External control in Markovian Genetic Regulatory Networks
External control in Markovian Genetic Regulatory Networks
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DOI：
10.1023/a:1023909812213
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发表时间：
2003-07-01
期刊：
影响因子：
7.5
通讯作者：
Dougherty, ER
中科院分区：
文献类型：
--
作者：
Datta, A;Choudhary, A;Dougherty, ER
概率布尔网络（PBN's）最近被引入作为一种基于规则的模式来建模基因调控网络。这些网络构成了马尔可夫遗传调控网络的一个子类，为研究不同基因之间的相互作用提供了一个方便的工具，同时允许这些关系知识的不确定性。本文研究了概率布尔网络中的控制问题。更准确地说，给定一个状态转移概率依赖于外部（控制）变量的一般马尔可夫遗传调控网络，本文开发了一个程序，通过该程序可以选择在有限步数上最小化给定性能指标的控制动作序列。该方法以受控马尔可夫链理论为基础，利用了经典的动态规划技术。有限范围性能指数的选择是由癌症治疗应用驱动的，理想情况下，人们希望只在有限的时间范围内进行干预，然后暂停治疗，在决定是否需要进一步干预之前，在一段额外的时间内观察效果。这里考虑的未折现有限地平线成本最小化问题是最容易制定和解决的问题，选择它主要是为了说明清楚，但在满足适当技术条件的情况下，也可以使用更复杂的成本。
Probabilistic Boolean Networks (PBN's) have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. Such networks, which form a subclass of Markovian Genetic Regulatory Networks, provide a convenient tool for studying interactions between different genes while allowing for uncertainty in the knowledge of these relationships. This paper deals with the issue of control in probabilistic Boolean networks. More precisely, given a general Markovian Genetic Regulatory Network whose state transition probabilities depend on an external ( control) variable, the paper develops a procedure by which one can choose the sequence of control actions that minimize a given performance index over a finite number of steps. The procedure is based on the theory of controlled Markov chains and makes use of the classical technique of Dynamic Programming. The choice of the finite horizon performance index is motivated by cancer treatment applications where one would ideally like to intervene only over a finite time horizon, then suspend treatment and observe the effects over some additional time before deciding if further intervention is necessary. The undiscounted finite horizon cost minimization problem considered here is the simplest one to formulate and solve, and is selected mainly for clarity of exposition, although more complicated costs could be used, provided appropriate technical conditions are satisfied.