CN107153771B - Synchronous control method of drug molecules and application thereof - Google Patents
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Abstract
The invention belongs to the technical field of gene information control, and discloses a synchronous control method of drug molecules and application thereof, wherein mathematical models are respectively established for randomly migrating cancer cells and freely diffusing drug molecules to obtain a cancer cell probability concentration equation and a drug molecule probability concentration equation; and (2) finding out the necessary coupling action between the drug molecules and the cancer cells based on the signal transmission phenomenon existing between the drug molecules and the cancer cells, adding a coupling equation to the established cancer cell probability concentration equation and the drug molecule probability concentration equation, and respectively bringing the coupling equation into the cancer cell probability concentration equation and the drug molecule probability concentration equation to obtain a reaction diffusion model for synchronously controlling the drug molecules. Realizes one-to-one synchronous control of the drug molecules on the cancer cells and reduces the damage of the drug molecules on the healthy cells.
Description
Technical Field
The invention belongs to the technical field of gene information control, and particularly relates to a synchronous control method of drug molecules and application thereof.
Background
Cancer cells seriously threaten human health and are a problem which is overcome by worldwide medical efforts, the cancer cells have diffusivity and disorder, the cell diffusion tracks are difficult to control, so the current treatment models adopt methods of radiotherapy and chemotherapy, the radiotherapy is a method for treating tumors by utilizing radioactive rays, including α, β and gamma rays generated by radioactive isotopes, and x rays, electron beams, proton beams and other particle beams generated by various x-ray treatment machines or accelerators, and the like, about 70 percent of cancer patients need to be treated by the radiotherapy in the process of treating the cancer, about 40 percent of the cancer can be radically treated by the radiotherapy, but the radiotherapy belongs to local treatment, is only effective to the tumors at the treatment part, and is difficult to effectively treat potential metastatic lesions and cancers which are already clinically metastatic.
Chemotherapy is a systemic treatment by killing cancer cells with chemotherapeutic drugs. Whatever the route of administration (oral, intravenous, body cavity, etc.), the chemotherapeutic agent is distributed throughout most organs and tissues throughout the body along with the blood circulation. Therefore, chemotherapy is the main treatment for some tumors prone to systemic dissemination and for tumors in the middle and late stages that have metastasized.
However, in both radiotherapy and chemotherapy, cancer cells are killed and healthy cells are also killed, and side effects such as vomiting, diarrhea, anemia and resistance reduction often occur to the treated person, and in order to reduce these side effects, it is urgently needed to develop a model and a method for one-to-one control of cancer cells by drug molecules.
Disclosure of Invention
The synchronous control method of the drug molecules and the application thereof provided by the invention realize one-to-one synchronous control of the drug molecules on cancer cells and reduce the damage of the drug molecules on healthy cells.
The first purpose of the invention is to provide a synchronous control method of drug molecules, which comprises the following steps:
s1, respectively establishing mathematical models for the cancer cells which are randomly migrated and the freely-diffused drug molecules to obtain a cancer cell probability concentration equation and a drug molecule probability concentration equation;
in the formula (1), (x, y) represents a plane position coordinate, P (x, y, t) represents a concentration value of a cancer cell in a plane-bounded region, Q (x, y, t) represents a concentration value of a drug molecule in a plane-bounded region, Δ P represents a diffusion action of the cancer cell itself, Δ Q represents a diffusion action of the drug molecule itself, D (x, y, t) represents a concentration value of a drug molecule in a plane-bounded region, D (x, y, t) represents a diffusion action of the cancer cell1Indicates the diffusion coefficient of cancer cells, D2Represents the diffusion coefficient of the drug molecule, h represents the absorption coefficient of the drug molecule, K represents the resistance coefficient to which the cancer cell is subjected when migrating, v (P, Q) represents the influence of the signal transmission between the cancer cell and the drug molecule on the concentration of the cancer cell, and u (P, Q) represents the influence of the signal transmission between the cancer cell and the drug molecule on the concentration of the drug molecule;
s2, finding out the necessary coupling action between the drug molecules and the cancer cells, namely determining the coupling terms to satisfy the established cancer cell probability concentration equation and the drug molecule probability concentration equation:
in the formula (2), D ═ D1+D2，ε1、ε2Is the system parameter that we want to adjust to achieve the goal of accurate control. To this end, let ε1、ε2Obeying the evolution law of equation (3):
in the formula (3), M, N is two constants;
s3, respectively substituting the coupling equation into a cancer cell probability concentration equation and a drug molecule probability concentration equation to obtain a reaction diffusion model for drug molecule synchronous control:
after bringing formula (3) and formula (2) into formula (1), we obtain the final reaction diffusion model as:
in the formula (4)
d＝D1+D2，K,h,D1,D2M and N are constant numbers, wherein K, h ∈ [0.1,1],D1、D2∈[0.01,0.1],M、N∈[100,500]；
S4, synchronously controlling the drug molecules and the cancer cells by using the reaction diffusion model described in the formula (4).
The second purpose of the invention is to provide the application of the synchronous control method of the drug molecules in the drug dosage selection for cancer cell chemotherapy.
Compared with the prior art, the synchronous control method of the drug molecules provided by the invention has the following beneficial effects: the model and the method for one-to-one control of the drug molecules on the cancer cells effectively reduce the side effects of methods such as chemotherapy, and the like, realize one-to-one synchronous control of the drug molecules on the cancer cells by establishing a reaction diffusion model for synchronous control of the drug molecules, reduce the damage of the drug molecules on healthy cells, and enable the dose application of the drug to be more scientific and the selection and the configuration of the drug to be more reasonable when the dose of the drug used for cancer cell chemotherapy is selected. Solves the problem that the existing radiotherapy and chemotherapy methods kill cancer cells and healthy cells simultaneously, thereby generating larger side effect.
Drawings
FIG. 1 is a planar motion diagram of cancer cells and drug molecules without coupling;
FIG. 2 is a schematic illustration of the coupling between cancer cells and drug molecules;
fig. 3 is a graph of the difference in concentration of cancer cells and drug molecules at [0,100] × [0,100] upon drug injection (t ═ 0);
fig. 4 is a graph of the difference in concentration of cancer cells and drug molecules at [0,100] × [0,100] when drug was infused 2s (t ═ 2 s);
fig. 5 is a graph of the difference in concentration of cancer cells and drug molecules at [0,100] × [0,100] when drug is infused for 5s (t ═ 5 s);
fig. 6 is a graph showing the difference in concentration between cancer cells and drug molecules at [0,100] × [0,100] when the drug is injected for 10s (t ═ 10 s).
Detailed Description
The invention is described in detail below with reference to the figures and the specific embodiments, but the invention should not be construed as being limited thereto. The following examples, if experimental methods without specific conditions noted, were carried out according to conventional methods and conditions in the art.
Example 1
The invention provides a synchronous control method of drug molecules, which takes tumor cancer cells as an example and comprises the following steps:
s1, respectively establishing mathematical models for the cancer cells which are randomly migrated and the freely-diffused drug molecules to obtain a cancer cell probability concentration equation and a drug molecule probability concentration equation.
The dynamic modeling is carried out on cancer cells which randomly walk and drug molecules which freely diffuse on a plane, the result is shown in figure 1, figure 1 is a motion state diagram of the cancer cells and the drug molecules on the plane under the condition of no coupling, a cancer cell probability concentration equation and a drug molecule probability concentration equation are referred to as an expression (1), the dynamic interaction process between the cancer cells and the drug molecules is represented as a macroscopic signal transmission process, and the effective transmission of signals between the cancer cells and the drug molecules means that the cancer is effectively treated, and the effective treatment is represented as a synchronous process of two dynamic systems (the probability concentration equation of the cancer cells and the probability concentration equation of the drug molecules).
In the formula (1), (x, y) represents a plane position coordinate, P (x, y, t) represents a concentration value of a cancer cell in a plane-bounded region, Q (x, y, t) represents a concentration value of a drug molecule in a plane-bounded region, Δ P represents a diffusion action of the cancer cell itself, Δ Q represents a diffusion action of the drug molecule itself, D (x, y, t) represents a concentration value of a drug molecule in a plane-bounded region, D (x, y, t) represents a diffusion action of the cancer cell1Indicates the diffusion coefficient of cancer cells, D2Represents the diffusion coefficient of the drug molecule, h represents the absorption coefficient of the drug molecule, K represents the resistance coefficient to which the cancer cell is subjected when migrating, v (P, Q) represents the effect of signal transmission between the cancer cell and the drug molecule on the concentration of the cancer cell, and u (P, Q) represents the effect of signal transmission between the cancer cell and the drug molecule on the concentration of the drug molecule. For simplicity, P (x, y, t) on the left side of the equation (1) equal sign is denoted as P on the right side of the equal sign, and Q (x, y, t) on the left side of the equation (1) equal sign is denoted as Q on the right side of the equal sign.
In 2013, nobel physiology awards 3 scientists who discovered the control mechanism of cellular vesicle transport, and the drug molecules injected into the body are surrounded by vesicles and are transported to the correct rake position at the correct time, and the 3 scientists preliminarily explain the mechanism process of vesicle for the precise identification, directional transport and destination unloading of the transported goods, wherein the role of the vesicles is equivalent to that of a coupling function in dynamics, which is the biological background of adding couplers to the two dynamics systems, and fig. 2 is shown.
S2, based on the signal transmission phenomenon existing between the drug molecules and the cancer cells, finding out the necessary coupling action between the drug molecules and the cancer cells (see figure 2 for the general idea), adding the coupling equation to the established cancer cell probability concentration equation and the drug molecule probability concentration equation:
in the formula (2), D ═ D1+D2，ε1、ε2Is the system parameter that we want to adjust to achieve the goal of accurate control. To this end, let ε1、ε2Obeying the evolution law of equation (3):
in the formula (3), M, N is two constants.
And S3, respectively substituting the coupling equation into a cancer cell probability concentration equation and a drug molecule probability concentration equation to obtain a reaction diffusion model for drug molecule synchronous control.
After bringing formula (3) and formula (2) into formula (1), we obtain the final reaction diffusion model as:
in the formula (4)
d＝D1+D2，K,h,D1,D2M and N are constant numbers, wherein K, h ∈ [0.1,1],D1、D2∈[0.01,0.1],M、N∈[100,500]。
It should be noted that the same letters in the above formulas (1) to (4) with the same subscripts or symbols represent the same meaning and also have a value range, and the description in each formula is not repeated.
The numerical simulation of equation (4) using Matlab software, observed the concentration difference of cancer cells and drug molecules at different times at [0,100] × [0,100], with the results shown in fig. 3, 4, 5, 6, fig. 3-6 are simulated graphs of the time variation of the concentration difference of cancer cells and drug molecules, and the vertical axis represents the concentration difference of cancer cells and drug molecules (fig. 3-6 correspond to the time t ═ 0s, t ═ 2s, t ═ 5s, t ═ 10s, respectively), and with the increase of time, the concentration difference approaches 0, i.e. the concentration difference of cancer cells and drug molecules approaches 0, with the extension of the time t of drug injection, i.e. the drug molecules and cancer cells reach a synchronized state by coupling, i.e. the theoretical analysis result is consistent with the precise treatment of cancer cells, i.e. the kinetic mechanism of signal transmission is effectively transmitted, we explain this from the therapeutic kinetic point of view, and verify that the theoretical analysis result is more correctly applied to cancer cells by the experimental mechanism of drug delivery, i.e. the theoretical analysis result of the drug molecules are more scientifically selected by the experimental mechanism of drug delivery, and the theoretical analysis of the drug delivery is more controlled by the theoretical cell-cancer cells.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (1)
1. A reaction diffusion model building method for synchronously controlling drug molecules is characterized by comprising the following steps:
s1, respectively establishing mathematical models for the cancer cells which are randomly migrated and the freely-diffused drug molecules to obtain a cancer cell probability concentration equation and a drug molecule probability concentration equation;
in the formula (1), (x, y) represents a plane position coordinate, P (x, y, t) represents a concentration value of a cancer cell in a plane-bounded region, Q (x, y, t) represents a concentration value of a drug molecule in a plane-bounded region, Δ P represents a diffusion action of the cancer cell itself, Δ Q represents a diffusion action of the drug molecule itself, D (x, y, t) represents a concentration value of a drug molecule in a plane-bounded region, D (x, y, t) represents a diffusion action of the cancer cell1Indicates the diffusion coefficient of cancer cells, D2Represents the diffusion coefficient of the drug molecule, h represents the absorption coefficient of the drug molecule, K represents the resistance coefficient to which the cancer cell is subjected when migrating, v (P, Q) represents the influence of the signal transmission between the cancer cell and the drug molecule on the concentration of the cancer cell, and u (P, Q) represents the influence of the signal transmission between the cancer cell and the drug molecule on the concentration of the drug molecule;
s2, finding out the necessary coupling action between the drug molecules and the cancer cells, namely determining the coupling terms to satisfy the established cancer cell probability concentration equation and the drug molecule probability concentration equation:
in the formula (2), D ═ D1+D2，ε1、ε2Is the system parameter that we want to adjust, let ε for this purpose1、ε2Obeying the evolution law of equation (3):
in the formula (3), M, N is two constants;
s3, respectively substituting the coupling equation into a cancer cell probability concentration equation and a drug molecule probability concentration equation to obtain a reaction diffusion model for drug molecule synchronous control:
after bringing formula (3) and formula (2) into formula (1), we obtain the final reaction diffusion model as:
in the formula (4)
d＝D1+D2，K,h,D1,D2M and N are constant numbers, wherein K, h ∈ [0.1,1],D1、D2∈[0.01,0.1],M、N∈[100,500]。
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