Fitzgerald Jeffrey D, Sharpee Tatyana O
Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, California 92037, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031914. doi: 10.1103/PhysRevE.80.031914. Epub 2009 Sep 23.
Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings between input signals and network states that allow the network to convey the maximal information about input signals drawn from a given distribution. This mapping also produces a set of linear equations for calculating the optimal Ising-model coupling constants, as well as geometric properties that indicate the applicability of the pairwise Ising model. We show that the optimal pairwise interactions are on average zero for Gaussian and uniformly distributed inputs, whereas they are nonzero for inputs approximating those in natural environments. These nonzero network interactions are predicted to increase in strength as the noise in the response functions of each network node increases. This approach also suggests ways for how interactions with unmeasured parts of the network can be inferred from the parameters of response functions for the measured network nodes.
最近有研究表明，几种类型的生物网络可以用具有成对相互作用的最大熵模型准确描述，该模型也被称为伊辛模型。在此，我们提出一种方法，用于找到输入信号与网络状态之间的最优映射，使网络能够传达来自给定分布的输入信号的最大信息。这种映射还会产生一组线性方程，用于计算最优伊辛模型耦合常数，以及表明成对伊辛模型适用性的几何特性。我们发现，对于高斯分布和均匀分布的输入，最优成对相互作用平均为零，而对于近似自然环境中的输入，它们不为零。预计随着每个网络节点响应函数中的噪声增加，这些非零网络相互作用的强度会增强。该方法还提出了如何从测量网络节点的响应函数参数推断与网络未测量部分相互作用的方法。
