Inference of a probabilistic Boolean network from a single observed temporal sequence.
Inference of a probabilistic Boolean network from a single observed temporal sequence.
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DOI：
10.1155/2007/32454
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Dougherty ER
中科院分区：
文献类型：
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作者：
Marshall S;Yu L;Xiao Y;Dougherty ER
基因调控网络的推断是基因组信号处理的一个关键问题。本文研究了基于网络状态时间序列的概率布尔网络（PBNs）的推理。由于PBN是由有限数量的布尔网络组成的，一个基本的观察是，一个没有扰动的布尔网络的特征可以由它的成对转移决定。由于网络函数是固定的，并且不存在扰动，所以给定的状态之后总是会在接下来的时间点有一个唯一的状态。因此，在数据序列上编译的转换计数矩阵将是稀疏的，每行只包含一个条目。如果网络也有摄动，且摄动概率很小，则转移计数矩阵中会有一些不显著的非零项代替部分（或全部）零。如果数据序列足够长，可以充分填充矩阵，那么确定模型底层的函数和输入就很简单了。当转换计数矩阵由来自多个布尔网络的数据组成时，困难就来了。我们分几个步骤来解决PBN推理过程：(1)将数据序列分离成对应于布尔网络组成的“纯”子序列；(2)给定子序列，推导布尔网络；(3)推断扰动的概率，在组成布尔网络之间存在切换的概率，以及在切换时选择哪个网络的选择概率。捕获概率布尔网络的全部动态行为，无论是二进制的还是多值的，都需要使用时间数据，而且是大量的时间数据。考虑到模型的复杂性和必须估计的过渡参数和静态参数的数量，这应该不足为奇。除了提供一种推理算法外，本文还证明，如果不希望推断切换、扰动和选择概率，则数据需求要小得多，并且对于相对较小的时间过程序列，可以以相当高的精度发现成分-网络连接。
The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1) separate the data sequence into "pure" subsequences corresponding to constituent Boolean networks; (2) given a subsequence, infer a Boolean network; and (3) infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm, this paper demonstrates that the data requirement is much smaller if one does not wish to infer the switching, perturbation, and selection probabilities, and that constituent-network connectivity can be discovered with decent accuracy for relatively small time-course sequences.