Rubin Katy J, Lawler Katherine, Sollich Peter, Ng Tony
Department of Mathematics, King׳s College London, Strand, London WC2R 2LS, UK.
Institute for Mathematical and Molecular Biomedicine, King׳s College London, Hodgkin Building, London SE1 1UL, UK.
J Theor Biol. 2014 Sep 21;357:245-67. doi: 10.1016/j.jtbi.2014.06.002. Epub 2014 Jun 11.
We show that in the generic situation where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger "bulk" network, the presence of the bulk causes not just extrinsic noise but also memory effects. This means that the dynamics of the subnetwork will depend not only on its present state, but also its past. We use projection techniques to get explicit expressions for the memory functions that encode such memory effects, for generic protein interaction networks involving binary and unary reactions such as complex formation and phosphorylation. Remarkably, in the limit of low intrinsic copy-number noise such expressions can be obtained even for nonlinear dependences on the past. We illustrate the method with examples from a protein interaction network around epidermal growth factor receptor (EGFR), which is relevant to cancer signalling. These examples demonstrate that inclusion of memory terms is not only important conceptually but also leads to substantially higher quantitative accuracy in the predicted subnetwork dynamics.
我们表明，在一般情况下，生物网络（例如蛋白质相互作用网络）实际上是嵌入在更大的“主体”网络中的子网络，主体的存在不仅会导致外在噪声，还会产生记忆效应。这意味着子网络的动态不仅取决于其当前状态，还取决于其过去状态。我们使用投影技术来获得编码此类记忆效应的记忆函数的显式表达式，用于涉及二元和一元反应（如复合物形成和磷酸化）的一般蛋白质相互作用网络。值得注意的是，在低内在拷贝数噪声的极限情况下，即使对于过去的非线性依赖关系，也可以获得此类表达式。我们用表皮生长因子受体（EGFR）周围的蛋白质相互作用网络中的例子来说明该方法，这与癌症信号传导相关。这些例子表明，纳入记忆项不仅在概念上很重要，而且在预测的子网络动态中还会导致更高的定量准确性。
