Generating Boolean networks with a prescribed attractor structure
Generating Boolean networks with a prescribed attractor structure
复制标题
DOI：
10.1093/bioinformatics/bti664
复制
发表时间：
2005-11-01
期刊：
影响因子：
5.8
通讯作者：
Dougherty, ER
中科院分区：
文献类型：
--
作者：
Pal, R;Ivanov, I;Dougherty, ER
动机：通过网络模型对基因调控进行动态建模是基因组学的一个关键问题。动力系统的长期特性是至关重要的，它们的确定是系统分析的一个主要方面。在另一个方向上，系统综合涉及构建一个具有给定属性集的网络。这就构成了反问题。一般来说，逆问题是不适定的，这意味着将有许多网络，或者可能没有网络，具有期望的性质。相对于长期行为，我们可能希望构建具有理想稳态分布的网络。本文讨论了布尔网络（BNs）的长期逆问题。结果：氮化硼的长期行为是由其吸引子决定的。状态转换图的其余部分被划分为水平集，第j个水平集由所有在j个转换中转换到一个吸引子状态的状态组成。给出了两种求解吸引子逆问题的算法。指定了吸引子，并且约束了预测集的大小和级别的数量。分析了算法的复杂度和性能。算法解有直接的应用价值。在假设采样来自稳态的情况下，检验所设计网络有效性的一个基本准则是模型的吸引子状态与数据状态是否一致。这个准则可以用来检验一种设计算法：随机选择一组状态作为数据状态；生成一个拥有选定状态作为吸引子的BN，可能会有一些额外的要求，例如对预测器数量和层次结构的限制；应用设计算法；并检查所设计网络的吸引子状态与数据状态之间的一致性。
Motivation: Dynamical modeling of gene regulation via network models constitutes a key problem for genomics. The long-run characteristics of a dynamical system are critical and their determination is a primary aspect of system analysis. In the other direction, system synthesis involves constructing a network possessing a given set of properties. This constitutes the inverse problem. Generally, the inverse problem is ill-posed, meaning there will be many networks, or perhaps none, possessing the desired properties. Relative to long-run behavior, we may wish to construct networks possessing a desirable steady-state distribution. This paper addresses the long-run inverse problem pertaining to Boolean networks (BNs).Results: The long-run behavior of a BN is characterized by its attractors. The rest of the state transition diagram is partitioned into level sets, the j-th level set being composed of all states that transition to one of the attractor states in exactly j transitions. We present two algorithms for the attractor inverse problem. The attractors are specified, and the sizes of the predictor sets and the number of levels are constrained. Algorithm complexity and performance are analyzed. The algorithmic solutions have immediate application. Under the assumption that sampling is from the steady state, a basic criterion for checking the validity of a designed network is that there should be concordance between the attractor states of the model and the data states. This criterion can be used to test a design algorithm: randomly select a set of states to be used as data states; generate a BN possessing the selected states as attractors, perhaps with some added requirements such as constraints on the number of predictors and the level structure; apply the design algorithm; and check the concordance between the attractor states of the designed network and the data states.