Rigorous Information-theoretic tools for Comparative Interactomics.

活细胞中的分子信号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定位我们基因中编码的大部分蛋白质。然而，在我们真正了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面临的主要挑战之一。分子通过与特定结合伙伴的相互作用来传递信息。结合诱导至少一个配对分子的构象变化，这触发了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是至关重要的，而信号转导过程中这种串扰的有效性在许多健康的生物过程和许多疾病(如癌症)中起着基础性的作用。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，并已保存在公开可用的数据库中。然而，目前的实验技术，如酵母双杂交(Y2H)和共亲和纯化结合质谱仪(AP-MS)，已经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。我们最近发展了一个理论上合理和准确的数学框架，用于比较相互作用组数据(PPI网络，PPIN)，并以一种公正的方式，根据宏观拓扑性质评估它们之间的距离。初步分析表明，相同物种和用相同方法采样的网络相似，比用相同方法但不同物种采样的网络更相似。因此，在相似的实验条件下产生的网络具有相似的拓扑特征，尽管它们与单独的PPI有很小的重叠。据我们所知，这一点还没有以如此明确和公正的方式表现出来。此外，通过比较不同方法采样的网络，我们可以清楚地看到，采样方法引起的数据偏差目前掩盖了物种相关的结构性质。同样，尽管文献中已经承认了方法学上的偏差，但我们通过使用客观距离测量来量化它们的影响的能力，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，我们试图为该理论增加一个进一步的基本成分：在我们的网络宏观特征中包括短环的统计信息(不仅仅是仅通过早期工作所基于的度统计和度相关性来量化结构)。其基本原理是，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着重要作用。为了推导出比我们在前面的PPIN比较中使用的公式更好的公式，我们现在需要解析地计算具有约束环的随机图的Shannon熵。从理论上讲，这一步是非常困难的，而且将涉及项目工期的一半。如果完全准确的评估要求太高，我们将转而求助于循环统计数据的定义明确和合理的近似。数值模拟将在适当构建的合成网络族上进行，生成的合成网络族与真实的PPIN相同或接近。这一步将被用作已开发理论的对照实验和/或验证。最后，该理论将应用于来自不同物种的大量PPIN收集。这里开发的方法论方法应该有助于实验者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.