CN113486952B - Multi-factor model optimization method of gene regulation network - Google Patents
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Abstract
The invention discloses a multi-factor model optimization method of a gene regulation network, which comprises the steps of utilizing a nonlinear differential equation model and a differential operation method of genes, combining a machine learning algorithm, deducing the gene regulation network, and optimizing key parameter attenuation rate based on a multi-objective optimization idea and a genetic algorithm. According to the invention, the effects of noise, attenuation rate and time delay are introduced on the basis of the traditional differential equation model, and a nonlinear regulation function is trained on the basis of a machine learning algorithm, so that the nonlinear dynamic process of gene expression can be better simulated; the provided algorithm is used for optimizing the attenuation rate and time delay of important parameters affecting gene expression, so that a more accurate and efficient mathematical model is constructed to infer a gene regulation network from gene expression data.
Description
Technical Field
The invention relates to the field of gene regulation networks, in particular to a multi-factor model optimization method of a gene regulation network.
Background
The development of the new generation high-throughput sequencing technology obtains rich gene expression data, the data conceals the dynamic process of genes and the interaction relationship between the genes, and understanding the dynamic process of the genes and the regulation relationship between the genes is helpful for understanding the regulation mechanism of organisms, and the system is used for understanding and understanding the transmission of biological genetic signals, cell division and other activity rules. The complex interaction relationship between the genes can be abstracted into a network structure called a gene regulation network, the regulation relationship between the genes can be found by correctly deducing the gene regulation network, the key regulation genes of pathological cells are identified, the diagnosis and treatment of complex diseases such as tumors and the research and development of targeted drugs are facilitated, and a plurality of reliable methods are proposed for deducing the gene regulation network at present, but a plurality of methods still need to be continuously optimized.
The construction of differential equation model based on machine learning algorithm is one of the common methods for deducing gene regulation network, it needs not to obtain clear differential equation mathematical expression, and it is suitable for the deduction of large-scale gene regulation network. However, most researchers have not considered two problems when using this approach to infer a gene regulatory network. Firstly, when a differential equation model is established, only the interaction among genes is analyzed, and the influence of multiple factors such as environment, actual regulation and control mechanisms and the like on gene expression is not considered. Secondly, no effective method is provided for optimizing key parameters involved in the model, so that the model is inaccurate and the calculation is complex.
Disclosure of Invention
The invention provides a multi-factor model optimization method of a gene regulation network, which aims to solve the technical problems of inaccurate model, complex calculation and the like.
In order to achieve the above object, the technical scheme of the present invention is as follows:
a multi-factor model optimization method of a gene regulation network is characterized by comprising the following steps:
step 1, constructing a differential equation model of gene expression data;
step 2, constructing a parameter data set by the attenuation rate data and the time delay data, and constructing a nonlinear differential equation model of the gene by combining a noise data set, a time sequence data set and a gene expression data differential equation model;
step 3, performing approximate differential operation on the nonlinear ordinary differential equation model by using a differential operation method;
step 4, obtaining a gene regulation network, an aupr value and an auroc value by utilizing a machine learning algorithm and combining a nonlinear ordinary differential equation model after approximate differential operation;
step 5, randomly generating a decay rate and a time delay first generation population in a parameter constraint range;
step 6, crossing, mutating and recombining the attenuation rate and time delay first generation population by utilizing a genetic algorithm to obtain an attenuation rate and time delay second generation population;
step 7, setting an aupr value and an auroc value as two objective functions, calculating the adaptation degree of the second generation population with the attenuation rate and the time delay and the first generation population with the attenuation rate and the time delay, and carrying out rapid non-dominant sorting to obtain a third generation population with the attenuation rate and the time delay;
step 8, screening out a fourth generation population with the attenuation rate from the third generation populations with the attenuation rate and the time delay by using a congestion degree calculation method;
step 9, repeating the steps 6 to 8, stopping operation after finishing the set iteration times to obtain fourth-generation populations with different attenuation rates and time delays, wherein the fourth-generation populations with different attenuation rates and time delays form an optimal attenuation rate and time delay population;
and 10, substituting the optimal attenuation rate and the attenuation rate and time delay parameters in the time delay population into a nonlinear differential equation model after approximate differential operation, deducing a gene regulation network in a noise environment, and selecting a group of attenuation rate and time delay parameters which are least sensitive to noise action as model optimal parameters.
Further, in step 1, when f i When the function is a nonlinear function, the formula for constructing the differential equation model of the gene expression data is as follows:
wherein χ is i Representing the expression value of a given gene i at time t, dχ i Dt represents the rate of change of the expression level of gene i at time t, function f i Representing internal regulatory mechanisms between genes, χ 1 ,χ 2 ，…，χ N And (3) representing candidate regulatory genes, wherein N represents the number of the candidate regulatory genes.
Further, in step 1, when f i When the function is a linear function, the formula for constructing the differential equation model of the gene expression data is as follows:
wherein the coefficient w i，j Representing the regulatory relationship between genes i and j, χ j Representing candidate regulatory genes, b i Representing the intensity of external disturbance, u i Representing an external disturbance.
Further, the formula of the nonlinear differential equation model for constructing the gene in the step 2 is as follows:
X TS ∈R T×P
wherein X is TS Represents time series data of gene expression, T is the number of time points, P is the number of genes, R represents linear space, τ i Represents the time delay of the lag regulation of gene j by regulatory gene i,represents the rate of change of the expression level of gene j at time t, c j Represents the decay rate of gene j>Representing the expression value of a given gene j at time t, χ -j P-1 candidate regulatory genes representing the gene except for j,>representing all candidate regulatory gene expression data under the action of time delay, n i Representing the amount of noise contained in the expression value of regulatory gene i.
Further, the formula for performing the approximate differential operation on the nonlinear ordinary differential equation model by using the differential operation method in the step 3 is as follows:
where h represents the order of the differential operation,represents the k+h time discrete point gene expression value,>represents the gene expression value, t, of the kth time discrete point k+h Represents the k+h time discrete point, t k Represents the kth time discrete point, n i Representing the amount of noise contained in the expression value of regulatory gene i.
Further, in the step 6, the crossover, mutation and recombination are performed on the attenuation rate and time delay first generation population by using a genetic algorithm, and then the attenuation rate and time delay second generation population is obtained specifically as follows: and crossing, mutating and recombining the attenuation rate and time delay first generation population in a binary form based on a genetic algorithm to obtain an attenuation rate and time delay second generation population.
The beneficial effects are that: according to the invention, the effects of noise, attenuation rate and time delay are introduced on the basis of the traditional differential equation model, and the nonlinear dynamic process of gene expression can be better simulated by training the nonlinear regulation function based on a machine learning algorithm; based on the multi-objective optimization thought and genetic algorithm, the parameter adjusting process is simpler and more convenient, the parameters are more accurate, and a more accurate and efficient mathematical model is constructed to infer a gene adjusting network from gene expression data.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments or the description of the prior art will be briefly described below, it will be obvious that the drawings in the following description are some embodiments of the present invention, and that other drawings can be obtained according to these drawings without inventive effort to a person skilled in the art.
FIG. 1 is a schematic diagram of the model optimization method of the present invention.
FIG. 2 is a graph showing the effect of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment provides a multi-factor model optimization method of a gene regulation network, as shown in fig. 1, which comprises the following specific steps:
step 1, constructing a differential equation model of gene expression data;
when f i When the function is a nonlinear function, the formula for constructing the differential equation model of the gene expression data is as follows:
wherein χ is i Representing the expression value of a given gene i at time t, dχ i Dt represents the rate of change of the expression level of gene i at time t, gene expression data for differential equation model, the expression value is required to be time series and cannot be negative, function f i Representing internal regulatory mechanisms between genes, χ 1 ，χ 2 ，…，χ N And (3) representing candidate regulatory genes, wherein N represents the number of the candidate regulatory genes. Function f i The structure of (a) indicates the internal regulatory mechanism between genes, i.e. regulatory networkStructure f i What expression is adopted indicates that genes act in a corresponding manner.
When f i When the function is a linear function, the formula for constructing the differential equation model of the gene expression data is as follows,
wherein the coefficient w i，j Representing the regulatory relationship between gene i and gene j, coefficient w i，j Positive numbers represent the relationship of gene j to gene i activation; negative numbers represent the relationship in which inhibition exists; if 0, no regulatory relationship exists. X-shaped articles j Representing candidate regulatory genes, b i Representing the intensity of external disturbance, u i Representing an external disturbance.
In most cases, interactions between genes exhibit complex nonlinear relationships, and thus nonlinear regulatory functions can more accurately infer gene regulatory networks. In the present invention, a nonlinear ordinary differential equation model is employed.
The differential equation model is a function composed of all potential regulated gene expression levels and external disturbances, and can quantitatively describe the dynamic characteristics of target gene expression. The model can accurately simulate the regulation and control behaviors among the real genes, considers the influence caused by external disturbance, and is favorable for accurately modeling the complex regulation and control relationship of the gene regulation and control network.
Step 2, constructing a parameter data set by the attenuation rate data and the time delay data, and constructing a nonlinear differential equation model of the gene by combining a noise data set, a time sequence data set and a gene expression data differential equation model;
the nonlinear differential equation model for constructing the gene is specifically:
X TS ∈R T×P
wherein X is TS Represents time series data of gene expression, T is the number of time points, P is the number of genes, R represents linear space, τ i Represents the time delay of the lag regulation of gene j by regulatory gene i,represents the rate of change of the expression level of gene j at time t, c j Represents the decay rate of gene j>Representing the expression value of a given gene j at time t, χ -j P-1 candidate regulatory genes representing the gene except for j,>representing all candidate regulatory gene expression data under the action of time delay, n i Representing the amount of noise contained in the expression value of regulatory gene i.
The model simultaneously considers three key influencing factors, namely noise, attenuation rate and time delay, and builds a nonlinear differential equation model which can better represent the biological dynamic process.
Step 3, performing approximate differential operation on the nonlinear ordinary differential equation model by using a differential operation method;
most of the obtained time series data are discrete data at time points, and differentiation is not easy to obtain, so that the approximate differentiation operation is carried out by using the differential operation, and the specific formula for carrying out the approximate differentiation operation on the nonlinear ordinary differential equation model is as follows:
where h represents the order of the differential operation,represents the k+h time discrete point gene expression value,>represents the gene expression value, t, of the kth time discrete point k+h Represents the k+h time discrete point, t k Represents the kth time discrete point, n i Representing the amount of noise contained in the expression value of regulatory gene i.
Step 4, obtaining a gene regulation network, an aupr value and an auroc value by utilizing a machine learning algorithm and combining a nonlinear ordinary differential equation model after approximate differential operation; the nonlinear regulation function can be easily trained by using a machine learning algorithm, and the regulation relation of genes can be better simulated.
Step 5, randomly generating a decay rate and a time delay first generation population in a parameter constraint range;
step 6, crossing, mutating and recombining the attenuation rate and time delay first generation population by utilizing a genetic algorithm to obtain an attenuation rate and time delay second generation population;
step 7, setting an aupr value and an auroc value as two objective functions, calculating the adaptation degree of the second generation population with the attenuation rate and the time delay and the first generation population with the attenuation rate and the time delay, and carrying out rapid non-dominant sorting to obtain a third generation population with the attenuation rate and the time delay;
step 8, screening out a fourth generation population with the attenuation rate from the third generation populations with the attenuation rate and the time delay by using a congestion degree calculation method;
step 9, repeating the steps 6 to 8, stopping operation after finishing the set iteration times to obtain fourth-generation populations with different attenuation rates and time delays, wherein the fourth-generation populations with different attenuation rates and time delays form an optimal attenuation rate and time delay population; according to the invention, the attenuation rate parameters of the aupr and the auroc are optimized based on the genetic algorithm, the optimization process is simpler and more convenient, the obtained parameters are more accurate, and the accuracy of the inference of the gene regulation network can be improved.
And 10, substituting the optimal attenuation rate and the attenuation rate and time delay parameters in the time delay population into a nonlinear differential equation model after approximate differential operation, deducing a gene regulation network in a noise environment, and selecting a group of attenuation rate and time delay parameters which are least sensitive to noise action as model optimal parameters. The method comprises the following steps: and calculating variation differences of the aupr and the auroc before and after the noise acts, and selecting the corresponding attenuation rate and time delay with the smallest difference as the optimal parameters of the model.
The conventional method is for parameter c j (decay Rate), τ i The estimation of (time delay) is not important, but the two parameters play an important role in the actual biological regulation and control process, accurate and reasonable value is required, and most people often adopt a grid search method to regulate the parameters, so that the parameter regulation is difficult, the calculation time is long, and the model accuracy is not high.
According to the invention, the effects of noise, attenuation rate and time delay are introduced on the basis of the traditional differential equation model, and the nonlinear dynamic process of gene expression can be better simulated by training the nonlinear regulation function based on a machine learning algorithm; the key parameter attenuation rate and the time delay are optimized based on the multi-objective optimization thought and the genetic algorithm, the parameter adjustment process is simple and convenient, the parameter is more accurate, the parameter adjustment is simple and convenient, the parameter is more accurate, and a more accurate and efficient mathematical model is further constructed to infer a gene regulation network from gene expression data.
The existing multi-objective optimization problem aims at that a model has a plurality of objective functions, all the objectives can have conflicts, the objectives can not be obtained at the same time, the coordination balance and compromise processing can only be carried out among the objectives, all the objective functions can be as optimal as possible, and the optimal balance among the objectives can be achieved by obtaining a Pareto optimal solution set through an evolutionary algorithm. The invention also comprises the steps of evaluating the accuracy of the model by adopting two indexes of the area under the correct rate-Recall curve (Area Under Precision-Recall Curves, AUPR) and the area under the receiver operation characteristic curve (Area Under Receiver Operating Characteristic, AUROC), respectively defined as S 1 (AUPR value) and S 2 (AUROC value), the value ranges are (0, 1), and the closer to 1, the higher the accuracy. For S 1 ,S 2 Two target optimizations defining decay rate c j And time delay tau i As decision variable χ, S 1 、S 2 Iterative acquisition of Paret for an objective function F (χ) based on genetic algorithmo parameter set.
The invention constructs a mathematical model of the multi-objective optimization problem as follows:
wherein f i (χ) represents the ith objective function, in order to make f i The value of (χ) is the smallest,is a constraint set of variables, namely the range of values of the variables. The key point is the design of objective function, the invention requires S 1 And S is 2 Maximum, equivalent to minimizing 1-S 1 1-S 2 Two objective functions are thus defined:
where χ= { c, τ } is the parameter set, c is the decay rate, τ is the time delay. Iterating in the parameter value range, and calculating and aiming functions 1-S based on genetic algorithm 1 And 1-S 2 And selecting a solution set which is least sensitive to noise from the optimal solution set as an optimal parameter corresponding to the optimal solution set, thereby obtaining an optimal gene regulation network model.
The method provided by the invention has better performance on the Dearm4 analog data set, and takes time series data of the InSilico_Size10 network in the Dearm4 challenge data set as an example to represent the advantages of the invention. It contains gene expression data at 21 time points, and the number of genes is 10. The attenuation ratio was set in a range of (0, 1) with a step of 0.1, and the obtained values of aupr and auroc are shown in fig. 2.
As can be seen with reference to fig. 2, the score that performs best is auroc:0.8707264957264957, aupr:0.5949663057780875, the corresponding decay rate is 0.5, and the result obtained based on the optimization algorithm of the invention is 0.0077976373398723, the time delay is 0, and the corresponding fraction is auroc:0.971153846153846, aupr:0.883662280701754.
it can be obviously seen that the optimized parameters are more accurate in value and the obtained score is better, so that the method for deducing the higher accuracy of the gene regulation network is shown to be very superior.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (6)
1. A multi-factor model optimization method of a gene regulation network is characterized by comprising the following steps:
step 1, constructing a differential equation model of gene expression data;
step 2, constructing a parameter data set by the attenuation rate data and the time delay data, and constructing a nonlinear differential equation model of the gene by combining a noise data set, a time sequence data set and a gene expression data differential equation model;
step 3, performing approximate differential operation on the nonlinear ordinary differential equation model by using a differential operation method;
step 4, obtaining a gene regulation network, an aupr value and an auroc value by utilizing a machine learning algorithm and combining a nonlinear ordinary differential equation model after approximate differential operation;
step 5, randomly generating a decay rate and a time delay first generation population in a parameter constraint range;
step 6, crossing, mutating and recombining the attenuation rate and time delay first generation population by utilizing a genetic algorithm to obtain an attenuation rate and time delay second generation population;
step 7, setting an aupr value and an auroc value as two objective functions, calculating the adaptation degree of the second generation population with the attenuation rate and the time delay and the first generation population with the attenuation rate and the time delay, and carrying out rapid non-dominant sorting to obtain a third generation population with the attenuation rate and the time delay;
step 8, screening out a fourth generation population with the attenuation rate from the third generation populations with the attenuation rate and the time delay by using a congestion degree calculation method;
step 9, repeating the steps 6 to 8, stopping operation after finishing the set iteration times to obtain fourth-generation populations with different attenuation rates and time delays, wherein the fourth-generation populations with different attenuation rates and time delays form an optimal attenuation rate and time delay population;
and 10, substituting the optimal attenuation rate and the attenuation rate and time delay parameters in the time delay population into a nonlinear differential equation model after approximate differential operation, deducing a gene regulation network in a noise environment, and selecting a group of attenuation rate and time delay parameters which are least sensitive to noise action as model optimal parameters.
2. The method of multi-factor model optimization of a gene regulatory network of claim 1 wherein in step 1, when f i When the function is a nonlinear function, the formula for constructing the differential equation model of the gene expression data is as follows:
wherein χ is i Representing the expression value of a given gene i at time t, dχ i Dt represents the rate of change of the expression level of gene i at time t, function f i Representing internal regulatory mechanisms between genes, χ 1 ，χ 2 ，...，χ N And (3) representing candidate regulatory genes, wherein N represents the number of the candidate regulatory genes.
3. The method of optimizing a multi-factor model of a gene regulatory network according to claim 2, wherein in step 1, when f i When the function is a linear function, the formula for constructing the differential equation model of the gene expression data is as follows:
wherein the coefficient w i，j Representing the regulatory relationship between gene i and gene j, x j Representing candidate regulatory genes, b i Representing the intensity of external disturbance, u i Representing an external disturbance.
4. The method for optimizing a multi-factor model of a gene regulatory network according to claim 3, wherein the formula for constructing a nonlinear differential equation model of a gene in step 2 is:
X TS ∈R T×P
wherein X is TS Represents time series data of gene expression, T is the number of time points, P is the number of genes, R represents linear space, τ i Represents the time delay of the lag regulation of gene j by regulatory gene i,represents the rate of change of the expression level of gene j at time t, c j Represents the decay rate of gene j>Representing the expression value of a given gene j at time t, χ -j P-1 candidate regulatory genes representing the gene except for j,>representing all candidate regulatory gene expression data under the action of time delay, n i Representing the amount of noise contained in the expression value of regulatory gene i.
5. The method for optimizing a multi-factor model of a gene regulation network of claim 4 wherein the formula for performing an approximate differential operation on a nonlinear ordinary differential equation model by means of a differential operation method in step 3 is:
where h represents the order of the differential operation,represents the k+h time discrete point gene expression value,>represents the gene expression value, t, of the kth time discrete point k+h Represents the k+h time discrete point, t k Represents the kth time discrete point, n i Representing the amount of noise contained in the expression value of regulatory gene i.
6. The method for optimizing a multi-factor model of a gene regulatory network according to claim 5, wherein the step 6 of crossing, mutating and recombining the attenuation rate and time delay first generation population by using a genetic algorithm to obtain the attenuation rate and time delay second generation population is specifically as follows: and crossing, mutating and recombining the attenuation rate and time delay first generation population in a binary form based on a genetic algorithm to obtain an attenuation rate and time delay second generation population.
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