CN106295150B - A kind of optimal control method of gene regulatory network - Google Patents
A kind of optimal control method of gene regulatory network Download PDFInfo
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Abstract
The present invention provides a kind of optimal control method of gene regulatory network, comprising: models in probabilistic model checking device PRISM to noisy and context-sensitive probability Boolean network, obtains the probability Boolean network model based on PRISM；Different state reporting values is set using state of the reward structure in the PRISM to the probability Boolean network, the state reporting value is used for characterization control cost function and terminal cost；Determine the first temporal logic formula and the second temporal logic formula for carrying out control cost optimization to limited range and infinite range respectively；The probability Boolean network model based on PRISM, the different state reporting value and first temporal logic formula and the second temporal logic formula are inputted in the probabilistic model checking device PRISM, optimal optimal control result is obtained.A kind of optimal control method of gene regulatory network provided by the invention can improve the efficiency for obtaining optimal optimal control result while occupying lower memory.
Description
Technical field
The present invention relates to bio-networks control technology field more particularly to a kind of optimal control sides of gene regulatory network
Method.
Background technique
Gene regulatory network is a kind of important bio-networks, modeling and analyze to be more fully understood bioprocess with
And the effective therapy intervention of development has great effect for human diseases.Currently, Boolean network and probability Boolean network are
Through being widely used in modeling gene regulatory network.Boolean network (Boolean Network, BN) is that kauffman exists
A kind of simple logic dynamical system proposed in 1969, and as a kind of important model for studying gene regulatory network
Dynamic behaviour.In Boolean network, the rules of interaction between the node and node of some binary values constitutes whole network
Topological structure.Assuming that the state of gene is divided into two kinds: " 0 " and " 1 ", wherein " 0 " represents gene and is not expressed, and " 1 " represents
Gene is expressed, and therefore, each node represents the state of a gene in Boolean network.The rule of interaction passes through cloth between node
You are indicated function.Boolean network can be expressed as B=(G, F).G={ V, E } is a digraph, wherein V={ x1,x2,
x3,…xnIndicate network in node set, E indicate node between incidence relation.Each node xi∈ { 0,1 } represents gene
The boolean state value of i.F={ f1,f2,f3,…,fnIt is a Boolean function set, it indicates all and is mutually related between gene
Regulate and control the rule of interaction, while defining the evolution rules of network.
On the basis of Boolean network, boolean can be constructed as control input by addition boolean control node and control net
Network (Boolean Control Network, BCN).Boolean controls network and refers to the Boolean network output and input.Output
For indicating desired network state.The purpose that addition boolean controls node is in order to by the value of manipulation boolean's control node
To change the state transition of Boolean network, run network in desired fashion.
Since there is biosystem random nature and the influence in complicated measurement process there are experimental noise to cause to use
Usually inaccurate in the data acquisition system of inference network structure.In 2002, Shmulevich proposed probability Boolean network
(Probabilistic Boolean Network, PBN).Probability Boolean network is on the basis of Boolean network by being every
A gene provides multiple Boolean functions, for handling the uncertainty from data and model selection aspect.At each moment, often
A gene randomly selects one according to given probability distribution from candidate Boolean function set, constitutes the differentiation of current network
Rule.Probability Boolean network can still indicate B=(G, F).Compared with Boolean network, Boolean function vector F={ F1,F2,F3...,
FnEach of Fi={ f1 (i),f2 (i),…,fl(i) (i)Represent the set being made of a Boolean function of l (i).fj (i)Table
Show j-th of Boolean function of gene i.Each fj (i):{0,1}k(i)The mapping of a state is realized in → { 0,1 }, determines gene i
Next moment possible state.For each fj (i), the value of k (i) may be different and the probability selected is Cj (i).It is apparent that Cj (i)Need to meet the condition of regression nature.
Currently, it when obtaining optimal control result by gene regulatory network, generally requires to occupy more memory, and
And the time of data processing is also relatively more long.Therefore, currently needing one kind being capable of optimal control that is quick and consuming lower memory
Method.
Summary of the invention
The purpose of the present invention is to provide a kind of optimal control methods of gene regulatory network, can occupy lower memory
While, improve the efficiency for obtaining optimal optimal control result.
To achieve the above object, the present invention provides a kind of optimal control method of gene regulatory network, the method packets
It includes: modeling, obtain to noisy and context-sensitive probability Boolean network in probabilistic model checking device PRISM
To the probability Boolean network model based on PRISM；Using the reward structure in the PRISM to the probability Boolean network
Different state reporting values is arranged in state, and the state reporting value is used for characterization control cost function and terminal cost；It determines and divides
Other the first temporal logic formula and the second temporal logic formula that control cost optimization is carried out to limited range and infinite range；It will
The probability Boolean network model based on PRISM, the different state reporting value and first temporal logic formula
It is inputted in the probabilistic model checking device PRISM with the second temporal logic formula, obtains optimal optimal control result.
Further, to noisy and context-sensitive probability boolean in probabilistic model checking device PRISM
Network is modeled, and is obtained the probability Boolean network model based on PRISM and is specifically included: will be each in the probability Boolean network
A Boolean function is converted to the polynomial form in real number field, includes multiple common nodes in the probability Boolean network and multiple
Control node；Default markov decision process is obtained, includes transition probability in the markov decision process, convert and open
Pass, probability of interference and interference incident；Respectively to the change-over switch, the interference incident, the common node and the control
Node processed is modeled, and the probability Boolean network model based on PRISM is obtained.
Further, modeling is carried out to the change-over switch to specifically include: set the value of the change-over switch as 0 or
1, wherein the value of the transition probability may make that the change-over switch value is 1, and following formula may make the change-over switch to take
Value is 0:
1-q
Wherein, q indicates the value of the transition probability；
When the change-over switch value is 1, the probability Boolean network randomly chooses a boolean according to probability distribution
Evolution rules of the network as network；When the change-over switch value is 0, keep current Boolean network constant.
Further, modeling is carried out to the interference incident to specifically include: set the value of the interference incident as 0 or
1, wherein the value of the transition probability may make that the interference incident value is 1, and following formula may make the interference incident to take
Value is 0:
1-q
Wherein, q indicates the value of the transition probability.
Further, first temporal logic formula are as follows:
Rmin=?: [C≤T+1]
Wherein, first temporal logic formula indicates the corresponding minimum accumulative return value of limited range, described to add up back
Report value is the control cost function value at each moment and cumulative, the R of terminal costminIndicating operator, C indicates the cumulative time,
T indicates integer variable,?: indicate conditional operator；
Second temporal logic formula are as follows:
Rmin=?: [F prop]
Wherein, second temporal logic formula indicates the corresponding minimum accessibility return value of infinite range, and F indicates timing
Logical word, prop indicate dbjective state.
The state evolution of probability Boolean network can be regarded as the Markov Chain of a discrete time by the present invention.General
Some nodes be can choose in rate Boolean network as control node, probability boolean is constituted and control network.Node is controlled each
A moment can choose a binary value non-determinedly, and the state transition that probability boolean controls network constitutes Markov and determines
Plan process (MDP).In order to use probabilistic model checking method to solve limited range and two class Optimal Control Problem of infinite range, this
Application needs the state evolution that probability boolean is controlled to network to be converted to a corresponding MDP model.Two class control problems difference
Limited range markov decision process and infinite range markov decision process are corresponded to, is then patrolled using corresponding timing
Formula is collected to be analyzed.In this application, according to the definition of Optimal Control Problem, using reward structure to MDP model extension
Carry out designated state return value, for expressing control cost function and terminal cost.Finally, by probability boolean's net based on PRISM
In network model, different state reporting values and temporal logic formula input probability model detector PRISM, so as to obtain
Optimal optimal control result.It is not difficult to find out that when applying this method in complicated probability Boolean network Optimal Control Problem
When, the efficiency for obtaining optimal optimal control result can be improved while occupying lower memory.
Detailed description of the invention
Fig. 1 is a kind of optimal control method flow chart of gene regulatory network provided by the invention；
Fig. 2 is the schematic diagram of limited range corresponding minimum accumulative return value when control node initial value is 0 in the present invention；
Fig. 3 is the schematic diagram of limited range corresponding minimum accumulative return value when control node initial value is 1 in the present invention.
Specific embodiment
In order to make those skilled in the art better understand the technical solutions in the application, below in conjunction with the application reality
The attached drawing in mode is applied, the technical solution in the application embodiment is clearly and completely described, it is clear that described
Embodiment is only a part of embodiment of the application, rather than whole embodiments.Based on the embodiment party in the application
Formula, all other embodiment obtained by those of ordinary skill in the art without making creative efforts, is all answered
When the range for belonging to the application protection.
Fig. 1 is a kind of optimal control method flow chart of gene regulatory network provided by the invention.As shown in Figure 1, described
Method may comprise steps of.
Step S1: to noisy and context-sensitive probability boolean's net in probabilistic model checking device PRISM
Network is modeled, and the probability Boolean network model based on PRISM is obtained.
In the present embodiment, each Boolean function in the probability Boolean network can be converted in real number field
Polynomial form includes multiple common nodes and multiple control nodes in the probability Boolean network.
For two Boolean variable δ1, δ2, then, following relationship is set up:
1)It is equivalent to 1- δ1；
2)δ1∨δ2It is equivalent to δ1+δ2-δ1δ2；
3)δ1∧δ2It is equivalent to δ1δ2。
In the present embodiment, given system can be described as a markov decision process, so as to obtain
Default markov decision process is taken, includes transition probability q, change-over switch s, probability of interference in the markov decision process
P and interference incident peri.
It in the present embodiment, can be respectively to the change-over switch, the interference incident, the common node and institute
It states control node to be modeled, to obtain the probability Boolean network model based on PRISM.
Specifically, when modeling to change-over switch s, specifically executing code can be as follows:
1)module switch
2)s:[0..1]init 1；
3) [csPBN] c=0- > q:(s'=1)+(1-q): (s'=0)；
4)endmodule
Wherein, the 2nd line code shows: change-over switch s can be respectively represented change-over switch in vain and be had with value 0 or 1
Effect, and assigning initial value is 1；3rd line code shows: change-over switch s becomes 1 with the probability of q, becomes 0 with the probability of 1-q.Work as s=
When 1, PBN is randomly chosen evolution rules of the Boolean network as network according to probability distribution；As s=0, keep current
Boolean network it is constant.
In the present embodiment, the execution code modeled to the interference incident can be as follows:
1)module perti
2)peri:[0..1]init 0；
3) [csPBN] c=0- > p:(peri'=0)+(1-p): (peri'=1)；
4)endmodule
Wherein, the 2nd line code shows: can respectively represent interference incident to any interference incident peri with value 0 or 1
Do not occur and occur, and assigning initial value is 0；The code of 3rd row shows that interference incident peri becomes 0 with the probability of p, with 1-p's
Probability becomes 1.
In the present embodiment, the code modeled to common node can be as follows:
1)module BNi
2)xi:[0..1]init 1；
3)di:[0..l(i)-1]init 0；
8) [csPBN] c=0&peri=1- > (xi'=0)；
9) [csPBN] c=0&peri=1- > (xi'=1)；
10)endmodule
Wherein, the 2nd line code shows that the value of node xi can take 0 or 1, and assigning initial value is 1；In 3rd line code
Di, i=0,1 ..., l (i) -1 are integer constants, and value range is to the selected boolean's letter of common node 1 from 0 to l (i) -
Several labels, assigning initial value is 0；The code of 4th row show when change-over switch open and interference incident do not occur when, xi node
Value withProbability depend onAnd be marked with di=0, the situation after plus sige is similar；5th row to the 7th row
Code show that when change-over switch is closed and interference incident is nonevent, the value of node xi depends on last moment by di
The Boolean function of label；The code of eighth row and the 9th row shows that the value of node xi jumps non-determinedly when interference incident occurs
To 0 and 1.
In the present embodiment, the code modeled to the control node can be as follows:
1)module inputi
2)ui:[0..1]init 0；
3) [csPBN] c=0- > (ui'=0)；
4) [csPBN] c=0- > (ui'=1)；
5)endmodule
Wherein, the code of the 2nd row shows: the value of control node ui is 0 or 1, and assigning initial value is 0；3rd row is to
The code of 4 rows shows: the value that each moment boolean controls node ui can take 0 and 1 non-determinedly.
Step S2: it is arranged using state of the reward structure in the PRISM to the probability Boolean network different
State reporting value, the state reporting value are used for characterization control cost function and terminal cost.
In the present embodiment, for solving optimization control problem, the reward structure of PRISM offer can be used to net
Different state reporting values is arranged in the state of network, controls cost function and terminal cost for illustrating.The code of specific implementation can
With as follows:
1)rewards"reward_name"
2)guard:reward；
3)endrewards；
Wherein, " guard " is the predicate formula in command statement, shows the condition that state reporting generates, " reward " is
One real number value, shows state reporting value.Return item " guard:reward ", which is meant, meets predicate formula guard to all
State be arranged a state reporting value reward.
Step S3: the first temporal logic formula for carrying out control cost optimization to limited range and infinite range respectively is determined
With the second temporal logic formula.
In the present embodiment, for the Optimal Control Problem of solution limited range, the first temporal logic formula can be used
“Rmin=?: [C≤T+1] " indicate the calculating to accumulation return, wherein and first temporal logic formula indicates limited range
Corresponding minimum accumulative return value, the accumulative return value are the control cost function value at each moment and tiring out for terminal cost
Add, RminIndicating operator, C indicates the cumulative time, and T indicates integer variable,?: indicate conditional operator.The purpose of the formula is
In order to obtain within the scope of T time, under the action of controlling list entries, optimal control cost caused by Network Evolution.It is public
The reason of " T+1 " being used in formula rather than " T " is Model Detection Algorithm in the calculating process of accumulation return, is not included to terminal
Moment state reporting adds up.According to it is accumulative return calculating process definition, calculated result be combine migration probability, to it is each when
It carves state reporting value and each state transition return value adds up.However, being returned due to only only specifying state in this application
Report value is for indicating control cost function and terminal cost, therefore, formula " Rmin=?: [C≤T+1] " calculating process meaning
Be to the cumulative of the control cost function value at each moment and terminal cost.Operator " Rmin" it is in MDP model
The smallest accumulative return, i.e. limited range optimal control cost are calculated from the action sequence of all various combinations.
In the present embodiment, for the Optimal Control Problem of solution infinite range, the second sequential logic public affairs can be used
Formula " Rmin=?: [F prop] " indicate the calculating returned accessibility, wherein and second temporal logic formula indicates unlimited model
Corresponding minimum accessibility return value is enclosed, F indicates that sequential logic word, prop indicate dbjective state.The purpose of the formula be in order to
It obtains from original state, under the action of controlling list entries, along the path that each can be performed, when arrival target-like
When state prop, optimal control cost caused by Network Evolution.The definition of calculating process is returned according to accessibility, calculated result is
It in conjunction with migration probability, adds up to each moment state reporting value and each state transition return value, meets until reaching
The state of prop.Similarly, since the application only only specify state reporting value for indicate control cost function and terminal cost,
Therefore, formula " Rmin=?: [F prop] " calculating process be meant to be network reach dbjective state before, to each moment
Control cost function value it is cumulative.Operator " Rmin" it is for the action sequence on MDP model from all various combinations
In calculate the return of the smallest accessibility, i.e. infinite range optimal control cost.
Step S4: by the probability Boolean network model based on PRISM, the different state reporting value and described
First temporal logic formula and the second temporal logic formula input in the probabilistic model checking device PRISM, obtain optimal excellent
Change control result.
In the present embodiment, the probability Boolean network model by described based on PRISM, the different state reporting value
And first temporal logic formula and the second temporal logic formula input in the probabilistic model checking device PRISM, it can be with
It is automatically solved by probabilistic model checking algorithm, so as to obtain optimal optimal control result.
In concrete application scene, using Apoptosis network as the research object of Optimal Control Problem, in this embodiment party
In formula, following Boolean network can be converted to probability boolean and control network:
X3(t+1)=X4(t)∨X2(t)
X4(t+1)=X4(t)
In above-mentioned formula, X1Represent the concentration level of IAP, X2Represent the concentration level of C3a, X3Represent the concentration water of C8a
It is flat, X4Represent the concentration level of TNF.Xi=1 indicates that high concentration is horizontal, Xi=0 indicates that low concentration is horizontal.In the above Boolean network
In, X can be chosen4Node u is controlled as boolean.Furthermore it is possible to combine mode to it using synchronized update and asynchronous refresh
Dynamic carries out probability extension, constructs probability boolean and controls network.The candidate Boolean function that all nodes are arranged is general by selection
Rate is 0.5, obtains following dynamical equation:
In this application, each Boolean function as shown above can be converted into the polynomial form in real number field, obtained
The Boolean function expression formula arrived are as follows: f11, f12, f21, f22, f31, f32.
Consider two Boolean variable δ1, δ2, then, following relationship is set up:
1)It is equivalent to 1- δ1
2)δ1∨δ2It is equivalent to δ1+δ2-δ1δ2
3)δ1∧δ2It is equivalent to δ1δ2
The result that above-mentioned dynamical equation is converted are as follows:
X1(t+1)=X1(t)~f f12=x1；
X2(t+1)=X2(t)~f22=x2；
X3(t+1)=u (t) ∨ X2(t)~f31=u+x2-u*x2；
X3(t+1)=X3(t)~f32=x3
Then, the probability boolean's control network model constructed can be described as a markov decision process, is
The influence for considering the stability and extraneous random disturbances of network, provides transition probability q, change-over switch s, probability of interference p, interferes
Event peri.
It is then possible to model to change-over switch s, specific embodiment is as follows:
1)module switch
2)s:[0..1]init 1；
3) [csPBN] c=0- > 0.3:(s'=1)+0.7:(s'=0)；
4)endmodule
2nd line code illustrates that change-over switch s can take binary value.3rd line command sentence shows to set transition probability q
=0.3.
It is then possible to model to interference incident, specific embodiment is as follows:
1)module pert1
2)per1:[0..1]init 0；
3) [csPBN] c=0- > 0.9:(per1'=0)+0.1:(per1'=1)；
4)endmodule
2nd line code illustrates that disturbance variable per1 can take binary value.3rd line command sentence shows to set probability of interference
P=0.1.
It is then possible to be modeled to the node x1 in model, wherein f11, f12 are the corresponding times of node x1 in model
Boolean function is selected, the probability that each candidate's Boolean function is selected is 0.5.Specific embodiment is as follows:
1)module BN1
2)x1:[0..1]init 1；
3)d1:[0..1]init 0；
4) [csPBN] c=0&s=1&per1=0- > 0.5:(x1'=f11) & (d1'=0)+0.5:(x1'=f12) &
(d1'=1)；
5) [csPBN] c=0&s=0&per1=0&d1=0- > (x1'=f11)；
6) [csPBN] c=0&s=0&per1=0&d1=1- > (x1'=f12)；
7) [csPBN] c=0&per1=1- > (x1'=0)；
8) [csPBN] c=0&per1=1- > (x1'=1)；
9)endmodule
The code of 4th row shows when change-over switch is opened and interference incident does not occur, the value of x1 node with 0.5 it is general
Rate depends on f11 and is marked with d1=0, and the situation after plus sige is similar；The code of 5th row to the 6th row show when turn
When changing switch closing and nonevent interference incident, the value of node x1 depends on the Boolean function marked by d1 last moment；
When (per1=1) occurs for interference incident, the value at boolean's node x1 next moment is non-determined for 7th row and eighth row code description
Ground becomes 1 or 0.
It is then possible to model to the control node u in model, specific embodiment is as follows:
1)module input
2)u:[0..1]init 0；
3) [csPBN] c=0- > (u'=0)；
4) [csPBN] c=0- > (u'=1)；
5)endmodule
The code of 3rd row to the 4th row shows: the value that each moment boolean controls node u can take 0 and 1 non-determinedly.
Then, for solving optimization control problem, the reward structure that PRISM offer can be used sets the state of network
Different state reporting values is set, controls cost function and terminal cost for illustrating.Specific embodiment is as follows:
1)rewards"cost"
2) x1=0&x2=0&x3=0&u=0:0；
3) x1=0&x2=0&x3=0&u=1:1；
4) x1+x2+x3=1&u=0:2；
5) x1+x2+x3=1&u=1:3；
6) x1+x2+x3=2&u=0:4；
7) x1+x2+x3=2&u=1:5；
8) x1=1&x2=1&x3=1&u=0:6；
9) x1=1&x2=1&x3=1&u=1:7；
10)endrewards
In the above PRISM code, can to network it is stateful be provided with different state reporting values.Network state
Variation range from [0,0,0] to [1,1,1].The code description of 2nd row to the 9th row is in all different states when network
When, boolean controls the corresponding control cost function value of node u=0 and u=1 difference.Meanwhile the code of the row of the 2nd, 4,6 and 8
Illustrate the terminal cost of all different conditions.In practice, state reporting value have to capture the cost of intervention with
And the opposite preference to different conditions.
It is then possible to be respectively indicated using probability calculation tree logic (PCTL) formula to limited range and infinite range optimization
The calculating for controlling cost, specifically includes:
Use probability calculation tree temporal logic formula R { " cost " }min=? [C≤T+1] indicates the optimization in limited range
Control cost.In the optimal control of limited range, T is an integer variable, and C represents the cumulative time.Set T variation range from
1 to 30 and increased step-length be 1.
Use probability calculation tree temporal logic formula R { " cost " }min=? [F x1=0&x2=0&x3=0] indicates unlimited
Optimal control cost in range.In the optimal control of infinite range, our dbjective states of specified network are [0,0,0].
In addition to this, we, which go back setting network and control the different initial value of node from four kinds of different original states and boolean respectively, goes out
Hair inquires into influence of these factors for two class optimal control costs of calculating.
Finally, can be by the model with interference and context-sensitive probability boolean control network based on PRISM, description
It controls the PRISM modeling code of the reward structure of cost and terminal cost and indicates the optimal control cost in limited range
Temporal logic formula R { " cost " }min=? [C≤T+1] and the sequential logic for indicating the optimal control cost in infinite range
Formula R { " cost " }min=? [F x1=0&x2=0&x3=0] is input in probabilistic model checking device PRISM, passes through probability mould
Type detection algorithm is automatically solved.
In the present embodiment, the corresponding minimum accessibility return of the infinite range sought using the second temporal logic formula
Value can be as shown in table 1.
Table 1 is using the corresponding minimum accessibility return value of infinite range that the second temporal logic formula is sought
From table 1 it follows that when being calculated by the optimal control method of gene regulatory network provided by the present application,
The time of consuming is less and the memory that consumes is also less, and so as to while occupying lower memory, it is optimal to improve acquisition
Optimal control result efficiency.
Fig. 2 and Fig. 3 are please referred to, Fig. 2 and Fig. 3 instantiate corresponding in the case where different control node initial values
The minimum of limited range adds up the schematic diagram of return value.Boolean's control node initial value is boolean's control node in 0, Fig. 3 in Fig. 2
Initial value is 1.The relationship that minimum expectation cost/return changes over time is instantiated in Fig. 2 and Fig. 3, it can from Fig. 2 and Fig. 3
To find out, as time increases, minimum expectation cost/return is also increasing, and different original states is in same time
Corresponding minimum expectation cost/return is also different at point.
Therefore the state evolution of probability Boolean network can be regarded as the Ma Erke of a discrete time by the present invention
Husband's chain.Some nodes be can choose in probability Boolean network as control node, probability boolean is constituted and control network.Control knot
Point can choose a binary value at each moment non-determinedly, and the state transition that probability boolean controls network constitutes horse
Er Kefu decision process (MDP).In order to use probabilistic model checking method to solve limited range and the optimization control of two class of infinite range
Problem processed, the application need the state evolution that probability boolean is controlled to network to be converted to a corresponding MDP model.The control of two classes
Problem respectively corresponds limited range markov decision process and infinite range markov decision process, then using correspondence
Temporal logic formula analyzed.In this application, according to the definition of Optimal Control Problem, using reward structure to MDP
Model extension carrys out designated state return value, for expressing control cost function and terminal cost.Finally, by based on the general of PRISM
In rate Boolean network model, different state reporting values and temporal logic formula input probability model detector PRISM, thus
It can obtain optimal optimal control result.It is not difficult to find out that when applying this method to complicated probability Boolean network optimization control
When in problem processed, the efficiency for obtaining optimal optimal control result can be improved while occupying lower memory.
Those skilled in the art are supplied to the purpose described to the description of the various embodiments of the application above.It is not
It is intended to exhaustion or be not intended to and limit the invention to single disclosed embodiment.As described above, the application's is various
Substitution and variation will be apparent for above-mentioned technology one of ordinary skill in the art.Therefore, although specifically begging for
Some alternative embodiments are discussed, but other embodiment will be apparent or those skilled in the art are opposite
It is easy to obtain.The application is intended to include all substitutions of the invention discussed herein, modification and variation, and falls in
Other embodiment in the spirit and scope of above-mentioned application.
Each embodiment in this specification is described in a progressive manner, same and similar between each embodiment
Part may refer to each other, what each embodiment stressed is the difference with other embodiments.
Although depicting the application by embodiment, it will be appreciated by the skilled addressee that there are many deformations by the application
With variation without departing from spirit herein, it is desirable to which the attached claims include these deformations and change without departing from the application
Spirit.
Claims (4)
1. a kind of optimal control method of gene regulatory network, which is characterized in that the described method includes:
It is modeled in probabilistic model checking device PRISM to noisy and context-sensitive probability Boolean network,
Obtain the probability Boolean network model based on PRISM；
Using state of the reward structure in the PRISM to the probability Boolean network, different state reporting values is set,
The state reporting value is used for characterization control cost function and terminal cost；
Determine the first temporal logic formula and the second timing for carrying out control cost optimization to limited range and infinite range respectively
Logical formula；
The probability Boolean network model based on PRISM, the different state reporting value and first timing are patrolled
It collects formula and the second temporal logic formula inputs in the probabilistic model checking device PRISM, obtain optimal optimal control result；
First temporal logic formula are as follows:
Rmin=?: [C≤T+1]
Wherein, first temporal logic formula indicates the corresponding minimum accumulative return value of limited range, the accumulative return value
For the control cost function value at each moment and cumulative, the Rmin expression operator of terminal cost, C expression cumulative time, T table
Show integer variable,?: indicate conditional operator；
Second temporal logic formula are as follows:
Rmin=?: [Fprop]
Wherein, second temporal logic formula indicates the corresponding minimum accessibility return value of infinite range, and F indicates sequential logic
Word, prop indicate dbjective state.
2. the method according to claim 1, wherein to noisy in probabilistic model checking device PRISM
And context-sensitive probability Boolean network is modeled, and is obtained the probability Boolean network model based on PRISM and is specifically included:
Each Boolean function in the probability Boolean network is converted into the polynomial form in real number field, the probability boolean
It include multiple common nodes and multiple control nodes in network；
Default markov decision process is obtained, includes transition probability, change-over switch, interference in the markov decision process
Probability and interference incident；
The change-over switch, the interference incident, the common node and the control node are modeled respectively, obtained
The probability Boolean network model based on PRISM.
3. according to the method described in claim 2, being specifically included it is characterized in that, carrying out modeling to the change-over switch:
The value of the change-over switch is set as 0 or 1, wherein the value of the transition probability may make the change-over switch to take
Value is 1, and following formula may make that the change-over switch value is 0:
1-q
Wherein, q indicates the value of the transition probability；
When the change-over switch value is 1, the probability Boolean network randomly chooses a Boolean network according to probability distribution
Evolution rules as network；
When the change-over switch value is 0, keep current Boolean network constant.
4. according to the method described in claim 2, being specifically included it is characterized in that, carrying out modeling to the interference incident:
The value of the interference incident is set as 0 or 1, wherein the value of the transition probability may make the interference incident to take
Value is 1, and following formula may make that the interference incident value is 0:
1-q
Wherein, q indicates the value of the transition probability.
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| External control in markovian genetic regulatory networks;Datta A等;《Journal of Chemical Physics》;20031130;第109卷(第11期);4569-4575 |
| Implementation of symbolic model checking for probabilistic systems;Parker David Anthony;《A thesis submitted to the Faculty of Science》;20031231;全文 |
| 基于模型检测的网络传播干预策略问题研究;余鹏;《中国优秀硕士学位论文全文数据库信息科技辑》;20160715;I141-19 |
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