Rigorous Information-theoretic tools for Comparative Interactomics.

活细胞中的分子信号可以在第一近似中主要归因于蛋白质-蛋白质相互作用（PPI）及其复杂的串扰。自从人类基因组计划最近完成以来，现在已经有可能识别和绘制我们基因中编码的大部分蛋白质。然而，在我们能够真正理解我们细胞系统的复杂生物学之前，需要揭示更多关于信号转导途径中所涉及的分子相互作用的细节。这是未来几年生物学和医学研究的主要挑战之一。分子通过与特异性结合伴侣相互作用来传递信息。结合诱导至少一个伴侣分子的构象变化，这触发信号级联中的下一个生物分子步骤。因此，蛋白质之间的相互作用机制对所有生物功能都至关重要，信号转导过程中这种串扰的有效性在许多“健康”生物过程和许多疾病（例如癌症）中起着重要作用。近年来，已经发表了几项大规模的实验研究，以检测不同物种的PPI，并已存入公开数据库。然而，目前的实验技术，如酵母双杂交（Y2 H）和共亲和纯化结合质谱（AP-MS），已被证明是相互作用数据空间的样本子集，只有非常有限的重叠。我们最近开发了一个理论上合理和准确的数学框架比较相互作用组数据（PPI网络，PPIN），并评估，在一个公正的方式，他们的距离在宏观拓扑性质。初步分析表明，相同物种和相同方法采样的网络是相似的，并且比相同方法但不同物种采样的网络更相似。因此，从相似的实验条件下生成的网络具有相似的拓扑特征，尽管它们的单个PPI的重叠很小。据我们所知，这一点还没有如此清楚地、以如此不偏不倚的方式显示出来。此外，我们可以很清楚地看到，在比较网络采样与不同的方法，数据偏差导致的采样方法目前掩盖了物种相关的结构特性。同样，尽管文献中已经承认了方法学偏差，但我们通过使用客观距离测量来量化其影响的能力为蛋白质组数据及其质量控制打开了一个强大的新窗口。在这个项目中，我们试图为理论增加一个更重要的组成部分：在我们对网络的宏观表征中包括短回路的统计（除了通过度统计和度相关性量化结构之外，早期的工作是基于这些）。基本原理是，涉及少量节点（通常为3-6个）的功能模块似乎在整个转导机制中发挥重要作用。为了推导出改进我们在前面的PPIN比较中使用的公式，我们现在需要解析地计算具有约束环的随机图的香农熵。这一步从理论上讲是非常困难的，将涉及项目工期的一半。如果完全精确的计算要求太高，我们将求助于循环统计的定义良好且合理的近似值。数值模拟将进行适当构造的合成网络，产生相同或接近现实的PPIN的家庭。该步骤将用作对照实验和/或验证所开发的理论。最后，该理论将被应用到一个大的收集PPIN从不同的物种。在这里开发的方法论的方法应有助于实验在设计和解释未来的研究。

Molecular signals in the living cell can be in a first approximation mostly attributed to Protein-Protein Interactions (PPI) and their complex cross-talk. Since the recent completion of the Human Genome project, it has now become possible to identify and map a large part of the proteins encoded in our genes. However, more details about the molecular interactions involved in signal transduction pathways need to be uncovered before we can truly understand the complex biology of our cellular system. This represents one of the major challenges for the next years of research in biology and medicine. Molecules signal information through interaction with specific binding partners. The binding induces a conformational change in at least one of the partner molecules, which triggers the next biomolecular step in the signaling cascade. The mechanisms of interaction between proteins are therefore crucial to all biological functions, and the effectiveness of this cross-talk during signal transduction plays a fundamental role in many 'healthy' biological processes and in many diseases (e.g. cancers). Several large-scale experimental studies have been published in recent years, to detect PPIs for diverse species, and have been deposited in publicly available databases. Current experimental techniques, such as yeast two-hybrid (Y2H) and co-affinity purification combined with mass spectrometry (AP-MS), have, however, been shown to samplesubsets of the interaction data space with only very limited overlap. We have recently developed a theoretically sound and accurate mathematical framework for comparing interactome data (PPI networks, PPIN) and to evaluate, in an unbiased way, their distance in terms of macroscopic topological properties. Preliminary analysis revealed that networks of the same species and sampled by the same method are similar, and more similar than networks sampled by the same method but different species. Therefore, networks generated from similar experimental conditions have similar topological features, despite their small overlap of the individual PPIs. To our knowledge this has not yet been shown so clearly and in such an unbiased way. Moreover, we could see very clearly, upon comparing networks sampled with different methods,that the data bias induced by the sampling method presently overshadows species related structural properties. Again, although methodological biases have been acknowledged in the literature, our ability to quantify their impact by using objective distance measures opens a powerful new window on proteome data and their quality control. In this project we seek to add a further essential ingredient to the theory: to include in our macroscopic characterizations of networks the statistics of short loops (beyond quantifying structure only via degree statistics and degree correlations, on which the earlier work was based). The rationale is that functional modules involving a small number of nodes (typically 3-6) appear to play an important role in the overall transduction mechanism. To derive formulae that improve upon those we have used in the previous PPIN comparison, we now need to calculate analytically the Shannon entropy for random graphs with constrained loops. This step is theoretically very difficult, and will involve half of the project duration. If fully exact evaluation is too demanding, we will resort to well-defined and sensible approximations of the loop statistics instead. Numerical simulations will be performed on suitably constructed families of synthetic networks, generated identically or close to those of realistic PPIN. This step will be used as control experiment and/or validation of the developed theory. Finally, the theory will be applied to a large collection of PPIN from different species. The methodological approach developed here should aid experimentalists in the design and interpretation of future studies.