基于概率模型检测和遗传算法的基因调控网络的无限范围优化控制

Infinite-horizon Optimal Control of Genetic Regulatory Networks Based on Probabilistic Model Checking and Genetic Algorithm

基因调控网络是一类基本且重要的生物网络,通过对其进行控制可以实现生物系统功能的调节。在生物系统中,通过外部的干预控制构造关于基因调控网络的控制理论成为了非常热门的研究主题。目前,作为一种重要的网络模型,带有干扰且上下文相关的概率布尔网络已经被广泛地应用于基因调控网络优化控制问题的研究中。针对无限范围的优化控制问题,文中提出了一种基于概率模型检测和遗传算法的近似最优控制策略的计算方法。首先,该方法将无限范围控制中定义的期望总成本归约为离散时间马尔科夫链上的平稳状态回报;然后,构建包含固定控制策略的带有干扰且上下文相关的概率布尔网络模型,采用带回报属性的时序逻辑公式表示固定控制策略的成本,采用概率模型检测器PRISM进行自动计算。进一步,采用遗传算法,将固定控制策略编码为遗传算法解空间中的个体,基于其控制成本,定义个体的适应度值,将PRISM作为求解器,通过在解空间上迭代地执行遗传操作获取近似最优解。将所提方法应用于WNT5A网络中,实验结果证明了该方法的有效性。

Genetic regulatory networks(GRNs)are the fundamental and significant biological networks,and the biologi-cal system function can be regulated by controlling them.In the field of biological system,one of the significant research topics is to construct the control theory of genetic regulatory networks by applying external intervention control.Currently,as an important network model,the context-sensitive probabilistic Boolean network with perturbation(CS-PBNp)has been widely used for the research of optimal control problem of GRNs.With respect to the infinite-horizon optimal control problem,this paper proposed an approach of approximate optimal control strategy based on probabilistic model checking and genetic algorithm.Firstly,the total expected cost defined in infinite-horizon control is reduced to the steady-state reward in a discrete-time Markov chain.Then,the model of CS-PBNp containing stationary control policy should be constructed,the cost of the fixed control strategy is represented by the temporal logic with reward property,and the automatic calculation is carried out by using probabilistic model checker PRISM.Next,stationary control policy is encoded as an individual in the solution space of genetic algorithm.The fitness of the individual can be computed by PRISM,and the optimal solution can be obtained by making use of the genetic algorithm to execute genetic operations iteratively.The experimental results generated by utilizing the proposed approach into the WNT5A network illustrate the correctness and effectiveness of this approach.