WO2020261154A1 - Computer implemented method for generating a culture protocol for bio-manufacturing - Google Patents

Abstract

A method is provided to generate via a computer a culture protocol of a biological system for a controlled culturing system, the method including providing a model of the biological system, generating a state space from said model, searching a given target state within the state space and collecting within the state space previous states leading to the target states.

Description

“Computer implemented method for generating a culture protocol for bio manufacturing”.

DESCRIPTION

OBJECT OF THE INVETION

The present invention relates generally to prediction of interactions of at least a first with a second cell within a biological system and to generate a biomanufacturing protocol from such prediction. The disclosed teachings are embodied in systems, methods and computer program products for predicting the progression of a biological system, and for prediction and optimization of culturing such biological system in order to obtain a pre-defmed effect. These systems, methods and computer program products are implemented for generating a production or culture, i.e. a biomanufacturing protocol, e.g. a culture protocol to be used in a cell culture system or a protocol for culturing in a controlled environment a bio-printed structure embedding biological material, such as tissues, organoids, organs or the like. In particular, according to the invention, it is possible to simulate and control both structural organization, e.g. via bioprinting techniques, and functional stimuli, e.g. via actuators and effectors of a bioreactor.

STATE OF THE ART

A culture protocol is often prepared with a trial-and-error process via in-vitro processes within a bio-reactor. Indeed, complexity of biological processes have so far led to in-vitro experiments rather than exploitation of in-silico simulations. A biological process may also take place in a bio-printed structure, e.g. a part of an organ for transplant. Such structure does not necessarily require to be subsequently processed in a bio-reactor, where the printed structure is stimulated by a number of effectors or actuators of the bioreactor. The bio-printed structure is cultured for example in a chamber having a simple control, e.g. keeping physical parameters such as humidity, temperature, pressure etc. constant. In order to provide predictions, models are known for modelling the cultured biological system, including its structural aspects, which spontaneously emerge and/or are determined artificially (for example, by bioprinting processes), as well as its functional evolution, which spontaneously emerge and/or is enforced via artificial stimuli (for example, provided by a bioreactor).

Some of the known biological modelling techniques are as follows.

Agent-based models center on the concept of agent, that is, an autonomous entity sensing the environment and taking decisions according to its individual set of rules. Groups of agents can interact among each other following the same paradigm. A group of agents and their relationships define an agent-based system, which can exhibit complex emergent behavior patterns such as competition and collaboration even in its simplest forms.

Every agent in the system is an explicit representation of an individual. This provides it with unique functioning and individual history. This can be exploited, in more complex agent-based systems, for learning and adaptation of the single agent.

In modeling biological systems, agents are provided with cellular functional structural features and behavior. Usually, agents modeling cells express cellular behaviors and possible evolutions, as well as physical and mechanical properties. And, the agent-based system models the interactions between cells. This corresponds to a very close representation to the physical system, and enables to reenact behaviors at different levels and scales, covering emergent behaviors encompassing all system levels. Agent-based models can be implemented with tools such as FLAME, REPAST, and SPARK.

Process Calculi (PC, or Process Algebras, PA) methods are based on is the algebraic formalism. This is reflected in the fact they are text-based languages, and their syntax uses symbols and rules from algebra and mathematics in general. Among the others, some implementations express spatiality and compartmentalization of the biological system. An example is Brane calculus, which focusses the simulation around biological membranes, which play the role of coordinators for the modeled processes. Another one is BioAmbients, which is provided with special operators able to specify merging, splitting, and communication between biological compartments, and is based on pi- calculus; BAM is a tool supporting stochastic simulations in BioAmbients.

Rule-based models are very abstract representations which focus on the rules underlying the system’s emergent behavior. They are particularly of use when the set of such rules is way simpler than the model it generates: the model is the enactment of a limited number of patterns repeating themselves. This language is particularly of use for modeling certain types of biological systems. In fact, its notation is very similar to that employed for representing chemical reactions and biochemical interactions between molecular species. They can easily cover, for example, reaction stoichiometry, and kinetic parameters of an interaction. Rule-based systems are very compact: each rule is an independent unit. This akes them easy to modify independently. Compactness helps accessibility: their simple syntax makes them human-readable, and possibly visually represented and modified with graphs. Existing tools for systems biology leverage these advantages, becoming accessible also for non-expert users. Some examples are BioNetGen, BIOCHAM, Kappa and Virtual Cell.

State charts are an easy-to-use, state-centered formalism recapitulating the representational style of state diagrams. Passages from one state to another are event driven, and each state corresponds to a particular set of parameters for the system. They support readable visual representation, with the possibility to easily highlight the interdependence between states in a reactive system. In systems biology, state charts are useful for they start from visually representing functional diagrams widely employed in biology. And, they augment them providing depth, hierarchy in states transitions and orthogonality between states. This allows to capture more of the biological system complexity, limiting the risk the number of possible states explodes.

In Boolean networks, nodes can assume one out of two states. Each node is a boolean variable, updated by a boolean function determining its truth value given the inputs from the neighbor nodes in the network. The most common application of this formalism to biology is the approximation of the dynamics of genetic regulatory networks. In these models, genes can be active or inactive, and boolean functions model regulatory relations between genes. This approach performs a strong abstraction from the complexity of the system, removing all quantitative aspects of gene activation, including the intermediate passages through gene products regulating target genes, and their respective kinetics. Yet, when dealing with large regulation networks, this can be a strategy for complexity reduction. And, it finds applications in studying the robustness and stability of gene regulation networks. Qualitative networks extend Boolean ones, devising a finite number of states each node can assume. Interesting examples of how Boolean networks can be used to analyze regulatory networks in systems biology are GINsim and BoolNet. An implementation of qualitative networks can be found in Bio Model Analyzer.

Petri Nets (PNs) collect many advantages of the previously described approaches for modeling distributed, concurrent processes. In addition, they have exact mathematical definition of their execution semantics, and support visual representation. They can easily encode process calculi and agent-based systems. Also, they can specify architectures recapitulating graph-based models such as qualitative and Boolean networks. PNs can also extend network-based formalisms by including quantitative aspects from the system. In fact, they support both qualitative aspects, encoded in the network architecture, and quantitative information, in quantification of resources and emergent network evolution. This is particularly of use in modeling biology. In fact, on one side it recapitulates and expands expressive power of all the other formalisms. On the other side, it allows to flexibly comprise in a model the diverse information characterizing systems biology as a knowledge domain. PNs come in different shades, from the low-level formalism, providing semiquantitative discrete representations of concurrent processes, to different high-level formalisms, supporting continuous information, timings, stochasticity and hierarchy.

In particular, it is also important to address spatiality of biological systems. For example, models are known to represent microscopic, mesoscopic and macroscopic levels, accounting for molecular interactions and networks, cell-cell and cell -environment communication and tissue- or organ-level phenomena. Compared to compartment-based models such as BioAmbients, which in a way also expresses spatiality, these formalisms provide a structure representing positions in space independently of the objects possibly occupying them. Lattice-based models are based over a regular repeated graph and are formed by identical n-dimensional grid sites. They have periodic or fixed boundary conditions in each direction over the grid.

Cellular automata are n-dimensional grids devising, for each position, either the presence or absence of a cell. Each cell has neighbors, and according to a mathematical function taking them as inputs, the whole model evolves in terms of state changes at each position. This allows to model pattern formation according to short- and long-range interactions between cells. In multiscale models of these kinds, the challenge is to set up a homogeneous representation, including communication between different model levels across multiple spatial scales. It is also necessary to reconsider specific asymptotic techniques for the analysis of the multiple time scales involved. Cellular Potts models combine the Monte Carlo method with a regular lattice-based model of spatiality. In general, cellular Potts models devise objects living in the lattice. These objects may be either discrete such as cells, or continuous, such as molecular gradients. Either way, their interactions, such as cell-cell communication, or cell-nutrient contact, are associated with an energy description. Energy minimization of a Hamiltonian function drive lattice rearrangements to simulate the evolution of the system, including its spatial architecture. CompuCelBD is a general modeling framework for cellular Potts models, which combines rigorous energetic and mechanical consideration of the system with usability and biology-centered representational capabilities.

Lattice-free models, on the other hand, represent spatial features of a system without specifying a spatial scaffold external to the system. For example, vertex models represent cell membranes as a set of polygonal points. Basing on tensions deriving from cell-cell adhesion forces and cell elasticity, during the simulation they update the position of each vertex.

Hybrid modelling approaches integrate state-based, event-driven discrete formalisms presented so far with the capability to represent continuous dynamics in each modeled state. The latter feature is usually supported by mathematical formalisms such as Ordinary Differential Equations. Hybrid systems can leverage the advantages of both mathematical and computational models, moving over the trade-off between expressivity and computational cost. In fact, they can accurately represent continuous phenomena with some model structures, and perform stronger abstractions, through discretization, in others. For this reason they are becoming relevant to systems biology, also in terms of adaptation of dedicated experimental procedures and knowledge exchange standards. Recently, knowledge of biological processes and complexity within biological systems has been deeply scrutinized to define and express functions and relations.

In particular, ontogenesis is one of the key concepts at the base of the developmental biology (Scott et al., 2001). It is defined as "[...] the development of a single individual, or a system within the individual, from the fertilized egg to maturation and death." (Said, 2018). Ontogenetic processes comprise complex and intertwined mechanisms at different levels, from the embryonic development of the organism as a whole to the differentiation of single cells. A particularly challenging task when modeling ontogenesis is to predict the outcome of a developmental process, simulating the formation of emergent morphological and phenotypic patterns from local inter-cellular interactions. This includes their organization in space, and the consecutive temporal stages characterizing the process. Each stage corresponds to a different conformation and regulative set-up involving multiple interacting cells. Since the regulatory states of these cells depend on the relations with their surroundings as well, such conformations dictate the communication schemes they engage into (Guglielmi and Renzis, 2017). This contributes to create a multi-dimensional, dynamic landscape of inter-dependent regulative states in which cells can fall into (Nepal et al., 2013; Huang, 2012).

Furthermore, in biology, each interaction context can contain and belong to other interaction contexts. In fact, a context can correspond to a specific set of interacting biological structures, being part of and being composed by other structures. Or, a context can define a bioprocess, separable into and contributing to other bioprocesses. Models of biological systems require efficient ways to represent context-dependent and flexible hierarchies. This implies the models are able to represent multi-level systems. Each level of organization may correspond to different dimensional ranges of interest, implying a model should support multi-scale information in both space and time dimensions.

Comprising multiple system levels brings on a systemic and holistic view considering all interconnections between subparts. For example, in a living organism some levels of interest can be that of molecules and molecular networks, the one of cells and cellular communications, the tissue and the organs levels respectively.

A good computational model has then a multi-level, hierarchical architecture, and represents separately each level of interest from the system. Still, biological actors from each level coexist on a spatio-temporal continuum in the actual system, and this draws necessary interconnections between levels, which a good model should then represent in a clear and consistent way.

Multi-level and multi-scale are not synonyms: the first refers to multiple organizational levels, the second to the fact biological systems, as well as each of their levels, can span over large time and space scales. The respective ranges do not univocally define the levels of interest, nor a level sets the boundaries for a certain scale range. Models need to express a wide range of parameter values, preserving dimensional consistency both intra- and cross-level in the model. Another aspect to consider is that system biology collects contributions from different scientific domains, organizing a multi-level scheme of existing or brand new knowledge corresponding to single system levels. This makes the model construction process complex. One of the approaches for comprising such diverse contributions is the composition of existing models into one with a larger scope (Bartocci and Lio, 2016). This raises consistency issues (Rogojin and Petre, 2016) as well as additional requirements to modeling formalisms, such as the capability to naturally support multi-level and hybrid models (Bardini et ah, 2017).

Existing computational approaches and tools for modeling biological complexity often recapitulate known practices and procedures from computer science, such as formal and static analyses, model checking, and runtime verification. A variety of modeling approaches based on different formalisms exist. Each of them has specific strengths when applied to computational systems biology (Bartocci and Lio, 2016; Fisher and Henzinger, 2007). While existing approaches may answer to general requirements from biological systems, they tend to fail at proper holistic modeling of ontogenesis, where not only physiology and phenotype emerge from the system subparts, but the subparts themselves self- reproduce, determining regulative and structural changes to themselves and the overall system.

More in general, limitations of current approaches emerge when targeting biological complexity with a systemic perspective. Considering modeling capabilities on one hand, current approaches fail to capture spatial patterns emerging from local interactions between biological entities. This is due to the huge computational complexity implied, and the lack of a modeling strategy specifically oriented to this specifically (Bartocci and Lio, 2016; Bartocci et al., 2015). Thinking of the modeling process on the other hand, for fine-tuning analysis and simulation, it is possible to combine different approaches, leveraging their specific capabilities for partial aspects of the same modeling problem. Yet, combining heterogeneous approaches in custom solutions follows a problem-specific paradigm.

Tissue engineering, food processing e.g. fermentation processes and cellular agriculture, generation of monoclonal antibodies, and production of pharmaceuticals e.g. insulin increasingly require increasing volumes of production, which can be satisfied via automated or partially automated biological system culturing units, an example of which is a bioreactor. The culturing unit may increase its productivity via the definition of a set of instructions, i.e. a culture protocol, acting on the actuators of the unit to automate the culturing process of a biological system. It is still unexplored how an efficient modelling approach for a biological system may benefit the automatic or semi-automatic generation of a culture protocol for a biological system. In particular, a semi-automatic generation of a culture protocol is experienced when one or more versions of a culture protocol are automatically generated and the latter are subsequently adjusted by experiments in order to provide a fully functioning or optimized culture protocol.

Furthermore, it is important to understand how different 3D geometries obtainable at the end of the bio-printing process affect biological processes of the cells embedded in the 3D printed structure in order to provide a more detailed biomanufacturing protocol. SCOPES AND BRIEF DESCRIPTION OF THE INVENTION

The scope of the present invention is achieved by a computer based method for generating a culture or production, i.e. a biomanufacturing protocol for a biological system of one or more cells within a culturing system for example a controlled bioreactor, comprising the steps of:

Providing a model of biological processes related to culturing between the at least two cells within a chamber of the culturing system; the model being and expressing 3D spatial functions between said cells and biological functions of the cells

- Generating at least a portion of a state space of the model via a biological model simulator;

Searching a target state condition within the generated state space and identifying at least a first and a second path of states within the state space including the at least one target condition and respective set of previous states leading to the target state condition, and

Selecting an optimal path between the at least first and second path via a fitness function

Generating a culture protocol based on said optimal path and set of previous states. According to the invention, it is possible to automatize the process of culture protocol generation using a model having 3D spatial functions, i.e. tracing the macroscopic evolution of the culture that is important in e.g. tissue engineering. Preferably the model is multi-level to use use different degrees of abstraction for different system parts. Examples of levels are: molecules (metabolites, transcripts, genes, proteins), cells, cell aggregates, tissues, organs, organisms, populations. By degree of abstraction (from low to high) it is meant a physical model of a biochemical reaction with quantitative parameters (with units), semi-quantitative functional model allowing to represent“high”, “medium”,“low” levels for molecules on an arbitrary scale, detailed qualitative model highlighting all relations but not their intensity, simplified functional model highlighting only some relations and variables in terms of presence/absence.

According to a preferred embodiment, the bio-manufaturing protocol is structured to include spatial and biological details of a starting condition for the given cell culturing process within the culturing system and a controlled machine, e.g. a 3D bio-printer, deposits biological material according to the starting condition information of the protocol. In particular, the protocol may provide as a starting condition information e.g. information about a structure that has been previously 3D bio-printed or includes instructions for the 3D bio-printing process and the subsequent culturing process. Therefore, the bio-fabrication process, in some instances, may include bioprinting to set up the structural aspects of the system, followed by the operation of a simple culture system keeping parameters constant during the entire culture process. In this instance, it is evident that the bio-printing phase in the beginning has the higher control over the system evolution. This example highlights the fact that a bio-fabrication protocol is structured so as to handle both the structural initial conditions, e.g. cell positioning, at culturing set-up, and the following functional stimuli to cells for triggering biological or bio-chemical processes in order to gain extensive control over the biological system. According to the invention, via a properly defined fitness function, it is possible to optimize also structural aspects, i.e. those controlled during the 3D bio-printing process, of a biological system such as an organoid.

According to a preferred embodiment, the method further comprises the step of executing the culture protocol on the controlled culturing system; collecting at least a parameter indicating a biological, chemical, biochemical or physical quantity at defined spatial coordinates during the protocol execution; adjusting the model based on such spatially organized measures.

In order to generate a further optimized culture protocol, it is possible at least an iteration where the generated protocol is executed on a controlled culturing system, collecting data used to refine the model.

According to a preferred embodiment of the present invention, the method further comprises the step of receiving input information about the culturing system, the model including at least a parameter based on said input information.

For example, input information comprise one or more parameters that are measured or calculated by the culturing system during execution of the protocol.

According to a preferred embodiment, the model expresses ontogenesis of the biological system, and comprises:

o At least one cell biological sub-model expressing at least one ontogenetic process by the combination of cell autonomous biological process between transcription and/or translation and/or enzymatic reaction and/or gene regulation and/or post-transcriptional regulation to express a biological process of interest; and

o At least a spatial sub-model (Interactive Spatial Grid) to explicitly represent a spatial grid architecture of the biological system and the surrounding environment within the chamber, together with at least an interaction taking place between a pair of spatial nodes in the grid when in both a biological entity sub-model is active or present; o The at least one cell sub-model and the at least spatial sub-model communicating via writing and reading functions to determine the activity of the at least one cell sub-model in a spatial node of the spatial sub-model to trigger the execution of a relationship function associated to the spatial nodes, wherein said function include at least one inductive relationship function expressing at least one of a cell movement, a molecular flow, a mitosis, an apoptosis, a signal sensing and a signal sending.

Ontogenesis is a well defined class of processes including bacterial cultures. According to the model, the spatiality - which is important for a correct representation of ontogenesis - is explicitly taken into consideration via an active model, i.e. including inductive functions that are important for a correct representation of ontogenesis. Furthermore, the spatial sub-model defines an interface with the culturing system, which provides stimuli and control during the execution of the in-vitro experiment and, therefore, needs to be taken into consideration in modeling.

According to a preferred embodiment of the invention, the model further comprises a process sub-model expressing a pre-defmed sequence of states of the biological system as a function of a biological parameter of the at least one cell sub-model and/or the at least one control parameter of the culturing system and wherein the writing and reading functions put in communication the process sub-model and the spatial and cell sub models to provide inputs and receive data to trigger a phenotypic switch from one state to another of the pre-defmed sequence.

The process sub-model includes a further interface between the culturing system and the biological system and structures the model to focus on states to increase control and monitoring of the simulation.

According to a preferred embodiment, at least one of the spatial sub-model and cell are multilevel so that, via the writing and reading function, the communication of a parameter of a lower level is transferred via each and every higher level.

In a multilevel structure, information to lower levels is conveyed only via higher levels and this helps to manage complexity, which is important in systems biology where complexity is an issue.

According to a preferred embodiment of the present invention, the at least one cell sub model expresses the at least one ontogenetic process by the combination of at least an biological process selected among a migration wave, an apoptotic wave, a proliferative phase, patterning.

In view of the main functions included in the biological entity sub-model, it is possible to model more complex functions.

According to a preferred embodiment of the present invention, the sub-models are expressed via Petri nets.

Such formalism has proven to be particularly effective to express a complex systems biology models.

In addition, a general-purpose method to model a biological system is given in claim 10. BRIEF DESCRIPTION OF THE DRAWINGS

The method of the present invention may be better understood from the following detailed description, in which reference is made to the attached drawings, which represent a preferred and non-limiting embodiment thereof, in which:

Figure 1 is a chart illustrating the flow of a process according to the present invention;

- Figure 2 is a sketch of the structure of a model for the method of the present invention including a spatial sub-model (ISG), a process sub-model (SL) and a set of biological entity sub-models (CELLS);

Figures 3-5 show diagrams of respective functions embedded in the model of figure 2;

- Figures 6-16 show diagrams of respective functions embedded in the spatial sub model;

Figures 17 to 20 show diagrams of a specific embodiment of the model in figure 2 for the process in figure 18; and

Figures 21-23 show tables of a state space of the specific example of figures 17- 20;

Figure 24 shows a second example of sub-model additional to that of figure 20; Figures 25-27 show with different highlighted information a portion of a state space generated based on sub-model of figure 24; and

Figure 28 shows a portion of a protocol according to a standard framework, e.g. IS088 - developed by Sartorius AG and used in bioreactors.

DETAILED DESCRIPTION OF THE INVENTION

Systems and methods have been disclosed for identifying optimal culture protocols for a biological system, using selected parameters. The techniques are based on biological knowledge, mathematical models, computer simulations, and optimization methods. According to figure 1, initially, a model 100 is created. This includes sub-models to simulate all the relevant biological processes based on e.g. both chemical and physical parameters such as those controllable within a culturing system for a biological material used in e.g. tissue engineering, food processing e.g. fermentation processes and cellular agriculture, generation of monoclonal antibodies, and production of pharmaceuticals e.g. insulin. These sub-models include mathematical models for processes that affect interaction of at least a first cell with a second cell via ontogenetic models of the following inductive functions, e.g. differentiation, transcription, translation, enzymatic reaction, post- transcriptional regulation, and a spatial model, including one or more of the following relationship functions, e.g. neighbor detection, cell movement, molecular flow, mitosis, apoptosis, signal sensing and signal sending, as will be discussed below in greater detail. A further block of the model describes a sequence of input states of selected parameters of the sub-models expressing the inductive and/or relationship functions.

Functions of the model are based on existing knowledge, e.g. literature, databases, experiments etc., and, optionally but preferably, on data measured within a controlled bioreactor 101. Example of existing knowledge sources are model databases made available by e.g. the National Center for Biotechnology Information, the European Bioinformatics Institute, the SenseLab of Yale University.

The combination of the above provides a detailed mathematical model of the overall biological system in a general sense and with a desired level of abstraction with respect to the real biological process. In particular, parameters of model 100 may be quantitative, e.g. kinetic models of biochemical reactions, gene transcription rates, to represent at a low level of abstraction the process or be qualitative such as a conditional rule that can be expressed e.g. by flags, tags or the like e.g. to express that the parameter is present or absent, the gene is transcribed or not, the protein is active or inactive, the transcript is present or absent etc. as will be explained below in greater detail. At least some of the quantitative parameters may be adjusted on the basis of measures from bioreactor 101.

A model may be of any kind where a state space can be generated. In particular, a non exhaustive list comprises computational models such as event-driven, state-based models, finite states machines, agent-based models; and mathematical models such as physical equations. Furthermore, where a spatial information is important for the prediction, such spatial information may be either implicit in the model, such as for example in case of a diffusion process, or explicit and include a grid with nodes where cells or another biological material is located and, via mathematical functions, may move from one node to another or to detect the presence or not in an adjacent node of a given sub-model of biological material, so as to explicitly provide a position information.

Then a state space 110 is generated using a state space generator. To do this, possible values of certain parameters such as, for example, photo or video tracking or chemical measures of overall cellular viability, presence of cells, culture medium pH, fluorescent signals for functional activations, for example the expression of phenotype markers, the production, accumulation or depletion of a metabolite, the secretion of a molecule, etc. are considered. Thus, a number of possible states is generated. This number could be very large because of the number of possible values or conditions of the parameters. The amount of possibilities depends on the number of parameters considered and their values' ranges or possible conditions. The number of parameters ultimately depends on the level of abstraction of model 100, which is flexible depending on the approach by the model’s author and can thus provide a reasonably limited state space also in case of a rather complex biological system.

After generation of the state space (or of a portion of interest of the state space), during state space exploration 120 suitable algorithms explore the state space to search one or more target conditions, that is for example a particular state of the model satisfying some condition(s) over variable values expressed under the chosen model syntax, for example “the level of GFP protein must exceed 5” will select all the states the model can reach which respect this constraint. Example of exploration algorithms are a Gaussian algorithm or a Neural Network algorithm. In particular, uniform search methods do not assume information about the state space and the target state location, e.g. traditional depth-first search, breadth-first search, iterative deepening, lowest-cost-first search. Heuristic search methods include information about the target state’s location in the form of a heuristic function, e.g. heuristic depth-first search, greedy best-first search, A* search.

Within the state space or portion of the state space, the target condition is at a certain step of a sequence or path including previous states starting from an initial given condition and following states to reach a final state. It is possible to identify such one or more paths or sequences via Design Space Exploration algorithms such as particles swarm, e.g. WSPSO, i-PSO, DPSO), simulated annealing, e.g. ASA, or genetic algorithms, e.g. Multi -Objective Genetic Algorithm MOGA-I, MOGA-II, NSGA-I, NSGA-II, SPEA2, SMPSO). As a matter of fact, such algorithms generate a state space where target conditions are more likely to be found. Therefore, only in very simple simulations or predictions the whole state space is generated and, afterwards, searched to find the target state.

All state paths including the target state or state combination are called target paths and shall then be processed via a fitness function, which is constructed by mathematically considering different possible factors, which may be influenced by the culturing scope. These may, for example, include the number of states in the target path e.g. which can be minimized in order to find the shortest path leading to the target condition, or the absence of a set of states in the path leading to the target state. In particular, the user can alter certain specific parameters in the fitness function so as to adjust this function to the user's specific goals. The user can be anybody, including a tissue engineer, a scientist or a drug developer. Based on the selected parameters, the fitness function is applied over the set of target paths. This results in the calculation of a fitness score for each and every target path. In this way, a subset of at least one optimal path is identified within the set of target paths. In general, the optimization step 130 is carried out in a path selector, either by search heuristics or by analytical methods, in order to select the optimal path from all the scored possibilities. The analytical methods include the use of Operations Research techniques such as the said use of a fitness function to prioritize or select the optimal target paths. In selecting the optimal path, which operationally corresponds to the optimal culture protocol, effects other than the duration of the protocol administration, represented by the number of intermediate states to reach the target state, are incorporated e.g. the number of necessary reagents for the protocol, the cost of said reagents, the quality of the regants to employ, intended as the level of understanding of their way of action, the easiness of use and the absence of unmanageable known counter-effects., as well as other objectives of said fitness function. The heuristics, or rules of thumb employed include computational complexity reduction. The optimal culture protocol is a combination of specifications of the bioreactor executing the protocol, the level of abstraction of the model, the predominant process of protocol, e.g. for culturing or bio-printing or both etc.

In this way, an effect and machine-specific, protocol may be obtained. The actual time it takes to generate the protocol once the parameters are entered may be negligibly short or up to hours, depending on the length of the simulated period, the level of abstractness of the model and the power of the specific search heuristics and the computational tools, making this a very feasible tool.

Such optimal selected path becomes the base for the generation of a culture protocol 140, which may need to be expressed in a standard accepted by a control unit of bioreactor 101, such as e.g. IS088. An example of conversion from the optimal path to a culture protocol is to express the sequence of states in the selected path as a sequence of corresponding instructions for controlled bioreactor 101. Such process can be automatic based on a database of instructions expressed to be compatible for execution by controlled bioreactor 101 and the corresponding state of model 100 (figure 28).

Once optimal protocol 140 is automatically generated according to the above, in a preferred embodiment of the present invention, the protocol is processed by controlled bioreactor 101. Preferably, bioreactor 101 comprises electronic hardware and software configured and programmed to monitor and adjust process parameters, preferably in real time, via suitable sensors and actuators, and to generate data time histories. Examples of actuators comprise pumps to control flow rates; at least an impeller for mixing; heating/cooling devices to control temperature.

According to a preferred embodiment, in order to prepare the biological material to be cultured in the cell culture system, spatial information about initial position of biological material, preferably 3D spatial information, object of the biological system model are the basis for a deposition process to provide a structure of the biological material, i.e, given initial positions and distances of cells that will afterwards be housed inside e.g. bioreactor 101 for culturing. For example, the structuring process of biological material according to initial spatial information of the culture protocol is carried out via a controlled machine, such as a 3D printer, depositing a gel -like substance, such as a bioink, embedding the starting biological material to be cultured and that was simulated via the model (spatial patterning). Before or immediately after the input of the protocol in controlled cell culture system, in a known manner a time for execution of the protocol and/or of each step of the protocol is estimated (temporal patterning).

In view of the high level of automation for culture protocol generation, according to a preferred embodiment, a further input of the method is one or more parameters that are measurable and/or controllable by the specific controlled bio-machine, e.g. bioreactor, that will execute the culture protocol, after generation of the latter. This ensures the highest compatibility of any bioreactor with the relative model and, thus, the highest efficiency of use for a given bioreactor.

To this regard, according to a further preferred embodiment, during execution of generated protocol 140, one or more data measured by bioreactor 101 are stored and collected, e.g. time histories, and used to fine tune model 100, which is expressed including the parameters that are measurable by bioreactor 101.

MODEL DESCRIPTION

An example of a model structured to generate a state space is provided in the following paragraphs.

Ontogenesis (or morphogenesis) is one of the key concepts at the base of the developmental biology. It can be defined as the origination and "[...] development of a single individual, or a system within the individual, from the fertilized egg to maturation and death.". Yet, ontogenesis concerns developing embryos of multicellular organisms as well as unicellular life forms not having an embryonic stage in their life cycle. In the invention, the focus is on the ontogenesis of a multi-cellular organism, which presents emergent architectural and phenotypic complexities and takes place following process stages.

Systems biology targets complexity with a holistic approach, considering a system as more than the sum of its parts. Under this perspective, ontogenesis comprises complex and intertwined processes at multiple system levels, from the development of the organism as a whole at the macroscale, to the differentiation of single cells at the microscale. In morphogenesis, emergent patterns, at the mesoscale, are aggregates of cells with different phenotypic identities grouped following a defined spatial organization. Patterns reshape after each developmental stage, and changes emerge from local interactions between cells, occurring over different distance and time ranges. It is possible to define the following classes of ontogenetic mechanisms:

•autonomous mechanisms, making the internal dynamics of the cell and resulting outward behaviors, such as division of an heterogeneous egg, and different mitotic spatio-temporal patterns. Or the evolution of cell identity, considered in reason of its functional markers;

• inductive mechanisms: cells affect each others’ autonomous mechanisms via either unilateral (hierarchical) or bilateral (emergent) signaling during pattern formation;

• morphogenetic mechanisms: phenomena changing the spatial architecture of cells (the form of a tissue) in a developing structure without directly affecting their internal dynamics. Some examples are directed mitosis, differential growth and adhesion, apoptotic and migration processes, contraction and matrix modification.

In a developmental process, each stage corresponds to a different architecture, regulative set-up or sub-process in the organism and its subparts. Architectural conformations, as a form of morphogenetic mechanism, dictate the communication schemes the cells participate in, setting up a scheme of relative positions between cells. This mediates cell cell communication, that is, inductive and subsequently cell autonomous mechanisms. Basic ontogenetic mechanisms are defined as "tractable and understandable phenomena", the result of a reductionist approach to complexity, which deconstructs the system to facilitate our understanding. According to the proposed approach, they are intended as building blocks for facilitating the construction of a model.

Yet, rather than a linear combination of sub-processes, a multi-dimensional, dynamic landscape of interdependent, diverse and complex regulation mechanisms underlies ontogenesis. At each developmental stage, the cellular microenvironment affects cell autonomous mechanisms. This defines the context cells live into under two main aspects. On one hand, the functional context includes neighboring cells, their architecture and environmental signals. On the other hand, the process context refers to the stage the cell lives into. In some circumstances, a regulation mechanism may overtake others, but the situation can be reversed when the context evolves.

In order to holistically comprise the resulting dynamic hierarchy of regulation layers, models of development need to consistently integrate multiple system levels. At the same time, reducing biological complexity to understandable phenomena, i.e. increasing the level of abstraction of a biological model, allows for easy knowledge interpretation and exchange.

Figure 2 is a sketch of a model to simulate via a computer a biological system to implement a method according to the present invention. Inputs for the creation of the model are:

Biological process of interest, e.g. optogenetic induction of transcription;

Culturing system involved to promote the biological process of interest, e.g. provided with a control unit to power on/off light sources (see the example below); Biological system setup of interest involving the biological process carried out by the culturing system, e.g. production of GTMl mRNA as a result of progressive illumination or contemporaneous illumination (see the example below).

The model comprises:

At least a biological entity sub-model: expresses at least a biological process of interest within the biological entity, e.g. a submodel of a cell expressing optogenetic induction of transcription;

A spatial sub-model (Interactive Spatial Grid): to explicitly represent the spatial architecture of the biological system and the surrounding environment, e.g. the chamber of a bio-reactor or another chamber of the culturing system, together with at least a relationship function expressing an interaction taking place between a pair of relevant nodes in the grid. The relationship function is pre-set during creation of the spatial sub-model and is executed depending on a first presence information associated to the sub-model of a first biological entity in a first relevant node and a second presence information associated to the sub-model of a second biological entity;

A process sub-model: includes selected states of the biological system and/or the culturing system arranged in a pre-set sequence to express at least a portion of interest of the biological process at stake. According to one aspect of the invention, the process sub-model may include both states of the biological system depending on a biological variable of one biological sub-model e.g. in order to observe the progress of the preferred biological process and on a chemical- physical variable controllable by the culturing system e.g. to impart an external input or condition at a pre-defmed stage of the biological process.

Sub-models relate to each other via pre-set reading functions to observe at least a variable processed during the execution of the model and writing functions to convey an information, e.g. the value of a variable processed during the execution of the model or the presence/absence of such variable or a signal or the like.

Examples of biological entity sub- models can be found is scientific literature or knowledge databases, such as BioModels database by EMBL-EPI, and can be found by the skilled man depending on the biological process of interest. As an alternative, in particular where the biological process of interest is not covered by literature or database, a biological sub-model of the biological process of interest can be generated via ad hoc experimental designs and the subsequent observations. Biological submodels may be stochastic, deterministic, etc.

Therefore the model aims at providing an approach to leverage existing information e.g. biological entity sub-models, and manage the complexity of having such sub-models interacting in space and receiving chemical-physical stimuli from a culturing system. For example stimuli are: physical e.g. light stimuli (with different wavelengths), temperature variations, pressure variations, fluid flow shear stress, rotation, mechanical forces; and/or chemical e.g. pH, osmolarity, nutrient concentration, molarity of different substances, inorganic substances (nanoparticles, ...); and/or biochemical e.g. diffusive molecular signals (biomolecules such as proteins, hormones, peptides, aminoacids, glucydes), static molecular signal (adhesion molecules, nanoparticles functionalizations ..)

This is particularly useful during the preparation or optimization of the culture protocol of a biological system for a preferred output of the system, i.e. a sequence of states of the biological system and stimuli provided by the culturing system, e.g. a bioreactor, a bio fluidic device or a semi-automatic culturing system where some operations are automatic and other operations are manual, in order to obtain the preferred output.

The spatial sub-model provides the 3-dimensional structure, including a culturing environment or environments controllable by suitable actuators of the culturing system and a spatial interaction between the biological entity sub-models and the culturing system is regulated by the spatial sub-model and a process interaction between the biological sub-model and the culturing system is regulated by the process sub-model. According to the present invention, the spatial sub-model preferably includes one or more of the following relationship functions:

Neighbor detection: provides neighborhood relations between two positions within the spatial grid, allowing a biological sub-model active in a spatial node of the grid to retrieve the identity and to functionally connect to a biological sub-model possibly active in one or more adjacent spatial nodes of the grid. In general, neighbor detection function activates when a given biological sub-model becomes active in a first spatial node of the grid and checks the presence of other biological sub-models active within an influence area having a pre-defmed extension with respect to the first spatial node;

Cell movement: provides step motion of a biological sub-model from a starting spatial node of the grid to another spatial node of the grid;

Molecular flow: provides step movement of a biomolecule from a spatial node of the grid to adjacent spatial node;

Mitosis: models the generation of two daughter cells from a single one. Preferably, it is ensured that cell division starts after specific markers signal the completion of previous mitotic phases. The newly generated biological sub-models of daughter cells occupy the starting spatial node and one of the adjacent ones respectively. The choice of the latter can be random. Or, contextual rules can affect the choice, including directionality over embryo axes, other neighbor biological sub-models of cells, and gradients of biomolecules over the surrounding places;

Apoptosis: models the regulated death of a cell with the elimination of the corresponding biological entity sub-model. Preferably, it is ensured the apoptotic process starts after specific regulations within the cell are in place and the respective markers arise;

Signal sensing: models the passage of a signal, carried by a biomolecule, from outside to inside a biological entity sub-model of a cell. The signal is acquired by the sub-model of the cell when both the cell and the biomolecule are active in the same spatial node in the grid;

Signal sending: models the passage of a signal, carried by a biomolecule, from inside to outside a biological entity sub-model of a cell.

Passage of a biological module signal requires the combination of a signal sending function, a molecular flow function and a signal sensing function.

The relationship functions check the respective presence condition, i.e. the presence of a first and a second biological entity in adjacent spatial nodes, at each step of execution of the model and are triggered when the condition is satisfied.

According to the present invention, the process sub-model preferably includes one or more of the following inductive, i.e. cells affect each others’ autonomous mechanisms via either unilateral (hierarchical) or bilateral (emergent) signaling during pattern formation, and cell autonomous, i.e. making the internal dynamics of the cell and resulting outward behaviors, such as division of an heterogeneous egg, and different mitotic space- temporal patterns or the evolution of cell identity considered in reason of its functional markers, ontogenetic functions:

Differentiative step (in general phenotypic switch): models the passage of cells or other biological entities from a state to another. It is dynamically assessed the state of the biological entity sub-models, and if they respond to the requirements, a state change takes place.

According to the present invention, the biological entity sub-model preferably includes one or more of the following inductive and cell autonomous ontogenetic functions:

Transcription: models the use of genetic information for producing protein-coding (mRNA) or non-coding transcripts;

Translation: models the consumption of a mRNA for producing an amino-acidic chain, or protein;

Enzymatic reaction: models the modification of the state or structure of a biomolecule through the intervention of an enzyme, which may be the same or another biomolecule; Gene regulation: models the interventions of regulatory molecules in the modulation of gene expression, e.g. activation or inhibition, on-off or graded; and

Post-transcriptional regulation: models the interventions of regulatory molecules, such as miRNAs, in the modulation of mRNA translation. Furthermore, higher-level functional modules for complex ontogenetic processes can be seen as combinations of the above functions or building blocks. They encompass multiple system levels, providing holistic representations of complex ontogenetic phenomena. According to the present invention, all model levels contribute to support functional modules, relying on cross-layer communication mechanisms, which ensure consistency in the resources and information flow across nets, and semantic coherence of the overall model.

As non-limiting examples:

Migration waves: can correspond to different biological mechanisms, all devising the active movement of cells, co-directed by other cells and environmental factors such as mechanical or chemical gradients. Cell movement, neighbor sensing, molecular flow and signal sensing building blocks combine to model this process;

Apoptotic waves involve a group of cells undergoing apoptosis in a regulated way, often inducing proliferation and migration in neighbor cells. Molecular flow, Signal sensing and apoptosis building blocks, over a set of adjacent spatial nodes in the spatial function underlie these processes;

Proliferative phases involve a selected population of cells undergoing mitotic processes in a regulated way, as a form of morphogenetic mechanism. Signal sensing and mitosis building blocks underlie this process, starting from spatial nodes in the spatial function and populating adjacent ones;

Patterning is the emergence of phenotype and architectural complexity from the local interactions between cells. It results from the combination of inductive mechanisms. For example, hierarchical signaling from a unique signal source can determine a chemical gradient over the architecture of receiver cells. In a distance-dependent way, cells receive a graded signal, having different effects at different concentrations. This can determine per se a pattern of different cell identities. Lateral signaling between neighbor receiver cells can affect the downstream effects of the signal.

According to a non-limiting embodiment of the invention, the sub-models are represented via Petri nets.

Low level Petri nets

The low-level PNs formalism supports a model combining usability and simplicity in model design with the capability of supporting dynamic simulations and formal, quantitative analysis. For these reasons low-level Petri Nets are a valuable state-of-the- art tool for computational biology.

Petri Nets at their core are bipartite, directed graphs consisting of two kinds of nodes: places, represented by circles, which can represent any state a resource can assume, including and not limiting to a physical point in space or a phase of a process it belongs to, and transitions, represented by boxes. A set of directed arcs connect the nodes, usually labeled with weights that represent the minimum tokens required to trigger the transition the place is an input for. A place that has an outgoing arc towards a transition is an input place for a transition. A place that has an incoming arc from a transition is an output place. As shown in Figure 3, each place can contain a number of tokens (black dots). Tokens provide a quantitative and discrete representation of resources, and they are another element of the PNs formalism.

At each moment along net evolution, the marking recapitulates the position of each token in the net. The initial marking models the starting conditions for system evolution. The marking evolves, according to transition firings, at each simulation step. Marking evolution models the emergent system dynamics over time.

Transitions function according to specific, local rules, regulating both enabling and firing. Rules define the conditions required for the transition to fire (e.g., a particular marking of the input places), and the effect of the transition (i.e., how tokens are moved when the transition fires). Firing transforms the current marking, and it can involve tokens in different ways: consuming them, putting them back, moving them or generating new ones to the output places, or a combination of these. This is established by the firing rules of the specific transition.

Net architecture organizes these rule-based functioning over the connections between input places, transitions and output places. The output place for a transition can work as an input place for another transition. In this way, several interlocked mechanisms find representation in a PNs model. Also, a transition can have multiple output places, linked to parallel downhill mechanisms. This supports the modeling and simulation of distributed systems and concurrent processes competing for resources, here modeled by tokens. A PN model comprises an arbitrarily large number of these structures, each with specific architecture, rules and connections to the other ones.

PNs easily model isolated biological mechanisms, such as biochemical reactions, representing semi-quantitative, stoichiometric relations between molecular species involved. In regulation networks such as genetic or metabolic ones, several reactions combine together, and further requirements emerge. A low-level PNs model meets these requirements too. In modeling regulation or metabolic networks, places can model molecular species and enzymes from biochemical reactions. Tokens can model biomolecules in a discretized way. Transitions can model the reaction processes, covering with their rules the stoichiometry and the biochemical transformation of resources in a semi-quantitative way.

High level Petri nets

Systems biology imposes to provide proper representation for the multiple organizational levels of biological systems: models need to express hierarchy. In general, biological processes are intrinsically stochastic: PNs models need to express stochasticity when executed.

To address this issue, a number of high-level PNs extend the low level formalism, supporting multi-level and nested models which properly handle information diversity, including more system complexity into models.

Colored Petri Nets (CPNs) support the representation of arbitrarily complex data structures attached to tokens. The information structures a model supports are defined as colors, and each place in the net supports a subset of colors, limiting the token types it accepts. In each place, the marking is defined as a multi-set over the color set attached to the place. In CPNs, each token can carry structured information, allowing to model different types of resources. This makes CPNs valuable visual modeling tools for complex systems as well, for they allow for non-redundant, more compact representations. This improves readability and averts modeling errors, while preserving the modeling capabilities of low-level PNs, which can be generated from CPNs models by automatic unfolding.

Timed Petri Nets (TPNs) extend the low-level formalism setting specific timings for transition firing. That is, once a transition is enabled, deterministic time delays can occur before actual firing, ordering different transition activations along net evolution. Delays are tunable parameters in the model. This allows to include in models mechanisms characterized by different timescales.

For modeling the inherent stochasticity in biological systems, stochastic PNs (SPNs) extend TPNs introducing probabilistic time delays. That is, time delays between enabling and actual firing are no more tunable parameters, but rather random variables. Their value can also depend on the current marking of the net, adding a representational layer for interdependencies within and across model levels. These capabilities prove useful in modeling biological systems.

Hierarchical (or nested) Petri Nets model multi-level biological systems. Representing parts and sub-parts in nested net architectures make the hierarchical relations between such parts explicit, allowing for arbitrarily high resolution in the description of mechanisms from different system levels. Nested PNs aim at representing a multi-level systems with single-level models. [Also, similarly to CPNs, they stick to a static paradigm: token colors correspond to static data structures, and nets have a static model architecture. Resources can change state only by moving from place to place, and mobility is devised for tokens but not for other model parts.

In fact, complex biological processes challenge the limitations of most high-level PNs. In fact, they consider biological systems as dynamic structures with multiple regulation set ups and structural conformations across different phases of the same process. This often involves evolutions of system architectural and functional patterns, including the movement and generation of new system parts, and decision making processes based on the outcome of previous process stages. This reflects into further requirements to computational models and the underlying formalisms.

Net within nets

Nets-within-nets (NWNs) can express all of the functionalities from other high-level PNs formalisms, such as stochasticity, timings, hierarchy, and quantitative information. In addition, they innovate PNs-based modeling strategies providing tokens with a PNs structure in turn. That is, NWNs go beyond the concept of static token color, by attaching dynamic information to tokens using the PNs formalism itself. Tokens specified in this way are called net tokens, or object nets. As Petri Nets, they evolve dynamically like the net holding them, which takes the name of system net. Also, they are able to hold net tokens in turn. This can be reiterated in a boundless way, allowing for open recursion in specifying the hierarchical organization of system levels with dedicated model layers (see Figure 3).

In other words, NWNs follow a paradigm similar to that of Obj ect-Oriented Programming (OOP): tokens in a NWNs model can be considered as instances of classes.

These classes can be specified with the NWNs formalism in turn, living within and being simulated concurrently with a higher-level NWNs model. As instances of NWN models, object nets can hold net tokens as well, and this can be repeated in a recursive way, specifying as many model levels as desired. This provides full expressivity, in a NWNs model, for representing system hierarchy.

Given their definition, NWNs are particularly suited to model distributed systems, which require hierarchy and encapsulation. Thanks to their capability to express encapsulation and selective communication, they can easily represent biological compartmentalization and semi-permeability of biological membranes. Moreover, by construction, the NWNs formalism recapitulates the OOP formalisms.

This facilitates the integration of models according to an embodiment of the invention with several modem programming languages.

The following paragraphs introduce features and capabilities of the NWNs formalism, as a premise for the presentation of the NWN-based modeling strategy.

Object systems: an elementary object system is defined as a single system net and its marking, which comprises either net tokens, with their markings, or simple black tokens. This draws a hierarchy of two levels: the system net on top, and the net tokens on bottom. In this hierarchy, net tokens are treated as objects of net classes. They can be instantiated within other net instances, creating a system of nets. Extending the concept of elementary object system, the same net token instance can live in different system nets. This allows for specifying different facets of the context to be modeled for the net token. Transports and interactions: different system nets can host the same net token, and each net token can navigate system nets following different mechanisms. Transitions in the system net can transport net tokens from a place to another one without determining any other changes. In this case, net tokens function independently and concurrently to the system net. In other cases, transitions from the different nets interlock: an interaction between them takes place. Interactions between different nets rely on communication mechanisms such as synchronous communication channels, which join transitions across nets. Each channel has two ends: the down-link and the up-link. The transition containing the down-link, when enabled, checks for the presence of the corresponding up-link in the nets system. If it finds it, they activate synchronously. Transitions containing an up-link, on the other hand, wait for the corresponding down-link to evoke their joint activation. A single down-link can activate multiple up-links at the same time. This defines, in a sense, a directionality for channels. Channels can also pass arguments, which can support token flow across nets. The direction of tokens flow between the down-link and the up-link transitions is independent from channel directionality.

Intra- and cross-layer interactions: in a hierarchical nets system, interactions involve transitions from both the same layer and different layers. They can result in either writing or reading mechanisms. That is, transitions activation can result either in the determination of the marking in the output place, or in the consideration of the marking in the input place for following evolutions. Combining these options, four categories of communication mechanisms take shape (figure 5):

• Intra-layer reading: a transition considers the marking at input places of another transition from the same model layer.

• Intra-layer writing: a transition affects the marking at output places of another transition from the same model layer. • Cross-layer reading: a transition considers the marking of a input place of another transition from a different model layer.

• Cross-layer writing: a transition affects the marking at output places of another transition from a different model layer.

These mechanisms allow communication between different nets, and combining them it is possible to build up a consistent hierarchical model of a multi-level system and the contexts for its dynamic evolution.

Application to an ontogenetic process

The fundamental blocks for models according to this approach are functional modules, modeling complex ontogenetic mechanisms thanks to the following features:

• they encompass one or more system levels of interest;

• they can function as scaffolds for a set of basic building blocks, mediating the combination of their functionalities within the multi-level hierarchy of the model;

• they have abstract architecture and adjustable parameters, making them both generalizable across different ontogenetic processes and fine-tunable to specific modeling applications;

• they can be combined forming models that naturally show consistency between time and space scales at all system levels.

In this way, the present approach supports generalization and knowledge exchange, as well as the gain of a deep, systemic insight over the system.

In the presented approach, functional modules and the overall model share an essential backbone centered on two system levels:

• the cells, and their internal regulation circuitry, including all relevant omics;

• the dynamic regulative landscape cells live into, as in their functional and process context. Referring back to figure 2, the presented approach structures models with two main levels. The top level hosts the spatial model and the process model as a set of two system nets, each one dealing with a different view over the complex regulatory landscape of the system.

Net tokens populate the bottom level, each one representing one of the cells biological sub-model from the system. Each net token instance lives in both system nets. At the bottom level, net tokens model cells composing the developing system; at the top level, the system nets represent their functional and process contexts. This reflects in different semantics for the different nets. Synchronous communication mechanisms make the whole model consistent.

According to the non -limiting embodiment of the present invention that includes PNs, for the spatial sub-model the following relations between model and system elements hold:

• Places model subparts of space (in either one, two or three dimensions). Each subspace holds a cell plus its pertinences;

• Transitions model transports or interactions between actors living either in the same or in adjacent places, also marking relations of mutual neighborhood between subspaces.

• Coloured tokens model biomolecules in the extracellular space;

• Net tokens model cells;

• Net architecture models the grid (either uni- bi- or three-dimensional) of subspaces, and their respective adjacencies and interactions.

Furthermore, according to the PNs formalism, functions of the spatial sub-model are defined as:

Neighbor detection: marks the neighborhood relations between two positions, allowing a net token occupying a place to retrieve the identity of (figure 6) and to connect for communication to (figure 7) the neighboring net token instances living in the adjacent places. It relies on intra- layer reading for neighbors identification, and on cross-layer reading and writing for communications between net tokens;

Cell movement: models the step movement of a cell in the defined space with the transport of a net token from a place to another in the grid (figure 8). It relies on intra-layer writing; Molecular flow: models the step movement of a biomolecule in the defined space with the transport of a coloured token from a place to another in the grid (figure 9). It relies on intra-layer writing;

Mitosis: models the generation of two daughter cells from a single one with the consumption or elimination of a net token and the following instantiation of two copies of it (figure 10). By cross-layer reading, a checkpoint block ensures cell division starts after specific markers signal the completion of previous mitotic phases. The newly generated net tokens model daughter cells and occupy the starting place and one of the adjacent ones respectively. The choice of the latter can be random. Or, contextual rules can affect the choice, including directionality over embryo axes, other neighbor cells, and gradients of biomolecules over the surrounding places;

Apoptosis: models the regulated death of a cell with the consumption of a net token from a place (figure 11). By cross-layer reading, a checkpoint ensures the apoptotic process starts after specific regulations within the cell are in place and the respective markers arise;

Signal sensing: models the passage of a signal, carried by a biomolecule, from outside to inside a cell. By cross-layer writing, the coloured token modeling thesignal flows into the net token modeling the cell when they both occupy the same place in the grid (figure 12); Signal sending: models the passage of a signal, carried by a biomolecule, from inside to outside a cell. By cross-layer writing, the coloured token modeling the signal flows from the net token modeling the cell to its place in the grid (figure 13). According to the preferred embodiment including PNs, the following relations between the process sub-model and system elements hold:

• Places model cell states, intended as functional identities or phenotypes;

• Transitions model passages from a cellular state to another one;

• Net tokens model cells or other biological entities, depending on the biological process;

• Net architecture models the landscape of differentiative trajectories underlying the ontogenetic process.

Furthermore, according to the PNs formalism, functions of the process sub-model are defined as:

Differentiative step: models the passage of cells from a state to another. By cross-layer reading, a checkpoint dynamically assesses the state of net tokens, and if they respond to the requirements, a state change takes place. Firing relies on intralayer writing for transporting the net token to the place modeling the following state (figure 14).

According to the embodiment including PNs, the following relations between a biological entity sub-model and the system elements hold:

• Places model biomolecules from all -omics and their possible states, including for example genes, mRNAs, ncRNAs, active and inactive proteins, and metabolites;

• Transitions model all kinds of biological processes, for example transcription, translation, genetic and epigenetic regulation, post-translational modification, enzymatic catalysis and protein degradation;

• Black tokens model biomolecules within the cell, whose identity changes depending on the place they live into;

• Net architecture models the scheme of relations between bioprocesses and the flow of resources along them.

Furthermore, according to the PNs formalism, functions of the biological entity sub- model are defined as:

Transcription: models the use of genetic information for producing protein-coding (mRNA) or non-coding transcripts. By intra-layer reading, a black token marking the presence of a gene allows, without being consumed, for the production of a variable number of black tokens in the places modeling the transcriptional products of that gene (figure 15 a);

Translation: models the consumption of a mRNA for producing an aminoacidic chain, or protein. A black token in the place modeling the mRNA is consumed for producing one (or more) black tokens in the place modeling the protein product (figure 15b);

Enzymatic reaction models the modification of the state or structure of a biomolecule through the intervention of an enzyme, which may be the same or another biomolecule. By intra-layer reading, it checks for the presence of the active enzyme. After that, it consumes black tokens from the place modeling the substrates for the reaction, and produces black tokens into the place modeling its products, following its stoichiometry. This can model a diversity of reactions, for example protein activation by post- translational modification, as well as metabolic cycles (figure 15c);

Gene regulation: models the interventions of regulatory molecules in the modulation of gene expression. This block can attach to a transcription block, which will consume black tokens from a place modeling the regulator (for instance, a transcription factor) to switch on, off or modulate the process (figure 15c and 16a);

Post-transcriptional regulation: models the interventions of regulatory molecules, such as miRNAs, in the modulation of mRNA translation. This block can attach to the place modeling coding transcripts in a translation block, and, consuming some black tokens from the place modeling miRNAs, take away some black tokens modeling mRNAs, according to the specific stoichiometry, and produces black tokens into the place modeling mRNA with miRNAs attached (figure 16b).

Example

Figures 17 to 20 show a cell sub-model, a spatial sub-model and a process sub-model for a specific example of optogenetic transcriptional regulation shown in figure 18.

In particular:

Cell sub-model: is a single cell submodel expressing the optogenetic transcriptional regulation of figure 18;

Spatial sub-model: shows in the same chart a first set-up of a culturing system wherein three spatial nodes are each illuminated by a respective light source and a second set-up where a single light source illuminates at the same time the three spatial nodes;

Process sub-model: shows in the same chart a process where the light sources are switched on in progression from spatial node 1 to spatial node 3 (left branch) and a process where the single blue light at the same time is switched on the three spatial nodes (right branch).

In particular, starting from the spatial sub-model, at first, an instance of the protocols generation ISG model is created in the central place. From here, the instance can undergo two paths: the one on the left and the one on the right.

Within the spatial sub-model ISG instance, three instances of the protocols generation cell model are created, and each one in a different place, modeling different adjacent positions: positionl, position2 and position3 respectively. Each one of these position places connects to:

- a channel taking care of position-specific signal administration;

- a channel, which is unique for all three positions, taking care of simultaneous signal administration to all cells.

Within each cell biological sub-model CELL, a channel takes care of sensing the signal. If the light signal is marked as "blue" light, the presence of a signal enables the transition modeling the homodimerization of VP EL222 monomers, which consumes two monomers to produce an homodimer. Homodimeric VP-EL222 enables, in turn, the transcription of the GLT1 Open Reading Frame (ORF), and for each homodimer the transcription of one mRNA takes place.

Going back to the process sub-model, the spatial sub-model ISG instance can take two paths.

PATH 1 - on the right

The spatial sub-model instance is assigned to the "cells" variable via the input arc of the transition. The inscription "cells:artificial_signal(light)" then activates the :artificial_signal(light) channel within the spatial sub-model instance. The argument is the variable "light", which the transition extracts from the double arc pointing to the "light" place. The String value "blue" is assigned to the "light" variable, and flows through the channel the transition activates.

Within the spatial sub-model ISG instance, the transition on the top, carrying the :artificial_signal(light) channel, interlocks with the transition from the process sub model, and it gets synchronously activated, passing to this instance the value "blue", which was assigned to the variable "light", which is the argument conveyed by the channel. The same argument flows through other channels linked to this transition: the celll :sensing(light), cell2:sensing(light), cell3:sensing(light) channels respectively. All of them activate synchronously to the first channel (and then, also with the process sub model transition), making the argument enter the three instances of the cell model, celll, cell2 and cell3 respectively, each one living in a specific position (position 1, position2, position3, respectively).

Within each cell model, the value assigned to the "light" variable provides the necessary condition for the homodimerization transition to activate. In particular, the inscription "guard light.equals("blue");" specifies this.

In this way, the signal ignited by the process sub-model instance and traveling through the spatial sub-model ISG instance sets up the condition for GLTl mRNA production synchronously for all the three positions, and then in all the three cell instances occupying them.

PATH 2 - on the left

The spatial sub-model ISG instance is assigned to the "cells" variable via the input arc of the transition. The inscription "cells:artificial_signal_p 1 (light)" then activates the :artificial_signal_pl (light) channel within the spatial sub-model ISG instance. The argument is the variable "light", which the transition extracts from the double arc pointing to the "light" place. The String value "blue" is assigned to the "light" variable, and flows through the channel the transition activates.

Within the spatial sub-model ISG instance, the transition on the top on positionl, carrying the :artificial_signal_pl (light) channel, interlocks with the transition from the process sub-model, and it gets synchronously activated, passing to this instance the value "blue", which was assigned to the variable "light", which is the argument conveyed by the channel. The same argument flows through the other channel linked to this transition: the celksensing(light) channel. This activates synchronously to the first channel (and then, also with the process sub-model transition), making the argument enter the instance of the cell model living in positionl.

Within the cell model, the value assigned to the "light" variable provides the necessary condition for the homodimerization transition to activate. In particular, the inscription "guard light.equals("blue");" specifies this.

In this way, the signal ignited by the process sub-model instance and traveling through the spatial sub-model ISG instance sets up the condition for GLTl mRNA production only for the cell model instance living in positionl.

The above is executed via a simulator that creates instances out of model classes according to the inscriptions they contain. In particular, it creates an instance of the process sub-model, which in turn creates an instance of the spatial sub-model, in which three instances of the cell model are created.

Each of these instances, following the template model of origin, have specific initial marking, setting the initial conditions for the overall model at the beginning of the simulation. This corresponds to a set of satisfied and unsatisfied enabling rules. After the beginning, at each step in the simulation, all transitions are evaluated for enabling, and out of all the enabled transitions the simulator shortlists some and put them in random order in a queue for firing. According to this order, they fire. This order randomization is the way the simulator of this particular implementation (based on the Renew tool) embeds stochasticity in model simulation. Step after step, the simulation goes on, and thanks to stochasticity, the same initial conditions can make different simulation outcomes emerge. In order to create the process sub-model, the state space shown in figures 21, 22, 23 has been automatically generated and subsequently scanned by a state space inference algorithm, such as a Gaussian algorithm or a Neural Network algorithm, in order to find the target condition that all three cells have indeed produced GLTl mRNA.

The algorithm found such a target condition in the space state, e.g. boxed cells in tables of figures 21-23. According to the simple example at stake, the path of states to obtain the target condition in the state space is given as input, i.e. either switching on the light with a pre-defmed progression or illuminating at the same time the three cells. It is however possible that a DSE algorithm, such as particles swarm, simulated annealing or genetic programming, expands the state space starting from the target states to find all paths resulting in the target space. Possibly enriching the process submodel in ways that do not descend directly from the current knowledge of the biological system.

The so-called path mentioned in previous paragraphs is a draft culture protocol that, after in-silico and subsequent experimental validation, becomes a set of instructions to be processed by the control unit of a culturing system, e.g. a bioreactor, in order to produce the desired biological output from the cultured biological system. In particular, transitions leading, state after state, to the target state are backtracked, and those among them which are operated by the automated culture system are translated into a set of successive instructions, e.g. parameter values of temperature, pressure, concentration etc., for the automated culture to guide the system from an initial state to the target state. Such instructions, in order to automatically operate the culture system, follow a suitable formalism such as IS9088. Between two subsequent states, conditions may be changed over time via interpolation functions compatible with actuators of the system. For example a linear interpolation can be used.

Figure 24 show an alternative structure of the biological model where process sub-model is more generic and describes the more general situation where three lights and a single light are respectively associated to a relative cell and to all cells. According to such a more general description of the situation, the execution of the model is not bound to a specific order of switching on the light with reference to the three blue lights and, therefore, the random execution generates a more complex state space than that of figures 21-23.

The target condition remaining the same as that of figures 21-23, i.e. all three cells produce at the same time GLTl mRNA, figures 25-27 show a portion of the state space where the target condition is found and the relative target paths are found and highlighted via an operational search algorithm e.g. a state space exploration (figure 26). In particular, the optimal target path is identified as the one having the minimum number of states to reach the target condition (figure 27).

According to a non illustrated example, model 100 and the consequent generation of a state space including target states can be applied to a bio-printing process, e.g. the production of an organoid. In such an instance, a bioprinter builds a 3D structure e.g. depositing a gel-like material, e.g. a bio-ink, where biological material e.g. cells is embedded. A position control system of the bio-printer provides a precise positioning of the biological material and such a position information including position and distance of one or more cells within the printed structure is an input for model 100. Furthermore, the printed structure is subsequently cultured and this contributes to the generation of a state space including different state paths, each starting from its own initial structure and leading to a previously identified biological target condition, such as e.g. cell percentage of survival. Therefore, the fitness function may be construed so as to identify, within the state space, the initial 3D structure to be cultured in order to obtain the target condition in a minimum number of states. It is also possible to associate to each state another parameter such as a culturing or production cost of that state or time involved by that state, so that optimum condition may be either to have minimum time to reach the target state or minimum cost to reach the target state. When a bioprinter or the like are used to set the initial position condition, e.g. spatial organization within a bio-printed structure, it is possible that the culturing system be very simple, such as a more controlled atmosphere chamber where physical parameters such as temperature, humidity etc. are kept constant during the culturing process so that the biological material is mainly subject to biological processes exemplified in model 100. The latter is therefore adjusted to include the conditions that e.g. temperature, humidity etc. are constant at a given initial value throughout the simulation.

Claims

1. Computer based method for generating a culture protocol for a biological system of two or more cells within a bio-manufacturing system, for example a controlled bioreactor, comprising the steps of:

- Providing a model of biological processes related to culturing between the at least two cells within a chamber of the culturing system; the model expressing 3D spatial functions between said cells and biological functions of the cells;

Generating at least a portion of a state space of the model via a biological model simulator;

- Searching a target state condition within the generated state space and identifying at least a first and a second path of states within the state space, each path including the at least one target condition and respective sets of previous states fulfilling the target state condition;

Selecting an optimal path between the at least first and second path via a fitness function;

Generating a culture protocol based on said optimal path and the respective previous states.

2. The method according to claim 1, further comprising the step of controlling a machine to deposit biological material based on a starting condition of the biological system, including spatial information including position of said cells at the beginning of the culturing process, the starting condition being expressed in the protocol.

3. The method according to any of the preceding claims, comprising the step of executing the culture protocol on the controlled bio-manufacturing system; sensing at least a biological, chemical, biochemical or physical parameter at defined and tracked spatial coordinates during the protocol execution; adjusting the model based on the sensed parameter.

4. The method according to any of the preceding claims, further comprising the step of receiving input information about the bio-manufacturing system, the model including at least a parameter based on said input information.

5. The method according to any of the preceding claims, wherein the model expresses ontogenesis of the biological system and comprises:

o At least one cell biological sub-model expressing at least one ontogenetic process by the combination of cell autonomous biological process between transcription and/or translation and/or enzymatic reaction and/or gene regulation and/or post-transcriptional regulation to express a biological process of interest; and

o At least a spatial sub-model (Interactive Spatial Grid) to explicitly represent a spatial grid architecture of the biological system and the surrounding environment within the chamber, together with at least an interaction taking place between a pair of spatial nodes in the grid when in both a biological entity sub-model is active or present;

o The at least one cell sub-model and the at least spatial sub-model communicating via writing and reading functions to determine the activity of the at least one cell sub-model in a spatial node of the spatial sub-model to trigger the execution of a relationship function associated to the spatial nodes, wherein said function include at least one inductive relationship function expressing at least one of a cell movement, a molecular flow, a mitosis, an apoptosis, a signal sensing and a signal sending.

6. Method according to claim 5, wherein the step of providing a model further comprises a process sub-model expressing a pre-defmed sequence of states of the biological system as a function of a biological parameter of the at least one cell sub-model and/or the at least one control parameter of the culturing system and wherein the writing and reading functions put in communication the process sub model and the spatial and cell sub-models to provide inputs and receive data to trigger a phenotypical switch from one state to another of the pre-defmed sequence.

7. Method according to any of the preceding claims, wherein at least one of the spatial sub-model and cell sub-model are multilevel so that, via the writing and reading function, the communication of a parameter of a lower level is transferred via each and every higher level.

8. Method according to any of the preceding claims, wherein the at least one cell sub-model expresses the biological process by the combination of at least a migration wave, an apoptotic wave, a proliferative phase, patterning.

9. Method according to any of the preceding claims, wherein the sub-models are expressed via Petri nets.

10. Computer based method of ontogenesis simulation of a biological system to be cultured in a culturing system, comprising the steps of:

acquiring at least a control parameter controllable via the culturing system;

providing a model of a pre-defmed ontogenesis process involving the biological system and the culturing system comprising:

At least one biological entity sub-model expressing at least one biological process by the combination of cell autonomous ontogenetic process between transcription and/or translation and/or enzymatic reaction and/or gene regulation and/or post- transcriptional regulation to express a biological process of interest; and At least a spatial sub-model (Interactive Spatial Grid) to explicitly represent a spatial grid architecture of the biological system and the surrounding environment within a chamber of the culturing system, together with at least an inductive relationship function expressing an interaction taking place between a pair of spatial nodes in the grid when in both a biological entity sub-model is active or present, the relationship functions including at least one of neighbor detection, cell movement, molecular flow, mitosis, apoptosis, signal sensing and signal sending;

The at least one biological entity sub-model and the at least spatial sub-model communicating via writing and reading functions to determine the activity of the at least one biological entity sub-model in a spatial node of the spatial sub-model to trigger the execution of the relationship function associated to the spatial node; Executing the model via a biological model simulator to provide an in-silico progression of states of the model expressed by at least a biological parameter of the biological entity sub-model and the at least one control parameter of the culturing system.

11. Method according to claim 10, wherein the step of providing a model further comprises a process sub-model expressing a pre-defmed sequence of states of the biological system as a function of a biological parameter of the at least one biological entity sub-model and/or the at least one control parameter of the culturing system and wherein the writing and reading functions put in communication the process sub-model and the spatial and biological entity sub models to provide inputs and receive data to trigger a phenotypical switch from one state to another of the pre-defmed sequence.

12. Method according to claim 11, comprising the further steps of: Acquiring a target condition within a space state of the pre-defmed ontogenesis process;

via a states space inference algorithm:

Generating at least a portion of a space state of the pre-defmed ontogenesis process;

Searching the target condition;

Acquiring at least one path of states including states satisfying the target condition; and

Assigning the at least one path as the pre-defmed sequence of states.

13. Method according to claim 12, wherein the step of acquiring comprises the step of generating, via the design space exploration algorithm, the at least one path.

14. Method according to any of claims 10 to 13, wherein at least one of the spatial sub-model and biological entity sub-model are multilevel so that, via the writing and reading function, the communication of a parameter of a lower level is transferred via each higher level.