CN116806262A

CN116806262A - Expression systems and methods for controlling network in cells and cells comprising the same

Info

Publication number: CN116806262A
Application number: CN202180089550.3A
Authority: CN
Inventors: 蒂莫西·托马斯·弗雷; 张景翔; 莫里斯·菲洛; 穆斯塔法·哈马什
Original assignee: Eidgenoessische Technische Hochschule Zurich ETHZ
Current assignee: Eidgenoessische Technische Hochschule Zurich ETHZ
Priority date: 2020-11-09
Filing date: 2021-11-09
Publication date: 2023-09-26

Abstract

The present application relates to an expression system for controlling a network in a cell, wherein the network comprises an activating molecule and an export molecule, wherein the activating molecule positively or negatively regulates the export molecule, wherein the expression system comprises a recombinant gene encoding a first control molecule, wherein the first control molecule positively or negatively regulates the activating molecule. The application also relates to cells comprising the expression system, cells for use as a medicament and methods of controlling a network in a cell.

Description

Expression systems and methods for controlling network in cells and cells comprising the same

The present application relates to expression systems, and methods for controlling regulatory networks in cells, and cells comprising the expression systems, as well as medical uses of the cells and expression systems.

The present application claims priority from european patent application EP20206417.6 filed 11/09 in 2020, incorporated herein by reference. The present application claims priority from european patent application EP21187316.1 filed on 22, 07, 2021, incorporated herein by reference.

The ability to maintain a stable internal environment in the presence of varying and uncertain outside world, known as homeostasis, is a defining feature of life systems. Homeostasis is maintained by various regulatory mechanisms, typically in the form of a negative feedback loop. The concept of homeostasis is particularly relevant in physiology and medicine, where loss of homeostasis is often due to the development of disease. In this regard, a deepened understanding of the molecular mechanisms controlling homeostasis will lead to the development of treatments for such diseases.

In engineering, when faced with disturbances to a desired state, the ability of a system to maintain another system in that state has been implemented using various control mechanisms and combinations thereof, resulting in, for example, integral, proportional derivative, and proportional integral derivative controllers that are frequently used in electronics.

In recent years, artificial genetic circuits have been introduced into the field of synthetic biology. These systems can be used to manipulate and artificially control networks in biological cells, such as gene regulatory networks. Basically, recombinant genes encoding cell regulators are introduced into these cells using molecular biological tools. This artificial genetic circuit provides a promising new therapy for a variety of diseases associated with deregulation of the cellular network.

However, many known artificial genetic circuits according to the prior art lack robustness against their environmental fluctuations, especially when very strict adjustments to the desired set point are required.

In view of these drawbacks of the known artificial genetic circuits, it is an object of the present invention to provide means and methods for controlling the network in cells in a robust and tightly controlled manner. This object is achieved by the subject matter of the independent claims of the present description, as well as by the further advantageous embodiments described in the dependent claims, examples, figures and general description of the present description.

The first aspect of the invention relates to a recombinant expression system for controlling a network in a cell, wherein the network comprises an activating molecule, in particular an activating protein, and an export molecule, in particular an export protein, wherein the export molecule is positively or negatively regulated by the activating molecule, and wherein the expression system comprises a nucleic acid comprising a recombinant gene encoding a first control molecule, wherein the first control molecule positively or negatively regulates the activating molecule.

In one embodiment, the first control molecule positively regulates the actuation molecule. The expression system further comprises a recombinant gene encoding a first antibody control molecule, wherein the first antibody control molecule down regulates, in particular inactivates, sequesters and/or annihilates the first control molecule, and wherein the first control molecule down regulates, in particular inactivates, sequesters and/or annihilates the first antibody control molecule. In case a), the actuator molecule positively regulates the output molecule, which positively regulates the first antibody control molecule. In case b), the actuator molecule negatively regulates the output molecule, which positively regulates the first control molecule.

In one embodiment, the first control molecule negatively regulates the actuation molecule. The expression system further comprises a recombinant gene encoding a first antibody control molecule, wherein the first antibody control molecule down regulates, in particular inactivates, sequesters and/or annihilates the first control molecule, and wherein the first control molecule down regulates, in particular inactivates, sequesters and/or annihilates the first antibody control molecule. In case a), the actuator molecule positively regulates the output molecule, and the output molecule positively regulates the first control molecule. In case b), the actuating molecule down-regulates the output molecule, which up-regulates the first antibody control molecule.

In particular, the expression system comprises or consists of one or several nucleic acids carrying at least one recombinant gene capable of being expressed in a cell. Wherein the expression particularly involves transcription of at least one recombinant gene into RNA, in particular messenger RNA (mRNA), and optionally subsequent translation of the mRNA into protein in the cell.

The cells may be prokaryotic (in particular bacterial) or eukaryotic (in particular fungal, plant or animal, more in particular mammalian) cells. Any suitable expression system known in the art may be used for the cell of interest. For example, the expression system may comprise one or several DNA vectors, such as plasmids, viruses or artificial chromosomes, as is known in the art of molecular biology.

As used herein, the term "network" describes at least two functionally linked biological entities (e.g., genes or proteins), one of which directly or indirectly affects the concentration and/or biological activity of any other entity of the network. For example, such a network may include at least one gene encoding a transcriptional regulator protein that activates or inhibits transcription of at least one other gene in the network. Furthermore, the biological entities in the network may be proteins that interact with each other, wherein one protein of the network activates or inhibits the biological activity (e.g., enzymatic activity) of another protein in the network.

In the cellular network according to the invention, the activating molecule (e.g. a protein) positively or negatively regulates the output molecule (e.g. a protein or a small molecule, e.g. a metabolite) directly or indirectly (i.e. by interaction with one or several further genes or proteins).

The actuation molecule may be a small molecule. The actuation molecule may be a protein.

The output molecule may be a small molecule. The export molecule may be a protein.

Wherein the term "modulate" refers to an actuator that directly or indirectly affects the concentration of an export molecule in a cell or its biological activity (e.g., enzymatic activity or binding to a target molecule) in a cell.

This regulation may occur through several mechanisms. For example, where the export molecule is a protein, modulation by the actuation molecule may occur by directly or indirectly activating or inhibiting transcription of the gene encoding the export molecule, directly or indirectly mediating or inhibiting degradation of the mRNA encoding the export molecule, directly or indirectly activating or inhibiting translation of the export molecule from the mRNA, directly or indirectly mediating or inhibiting degradation, post-translational modification, complex formation, cellular secretion or intracellular transport of the export molecule, or activating or inhibiting biological activity of the export molecule. Likewise, where the output molecule is a small molecule, positive or negative modulation may, for example, directly or indirectly affect the synthesis, degradation, transport, or modification of the small molecule.

According to the invention, the expression system is used to introduce nucleic acids encoding recombinant molecule controllers (at least a first control molecule and optionally also feedback molecules, a first anti-control molecule, a second control molecule and a second anti-control molecule, see below) into a cell of interest to control the output molecules (controlled species) of the network by manipulation of the actuation molecules (process inputs). In particular, the purpose of this control is to achieve a desired set point, i.e. a desired concentration and/or activity of the output molecules, regardless of fluctuations in the network balance and external disturbances.

In certain embodiments, the expression system further comprises a nucleic acid comprising a recombinant gene encoding a feedback molecule, wherein the output molecule positively regulates the feedback molecule, and wherein in the event that the output molecule is positively regulated by the actuator molecule, the feedback molecule negatively regulates the actuator molecule, and in the event that the output molecule is negatively regulated by the actuator molecule, the feedback molecule positively regulates the actuator molecule.

The case where the actuator molecules positively regulate the output molecules is also referred to herein as a "positive gain process", while the case where the actuator molecules negatively regulate the output molecules is also referred to herein as a "negative gain process".

Advantageously, the feedback molecules artificially introduce molecular feedback into the network, thereby increasing the stability of the concentration and/or activity of the output molecules against disturbances to the network. In terms of control theory, the feedback molecule introduces proportional control into the network, in other words, the correction applied to the controlled species (output molecule) is proportional to the measured value.

Instead of or in addition to introducing feedback molecules into cells to achieve artificial feedback regulation of the network, naturally occurring (i.e., non-recombinant) feedback of the network may also be utilized to achieve stability of regulation. That is, if the network itself is naturally feedback regulated, it is possible to implement a proportional-integral controller, for example, by introducing only the first control molecule and the first anti-control molecule (the opposite motif leading to integral control, see below) without introducing a recombinant feedback molecule. In this case, for example, proportional control would be achieved through a naturally occurring (i.e., non-recombinant) feedback mechanism.

In certain embodiments, where the actuation molecule positively regulates the output molecule (in other words, where the positive gain process), the feedback molecule is a microrna that negatively regulates the production of the actuation molecule, particularly by inhibiting translation of and/or promoting degradation of the mRNA encoding the actuation molecule.

In certain embodiments, where the actuation molecule positively regulates the output molecule (in other words, in the case of a positive gain process), the feedback molecule is an RNA binding protein that negatively regulates the production of the actuation molecule, in particular by binding to an untranslated region of the mRNA encoding the actuation molecule and inhibiting translation of the mRNA.

In certain embodiments, where the actuation molecule negatively regulates the output molecule (in other words, where the negative gain process), the feedback molecule is an additional mRNA encoding the actuation molecule. Wherein the term "additional mRNA" refers to a transcript of an additional recombinant gene introduced into a cell in addition to the transcript of the naturally occurring (i.e., non-recombinant) gene encoding the activating molecule.

In certain embodiments, the first control molecule positively regulates an activating molecule, wherein the expression system further comprises a nucleic acid comprising a recombinant gene encoding a first antibody control molecule, wherein the first antibody control molecule negatively regulates the first control molecule, and wherein the first control molecule negatively regulates the first antibody control molecule. In particular, the first antibody control molecule inactivates, sequesters, and/or annihilates the first control molecule, and the first control molecule inactivates, sequesters, and/or annihilates the first antibody control molecule.

In case the actuator molecule is regulating the output molecule (in other words in case of a positive gain process), the output molecule is regulating the first antibody control molecule. Alternatively, in case the actuator molecule negatively regulates the output molecule (in other words, in case of a negative gain process), the output molecule positively regulates the first control molecule. In this way, a closed control loop between the actuator molecule and the output molecule is formed by the first control molecule and the first anti-control molecule.

This type of control, which may also be referred to herein as a "p-motif", enables integral control of the network, in other words, the correction applied to the controlled species (output molecule) depends on the integral of the difference between the setpoint and the measured value. In this implementation, in particular, the set point may be controlled by the ratio between the rate of production of the control molecules and the rate of production of the anti-control molecules in the control unit.

In certain embodiments, the first antibody control molecule deactivates, particularly fully deactivates, the first control molecule, and the first control molecule deactivates, particularly fully deactivates, the first antibody control molecule. In particular, the inactivation reaction between the first control molecule and the first antibody control molecule is stoichiometrically fixed, in other words, a given number of first antibody control molecules inactivate a fixed number of first control molecules and/or a given number of first control molecules inactivate a fixed number of first antibody control molecules. Wherein, "stoichiometrically immobilized" means that the ratio of the number of first control molecules to the number of first anti-control molecules does not change over time.

In the context of the present specification, the "inactivation" of the second molecule by the first molecule means that the first molecule eliminates the biological function of the second molecule. Such biological functions may be, for example, the binding of transcription regulatory factors to target DNA, the binding of translation regulatory factors to target mRNA, the binding of proteins to target molecules or the enzymatic activity of enzymes.

In certain embodiments, the first antibody control molecule and the first control molecule physically interact, in particular bind to each other (e.g., in the case of a protein) or hybridize (e.g., in the case of a nucleic acid) to down-regulate, in particular inactivate, each other.

In certain embodiments, the first antibody control molecule and the first control molecule physically interact to inactivate each other, wherein the first antibody control molecule eliminates a biological function of the first control molecule, particularly binding activity of the first control molecule to a target molecule (e.g., target DNA, RNA, or protein), wherein the first control molecule sequesters the first antibody control molecule.

In the context of this specification, the term "sequestered" describes a first molecule bound to a second molecule such that the physical interaction of the second molecule with another molecule is eliminated (e.g., a single first control molecule binds to a single first anti-control molecule to eliminate the binding of the first anti-control molecule to other first control molecules).

In certain embodiments, the first antibody control molecule and the first control molecule annihilate with each other to down-regulate, and in particular inactivate, each other.

In the context of the present specification, the term "annihilation" describes an interaction between a first molecule and a second molecule, which results in degradation of the first molecule and the second molecule.

In certain embodiments, the first control molecule comprises either a sense mRNA encoding an activating molecule or a sense mRNA encoding an activator, e.g., a transcriptional activator of a gene encoding an activating molecule, which upregulates the activating molecule, and wherein the first anti-control molecule comprises or comprises an antisense RNA of a sequence complementary to the sense mRNA sequence. Hybridization of sense mRNA to antisense RNA results in inhibition of translation of sense mRNA (resulting in inactivation). At the same time, hybridization prevents the antisense RNA from interacting (i.e., sequestering) with other sense mRNA molecules.

In certain embodiments, the first control molecule is an activator protein that positively modulates production of the activator molecule, for example, by activating transcription of a gene encoding the activator molecule, activating translation of an mRNA encoding the activator molecule, or inhibiting degradation of the activator molecule, or by a suppressor that negatively modulates a function of the activator molecule, and wherein the first anti-control molecule is an anti-activator protein, wherein the activator protein and the anti-activator protein form a protein-protein complex, wherein positive modulation of the activator molecule by the activator protein is inhibited by formation of the complex (resulting in inactivation). At the same time, complex formation prevents the anti-activin from interacting (i.e., sequestering) with other activin molecules.

In one embodiment, the first control molecule is a sense mRNA encoding an inhibitor of a negative regulator actuator molecule, and wherein the second control molecule comprises an antisense RNA comprising a sequence complementary to the sequence of the sense mRNA.

In one embodiment, the first control molecule is an inhibitor protein that down-regulates production of the actuator molecule by inhibiting translation of mRNA encoding the actuator molecule or activating degradation of the actuator molecule or by positively regulating an inhibitor of the function of the actuator molecule, and wherein the first control molecule is an anti-activator protein, wherein the activator protein and the anti-activator protein form a complex, wherein down-regulation of the actuator molecule by the inhibitor protein is activated by formation of the complex.

In particular, this pair of motifs can be combined with a feedback mechanism that feeds back the molecules to implement a molecular proportional integral controller (PI controller).

In certain embodiments, to provide a molecular PI controller, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a first anti-control molecule, and in particular a feedback molecule, wherein the actuating molecule positively regulates the output molecule, i.e., in the case of a positive gain process (N-type PI controller)

The first control molecule positively regulates the actuator molecule, the first anti-control molecule negatively regulates the first control molecule, the first control molecule negatively regulates the first anti-control molecule (opposite motif), and the output molecule positively regulates the first anti-control molecule (resulting in integral control), an

The output molecule positively regulates the feedback molecule and the feedback molecule negatively regulates the actuator molecule, or (in case no feedback molecule is provided) the output molecule negatively regulates the actuator molecule, in particular directly (leading to a proportional control).

Alternatively, in the case of an actuation molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type PI controller)

The first control molecule positively regulates the actuator molecule, the first anti-control molecule negatively regulates the first control molecule, the first control molecule negatively regulates the first anti-control molecule (opposite motif), and the output molecule positively regulates the first control molecule (resulting in integral control), an

The output molecule upregulates the feedback molecule and the feedback molecule upregulates the actuator molecule, or (in case no feedback molecule is provided) the output molecule upregulates the actuator molecule, in particular directly (leading to proportional control).

In certain embodiments, the actuator molecule positively regulates the output molecule (in other words, the network between the actuator molecule and the output molecule represents a positive gain process), wherein the output molecule positively regulates the first control molecule.

In certain embodiments, the actuating molecule negatively modulates the output molecule (in other words, the network between the actuating molecule and the output molecule represents a negative gain process), wherein the output molecule positively modulates the first antibody control molecule.

By this additional linkage between the output molecule and the first control or anti-control molecule, differential control can be achieved in addition to proportional-integral control by the opposite motif. As used herein, differential control is a control mechanism in which the correction applied to the controlled species (output molecule) depends on the derivative of the measured value (output). In combination with a feedback loop to achieve proportional control, this can be used to achieve a molecular second order Proportional Integral Derivative (PID) controller (second order due to the presence of two controller species, a first control molecule and a first anti-control molecule).

In one embodiment, the actuating molecule positively regulates the output molecule, and wherein the output molecule positively regulates the first antibody control molecule.

In one embodiment, the actuation molecule negatively regulates the output molecule, and wherein the output molecule positively regulates the first control molecule.

In certain embodiments, to implement a second order PID controller, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a second control molecule and in particular a feedback molecule, wherein in the case of an actuation molecule upregulating the output molecule, i.e. in the case of a positive gain process (N-type second order PID controller)

The first control molecule positively regulates the actuator molecule, the first anti-control molecule negatively regulates the first control molecule, the first control molecule negatively regulates the first anti-control molecule (opposite motif), and the output molecule positively regulates the first anti-control molecule (resulting in integral control),

the output molecule positively regulates the feedback molecule and the feedback molecule negatively regulates the actuator molecule, or (in case no feedback molecule is provided), the output molecule negatively regulates the actuator molecule, in particular directly (resulting in a proportional control), and

the output molecules positively regulate the first control molecules (this component combined with the proportional component results in filtered PD control).

Alternatively, in the case of an actuation molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (a P-type second order PID controller)

The first control molecule positively regulates the actuating molecule, the first anti-control molecule negatively regulates the first control molecule, the first control molecule negatively regulates the first anti-control molecule (opposite motif), and the output molecule positively regulates the first control molecule (resulting in integral control),

the output molecule upregulates the feedback molecule and the feedback molecule upregulates the actuator molecule, or (in case no feedback molecule is provided), the output molecule upregulates the actuator molecule, in particular directly (leading to proportional control), and

The output molecules positively regulate the first antibody control molecules (this component combined with the proportional component results in filtered PD control).

In certain embodiments, the expression system further comprises a nucleic acid comprising a recombinant gene encoding a second control molecule.

In certain embodiments, where the actuator molecule positively modulates the output molecule (positive gain process), the output molecule positively or negatively modulates the second control molecule, and the second control molecule negatively modulates the actuator molecule.

In certain embodiments, where the actuator molecule positively modulates the output molecule (positive gain process), the output molecule negatively modulates the second control molecule, and the second control molecule positively or negatively modulates the actuator molecule.

In certain embodiments, where the actuation molecule negatively regulates the output molecule (negative gain process), the output molecule positively or negatively regulates the second control molecule, and the second control molecule positively regulates the actuation molecule.

In certain embodiments, where the actuation molecule negatively regulates the output molecule (negative gain process), the output molecule positively regulates the second control molecule, and the second control molecule positively or negatively regulates the actuation molecule.

Differential control is achieved in the network by an additional second control molecule. In combination with integral control (e.g., via a counter motif) and proportional control (e.g., using an artificial feedback loop), a molecular third-order proportional-integral-derivative (PID) controller can be implemented. As three species are involved: a first control molecule, a first antibody control molecule, a second control molecule, which controllers are third order controllers.

In certain embodiments, to implement a molecular third-order PID controller, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a first anti-control molecule, a second control molecule and in particular a feedback molecule, wherein in case the actuating molecule is upregulating the output molecule, i.e. in case of a positive gain process (N-type third-order PID controller):

the first control molecule positively regulates the actuating molecule, the first anti-control molecule negatively regulates the first control molecule, the first control molecule negatively regulates the first anti-control molecule (opposite motif), and the output molecule positively regulates the anti-control molecule (resulting in integral control),

the output molecule either positively or negatively regulates the second control molecule and the second control molecule negatively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller), or the output molecule negatively regulates the second control molecule and the second control molecule either positively or negatively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller). In both cases, the filtered PD controller approximates a pure PD controller when the modulation of the second control molecule and the modulation of the actuation molecule have opposite signs (one positive and the other negative). When the symbols are the same, the filtered PD controller approximates a so-called LAG controller.

Alternatively, in the case of an actuator molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type third-order PID controller)

the output molecule positively or negatively regulates the second control molecule and the second control molecule positively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller), or the output molecule positively or negatively regulates the second control molecule and the second control molecule positively or negatively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller). In both cases, the filtered PD controller approximates a pure PD controller when the modulation of the second control molecule and the modulation of the actuation molecule have opposite signs (one positive and the other negative). When the symbols are the same, the filtered PD controller approximates a so-called LAG controller.

In certain embodiments, the expression system further comprises a nucleic acid comprising at least one recombinant gene encoding a second antibody control molecule, wherein the second antibody control molecule negatively regulates, in particular inactivates, sequesters and/or annihilates the second control molecule, and wherein the second control molecule negatively regulates, in particular inactivates, sequesters and/or annihilates the second antibody control molecule, wherein the second control molecule is negatively regulated by the output molecule in case the output molecule is positively regulated by the actuator molecule, i.e. in case of a positive gain process, and the second control molecule is positively regulated by the output molecule in case the output molecule is negatively regulated by the actuator molecule, i.e. in case of a negative gain process.

According to this embodiment, the second control molecule and the second antibody control molecule form a second pair of motifs, which are particularly useful for implementing a molecular fourth-order proportional-integral-derivative (PID) controller to control a network in a cell.

In certain embodiments, the second control molecule down-regulates itself.

In certain embodiments, to implement a fourth-order PID controller, the expression system includes a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a first antibody control molecule, a second antibody control molecule, and a feedback molecule, wherein in the case of an actuation molecule upregulating an output molecule, i.e., in the case of a positive gain process (an N-type fourth-order PID controller),

A first control molecule positively regulates the actuator molecule, a first anti-control molecule negatively regulates the first control molecule, a first control molecule negatively regulates the first anti-control molecule (first pair motif), an output molecule positively regulates the first anti-control molecule (resulting in integral control),

second control molecule down-regulates the actuation molecule, second antibody control molecule down-regulates the second control molecule, second control molecule down-regulates the second antibody control molecule (second opposite motif), output molecule down-regulates the second control molecule, and second control molecule down-regulates itself (resulting in differential control).

Alternatively, in the case of an actuation molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type fourth-order PID controller)

the second control molecule positively regulates the actuation molecule, the second antibody control molecule negatively regulates the second control molecule, the second control molecule negatively regulates the second antibody control molecule (second opposite motif), the output molecule positively regulates the second control molecule, and the second control molecule negatively regulates itself (resulting in differential control).

In certain embodiments (particularly in the case of any of the N-type or P-type PI controllers, N-type or P-type second, third or fourth order PID controllers described above), the first antibody control molecule deactivates, particularly fully deactivates, the first antibody control molecule, and the first control molecule deactivates, particularly fully deactivates, the first antibody control molecule. In particular, the inactivation reaction between the first control molecule and the first antibody control molecule is stoichiometrically fixed.

In certain embodiments (particularly in the case of any of the above-described N-type or P-type PI controllers, N-type or P-type secondary, tertiary or quaternary PID controllers), the first anti-control molecule and the first control molecule physically interact, particularly bind to each other (e.g., in the case of proteins) or hybridize (e.g., in the case of nucleic acids) to down-regulate, particularly inactivate, each other.

In certain embodiments, (particularly in the case of any of the N-type or P-type PI controllers, N-type or P-type secondary, tertiary or quaternary PID controllers described above), the first anti-control molecule and the first control molecule physically interact to inactivate each other, wherein the first anti-control molecule abrogates the biological function of the first control molecule, particularly the binding activity of the first control molecule to a target molecule (e.g., target DNA, RNA or protein), wherein the first control molecule sequesters the first anti-control molecule.

In certain embodiments (particularly in the case of any of the above-described N-type or P-type PI controllers, N-type or P-type second, third or fourth order PID controllers), the first antibody control molecule and the first control molecule annihilate each other to down regulate, particularly inactivate, each other.

In certain embodiments, the second control molecule is a sense mRNA encoding a regulatory protein, in particular a transcriptional activator or transcriptional repressor, that modulates expression of the activating molecule, wherein the second anti-control molecule is an antisense RNA comprising a sequence complementary to the sequence of the sense mRNA encoding the regulatory protein, wherein the sense mRNA may encode a regulatory protein that negatively modulates expression of the additional mRNA encoding the activating molecule, in particular where the feedback molecule is the additional mRNA encoding the activating molecule (e.g., for a P-type controller in the case of a negative gain process).

In certain embodiments, the second control molecule is an RNA-binding protein that binds to an untranslated region of an mRNA encoding an actuation molecule, thereby negatively or positively modulating the actuation molecule, e.g., by inhibiting or activating translation or promoting or inhibiting degradation of the mRNA, and wherein the second anti-control molecule is an anti-RNA-binding protein, wherein the RNA-binding protein and the anti-RNA-binding protein form a complex, wherein negative or positive modulation of the actuation molecule by the RNA-binding protein is inhibited by forming the complex.

The anti-RNA binding protein may be a protein capable of forming a complex with the RNA binding protein. The complex formed can down-regulate the RNA binding protein. In particular, the complex inhibits RNA binding proteins. Negative or positive regulation of the actuator molecule by the RNA-binding protein may be inhibited by forming a complex comprising the RNA-binding protein and the anti-RNA-binding protein.

In certain embodiments, where the actuator molecule positively modulates the output molecule (positive gain process), the output molecule positively or negatively modulates the first control molecule, and the first control molecule negatively modulates the actuator molecule.

In certain embodiments, where the actuator molecule positively modulates the output molecule (positive gain process), the output molecule negatively modulates the first control molecule, and the first control molecule positively or negatively modulates the actuator molecule.

In certain embodiments, where the actuation molecule negatively regulates the output molecule (negative gain process), the output molecule positively or negatively regulates the first control molecule, and the first control molecule positively regulates the actuation molecule.

In certain embodiments, where the actuating molecule negatively regulates the output molecule (negative gain process), the output molecule positively regulates the first control molecule, and the first control molecule positively or negatively regulates the actuating molecule.

In this way, a molecular differential controller can be implemented using only one controller species (the first control molecule). Whether the output molecule positively or negatively regulates the first control molecule is determined by a parameter of the network. In particular, this type of differential control may be combined with proportional control by means of a manual feedback loop to implement a molecular PD controller.

In certain embodiments, to implement a Proportional Differential (PD) controller, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule and in particular a feedback molecule, wherein in the case of an actuating molecule positively regulating the output molecule, i.e. in the case of a positive gain process (N-type PD controller),

The output molecule either positively or negatively regulates the first control molecule and the first control molecule negatively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller), or the output molecule negatively regulates the first control molecule and the first control molecule either positively or negatively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller). In both cases, the filtered PD controller approximates a pure PD controller when the modulation of the first control molecule and the modulation of the actuation molecule have opposite signs (one positive and the other negative). When the symbols are the same, the filtered PD controller approximates a so-called LAG controller.

Alternatively, in the case of an actuation molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type PD controller)

the output molecule positively or negatively regulates the first control molecule and the first control molecule positively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller), or the output molecule positively or negatively regulates the first control molecule, the first control molecule positively or negatively regulates the actuation molecule (together with the proportional controller resulting in a filtered PD controller). In both cases, the filtered PD controller approximates a pure PD controller when the modulation of the first control molecule and the modulation of the actuation molecule have opposite signs (one positive and the other negative). When the symbols are the same, the filtered PD controller approximates a so-called LAG controller.

The second aspect of the invention relates to a cell comprising the expression system of the first aspect of the invention.

In certain embodiments, the cell is a mammalian cell, particularly a human cell.

In certain embodiments, the cell is a T cell, particularly a T cell expressing a Chimeric Antigen Receptor (CAR).

CAR T cells are often used in cancer therapy, wherein an engineered chimeric antigen receptor interacts with an antigen expressed by a cancer cell of interest and is then specifically targeted by the CAR T cell.

In certain embodiments, the concentration of the export molecule in the cell is indicative of the concentration of at least one inflammatory cytokine in the cell, wherein the actuation molecule upregulates the production or release of at least one immunosuppressant in the cell. During CAR T cell therapy, a condition known as Cytokine Release Syndrome (CRS) often occurs. CRS is a form of systemic inflammatory response syndrome that may be life threatening due to high inflammation, hypotensive shock and multiple organ failure. During CRS, positive feedback activates T cells and other immune cells, resulting in cytokine storms.

In particular, expression systems and cells according to the invention can be used to counteract CRS during CAR T cell therapy by controlling and stabilizing the network responsible for immune responses during CRS:

To this end, in particular, a molecule whose presence or concentration or activity is indicative of the concentration of at least one inflammatory cytokine in the cell may be selected as output molecule, which output is sensed by the control molecule according to the invention. In addition, molecules that are part of the same network as the export molecule and that upregulate the production or release of at least one immunosuppressant in the cell may be selected as the actuation molecules that stabilize the immune response and mitigate CRS. For example, the actuator molecules may act as antagonists of IL-6 or IL-1 receptors, which have been shown to be effective against CRS.

By the control means of the present invention, the desired set point of this antagonistic function can be reached to avoid both too little immunosuppressive effect, which is ineffective against immunosuppression, and too much immunosuppressive effect, which inhibits the efficacy of the anti-tumor response. Furthermore, adaptation to patient-specific doses can be achieved using the control mechanism according to the invention.

A third aspect of the invention relates to a cell comprising a network, wherein the network comprises an activating molecule and an export molecule, wherein the export molecule is positively or negatively regulated by the activating molecule, and wherein the cell expresses a recombinant gene encoding a first control molecule, wherein the first control molecule positively or negatively regulates the activating molecule.

In certain embodiments, the cell is a prokaryotic (particularly bacterial) or eukaryotic (particularly fungal, plant or animal, more particularly mammalian) cell.

In certain embodiments, the cell expresses a recombinant gene encoding a feedback molecule, wherein the feedback molecule is positively regulated by the output molecule, and wherein in the event that the actuator molecule positively regulates the output molecule, the feedback molecule negatively regulates the actuator molecule, and in the event that the actuator molecule negatively regulates the output molecule, the feedback molecule positively regulates the actuator molecule.

In certain embodiments, where the actuation molecule positively regulates the output molecule (in other words, where the positive gain process), the feedback molecule is a microrna that negatively regulates the production of the actuation molecule, particularly by inhibiting translation of or promoting degradation of mRNA encoding the actuation molecule.

In certain embodiments, the first control molecule positively regulates an activating molecule, wherein the cell expresses a recombinant gene encoding the first antibody control molecule, wherein the first antibody control molecule negatively regulates the first control molecule, and wherein the first control molecule negatively regulates the first antibody control molecule. In particular, the first antibody control molecule inactivates, sequesters, and/or annihilates the first control molecule, and the first control molecule inactivates, sequesters, and/or annihilates the first antibody control molecule. In particular, the first antibody control molecule inactivates, sequesters, and/or annihilates the first control molecule, and the first control molecule inactivates, sequesters, and/or annihilates the first antibody control molecule. In case the actuator molecule is regulating the output molecule (in other words in case of a positive gain process), the output molecule is regulating the first antibody control molecule. Alternatively, in case the actuator molecule negatively regulates the output molecule (in other words, in case of a negative gain process), the output molecule positively regulates the first control molecule. In this way, a closed control loop between the actuator molecule and the output molecule is formed by the first control molecule and the first anti-control molecule.

In certain embodiments, the first antibody control molecule deactivates, particularly fully deactivates, the first control molecule, and the first control molecule deactivates, particularly fully deactivates, the first antibody control molecule. In particular, the inactivation reaction between the first control molecule and the first antibody control molecule is stoichiometrically fixed.

In certain embodiments, the first control molecule comprises either a sense mRNA encoding an activating molecule or a sense mRNA encoding an activator, e.g., a transcriptional activator of a gene encoding an activating molecule, which upregulates the activating molecule, and wherein the first anti-control molecule comprises or comprises an antisense RNA of a sequence complementary to the sense mRNA sequence. Hybridization of sense mRNA to antisense RNA results in inhibition of translation of sense mRNA. At the same time, hybridization prevents the antisense RNA from interacting with other sense mRNA molecules.

In certain embodiments, the first control molecule is an activator protein that positively modulates production of the activator molecule, for example, by activating transcription of a gene encoding the activator molecule, activating translation of an mRNA encoding the activator molecule, or inhibiting degradation of the activator molecule, or by a suppressor that negatively modulates a function of the activator molecule, and wherein the first anti-control molecule is an anti-activator protein, wherein the activator protein and the anti-activator protein form a complex, wherein positive modulation of the activator molecule by the activator protein is inhibited by the formation of the complex. At the same time, the formation of complexes prevents the interaction of the anti-activin with other activin molecules.

In certain embodiments, to provide a molecular PI controller, the cell expresses at least one recombinant gene encoding a first control molecule, a first anti-control molecule and in particular a feedback molecule, wherein in case the actuating molecule upregulates the output molecule, i.e. in case of a positive gain process (N-type PI controller)

-the first control molecule positively regulates the actuator molecule, the first anti-control molecule negatively regulates the first control molecule, the first control molecule negatively regulates the first anti-control molecule (opposite motif), and the output molecule positively regulates the first control molecule (resulting in integral control), and

In certain embodiments, to implement a second order PID controller, the cell expresses at least one recombinant gene encoding a first control molecule, a second control molecule and in particular a feedback molecule, wherein in case the actuating molecule positively regulates the output molecule, i.e. in case of a positive gain process (an N-type second order PID controller)

In certain embodiments, the cell also expresses a recombinant gene encoding a second control molecule.

In certain embodiments, to implement a molecular third-order PID controller, the cell expresses at least one recombinant gene encoding a first control molecule, a first anti-control molecule, a second control molecule and in particular a feedback molecule, wherein in case the actuating molecule positively regulates the output molecule, i.e. in case of a positive gain process (N-type third-order PID controller):

In certain embodiments, the cell further expresses at least one recombinant gene encoding a second antibody control molecule, wherein the second antibody control molecule negatively regulates the second control molecule, and wherein the second control molecule negatively regulates the second antibody control molecule, wherein the output molecule negatively regulates the second control molecule in the event that the output molecule is positively regulated by the actuator molecule, i.e., in the event of a positive gain process, and the second control molecule is positively regulated by the output molecule in the event that the output molecule is negatively regulated by the actuator molecule, i.e., in the event of a negative gain process.

In certain embodiments, the second control molecule down-regulates itself.

In certain embodiments, to implement a fourth-order PID controller, the cell expresses at least one recombinant gene encoding a first control molecule, a first anti-control molecule, a second anti-control molecule and in particular a feedback molecule, wherein in case the actuator molecule is upregulating the output molecule, i.e. in case of a positive gain process (N-type fourth-order PID controller),

a second control molecule positively regulates the actuation molecule, a second anti-control molecule negatively regulates the second control molecule, a second control molecule negatively regulates the second anti-control molecule (second opposite motif), a second control molecule negatively regulates itself, and an output molecule positively regulates the second control molecule (resulting in differential control).

In certain embodiments, the second control molecule down-regulates itself.

In certain embodiments, to implement a Proportional Differential (PD) controller, the cell expresses at least one recombinant gene encoding a first control molecule and in particular a feedback molecule, wherein in case the actuator molecule positively regulates the output molecule, i.e. in case of a positive gain process (N-type PD controller),

A fourth aspect of the invention relates to a cell according to the second or third aspect of the invention or an expression system according to the first aspect of the invention for use as a medicament.

A fifth aspect of the invention relates to a cell according to the second or third aspect of the invention or an expression system according to the first aspect of the invention for use in a method of treating or preventing an immune disorder, in particular cytokine release syndrome or rheumatoid arthritis.

A sixth aspect of the invention relates to a cell according to the second or third aspect of the invention or an expression system according to the first aspect of the invention for use in a method of treating or preventing a metabolic or endocrine disorder, in particular diabetes.

The seventh aspect of the invention relates to a method for controlling a network in a cell, in particular a cell according to the second or third aspect, wherein the method comprises expressing at least one recombinant gene of the expression system according to the first aspect of the invention in the cell.

The method may be an ex vivo method.

An eighth aspect of the invention relates to the use of a cell according to the second or third aspect or an expression system according to the first aspect in the manufacture of a medicament.

A ninth aspect of the invention relates to the use of a cell according to the second or third aspect or an expression system according to the first aspect for the manufacture of a medicament for the treatment or prevention of an immune disorder, in particular cytokine release syndrome or rheumatoid arthritis.

A tenth aspect of the invention relates to the use of a cell according to the second or third aspect or an expression system according to the first aspect for the manufacture of a medicament for the treatment or prevention of a metabolic or endocrine disorder, in particular diabetes.

Where alternatives to individual separable features are provided as "embodiments" wherever herein appears, it should be understood that such alternatives can be freely combined to form discrete embodiments of the invention disclosed herein.

The invention is further illustrated by the following examples and figures, from which other embodiments and advantages can be derived. These examples are intended to illustrate the invention and not to limit its scope.

In certain embodiments, where the actuator molecule positively modulates the output molecule (positive gain process), a second control molecule is constitutively generated to positively modulate the actuator molecule and negatively modulate itself. In addition, the output molecule negatively regulates the actuator molecule and positively regulates the first control molecule.

In certain embodiments, where the actuating molecule negatively regulates the output molecule (negative gain process), a second control molecule is constitutively generated to regulate the actuating molecule and negatively regulate itself. In addition, the output molecule positively regulates the actuator molecule and the first control molecule.

Differential control is achieved in the network by an additional second control molecule. In combination with integral control (e.g., via a counter motif) and proportional control (e.g., using an artificial feedback loop), a molecular outflow proportional-integral-derivative (PID) controller can be implemented. This controller is an outflow controller, since only the outflow of the second control molecule is regulated.

In certain embodiments, to achieve molecular efflux PID controllers, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a first anti-control molecule, a second control molecule and in particular a feedback molecule, wherein in case the actuating molecule is upregulating the output molecule, i.e. in case of a positive gain process (N-type efflux PID controller):

the second control molecule positively regulates the actuator molecule and negatively regulates itself. In addition, the output molecule negatively regulates the actuator molecule and positively regulates the first control molecule, resulting in differential control.

Alternatively, in the case of an actuation molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type outflow PID controller),

the second control molecule positively regulates the actuator molecule and negatively regulates itself. In addition, the output molecules positively regulate the actuator molecules and positively regulate the first control molecules, resulting in differential control.

In certain embodiments, where the actuator is regulating the output molecule (positive gain process), the second control molecule is regulating itself and the actuator. In addition, the output molecule positively regulates the actuator molecule and the first control molecule.

In certain embodiments, where the actuating molecule negatively regulates the output molecule (negative gain process), the second control molecule positively regulates itself and the actuating molecule. In addition, the output molecule negatively regulates the actuator molecule and the first control molecule.

Differential control is achieved in the network by an additional second control molecule. In combination with integral control (e.g., via a counter motif) and proportional control (e.g., using an artificial feedback loop), a molecular inflow proportional-integral-derivative (PID) controller can be implemented. This controller is an inflow controller, since only the inflow of the second control molecule is regulated.

In certain embodiments, to achieve molecular inflow PID controllers, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a first anti-control molecule, a second control molecule and in particular a feedback molecule, wherein in case the actuating molecule is upregulating the output molecule, i.e. in case of a positive gain process (N-type inflow PID controller):

The second control molecule positively regulates the actuator molecule and itself. In addition, the output molecule negatively regulates the actuator molecule and the first control molecule, resulting in differential control.

Alternatively, in the case of an actuator that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type inflow PID controller),

In certain embodiments, where the actuator molecule positively modulates the output molecule (positive gain process), the second control molecule positively and negatively modulates itself. The second control molecule also positively regulates the actuation molecule. In addition, the output molecule negatively regulates the actuator molecule and positively regulates the first control molecule.

In certain embodiments, where the actuating molecule negatively regulates the output molecule (negative gain process), the second control molecule positively and negatively regulates itself. The second control molecule also positively regulates the actuation molecule. In addition, the output molecule positively regulates the actuator molecule and negatively regulates the first control molecule.

Differential control is achieved in the network by an additional second control molecule. In combination with integral control (e.g., through a para motif) and proportional control (e.g., using an artificial feedback loop), a molecular autocatalytic proportional-integral-derivative (PID) controller can be implemented. This controller is an autocatalytic controller because the autocatalytic generation of the second controller is a key mechanism to achieve differential control.

In certain embodiments, to implement a molecular autocatalytic PID controller, the expression system comprises a nucleic acid comprising at least one recombinant gene encoding a first control molecule, a first anti-control molecule, a second control molecule and in particular a feedback molecule, wherein in case the actuating molecule is upregulating the output molecule, i.e. in case of a positive gain process (an N-type autocatalytic PID controller):

the second control molecule positively and negatively regulates itself. The second control molecule also positively regulates the actuation molecule. In addition, the output molecule negatively regulates the actuator molecule and positively regulates the first control molecule, resulting in differential control.

Alternatively, in the case of an actuation molecule that negatively regulates the output molecule, i.e. in the case of a negative gain process (P-type autocatalytic PID controller),

the second control molecule positively and negatively regulates itself. The second control molecule also positively regulates the actuation molecule. In addition, the output molecules positively regulate the actuator molecules and negatively regulate the first control molecules, resulting in differential control.

Brief description of the drawings

FIG. 1 illustrates an embodiment of a molecular N-type integral controller according to the present invention;

FIG. 2 illustrates an embodiment of a molecular N-type PI controller according to this invention;

FIG. 3 illustrates an embodiment of a molecular N-type second order PID controller according to the invention;

FIG. 4 illustrates an embodiment of a molecular N-type third-order PID controller according to the invention;

FIG. 5 illustrates an embodiment of a molecular N-type fourth-order PID controller according to the invention;

FIG. 6 illustrates an embodiment of a molecular P-type integral controller according to the present invention;

FIG. 7 illustrates an embodiment of a molecular P-type PI controller according to this invention;

FIG. 8 illustrates an embodiment of a molecular P-type second order PID controller according to the invention;

FIG. 9 illustrates an embodiment of a molecular P-type third-order PID controller according to the invention;

FIG. 10 illustrates an embodiment of a molecular P-type fourth-order PID controller according to the invention;

FIG. 11 illustrates another embodiment of a molecular N-type integral controller according to the present invention;

FIG. 12 illustrates another embodiment of a molecular N-type PI controller according to this invention;

FIG. 13 illustrates another embodiment of a molecular N-type second order PID controller according to the invention;

FIG. 14 illustrates another embodiment of a molecular N-type third-order PID controller according to the invention;

FIG. 15 illustrates another embodiment of a molecular N-type fourth-order PID controller according to the invention;

FIG. 16 illustrates another embodiment of a molecular P-type integral controller according to the present invention;

FIG. 17 illustrates another embodiment of a molecular P-type PI controller according to this invention;

FIG. 18 illustrates another embodiment of a molecular P-type second order PID controller according to the invention;

FIG. 19 illustrates another embodiment of a molecular P-type third-order PID controller according to the invention;

FIG. 20 illustrates another embodiment of a molecular P-type fourth-order PID controller according to the invention;

fig. 21 shows the network topology of an arbitrary molecular network with embedded opposite integration feedback motifs for positive gain processes (N-type controller, left) and negative gain processes (P-type controller, right).

FIG. 22 shows a comparison of open-loop and closed-loop dynamics (A) and the dynamics of the opposite motif given by the ordinary differential equation set (B);

figure 23 shows data illustrating perfect adaptation of synthetic counter-integral feedback loops in mammalian cells.

Fig. 24 shows data illustrating a response to a disturbance of the regulated network.

Fig. 25 shows an implementation of a proportional-integral controller according to the invention.

Fig. 26 shows a mathematical model describing the closed-loop and open-loop integration control and the corresponding fitting results.

FIG. 27 shows a list of biochemical species used in a mathematical model;

FIG. 28 shows a detailed biochemical reaction network used in describing a mathematical model of a controller according to the present invention;

FIG. 29 shows a schematic representation of a mathematical model depicting a molecular PI controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with this invention;

FIG. 30 shows a schematic representation of a mathematical model depicting a molecular PD controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with the present invention;

FIG. 31 shows a schematic representation of a mathematical model depicting a molecular second-order PID controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with the invention;

FIG. 32 shows a schematic representation of a mathematical model depicting a molecular third-order PID controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with the invention;

FIG. 33 shows a schematic representation of a mathematical model describing a molecular fourth-order PID controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with the invention;

FIG. 34 illustrates an embodiment of a molecular N-type outflow PID controller according to the invention;

FIG. 35 illustrates an embodiment of a molecular N-type inflow PID controller according to the invention;

FIG. 36 illustrates an embodiment of a molecular N-type autocatalytic PID controller according to the invention;

FIG. 37 illustrates an embodiment of a molecular P-type outflow PID controller according to the invention;

FIG. 38 illustrates an embodiment of a molecular P-type inflow PID controller according to the invention;

FIG. 39 illustrates an embodiment of a molecular P-type autocatalytic PID controller according to the invention;

FIG. 40 illustrates another embodiment of a molecular N-type outflow PID controller according to the invention;

FIG. 41 illustrates another embodiment of a molecular N-type inflow PID controller according to the invention;

FIG. 42 illustrates another embodiment of a molecular N-type autocatalytic PID controller according to the invention;

FIG. 43 illustrates another embodiment of a molecular P-type outflow PID controller according to the invention;

FIG. 44 illustrates another embodiment of a molecular P-type inflow PID controller according to the invention;

FIG. 45 illustrates another embodiment of a molecular P-type autocatalytic PID controller according to the invention;

FIG. 46 shows a schematic representation of a mathematical model describing a molecular outflow PID controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with the invention;

FIG. 47 shows a schematic representation depicting a mathematical model of molecular inflow PID controllers for positive gain processes (left, N-type controllers) and negative gain processes (right, P-type controllers) in accordance with the invention;

FIG. 48 shows a schematic representation of a mathematical model depicting a molecular autocatalytic PID controller for use in a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) in accordance with the invention;

FIG. 49 shows a scheme of eight different interaction networks comprising opposite motifs;

FIG. 50 shows a schematic representation of a mathematical model describing a negative-actuated opposition-integral feedback motif with a positive gain process;

FIG. 51 shows an embodiment of a molecular N-type integral controller based on a opposite integral feedback motif formed by repressing sense mRNA z1 (first control molecule) and antisense RNA z2 (first anti-control molecule) according to the invention.

FIG. 52 illustrates an embodiment of a molecular N-type integral controller according to the present invention;

fig. 53 shows data of an exemplary experiment.

Detailed description of the drawings

FIG. 1 shows an embodiment of a molecular N-type integral controller based on a opposite integral feedback motif formed by activating sense mRNA z1 (first control molecule) and antisense RNA z2 (first anti-control molecule) according to the present invention. The cloud on the right side of fig. 1 symbolizes a regulatory network in a biological cell comprising an actuator X1 and an output XL, wherein the actuator X1 positively regulates the output XL (positive gain process), in particular indirectly, i.e. via a plurality of further molecules of the network. Activating sense mRNA z1 is the product of the first recombinant gene expressed in the cell under a constitutive promoter (construct and branching marker "2"). In the described embodiment, the activating sense mRNA z1 is translated to produce an activating protein Act, which is a positive transcriptional regulator of the recombinant gene (construct and branch marker "3") encoding activating mRNA X1 (activating molecule), i.e., the gene encoding X1 has an activator-responsive promoter. The second gene encoding antisense RNA z2 (construct and branch marker "1") is expressed recombinantly in cells under the promoter upregulated by the export molecule XL. Antisense RNA has a sequence complementary to that of activating sense RNA z1 and therefore hybridizes to z1, producing an inactive complex z1-z2, blocking translation of z1, and ultimately leading to degradation of z1 and z2 (opposite motifs).

Fig. 2 shows an embodiment of a molecular N-type proportional-integral controller according to the present invention. Integral control was performed by the same RNA-based opposite motif as shown in figure 1 and described above (constructs and branches 1 to 3). In addition, another recombinant gene (construct and branch marker "4") encoding micrornas (feedback molecules) is expressed in cells under a promoter upregulated by export molecule XL. Micrornas bind to the untranslated region of the actuator mRNA X1, blocking translation and triggering degradation of the actuator mRNA. Thus, negative feedback between XL and X1 is achieved, resulting in proportional control other than integral control through the opposite motif.

Fig. 3 shows an embodiment of a molecular N-type second order PID controller according to the present invention. RNA-based opposite motifs and negative feedback mechanisms were implemented as shown in FIGS. 1 and 2 and described above (constructs and branches 1 to 4). Furthermore, to obtain differential control, another recombinant gene (construct and branching marker "5") encoding another copy of the activating sense mRNA z1 (first control molecule) is expressed in the cell under the control of a promoter upregulated by the output molecule XL.

Fig. 4 shows an embodiment of a molecular N-type third-order PID controller according to the present invention. RNA-based opposite motifs and negative feedback mechanisms were implemented as shown in FIGS. 1 and 2 and described above (constructs and branches 1 to 4). In addition, another recombinant gene (construct and branch marker "5") encoding regulatory mRNA z3 (second control molecule) is expressed in the cell under the control of a promoter upregulated by output molecule XL. The regulatory mRNA encodes a regulatory protein, which is a transcriptional activator or repressor of another recombinant gene (construct "6" with a regulatory protein-inducible promoter and branch "6") encoding another copy of regulatory mRNA X1.

Fig. 5 shows an embodiment of a molecular N-type fourth-order PID controller according to the present invention. RNA-based opposite motifs and negative feedback mechanisms were implemented as shown in FIGS. 1 and 2 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding repressor sense mRNA z5 (construct "5") is expressed in the cell under the promoter upregulated by the export molecule XL. Repressor sense mRNA z5 is translated into repressor Rep, which represses transcription of the recombinant gene encoding an additional copy of promoter mRNA X1 (construct "6" with Rep-responsive promoter). In addition, the recombinant gene encoding the repressor sense mRNA z4 (second control molecule) is expressed under the negative control of the repressor Rep (Rep-inducible promoter) (construct "7"), and the recombinant gene encoding the antisense RNA z3 complementary to mRNA z4 (second anti-control molecule) is expressed under the constitutive promoter (construct "8"). mRNA z4 hybridizes to antisense RNA z3 and forms an inactive complex that blocks translation of mRNA z4 and leads to degradation. Thus, z3 and z4 form further opposing motifs involved in differential control of the network.

FIG. 6 shows an embodiment of a molecular P-type integral controller based on a counter-integral feedback motif formed by activating sense mRNA z2 and antisense RNA z1 according to the present invention. In this embodiment, the actuating molecule X1 negatively regulates the output molecule XL (negative gain process). Recombinant expression (construct "1") activates sense mRNA z2 (the first control molecule) under a promoter upregulated by output molecule XL. Activating sense RNA z2 is translated to produce activator protein Act, which is a positive transcriptional regulator of mRNA m1 expressed recombinantly (construct "3") in cells under the activator Act-responsive promoter. The gene product of mRNA m1 upregulates (directly or indirectly) the production of the actuator molecule X1. Antisense RNA z1 (first anti-control molecule) is expressed under a constitutive promoter (see construct "2") having a sequence complementary to z2 such that z1 and z2 form an inactive complex, interfering with translation of z2 (and thus reducing Act protein production) and leading to RNA degradation of the complex. Thus, z1 and z2 form opposite motifs leading to integral control of the network.

Fig. 7 shows an embodiment of a molecular P-type PI controller (controlling the negative gain process) according to the present invention, which includes all of the components shown in fig. 6 and described above. In addition, another mRNA m2 (feedback molecule) from the construct labeled "4" is expressed recombinantly in the cell under the control of a promoter upregulated by the export molecule XL (export inducible promoter). mRNA m2 encodes a protein that upregulates (directly or indirectly) the production of the actuator molecule X1 (either from its native gene or from an additional copy of the recombinant gene). This results in a feedback loop between the output molecule XL and the actuating molecule X1, leading to proportional control of the network in addition to integral control mediated by the opposite motif.

Fig. 8 shows an embodiment of a molecular P-type secondary PID controller according to the present invention, which includes all the components (configurations 1 to 4) shown in fig. 6 and 7. In addition, another copy of antisense RNA z1 (the first control molecule) is expressed (constructs "5") in the cell under a promoter upregulated by the export molecule XL to achieve differential control of the network.

Fig. 9 shows an embodiment of a molecular P-type third-order PID controller according to the present invention, which includes all the components (configurations 1 to 4) shown in fig. 6 and 7. In addition, sense mRNA z3 (second control molecule) is regulated by recombinant expression (construct "5") in cells under a promoter upregulated by export molecule XL. Regulation of sense mRNA z3 produces the regulatory protein Reg (transcriptional activator or repressor). In addition, mRNA m2 (positive regulator of the actuator molecule X1) is expressed recombinantly (construct "6") in cells under the control of a promoter positively or negatively regulated by the regulatory protein Reg

Fig. 10 shows an embodiment of a molecular P-type fourth-order PID controller according to the present invention, which includes all the components (configurations 1 to 4) shown in fig. 6 and 7. In addition, repressor mRNA z4 (second control molecule) producing repressor Rep is recombinantly expressed in cells from construct "5" under the control of a promoter that is upregulated by export molecule XL and downregulated by the repressor. Another construct "6" encoding mRNA m2 is expressed recombinantly in cells under a promoter that is upregulated by the export molecule XL and downregulated by the repressor protein. mRNA m2 upregulates the transcription of the promoter molecule X1, for example by activating another copy from the gene encoding the promoter molecule. In addition, antisense RNA z3 (second antibody control molecule) having a sequence complementary to repressor mRNA z4 was expressed from a constitutive promoter (construct "7"). As described above, with respect to z1 and z2, z3 and z4 form complexes, interfering with translation of z4 and ultimately leading to degradation of mRNA z3 and z 4. Thus, z3 and z4 form additional opposing motifs that facilitate differential control of the network.

Fig. 11 depicts another embodiment of a molecular N-type integral controller according to the present invention. In contrast to the controller shown in fig. 1, the opposite motif is achieved by protein-protein interactions. In the cellular network represented by the cloud on the right hand side of fig. 11, the actuating molecule X1 is positively regulating the output molecule XL, in other words, the positive gain process is controlled. mRNA z1 is activated from recombinant expression of the constitutive promoter in the cell (see construct "2"). mRNA Z1 is translated to produce activator protein Z1 (the first control molecule, also known as Z1 (Act)). The actuator mRNA m1 of actuator molecule X1 is upregulated by recombinant expression (see construct "3") from the promoter upregulated by activator protein Z1. In addition, the anti-activator mRNA z2 is expressed recombinantly under the control of a promoter upregulated by the export molecule XL (see construct "1"). The anti-activator mRNA Z2 is translated into an anti-activator protein Z2 (primary antibody control molecule) that specifically interacts with activator protein Z1 to sequester and inactivate Z1, resulting in reduced or lost transcriptional activation of m1 by Z1. Proteins Z1 and Z2 implement protein-based opposite motifs that lead to integral control of the network.

Fig. 12 shows another embodiment of a molecular N-type PI controller according to the invention. The controller includes all the components shown in fig. 11 (configurations 1 to 3). In addition, mRNA z3 encoding the RNA binding protein RBP (feedback molecule) is expressed recombinantly (from construct "4") in cells under the control of a promoter upregulated by export molecule XL. The mRNA is translated to produce the RNA-binding protein RBP, which binds to the untranslated region of the mRNA encoding the actuation molecule X1 and inhibits translation of the X1 mRNA, thereby down-regulating X1. In this way, a negative feedback loop between XL and X1 is achieved, resulting in proportional control.

Fig. 13 shows another embodiment of a molecular N-type second order PID controller according to the present invention. The controller includes all the components shown in fig. 11 and 12 (configurations 1 to 4). In addition, the promoter recombination upregulated by the output molecule XL expresses the second copy z1 of the activating mRNA described above (see construct "5", which in combination with the proportional component results in filtered PD control).

Fig. 14 shows another embodiment of a molecular N-type third-order PID controller according to the present invention. The controller includes all the components shown in fig. 11 and 12 (configurations 1 to 4). In addition, mRNA z4 is regulated in the cell by recombinant expression from the promoter upregulated by export molecule XL. mRNA z4 is translated into a regulatory protein Reg (second control molecule), which may be a translational repressor or activator. The regulatory protein Reg negatively or positively regulates translation of mRNA encoding the actuator molecule X1 (this component in combination with the proportional component results in filtered PD control).

Fig. 15 shows another embodiment of a molecular N-type fourth-order PID controller according to the present invention. The controller includes all the components shown in fig. 11 and 12 (configurations 1 to 4). In addition, repressed mRNA z5 (construct "5") is expressed recombinantly in cells under the control of a promoter upregulated by export molecule XL. In addition, repressor/RBP sense mRNA z4 (second control molecule) is expressed recombinantly in cells (construct "6"). The translation product of z4 is a Rep protein (repressor and RNA binding protein) that has the dual function of acting as a repressor of z4 self transcription and as another RNA binding protein (in addition to RBP expressed by construct 4) that binds to the untranslated region of the mRNA encoding the actuation molecule X1, thereby inhibiting translation of X1. mRNA z4 was expressed from construct 5 under a Rep-inducible promoter that was inhibited by Rep protein. Finally, antisense RNA z3 (second antibody control molecule) with a sequence complementary to z4 is expressed recombinantly in cells under the action of constitutive promoters (construct "7"). Antisense RNA z3 forms a complex with mRNA z4, which interferes with translation of z4 (and thus reduces Rep protein concentration), and ultimately leads to degradation of z3 and z4. Thus, Z3 and Z4 form a second (RNA-based) opposing motif, contributing to differential control of the network.

Fig. 16 shows another embodiment of a molecular P-type integral controller according to the present invention. Here, the negative gain process is regulated, i.e. the actuator molecule X1 negatively regulates the output molecule XL. Recombinant expression activates mRNA z2 (construct "1") in cells under the control of a promoter upregulated by export molecule XL. The translation product of Z2 is activator protein Z2 (first control molecule). The anti-activator mRNA z1 (construct "2") was expressed recombinantly in cells under constitutive promoters. mRNA Z1 is translated into anti-activin Z1 (primary anti-control molecule) which specifically binds to activin Z2, thereby sequestering and inactivating activin (the opposite motif based on protein-protein interactions). The activator mRNA m1 (construct "3") was further expressed recombinantly in cells under the activator protein Z2 upregulated promoter. mRNA m1 upregulates (directly or indirectly) the production of the actuator molecule X1.

Fig. 17 shows another embodiment of a molecular P-type PI controller according to the invention. In addition to the components shown in fig. 16 and described above (constructs 1 to 3), the controller contains another construct (labeled "4") for recombinantly expressing in the cell an actuator mRNA m2 (feedback molecule) encoding an actuator molecule X1 (another copy of the X1 gene) under a promoter that is positively regulated by the output molecule XL to achieve a negative feedback loop between XL and X1, resulting in proportional control of the network.

FIG. 18 shows another embodiment of a molecular P-type second order PID controller according to the invention. The controller includes all the components shown in fig. 16 and 17 and described above (configurations 1 to 4). In addition, another copy of the gene encoding the anti-activator mRNA z1 was introduced into the cell by constructing "5". Thus, the anti-activator mRNA z1 is expressed recombinantly under the control of a promoter upregulated by the output molecule XL to achieve differential control.

FIG. 19 shows another embodiment of a molecular P-type third-order PID controller according to the invention. The controller includes all the components shown in fig. 16 and 17 and described above (configurations 1 to 4). In addition, mRNA z3 is regulated in the cell from the recombinant expression of construct "5" under the control of a promoter upregulated by the export molecule XL. The regulatory mRNA is translated into regulatory protein Z3 (a second control molecule, also referred to as Z3 (Reg) in fig. 19), which may be a transcriptional activator or repressor. In addition, another copy of regulatory mRNA m2 is expressed recombinantly from construct "6" under the control of a promoter that activates or inhibits regulatory protein Z3. This results in differential control of the network.

FIG. 20 shows another embodiment of a molecular P-type fourth-order PID controller according to the invention. The controller includes all the components shown in fig. 16 and 17 and described above (configurations 1 to 4). Furthermore, construct "5" was introduced, which encodes RBP-actuator mRNA Z4, which in tandem encodes RNA binding protein Z4 (second control molecule) and actuator molecule X1, such that they are co-expressed in the cell under the control of a promoter upregulated by output molecule XL. RNA binding protein Z4 binds to the untranslated region of RBP actuator mRNA Z4 and inhibits its translation into Z4 and X1. In addition, anti-RBP mRNA z3 was expressed recombinantly in cells from constitutive promoters (see construct "6"). The translation product of Z3 is the anti-RBP protein Z3 (second antibody control molecule), which forms a complex with the RNA binding protein Z4, resulting in inhibition of the RNA binding function of Z4. Thus, the second protein-based opposite motif is implemented by Z3 and Z4, contributing to differential control of the network.

Fig. 21 shows the network topology of an arbitrary molecular network with embedded opposite integration feedback motifs for positive gain processes (N-type controller, left) and negative gain processes (P-type controller, right). The nodes marked with Z1 and Z2 (first control molecule and first antibody control molecule) together form the opposite motif. Species Z1 is produced at a rate μ, and when it is at a rate η andspecies Z2 functionally annihilates when interacting. Furthermore, it interacts with the controlled network by facilitating the production of species X1 (the actuator molecule). To close the feedback loop to react with θ and output species X _L The proportional reaction rate (of the output molecule) yields species Z2.

Fig. 22a shows a comparison of open loop and closed loop dynamics. Both open loop (bottom) and closed loop (top) systems track the desired set point without any disturbance to the controlled network. However, when the disturbance occurs and persists, the open loop deviates from the desired set point, and the closed loop system returns after some transient deviation. This is also the case when the interference is reduced after a period of time but still persists. The dynamics of the opposite motif are given by the system of ordinary differential equations shown in fig. 22 b. From for species Z ₁ Is subtracted from the differential equation for species Z ₂ Is disclosed, which ensures that the steady state of the output converges to a value independent of the device parameter. The long-term performance of the output is given by the ratio of the two reaction rates μ and θ. Importantly, this steady state is independent of any rate in the controlled network and is therefore robust to any interference in these rates.

Figure 23 shows data illustrating perfect adaptation of synthetic counter-integral feedback loops in mammalian cells. Figure 23a shows a genetic implementation of open and closed loops. The two loops consist of two genes implemented on separate plasmids. The gene in the activating plasmid (first control molecule) encodes the fluorescent protein mcitrane and the chemically induced degradation tag (SMASh) labeled synthetic transcription factor tTA (tetracycline transactivator). Its expression is composed of a strong constitutive promoter (P _EF-1 Alpha) actuation. Genes in antisense plasmids were replaced in the tTA-reactive promoter (P _TRE ) Under the control of (a) expression antisense RNA (a first antibody control molecule). In the open loop configuration, the TRE promoter is replaced with a non-reactive promoter. In this case, the controlled species is the tTA protein, which can be subjected to external perturbation by the addition of Ataprevir (ASV), a chemical inducer of SMASh degradation of the tag. FIG. 23b shows the steady state level of output (mCitrine) at increasing plasmid proportions. At different molar ratios (setting The point: =activator/antisense) transient transfection of the genetic realization of the closed loop as shown in figure (a). Data were collected 48 hours post-transfection and shown as an average for each condition normalized to the lowest set point (1/16) ±s.e., n=3 replicates. This suggests that increasing the plasmid ratio increases the steady state output level. Fig. 23c shows steady state response of open loop and closed loop implementations to degradation caused by ASV. Genetic realizations of the open and closed loops shown in FIG. 23a were transiently transfected at different molar ratios and perturbed with ASV at 0.033. Mu.M. Data were collected 48 hours post-transfection and shown as averages for each condition, normalized to the undisturbed condition for each set point. This demonstrates the anti-jamming capability of the closed loop and indicates that the open loop is not adaptive.

Fig. 24 shows data illustrating a response to a disturbance of the regulated network. Fig. 24a schematically shows an extension of the network topology with a negative feedback loop. By expressing the RNA binding protein L7Ae under the control of the tTA-responsive TRE promoter, a negative feedback loop is added from tTA-mCitrine to itself. This protein binds to the 5' untranslated region of the sense mRNA species, inhibiting translation of tTA. Fig. 24b shows data demonstrating that the closed loop is fair to the topology of the regulated network. The closed and open loops were perturbed by co-transfection network perturbation and addition of ASV of 0.033 μm. This is done at two setpoints 1/2 and 1 (setpoint: = activator/antisense). HEK293T cells were measured using flow cytometry 48 hours after transfection, data shown as mean values for each condition, normalized to undisturbed network and no ASV condition ± s.e., n=3 replicates.

Fig. 25 shows an implementation of a proportional-integral controller according to the invention. Fig. 25a shows the genetic implementation of an independent proportional (P) controller and Proportional Integral (PI) controller. A negative feedback loop from the RNA binding protein L7Ae (which is an alternative to tTA-mCitrine because it is produced simultaneously from the same mRNA) was added to the opposite motif. This protein binds to the 5' untranslated region of the sense mRNA species while inhibiting tTA and its own translation. A stronger proportional feedback is achieved by adding additional L7Ae binding hairpins. Fig. 25b shows data that demonstrate that the PI controller does not destroy the adaptation characteristics. PI and P loops were perturbed by co-transfection network perturbation and by addition of ASV at 0.033 μm. HEK293T cells were measured using flow cytometry 48 hours after transfection, and the data showed an average for each condition normalized to undisturbed (ASV-free) condition ± s.e., n=3 replicates. Obviously, a controller without integral feedback cannot meet the adaptation criteria. However, the PI controller ensures adaptation.

Fig. 26 shows a mathematical model describing the closed-loop and open-loop integration control and the corresponding fitting results. Fig. 26a is a schematic and mathematical description of a simplified model. Sense mRNA Z ₁ Produced constitutively at a rate μ which depends on total (free and bound) plasmid concentration,And a shared transcription source P (e.g., a polymerase). Then, Z ₁ Translation into Green fluorescent protein X at a Rate k ₂ The rate k depends on Z ₁ Concentration of translation source R (e.g., ribosome), and total drug concentration G as inhibitor _T 。X ₂ Protein dimerization, Z as an activating antisense RNA ₂ A transcribed transcription factor. The transcription rate represented by θ is X ₂ Function of P and total plasmid concentration. Antisense RNA to depend on Z ₂ And the rate ν of R translates into red fluorescent protein Y. Z is Z ₁ And Z ₂ Isolated from each other at a rate η to close the ring. The open loop setting is obtained by setting η=0. The transcription/translation burden is imposed by the shared resource. By either making P and R constant, or allowing them to depend on other species, the load can be eliminated or included in the model, as shown in the table. Fig. 26b shows the fitting of the model to experimental data. Using green and red fluorescence measurements, the parameters of the model considering only translation burden were best fitted (p=pt). Displaying an unloaded scene does not fit the data properly, while a fully loaded scene does not significantly increase model fitting accuracy. The fitted model shows the plasmid ratio +. >On the good one of the dataAnd (5) sex. This mathematically implies that the system only represents a translation burden.

FIG. 27 shows a list of biochemical species used in a mathematical model;

fig. 29 shows a schematic representation of a mathematical model describing a molecular PI controller based on opposite motifs with additional feedback control for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) according to the present invention. X1 represents an actuating molecule, XL represents an output molecule, Z1 represents a first control molecule (left panel) or a first anti-control molecule (right panel), and Z2 represents a first anti-control molecule (left panel) or a first control molecule (right panel). μ is the rate of formation of Z1, and η is the rate of complex formation/annihilation of Z1 and Z2.

Fig. 30 shows a schematic representation of a mathematical model describing a molecular PD controller for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) according to the present invention. X1 represents an actuation molecule, XL represents an output molecule, and Z represents a first controller molecule. Mu is the rate of Z formation, and gamma _Z Is the degradation rate of Z.

Fig. 31 shows a schematic representation of a mathematical model describing a molecular second order PID controller based on opposite motifs with additional feedback control for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) according to the present invention. X1 represents an actuator molecule, XL represents an output molecule, Z1 represents a first control molecule, and Z2 represents a first anti-control molecule. η is the complex formation/annihilation rate of Z1 and Z2.

Fig. 32 shows a schematic representation of a mathematical model describing a molecular third-order PID controller based on opposite motifs with additional feedback control for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) according to the present invention. X1 represents an actuator molecule, XL represents an output molecule, Z1 represents a first control molecule, Z2 represents a first anti-control molecule, and Z3 represents a second control molecule. η is the complex formation/annihilation rate of Z1 and Z2.

Fig. 33 shows a schematic representation of a mathematical model describing a molecular fourth-order PID controller based on two opposite motifs with additional feedback control for a positive gain process (left, N-type controller) and a negative gain process (right, P-type controller) according to the present invention. X1 represents an actuator molecule, XL represents an output molecule, Z1 represents a first control molecule, Z2 represents a first antibody control molecule, Z3 represents a second control molecule, and Z4 represents a second antibody control molecule. η is the complex formation/annihilation rate of Z1 and Z2.

Fig. 34 shows an embodiment of a molecular N-type outflow PID controller according to the present invention. RNA-based opposite motifs and negative feedback mechanisms were implemented as shown in FIGS. 1 and 2 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding RNA Binding Protein (RBP) mRNA z4 (construct "5") is expressed in cells under the control of a promoter upregulated by export molecule XL. RBP mRNA z4 is translated into RNA binding protein RBP, which inhibits translation of mRNA z3 encoding the activator Act linked to endonuclease ERN (Act-P2A-ERN mRNA). mRNA z3 is transcribed from the recombinant gene (construct "6" with constitutive promoter) and degraded by the endonuclease ERN.

FIG. 35 shows an embodiment of a molecular N-type inflow PID controller according to the invention. RNA-based opposite motifs and negative feedback mechanisms were implemented as shown in FIGS. 1 and 2 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding the activator 2mRNA z4 (construct "5") is expressed in the cell under the promoter upregulated by the export molecule XL. The activator 2mRNA z4 is translated into activator protein Ac2, which positively regulates transcription of another copy of the activator 2mRNA z3 encoded in another recombinant gene (construct "7" with Act 2-inducible promoter). In addition, act2 activates transcription of a recombinant gene encoding another copy of the actuator mRNA X1 (construct "6" with an Act2 inducible promoter).

Fig. 36 shows an embodiment of a molecular N-type autocatalytic PID controller according to the present invention. RNA-based opposite motifs and negative feedback mechanisms were implemented as shown in FIGS. 1 and 2 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding RNA Binding Protein (RBP) mRNA z4 (construct "5") is expressed in cells under the control of a promoter upregulated by export molecule XL. RBP mRNA z4 is translated into RNA binding protein RBP, which inhibits translation of mRNA z3 encoding activator Act1 linked to endoribonuclease ERN, internal ribosome entry site IRES and another activator Act2 (Act 1-P2A-ERN-IRES-Act2 mRNA). Transcription of mRNA z3 is upregulated by the activator Act2 and degraded by the endonuclease ERN by the recombinant gene (construct "6" with the Act 2-inducible promoter). In addition, act1 activates transcription of a recombinant gene (construct "3" with an activator-responsive promoter) encoding another copy of the promoter mRNA X1.

Fig. 37 shows an embodiment of a molecular P-type outflow PID controller according to the present invention, which includes all the components (configurations 1 to 4) shown in fig. 6 and 7. In addition, a recombinant gene encoding mRNA z4 encoding an activator Act linked to an endonuclease ERN (Act-P2A-ERN mRNA) is expressed in cells under the action of a promoter upregulated by the export molecule XL (construct "5"). In addition, another recombinant gene (construct "6" with constitutive promoter) transcribes another copy of mRNA, which encodes an activator Act linked to endoribonuclease ERN (Act-P2A-ERN mRNA) and denoted as z3, which is translated into activator Act and endoribonuclease ERN that degrades z 3.

Fig. 38 shows an embodiment of a molecular P-type inflow PID controller according to the present invention, which includes all the components (configurations 1 to 4) shown in fig. 6 and 7. In addition, a recombinant gene encoding RNA Binding Protein (RBP) mRNA z4 (construct "5") is expressed in cells under the control of a promoter upregulated by export molecule XL. RBP mRNA z4 is translated into RNA binding protein RBP, which inhibits translation of mRNA z3 encoding activator Act2. mRNA z3 was transcribed from the recombinant gene upregulated by activator protein Act2 (construct "7" with activator 2-responsive promoter). In addition, activator protein Act2 upregulates the recombinant gene encoding m2 mRNA (construct "6" with activator 2-inducible promoter).

Fig. 39 shows an embodiment of a molecular P-type autocatalytic PID controller according to the present invention comprising all components (configurations 1 to 4) shown in fig. 6 and 7. In addition, a recombinant gene encoding mRNA z4 of activator Act1 linked to endoribonuclease ERN (Act 1-P2A-ERN mRNA) was expressed in cells under the promoter upregulated by export molecule XL (construct "5"). In addition, the recombinant gene (construct "6" with activator 2-inducible promoter) transcribes mRNA encoding activator protein Act1 linked to an endoribonuclease ERN linked to additional activator protein Act2 (Act 1-P2A-ERN-P2A-Act2 mRNA) and denoted as z3, which is translated into activator protein Act1, endoribonuclease ERN degrading z3 and activator protein Act2 upregulating z3 expression.

FIG. 40 shows another embodiment of a molecular N-type outflow PID controller according to the invention. Protein-based opposite motif and negative feedback mechanisms were implemented as shown in fig. 11 and 12 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding mRNA z4 encoding activator Act2 linked to endoribonuclease ERN (Act 2-P2A-ERN mRNA) was constitutively expressed in the cell (construct "5"). Translation of z4 inhibited by the RNA binding protein RBP produces the activator protein Act2 and the endonuclease ERN which degrades z 4.

FIG. 41 shows another embodiment of a molecular N-type inflow PID controller according to the invention. Protein-based opposite motif and negative feedback mechanisms were implemented as shown in fig. 11 and 12 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding mRNA z5 of activator Act2 (construct "5") was expressed in cells under an output-inducible promoter. Another recombinant gene (construct "6" with activator 2-responsive promoter) was upregulated by activator protein Act2 to transcribe mRNA z 4. Both z4 and z5 translate into activator protein Act2.

FIG. 42 shows another embodiment of a molecular N-type autocatalytic PID controller according to the invention. Protein-based opposite motif and negative feedback mechanisms were implemented as shown in fig. 11 and 12 and described above (constructs and branches 1 to 4). In addition, a recombinant gene encoding mRNA z4 encoding activator Act2 linked to endoribonuclease ERN, internal ribosome entry site IRES and activator Act3 (Act 2-P2A-ERN-IRES-Act3 mRNA) was expressed in cells under upregulation of activator Act3 by Act 3-sensor protein (construct "5"). Translation of z4 inhibited by the RNA binding protein RBP produces the activator protein Act2, which upregulates expression of the endoribonuclease ERN that actuates mRNA m1, degrades z4, and activator protein Act 3.

Fig. 43 shows another embodiment of a molecular P-type outflow PID controller according to the present invention, comprising all the components shown in fig. 6 and 7 (configurations 1 to 4). In addition, a recombinant gene encoding mRNA z4 encoding the activator Act2 linked to endonuclease ERN (Act 2-P2A-ERN mRNA) was expressed in cells under the action of the output-sense promoter (construct "5"). Another recombinant gene (construct "6" with constitutive promoter) expresses another copy of mRNA z3, which encodes the activator Act2 linked to endonuclease ERN (Act 2-P2A-ERN mRNA). Both z3 and z4 translate into activator protein Act2, which upregulates the expression of mRNA m1, and endoribonuclease ERN that degrades mRNA z3.

Fig. 44 shows another embodiment of a molecular P-type inflow PID controller according to the present invention, which includes all the components (configurations 1 to 4) shown in fig. 6 and 7. In addition, a recombinant gene encoding RNA Binding Protein (RBP) mRNA z4 (construct "5") is expressed in cells under the control of a promoter upregulated by export molecule XL. RBP mRNA z4 is translated into RNA binding protein RBP, which inhibits translation of activator protein Act 2. mRNA z3 was transcribed from the recombinant gene upregulated by activator protein Act2 (construct "6" with activator 2-responsive promoter). In addition, the recombinant gene encoding m1 mRNA (construct "3" with the Act1/Act2 inducible promoter) is upregulated by the activator protein Act2 (and Act 1).

Fig. 45 shows another embodiment of a molecular P-type autocatalytic PID controller according to the present invention comprising all components (configurations 1 to 4) shown in fig. 6 and 7. In addition, a recombinant gene encoding mRNA z4 encoding the activator Act2 linked to endonuclease ERN (Act 2-P2A-ERN mRNA) was expressed in cells under the action of the output-sense promoter (construct "5"). Another recombinant gene (construct "6" with activator 3-inducible promoter) expresses mRNA z3 encoding activator Act2 linked to endoribonuclease ERN linked to another activator Act3 (Act 2-P2A-ERN-P2A-Act3 mRNA). Both z3 and z4 translate into activator protein Act2, which upregulates the expression of mRNA m1, and endoribonuclease ERN that degrades mRNA z 3. In addition, z3 translates into another activator protein Act3, which positively regulates its own expression.

Fig. 49 shows eight different effective interaction profiles including the opposite motif. In the control theory, it is assumed that the structure of the process to be controlled cannot be changed. Thus, in order to be able to control a given process, the control system must interact with it via its available inputs and outputs. In a living molecular system, the interaction may be positive, particularly if one molecule is converted to another molecule, increased production of another molecule, or decreased removal of another molecule. The interaction may be negative, particularly if the presence of one molecule increases the removal of another molecule or reduces the production of another molecule.

Fig. 49 shows three embodiments of direct or indirect interactions discussed. It is shown how the actuator can influence the output molecules, how the output molecules can act on the control network and how the control network can act on the actuator molecules. Based on the process to be controlled and the available implementation of the opposing core motif, the most appropriate profile for a given configuration can be selected from a set of all combinations.

The control network comprises a first control molecule (Z1) and a first antibody control network (Z2). The controlled network may interact with the control network through the output molecules (O) and the actuation molecules (a). In fig. 49, normal arrows indicate positive interactions, while flat headed arrows indicate negative interactions.

Fig. 49 i): the positive influence of the first control molecule (Z1) on the actuator molecule (A).

Fig. 49 ii): negative influence of the first control molecule (Z1) on the actuator molecule (A).

Fig. 49i a), ii a): the positive influence of the actuator molecule (a) on the output molecule (O).

Fig. 49i b), ii b): negative influence of the actuator molecule (A) on the output molecule (O).

Fig. 49 left column: the positive influence of the output molecule (O) on the first control molecule (Z1) (ib, iia) or the first anti-control network (Z2) (ia, iib).

Right column of fig. 49: the negative influence of the output molecule (O) on the first control molecule (Z1) (ia, iib) or the first anti-control network (Z2) (ib, iia).

Fig. 50 shows a schematic representation of a mathematical model describing a negative-actuated opposition-integral feedback motif with a positive gain process. The nodes marked with Z1 and Z2 (the first control molecule and the first anti-control molecule, respectively) together form the opposite motif. Species Z2 is produced at a rate μ and functionally annihilates when it interacts with species Z1 at a rate η. Furthermore, species Z1 can interact with the controlled network by inhibiting the production of species X1 (the actuator molecule) at a rate (α/(z1+κ)). To close the feedback loop, in the example shown, species Z1 is generated at a reaction rate proportional to θ and output species XL (output molecule).

FIG. 51 shows an embodiment of a molecular N-type integral controller according to the present invention based on the opposing integral feedback motif formed by repressing sense mRNA z1 (first control molecule) and antisense RNA z2 (first anti-control molecule). The cloud on the right side of fig. 51 symbolizes a regulatory network in biological cells, which comprises an actuator and an output, wherein the actuator positively regulates the output (positive gain process), in particular indirectly, i.e. through a plurality of further molecules of the network. In this example, repressed sense mRNA z1 is the product of a first recombinant gene (construct and branching marker 1) expressed in the cell under a promoter that is upregulated by the export molecule. In the described embodiment, the repressor sense mRNA z1 is translated to produce the repressor Rep, which is the negative transcriptional regulator of the recombinant gene (construct and branch marker 3) encoding the promoter mRNA (promoter), i.e.the gene encoding the promoter has a repressor-inducible promoter. In this example, a second gene encoding antisense RNA z2 (construct and branch marker 2) is expressed recombinantly in cells under the influence of a constitutive promoter. Antisense RNA has a sequence complementary to repressed sense RNA z1 and therefore hybridizes to z1, producing an inactive complex z1-z2, blocking translation of z1 and causing degradation of z1 and z2 (opposite motifs).

Fig. 52 shows an embodiment of a molecular N-type integral controller according to the present invention. In contrast to the controller shown in fig. 51, the opposite motif is achieved by protein-protein interactions. In the cellular network represented by the cloud on the right hand side of fig. 52, the actuation molecules are positively regulating the output molecules, in other words, the positive gain process is controlled. In this example, a promoter upregulated by the export molecule recombinantly expresses repressed mRNA z1 in the cell (see construct 1). mRNA Z1 is translated to produce repressor Z1 (the first control molecule, also known as Z1 (Rep)). The actuator mRNA m1 of the actuator molecule is upregulated by recombinant expression from the promoter that is upregulated by repressor Z1 (see construct 3). In addition, anti-repression mRNA z2 is expressed recombinantly under the control of constitutive promoters (see construct 2). Anti-repression mRNA Z2 is translated into anti-repressor Z2 (primary anti-control molecule) that specifically interacts with repressor Z1 to sequester and inactivate Z1, resulting in reduced or lost transcriptional repression of m1 by Z1. Proteins Z1 and Z2 implement protein-based opposite motifs that lead to integral control of the network.

Fig. 53 shows data of an exemplary experiment. In this example, the effectiveness of a PID controller in an experimental optogenetic environment described in the "cyberloop" setting of FIG. (a) is illustrated. An exemplary network to be controlled is genetically engineered in Saccharomyces cerevisiae. The control network is implemented in a computer that mimics the random dynamics of the biomolecules I, PI and/or fourth order PID controllers. The controlled network includes a gene expression loop that is initiated by optogenetic induction (blue light) to initiate the production of nascent RNA that can be measured under a microscope by fluorescent proteins. In this embodiment, these single cell measurements are performed in real time and sent to a computer to simulate the random dynamics of the controller of each cell. The experimental results for each of the three controllers are depicted in graph (B). The top graph shows the average time response of the I controller (across 168 units), PI controller (across 128 units), and fourth order PID controller (across 131 units). This figure shows the effectiveness of the PI controller in reducing oscillations of the average response over the cell. It also demonstrates the additional benefit of a PID controller in reducing overshoot. The bottom plot shows the Power Spectral Density (PSD) of the various responses. PSD is useful in revealing random oscillations at the single cell level: spikes in PSD reveal the persistence of random single cell oscillations. The examples provided demonstrate the effectiveness of the PID controller in smoothing peaks and thus significantly reducing single cell oscillations.

Examples

Example 1: opposing proportional-integral feedback control in mammalian cells

Perfect adaptation is demonstrated in sense/antisense mRNA implementation of the opposing integration feedback loop in mammalian cells, and the display controller is agnostic to the system it regulates.

Materials and methods

Plasmid construction

Mammalian adapted modular cloning (MoClo) yeast kit standard (Michael E Lee, william C DeLoache, bernardo Cervantes, and John E Dueber.A highly characterized yest toolkit for modular, multipart assembly.ACS synthetic biology,4 (9): 975-986, 2015) was used. Custom parts of the kits were generated by PCR amplification (Phusion Flash High-Fidelity PCR Master Mix; thermo Scientific) and assembled into kit carriers by Golden Gate modules (Carola Engler, romy Kandzia, and Sylvestre Marillonnet.A. one spot, one step, precision cloning method with high throughput capability. PloS one,3 (11), 2008). All enzymes used to carry out the moco procedure were obtained from New England Biolabs (NEB).

Cell culture

HEK293T cells (ATCC, strain No. CRL-3216) were cultured in Dulbecco's modified Eagle's medium (DMEM; gibco) supplemented with 10% FBS (Sigma-Aldrich), 1X GlutaMAX (Gibco) and 1mM sodium pyruvate (Gibco). Cells were maintained at 37℃and 5% CO2. Cells were passaged every 2 to 3 days into fresh T25 flasks. When required, the remaining cells were seeded into 96-well plates at 100 μl, 1×104 cells per well for transfection.

Transfection

Cells used in transfection experiments were plated approximately 24 hours prior to treatment with the transfection solution. The transfection solution was prepared with Polyethylenimine (PEI) "MAX" (MW 40000; polysciences, inc.) in a ratio of 1:3 (μg DNA to μg PEI) with a total amount of plasmid DNA per well of 100ng. Solutions were prepared in Opti-MEM I (Gibco) and incubated for about 25 minutes before addition of the cells.

Flow cytometry

Approximately 48 hours after transfection, cells were collected in 60. Mu.L Actutase solution (Sigma-Aldrich). Fluorescence was measured on a Beckman Coulter CytoFLEX S flow cytometer using 488nm laser with 525/40+OD1 bandpass filter. For each sample, whole cell suspensions were collected. In each measurement, additional unstained and single color (mcitrane only) controls were collected for gating and compensation.

Data analysis

The acquired data is analyzed using a custom analysis pipeline implemented in the R programming language. The measured events are automatically gated and compensated for further mapping and analysis.

Results

A schematic of the sense/antisense RNA implementation of the opposing integration feedback loop is shown in fig. 23A. The basic loop consists of two genes, which are encoded on separate plasmids. The gene in the activator plasmid is the synthetic transcription factor tTA (tetracycline transactivator) fused to the green fluorescent protein mCitine. Expression of this gene is driven by a strong mammalian EF-1 alpha promoter. This transcription factor actuates the expression of another gene in the antisense plasmid. This gene expresses antisense RNA complementary to the activating mRNA. Hybridization of these two species effects an annihilation reaction and closes the feedback loop. As a control that failed to produce integrated feedback, an open loop analog of a closed loop was established in which the tTA-responsive TRE promoter was replaced with a non-responsive promoter. A closed loop configuration was established to regulate the expression level of the activator tTA-mCitrine. In order to introduce specific perturbation to the activator, an Atazanavir (ASV) induced degradation tag (SMASh) was additionally fused to tTA-mcitrane.

To show that our genetically implemented circuits performed integrated feedback, ASV constant perturbation at a concentration of 0.033 μm was applied to HEK293T cells transiently transfected either with an open loop or with a closed loop. In addition, the set point was changed by transfecting the two genes in a ratio of 1/16 to 1/2. Fluorescence of the cells was measured 48 hours after transfection using flow cytometry. As the setpoint ratio increases, so does the fluorescence of ttamcitrane, indicating that the loop allows setpoint control (fig. 23B). A loop is considered adaptive if its normalized fluorescence intensity remains within 0.1 of the control without interference. Under this criterion, adaptation is achieved for all setpoints tested in the closed loop configuration, while none of the open loop configurations is managed to meet the adaptive criterion (fig. 23C).

Next, attempts were made to demonstrate that the implementation of a opposition integrator controller would provide immunity at different set points, regardless of its regulated network topology. Thus, a negative feedback loop was added from tTA-mCitrine to its own product. This negative feedback was achieved by the RNA-binding protein L7Ae, which was expressed under the control of the tTA-reactive TRE promoter and bound to the 5' untranslated region of the sense mRNA to inhibit translation (fig. 24A).

Either closed and open loops were transiently transfected with or without this negative feedback plasmid to introduce perturbation into the regulatory network. Set points 1/2 and 1 were tested by transfecting the appropriate ratio of activator to antisense plasmid as described previously. These different conditions were further perturbed at the molecular level by inducing tTA-mCitrine degradation by addition of 0.033 μm ASV. As shown in fig. 24B, in most cases, the closed loop resists both disturbances, and the open loop again fails to adapt. However, a closed loop with a set point of 1/2 of two disturbances also fails to meet the adaptation requirements. However, under the same conditions, it still remains much closer to the desired value for the open loop.

The ability of the opposing integration controller to resist topology network disturbances, as previously demonstrated in fig. 24, allows for further improvement of controller performance by increasing its complexity. In particular, a general control strategy is implemented, which is widely used in various engineering disciplines, and is called Proportional Integral (PI) control. This control strategy adds proportional (P) feedback actions to the integral (I) controller to enhance overall performance, such as transient dynamics and variance reduction, while maintaining adaptive characteristics. To achieve proportional feedback control with faster action than integral feedback, an alternative protein, the RNA-binding protein L7Ae, was used, which was produced from a single mRNA in parallel with mcitrane-tTA by using P2A self-cleaving peptide (fig. 25A). Thus, the expression level of L7Ae is expected to reflect the level of tTA-mCitrine proportionally. Thus, negative feedback is achieved by binding to the 5' untranslated region of the sense mRNA to inhibit translated surrogate proteins. Note that in contrast to the loop in fig. 24A, the production of L7Ae in the PI controller is not regulated by the tTA responsive TRE promoter. In fact, it is directly controlled by sense mRNA. Furthermore, the proportional feedback implemented in the PI controller is expected to be faster than the feedback achieved by the tTA-dependent generation of L7Ae (fig. 24), since it does not require additional transcription and translation steps.

As shown in fig. 25B, the controller without integral feedback cannot meet the adaptive criteria. On the other hand, as shown in fig. 25, the expression of tTA-mcitrane is ensured to be robust against induced drug interference using a Proportional Integral (PI) controller. This suggests that the additional proportional feedback does not disrupt the adaptive characteristics of the opposing integrating controller.

For a better understanding of the mathematical operation of the basic circuit depicted in fig. 23A, a detailed mechanical model is derived starting from the basic principle of mass-acting kinematics. Capital letters are used to indicate the concentration of species represented by their corresponding bold letters.

The detailed model shown in fig. 27 and 28 captures transcription of both plasmids (in D ₁ And D ₂ Represented) and translation of sense and antisense RNAs (represented by Z1 and Z2, respectively). Translation of sense mRNA produces a protein consisting of tTA, mCitrine and SMAshTag fused together (with X ₁ Representation). SMAShTag recruitment drug (denoted G), which in turn degrades complex X ₁ . The drug-escaping protein releases SMAShTag, leaving tTA and mcitrane fused together (with X ₂ Representation). When the latter dimerizes, it acts as a transcription factor that activates antisense RNA production. The model also captures the participation of resources shared between different transcription/translation processes. The transcriptional source (e.g., polymerase) is denoted by P and the translational source (e.g., ribosome) is denoted by R. Note that an additional translation step is added here compared to the loop of fig. 23A, where the antisense RNA is translated into a protein containing mriby 3 (denoted by Y). This allows an additional set of measurements (red fluorescence) to be obtained to better mathematically characterize the system.

To obtain a simpler mathematical model, a completely detailed model is simplified based on three mild assumptions (see "model simplified" section below). The simplified model is schematically and mathematically depicted in FIG. 26A, whereG ^T 、P ^T And P ^T The total concentration of plasmid, drug, and resource are expressed separately and assumed to be constant. The simplified model takes the form of a dynamic system that can be divided into controller modules that are feedback connected to the device modules to be controlled. The open loop (correspondingly closed loop) setting is achieved by setting the isolation rate η=0 (correspondingly η>>0) But is mathematically implemented.

The mathematical complexity of the reduced model depends on the level of modeling detail of the load imposed by the shared transcription and translation resources P and R. In the simplest case, the system is assumed to be unbraked. That is, resources P and R are approximately constant and are not affected by loops. In the second case, it is assumed that the burden is derived from only shared translation resources R. Mathematically, this is accomplished by letting R be Z as shown in the table of FIG. 26A ₁ And Z ₂ Is realized by a hill function. In both cases, by X ₂ ；Y、Z ₁ And Z ₂ A set of Ordinary Differential Equations (ODE) in (a) to describe dynamics, where p=p ^T . Finally, in the last case, the transcription burden is also considered. This is achieved mathematically by adding algebraic constraints as shown in the table of fig. 26A. This gives an implicit equation for P and thus produces a set of Differential Algebraic Equations (DAE). The detailed derivation of the reduced model is given in the "model reduced" section below.

Next, model fitting was performed for three different cases. Green fluorescence represents all of the genes involved in mcitrane (X ₁ +X ₂ +dimerization X ₂ ) Red fluorescence represents a molecule that involves mriby 3 (Y). The display (the "model fitting" section below) is not burdened with an adequate fit to the available data. However, the translation burden is sufficient to fit the data, so FIG. 26B shows the best of the translation burden casesAnd (5) parameter fitting. In fact, for both open/closed loop settings, with/without interference, green/red fluorescence, and in plasmid ratiosThe model successfully fits the data. Note that increasing the transcription load only yields a slightly better fit (due to the extra degrees of freedom) and is therefore not considered here.

It can be observed that in the open loop setting, the green fluorescence is near saturation for high plasmid ratios and the red fluorescence is saturated and begins to decrease for high plasmid ratios. This behavior is a consequence of the burden and cannot be captured with an unbiased model. Furthermore, in the closed loop setting, it was observed that the interference resistance was nearly perfect for low plasmid ratios, but began to worsen for higher plasmid ratios. This is expected because the loop exhibits a functional dynamic range that places limits on the allowable set point. This limitation is Z ₁ And Z ₂ As a result of the degradation/dilution of the burden imposed by the shared resource. Finally, it can be observed that the red fluorescence in the closed loop setting is very small compared to the open loop setting. This suggests that sense-antisense RNA isolation is efficient and as a result, the loop shows strong feedback. In fact, sense mRNA, produced constitutively, effectively sequesters antisense RNA and keeps it at very low concentrations.

Discussion of the invention

This study demonstrates the first realization of opposing integral feedback in mammalian cells. The principle verification loop is utilized to lay a foundation for robust and predictable control system engineering in biology.

Based on the opposite motif (fig. 21), a perfect adaptation of the proof of concept loop was designed and constructed. This is achieved by using hybridization of the mRNA molecules with complementary antisense RNA. The resulting translational suppression implements a central isolation mechanism. Specifically, antisense RNA is expressed by a promoter activated by the transcription factor tTA. This antisense RNA was complementary to and bound to tTA mRNA, thus blocking the negative feedback loop (FIG. 23A). By showing the loop to allow for different setpoints in the range of about 3.5 times (fig. 23B), the nature of the integral feedback control is highlighted. By further optimizing the loop parameters, it is likely that this folding dynamic range can be improved.

By modulating the disturbance of the species, it has been shown that closed loop achieves adaptability and is superior to similar open loop (fig. 23C). Furthermore, it has been shown that adaptation is also achieved when changing the set point of the loop.

Furthermore, it has also been shown that the implementation of the opposite integration feedback motif is largely unknown to the network structure of the species being regulated. This is achieved by introducing disturbances to the network of the controlled species itself (fig. 24B). Furthermore, it has been demonstrated that the closed loop is resistant to interference even in the presence of such additional disturbances to the network. In an open loop, disturbances, perturbation and perturbation with disturbances lead to a continuously stronger decrease in tTA-mCitrine expression.

Finally, to improve the performance of the opposite integral controller, proportional feedback is added (fig. 25). It has been shown that independent proportional controllers can reduce the steady state error of the tTA-mcitrane expression but cannot reduce it enough to meet the adaptation criteria. On the other hand, proportional Integral (PI) controllers have been shown to not disrupt the adaptive properties of the independent opposite motifs. It is expected that adding this additional proportional feedback will enhance performance, such as transient dynamics and variance reduction.

In addition to being able to produce overall feedback control, the implementation of sense and antisense RNAs is very adaptable and very universally applicable. Both sense and antisense are fully programmable, the only requirement being that they have sufficient sequence homology to hybridize and inhibit translation. Thus, the mRNA of an endogenous transcription factor can be easily converted to the opposite motif simply by expressing its antisense RNA from a promoter activated by the transcription factor. It should be noted, however, that in this case, the setting point of the transcription factor will be lower than in the absence of antisense RNA due to negative feedback, and in addition, if the mRNA of the endogenous transcription factor is not very stable, the integrator is expected to function poorly.

It is believed that the ability to accurately and robustly regulate gene expression in mammalian cells will find many applications in industrial biotechnology and biomedical applications.

Complete model

A detailed biochemical reaction network (fig. 27) describing interactions between various biochemical species is given in fig. 28.

Model simplification

In this section, the complete model given in fig. 28 is mathematically reduced to the model given in fig. 27, which has been used for the fitting shown in fig. 26B. The model reduction flow is based on the following assumptions:

Suppose 1. The binding reaction is fast.

Suppose that smashtag is released rapidly.

Suppose that the concentration of complex tTA: mCitrine: SMAshTag is low.

Assumption 1 and assumption 2 are based on the time scale separation principle, exploiting the fact that the binding reaction and the unique conversion reaction are much faster than the other reactions in the system.

As a result, quasi-steady state approximation (QSSA) is applied. It is emphasized that QSSA gives a simplified model of dynamic approximation, but steady state behavior is still accurate.

Suppose 3 is based on the fact that the complex tTA, mCitrine, SMASTTag (X ₁ ) It is very unstable, i.e. it either rapidly loses SMAShTag (in the conversion reaction) or rapidly binds to the drug, but this in turn rapidly breaks it. More precisely, mathematically, hypothesis 3 is converted into the following asymptotic inequality: x is X ₁ ＜＜κ ₃ . Hypothesis 3, which is different from hypotheses 1 and 2, yields an approximate reduced model, which is inaccurate in steady state systems.

Now, a mathematical derivation of the reduced model is shown. The law of conservation is given by

Since the binding reaction is much faster than the other reactions in the network (hypothesis 1), the following quasi-steady state approximation (QSSA) can be invoked

Wherein various dissociation constants (. Kappa.) are used ₁ 、κ ₂ 、κ ₃ 、κ′ ₁ 、κ′ ₂ 、κ′、And κ0) are both shown in fig. 28.

Law of conservation And->Is->And->The following expression is obtained:

similarly, by substituting conservation lawAnd->Is->And->We obtain a quasi-steady state approximation of (1)

The remaining sole law of conservation is represented byGiven the law of conservation of RNA polymerase.

By substitution intoAnd a quasi-steady state approximation of A, resulting in the algebraic equation

Wherein the method comprises the steps ofIt is desirable to write P as a function of X2. However, since this is a cubic polynomial of P, it is tedious to explicitly write closed-form solutions. Thus, this equation is implicit in P and X2.

In the case of a quasi-steady state approximation, a set of Differential Algebraic Equations (DAE) describing the evolution of X1, X2, Z1, Z2, P and Y can be written.

The set of DAEs can be compactly rewritten as

Wherein the method comprises the steps of

A final approximation can also be performed by invoking assumptions 2 and 3, i.e., X ₁ ＜＜κ ₃ Andwe have

And->

As a result, we can derive from the differential equationRemove->To obtain the following DAE

Wherein, in case of a slight misuse of the sign, the definition of the function k is modified to incorporate the drug effect as

Finally, the step of obtaining the product,can be rewritten into a more convenient form of

Wherein:

and n=2 is the hill coefficient. Note that toThe dissociation constant corresponding to the basal expression is greater than that corresponding to the expression in the presence of the activator, i.e., κ ₀ >κ ₂ Thus for any P>0，α(P)>0。

The simplified model is shown in fig. 26A.

Model fitting

In this section, we show that the no-load model is insufficient to fit the data shown in fig. 26B. The no-load model in the open loop setting (η=0) is described by the following ODE set.

Wherein:α ₀ ∶＝α ₀ (P ^T )，α ₁ ∶＝α ₁ (P ^T )，α∶＝α(P ^T )，κ∶＝κ(P ^T )。

calculating the fixed point of open loop dynamics by setting the time derivative to zeroX ₂ ,Z ₁ ,Z ₂ ,Y) To obtain

The green and red fluorescence measured in the experiment were measured with M respectively _G And M _R The expression is given by

Wherein c _G And c _R Is a proportionality constant that maps the concentration to green and red fluorescence, respectively. Note that a representsX ₂ Is also green fluorescent as a transcription factor. Indicating that its concentration in steady state is defined by(for detailed explanation, refer to the "simplified model" section). M is observed _G In->Is increased in a quadratic manner (becauseX ₂ At->In a linear increase). In addition, M was observed _R Is thatX ₂ Is a monotonically increasing Hill function of ∈so that ∈>Is a monotonically increasing hill function of (1). These two observations are contradictory to the data shown in FIG. 26B, because the green fluorescence saturation is high +. >While the red fluorescence is at high +.>And then starts to decrease. As a result, the no-load model cannot capture both behaviors.

Example 2: mathematical description of PI, PD and PID molecular controllers

We want to control the process with L dynamically interacting species at concentrations consisting of: x is X ₁ 、……、X _L Given. Where X is ₁ Is assumed to be the concentration of the actuated species (process input), X _L Is the concentration of the species being regulated (process output). Assuming that the molecular controller has n species whose concentration is defined by Z ₁ 、……、Z _n Given. We control the process by affecting X ₁ (see above figures). In particular, it is a combination of two or more of the above-mentioned

The function U may depend on X _L To allow feedback and may depend on the actuated species to allow the actuated species to be generated or eliminated in a manner dependent on its concentration.

The variables involved in the control are indicated by arrows or T-lines. In FIGS. 29-33, for example, arrows represent X as a function of the variables associated with the arrows ₁ An increase in the rate of production. This can be achieved by various means, for example increasing its expression or activation, reducing its degradation or inhibiting X ₁ Etc. On the other hand, a line ending with T represents X ₁ The decrease in the rate of production as a function of the T-line related variable may be achieved by reverse processes such as decreased expression, decreased activation, increased inhibition, increased degradation, etc. In the embodiment shown in the drawings to be carried out,

U＝U(Z ₁ ,Z ₂ ,X ₁ ,X _L )，

U is Z near the operating point ₁ And Z ₂ And X _L Is a decreasing function of (a). For linear analysis, and without loss of generality, one can simply assume the following form of U:

U＝h ₀ (XL；X ₁ )+h ₁ (Z ₁ ；X ₁ )+h ₂ (Z ₂ ；X ₁ )

wherein h is ₀ And h ₁ Is a monotonically increasing function (consistent with arrow) of their arguments and h ₂ Is monotonically decreasing (consistent with a T-line). In fact, at a given fixed point, the linearization of the two expressions of U described above has the same form. For our next analysis, U versus X ₁ The dependency of (c) will be suppressed to simplify the explanation. In other words, we will make

U＝h ₀ (X _L )+h ₁ (Z ₁ )+h ₂ (Z ₂ )

By inhibiting the reaction of X ₁ The possible dependencies of (a) do not lead to a loss of generality and as long asOur U implementation (e.g., activation/inhibition/expression/degradation of the actuating species) depends on the actuating species concentration X ₁ Analysis can be similarly easily performed.

PI controller

There are two implementation types to consider: n-type and P-type. The N-type controller is suitable for positive processes, while the P-type controller is suitable for negative processes. This ensures that the entire control loop achieves negative feedback.

1.1 second order implementation of PI controllers

1.1.1 methods with negative gain

These processes require a P-type controller to achieve stability. The method is described as follows

Given a desired set point We assume that there is a corresponding non-zero fixed point +.>

The P-type PI controller dynamics are as follows (see fig. 29, right):

U＝h ₂ (Z ₂ )+h ₀ (X _L )

we will let h ₀ And h ₂ Monotonically increasing.

And (5) lemma: closed loop with non-negative fixed pointIs that

h ₂ (0)<U ^* -h ₀ (μ/θ)<h ₂ (∞)

At this fixed point linearization dynamics we have:

wherein h' ₀ And h' ₂ Respectively is h evaluated at a fixed point ₀ And h ₂ Is a derivative of (a).

Let u' ₂ ＝h′ ₂ (*)z ₂ +h′ ₀ (*)x _L . From X _L The conversion function to u is given by

1.1.2 method with positive gain

These processes require an N-type controller to achieve stability. The method is described as follows

Given a desired set pointWe assume that there is a corresponding non-zero fixed point +.>

The N-type PI controller dynamics are as follows (see fig. 29, left panel):

U＝h ₁ (Z ₁ )+h ₀ (X _L )

we will let h ₀ Monotonically decreasing and h ₁ Monotonically increasing.

And (5) lemma: closed loop with non-negative fixed pointIs that

h ₁ (0)<U ^* -h ₀ (μ/θ)<h ₁ (∞)

At this fixed point linearization dynamics we have:

wherein h' ₀ And h' ₁ Respectively is h evaluated at a fixed point ₀ And h ₁ Is a derivative of (a). Let u: =h' ₂ (*)z ₂ +h′ ₀ (*)x _L . From x _L The conversion function to u is given by

Note that: this controller is proportional to the filter integral. However, the filter cut-off frequency is large forIs high and therefore the filter can be omitted in this case.

PD controller

2.1 negative gain method

These processes are described as follows (fig. 30, right):

we assume that there are non-zero fixed points

The P-type PD controller dynamics are as follows (see fig. 30, right):

U＝h(Z)+h ₀ (X _L )

let us assume h ₀ G when h monotonically increases ₀ Monotonically decreasing or increasing (depending on the desired PD parameters).

Linearization dynamics

It follows that

2.2 positive gain method

These processes are described as follows (fig. 30, left panel):

we assume that there are non-zero fixed points

The N-type PD controller dynamics are as follows (see fig. 30, left panel):

U＝h(Z)+h ₀ (X _L )

let us assume h ₀ G when h monotonically decreases ₀ Monotonically decreasing or increasing (depending on the desired PD parameters).

The linearization dynamics are as follows:

PID controller

We present three implementations, one is a second order implementation that requires two species, another is a third order implementation that requires three species, and the last is a fourth order implementation that requires four species. The second order controller implementation is simpler, but it covers only a subset of all PID controllers, while the third order implementation for all practical purposes covers all possible PID controller parameters with filtered PD components. The fourth order implementation is most general and covers all PID controllers with a filtered D component. It is the controller that most closely matches the PID industrial controller.

3.1 second order PID implementation

3.1.1 methods with negative gain

Negative gain processes are those with reduced dose response. These processes require a P-type controller to achieve stability. We assume that the method is described as

The P-type PID controller is dynamic as follows (see FIG. 31, right panel):

U＝h ₀ (X _L )+h ₂ (Z ₂ )

we will let h ₀ And h ₂ Monotonically increasing.

And (5) lemma: closed loop with non-negative fixed pointIs that

h ₂ (0)<U ^* -h ₀ (μ/θ)<h ₂ (∞)

At this fixed point linearization dynamics we have:

wherein h' ₀ And h' ₂ Respectively is h evaluated at a fixed point ₀ And h ₂ Is a derivative of (a). Let u: =h' ₂ (*)z ₂ +h′ ₀ (*)x _L . From x _L The conversion function to u is given by

3.1.2 method with positive gain

Positive gain processes are those with increased dose response. These processes require an N-type controller to achieve stability. We assume that the method is described as

The N-type PID controller dynamics are as follows (see fig. 31, left panel):

U＝h ₀ (X _L )+h ₁ (Z ₁ )

we will let h ₀ Monotonically decreasing and h ₁ Monotonically increasing.

And (5) lemma: closed loop with non-negative fixed pointIs that

h ₁ (0)<U ^* -h ₀ (μ/θ)<h ₁ (∞)

At this fixed point linearization dynamics we have:

Wherein h' ₀ And h' ₁ Respectively is h evaluated at a fixed point ₀ And h ₁ Is a derivative of (a).

Let u: =h' ₁ (*)z ₁ +h′ ₀ (*)x _L . From x _L The conversion function to u is given by

Wherein K is _D ＝-h′ ₀ (*)>0,(when alpha is selected to be sufficiently small)And (2) and

3.2 third order PID implementation

3.2.1 method with negative gain

These processes typically require a P-type controller to achieve stability. We assume that the method is described as

Given a desired set pointWe assume that there is a corresponding non-zero fixed point +.>The P-type PID controller dynamics are as follows (see FIG. 32, right panel):

U＝h ₀ (X _L )+h ₂ (Z ₂ )+h ₃ (Z ₃ )

we will let h ₂ Monotonically increasing.

And (5) lemma: closed loop with non-negative fixed pointIs that

At this fixed point linearization dynamics we have:

wherein g' ₀ (*)、h′ ₀ (*)、h′ ₁ (, and h' ₃ G is evaluated at a fixed point ₀ 、h ₀ 、h ₁ And h ₃ Is a derivative of (a).

Let u: =h' ₂ (*)z ₂ +h′ ₃ (*)z ₃ +h′ ₀ (*)x _L From x + _L The conversion function to u is given by

Wherein select h ₀ 、h ₂ 、h ₃ And g ₀ So as to K _I ＝θh′ ₂ (*),K _D ＝h′ ₀ (, and K) _P ＝γh′ ₀ (*)+h′ ₃ (*)g′ ₀ (*). After choosing the functions to satisfy the conditions, addingThere is some flexibility in the presence of conditions at the fixed point in the up-draw. For example, h ₂ (Z ₂ )＝k ₂ Z ₂ 、h ₃ (Z ₃ )＝k ₃ Z ₃ 、 (or->)。

3.2.2 method with positive gain

Given a desired set pointWe assume that there is a corresponding non-zero fixed point +. >

The N-type PID controller dynamics are as follows (see fig. 32, left panel):

U＝h ₀ (X _L )+h ₁ (Z ₁ )+h ₃ (Z ₃ )

we will let h ₀ And h ₃ Monotonically decreasing, and h ₁ Monotonically increasing.

Closed loop with non-negative fixed pointIs +.>And is also provided with

At this fixed point linearization dynamics we have:

let u: =h' ₁ (*)z ₁ +h′ ₃ (*)z ₃ +h′ ₀ (*)x _L From x _L The conversion function to u is given by

Wherein select h ₀ 、h ₂ 、h ₃ And g ₀ So as to K _I ＝θh′ ₁ (*),K _D ＝-h′ ₀ (, and K) _P ＝-γh′ ₀ (*)-h′ ₃ (*)g′ ₀ (*)。

3.3 fourth order PID controller

We propose a fourth-order PID controller based on two opposite motifs. The implementation is a PI plus filtered D controller. Since the derivative must always be filtered, this is the most versatile and least restrictive architecture, and it allows all possible PID controller parameters and filter cut-off parameters. This is the most common PID structure.

3.3.1 method with negative gain

The P-type PID controller dynamics are as follows (see FIG. 33, right panel):

we will let h ₀ And h ₂ Strictly monotonically increasing, and g (Z) ₄ ；X _L ) At X _L Strictly monotonically increasing in Z ₄ Is strictly monotonically decreasing. For exampleOr->Or->Etc.

Lemma 1: closed loop with non-negative fixed point Necessary and sufficient conditions of (2)

Is that

g(∞,μ/θ)<μ ₀ <g(0,μ/θ)

And is also provided with

h ₂ (0)<[U ^* -h ₀ (μ/θ)-μ ₀ ]<h ₂ (∞)

And (4) lemma 2:independent of η and positive. When eta → +.>

At this fixed point linearization dynamics we have:

wherein h' ₀ (*)、h′ ₂ H is estimated at a fixed point ₀ 、h ₂ Is a derivative of (2); θ _z g and theta _x g is the g evaluated at a fixed point relative to Z, respectively ₄ And X _L Is a partial derivative of (c).

We next calculate the slave x _L To u: =u _P +u _I +u _D Is a function of the conversion function of (a). From x _L To u _P Is defined by the conversion function of (2)Given, wherein K _P ＝h′ ₀ (*). From x _L To u _I The conversion function of (2) is given by

To calculate the slave x _L To u _D We first calculate the conversion function from u _D To z ₄ Is a function of the conversion function of (a).

And this is combined withIn fact, we get the slave x immediately _L To u _D Is a conversion function of (2)

Wherein K is _D ＝θ _x And (x) andnote gamma>0。

It follows that

3.3.2 method with positive gain

These processes typically require an N-type controller to achieve stability. We assume that the method is described as

The N-type PID controller dynamics are as follows (see fig. 33, left panel):

we will let h ₀ Strictly monotonically decreasing, h ₂ Strictly monotonically increasing, and g (Z) ₄ ,X _L ) At X _L And Z ₄ Is strictly monotonically decreasing. For exampleOr->Etc.

Lemma 1: closed loop with non-negative fixed pointNecessary and sufficient conditions of (2)

Is that

g(∞,μ/θ)<μ ₀ <g(0,μ/θ)

And is also provided with

h ₂ (0)<[U ^* -h ₀ (μ/θ)-μ ₀ ]<h ₂ (∞)

And (4) lemma 2:independent of η and positive. When eta is 0->

At this fixed point linearization dynamics we have:

wherein h' ₀ (*),h′ ₂ H is estimated at a fixed point ₀ 、h ₁ Is a derivative of (2);and->G evaluated at a fixed point is relative to Z, respectively ₄ And X _L Is a partial derivative of (c).

We next calculate the slave x _L To u:=u _p +u _I +u _D Is a function of the conversion function of (a). From x _L To u _P Is defined by the conversion function of (2)Given, wherein K _P ＝-h′ ₀ (*)>0. From x _L To u _I The conversion function of (2) is given by

This is combined with the fact that we immediately get the slave x _L To d _u Is a conversion function of (2)

Wherein the method comprises the steps ofAnd->Note that K _D ,γ>0。

It follows that

Example 4: mathematical description of inflow, outflow and autocatalytic PID molecular controllers

Differential operation of the second and third order PID controllers is achieved by a non-coherent feed forward loop. With respect to fourth-order PID controllers, the differentiation operators we call the opposite differentiators are fundamentally different. It is achieved by placing the opposite integration motif in its own feedback loop. This is an alternative technique to implement a differentiator using an integrator. Of course, since pure derivatives cannot be physically achieved, the resulting differentiator is low pass filtered: the pure derivative requires access to future inputs. Here we show that this skill can be achieved by using different integrators (in addition to the counter integrator) to construct other differentiators.

1. Outflow PID controller

1.1 Positive gain method

The N-type outflow PID controller dynamics are as follows (see fig. 46, left):

U＝h(Z ₁ ,X _L ,U _D )；U _D ＝g(Z ₃ ,X _L )

we will have h at Z ₁ And U _D Monotonically increasing in X _L Is monotonically decreasing. Furthermore, we will have g at Z ₃ Monotonically increasing and at X _L Is monotonically decreasing.

Linearizing the dynamics at this fixed point and assuming (κ) ₀ ＜＜Z ₃ ) We have:

wherein the method comprises the steps ofRepresenting the partial derivative of f with respect to x estimated at a fixed point.

From x _L The conversion function to u can be calculated directly and displayed as

Note that: this controller is a proportional-integral controller with a low-pass filtered derivative, where ω ₀ Representing the cut-off frequency.

1.2 negative gain method

Given a desired set pointWe assume that there is a corresponding non-zero fixed point +.>The P-type outflow PID controller dynamics are as follows (see FIG. 46, right):

U＝h(Z ₂ ,X _L ,U _D )；U _D ＝g(Z ₃ ,X _L )

we will have h at Z ₂ 、X _L And U _D Is monotonically increasing. Furthermore, we will have g at Z ₃ And X _L Is monotonically increasing.

2. Inflow PID controller

2.1 Positive gain method

The N-type inflow PID controller dynamics are as follows (see FIG. 47, left panel):

U＝h(Z ₁ ,X _L ,U _D )；U _D ＝g(Z ₃ ,X _L )

we will have h at Z ₁ And U _D Monotonically increasing in X _L Is monotonically decreasing. Furthermore, we will have g at Z ₃ And X _L Is monotonically increasing. Linearizing the dynamics at this fixed point and assuming (κ) ₀ ＜＜Z ₃ ) We have:

2.2 negative gain method

The P-type outflow PID controller dynamics are as follows (see FIG. 47, right panel):

U＝h(Z ₂ ,X _L ,U _D )；U _D ＝g(Z ₃ ,X _L )

3. Autocatalytic PID controller

3.1 Positive gain method

The N-type autocatalytic PID controller is dynamic as follows (see FIG. 48, left panel):

U＝h(Z ₁ ,X _L ,U _D )；U _D ＝g(Z ₃ ,X _L )

Note that there are two fixed points:and->It can be seen that the function g can be designed to produce an unstable fixation point +.>Therefore, for the rest of the analysis we assume +.>And->

At this fixed point linearization dynamics we have:

wherein the method comprises the steps of Representing the partial derivative of f with respect to x estimated at a fixed point.

3.2 negative gain method

The P-type autocatalytic PID controller dynamics are as follows (see fig. 48, right):

U＝h(Z ₂ ,X _L ,U _D )；U _D ＝g(Z ₃ ,X _L )

At this fixed point linearization dynamics we have:

Claims

1. An expression system for controlling a network in a cell, wherein the network comprises an activating molecule and an export molecule, wherein the activating molecule positively or negatively modulates the export molecule, wherein the expression system comprises a recombinant gene encoding a first control molecule, wherein the first control molecule positively or negatively modulates the activating molecule,

i) Wherein the first control molecule positively regulates the actuation molecule, and wherein the expression system further comprises a recombinant gene encoding a first anti-control molecule, wherein the first anti-control molecule negatively regulates, in particular inactivates, sequesters and/or annihilates the first control molecule, and wherein the first control molecule negatively regulates, in particular inactivates, sequesters and/or annihilates the first anti-control molecule, wherein

a. In the case where the actuating molecule is upregulating the output molecule, the output molecule is upregulating the first antibody control molecule, and

b. in case the actuating molecule down-regulates the output molecule, the output molecule up-regulates the first control molecule, or

ii) wherein the first control molecule down regulates the actuation molecule, and wherein the expression system further comprises a recombinant gene encoding a first anti-control molecule, wherein the first anti-control molecule down regulates, in particular inactivates, sequesters and/or annihilates the first control molecule, and wherein the first control molecule down regulates, in particular inactivates, sequesters and/or annihilates the first anti-control molecule, wherein

a. In the case where the actuating molecule is upregulating the output molecule, the output molecule is upregulating the first control molecule, and

b. In the case where the actuating molecule negatively modulates the output molecule, the output molecule positively modulates the first antibody control molecule.

2. The expression system of claim 1, wherein the expression system further comprises a recombinant gene encoding a feedback molecule, wherein the output molecule upregulates the feedback molecule, and wherein

a. In the case where the actuator molecule positively regulates the output molecule, the feedback molecule negatively regulates the actuator molecule, an

b. In the case where the actuating molecule negatively regulates the output molecule, the feedback molecule positively regulates the actuating molecule.

3. The expression system of claim 2, wherein

a. In the case where the actuator molecule is regulating the output molecule, the feedback molecule is

microRNA which down-regulates the production of the actuator molecule, or

RNA binding proteins which down-regulate the production of the actuator molecule, or

b. In the case where the actuation molecule down-regulates the output molecule, the feedback molecule is an additional mRNA encoding the actuation molecule.

4. The expression system of claim 1, wherein

a. The first control molecule is a sense mRNA encoding the activating molecule or a sense mRNA encoding an activator that upregulates the activating molecule, wherein the second control molecule comprises an antisense RNA comprising a sequence complementary to the sense mRNA sequence, or,

b. The first control molecule is an activator protein that upregulates production of the activator molecule by activating translation of mRNA encoding the activator molecule, or inhibiting degradation of the activator molecule, or a suppressor that down-regulates the function of the activator molecule, and wherein the first anti-control molecule is an anti-activator protein, wherein the activator protein and the anti-activator protein form a complex, wherein upregulation of the activator molecule by the activator protein is inhibited by the formation of a complex, or

c. The first control molecule is a sense mRNA encoding a suppressor that down-regulates the actuation molecule, and wherein the second control molecule comprises an antisense RNA comprising a sequence complementary to the sequence of the sense mRNA, or

d. The first control molecule is an inhibitor protein that down-regulates production of the actuator molecule by inhibiting translation of mRNA encoding the actuator molecule, or activating degradation of the actuator molecule, or an inhibitor that positively regulates the function of the actuator molecule, and wherein the first control molecule is an anti-activator protein, wherein the activator protein and the anti-activator protein form a complex, wherein down-regulation of the actuator molecule by the inhibitor protein is activated by formation of the complex.

5. The expression system according to any one of claims 1 to 4, wherein

a. The actuation molecule upregulates the output molecule, and wherein the output molecule upregulates the first control molecule,

b. the actuation molecule down-regulates the output molecule, and wherein the output molecule up-regulates the first antibody control molecule.

6. The expression system according to any one of claims 1 to 4, wherein

a. The actuation molecule upregulates the output molecule, and wherein the output molecule upregulates the first antibody control molecule,

b. the actuation molecule negatively regulates the output molecule, and wherein the output molecule positively regulates the first control molecule.

7. The expression system according to any one of claims 1 to 6, wherein the expression system further comprises a recombinant gene encoding a second control molecule,

a. in the case where the actuating molecule is regulating the output molecule,

i. the output molecule positively or negatively modulates the second control molecule, and the second control molecule negatively modulates the actuating molecule, or

Said output molecule down-regulates said second control molecule and said second control molecule either positively or negatively regulates said actuation molecule,

And, in addition, the processing unit,

b. in the case where the actuating molecule down-regulates the output molecule,

i. the output molecule positively or negatively modulates the second control molecule, and the second control molecule positively modulates the actuating molecule, or

The output molecule positively regulates the second control molecule, and the second control molecule positively or negatively regulates the actuation molecule.

8. The expression system according to claim 7, wherein the expression system further comprises a recombinant gene encoding a second antibody control molecule, wherein the second antibody control molecule down regulates, in particular inactivates, sequesters and/or annihilates the second control molecule, wherein the second control molecule down regulates, in particular inactivates, sequesters and/or annihilates the second antibody control molecule, and wherein the second control molecule down regulates itself, and wherein

a. In the case where the actuating molecule negatively regulates the output molecule, the output molecule positively regulates the second control molecule, an

b. In the case where the actuating molecule positively modulates the output molecule, the output molecule negatively modulates the second control molecule.

9. The expression system of claim 8, wherein

a. The second control molecule is a sense mRNA encoding a regulatory protein that regulates expression of the activator molecule, wherein the second anti-control molecule is an antisense RNA comprising a sequence complementary to the sense mRNA sequence encoding the regulator molecule, wherein in particular, in the case where the feedback molecule is an additional mRNA encoding the activator molecule, the regulator protein regulates expression of the additional mRNA encoding the activator molecule, or

b. The second control molecule is an RNA binding protein that binds to an untranslated region of an mRNA encoding the actuation molecule, thereby negatively or positively modulating the actuation molecule, and wherein the second anti-control molecule is an anti-RNA binding protein, wherein the RNA binding protein and the anti-RNA binding protein form a complex, wherein the negative or positive modulation of the actuation molecule by the RNA binding protein is inhibited by forming the complex.

10. The expression system according to claim 1 or 2, wherein

a. In the case where the actuating molecule is regulating the output molecule,

i. the output molecule positively or negatively modulates the first control molecule, and the first control molecule negatively modulates the actuating molecule, or

Said output molecule down-regulates said first control molecule and said first control molecule either positively or negatively regulates said actuation molecule,

and, in addition, the processing unit,

b. in the case where the actuating molecule down-regulates the output molecule,

i. the output molecule positively or negatively modulates the first control molecule, and the first control molecule positively modulates the actuating molecule, or

The output molecule positively regulates the first control molecule and the first control molecule positively or negatively regulates the actuation molecule.

11. The expression system according to any one of claims 1 to 10, wherein the actuatable molecule is an actuatable protein or a small molecule and/or the export molecule is selected from the group consisting of a protein, a small molecule.

12. A cell comprising the expression system according to any one of claims 1 to 11.

13. The cell according to claim 12, wherein the cell is a mammalian cell, in particular a human cell.

14. The cell according to claim 12 or 13, wherein the cell is a T cell, in particular a T cell expressing a chimeric antigen receptor CAR, in particular wherein the concentration of the export molecule in the cell is indicative of the concentration of at least one inflammatory cytokine in the cell, and wherein the actuation molecule is upregulating the production or release of at least one immunosuppressant in the cell.

15. The cell according to any one of claims 12 to 14 for use as a medicament, in particular in a method for the treatment of an immune disorder, in particular cytokine release syndrome or rheumatoid arthritis, or in a method for the treatment of a metabolic or endocrine disorder, in particular diabetes.

16. A method for controlling a network in a cell, in particular an ex vivo method, wherein the method comprises expressing in the cell at least one recombinant gene of the expression system according to any one of claims 1 to 11.