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Generating probabilistic Boolean networks from a prescribed stationary distribution

机译:根据规定的平稳分布生成概率布尔网络

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摘要

Modeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods.
机译:基因调控的建模是基因组研究中的重要问题。布尔网络(BN)及其泛化概率布尔网络(PBN)已被提出来模拟遗传调控相互作用。 BN是确定性模型,而PBN是随机模型。一方面,在PBN中,其固定分布可提供有关网络的长期行为的重要信息。另一方面,可能对系统综合感兴趣,该系统综合需要从观察到的固定分布中构造网络。这导致不适的问题和挑战性的逆问题。因为可能有许多网络,或者没有网络具有给定的属性,所以反问题的规模很大。在本文中,我们考虑了从给定的固定分布和一组给定的布尔网络(BN)构造PBN的问题。我们首先将反问题表述为约束最小二乘问题。然后,我们提出了一种基于共轭梯度(CG)算法的启发式方法(一种迭代方法)来解决由此产生的最小二乘问题。我们还介绍了PBN参数的估计方法。数值例子说明了所提方法的有效性。

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