From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200

Exploring hierarchical and overlapping modular structure in the yeast protein interaction network

<p>Abstract</p> <p>Background</p> <p>Developing effective strategies to reveal modular structures in protein interaction networks is crucial for better understanding of molecular mechanisms of underlying biological processes. In this paper, we propose a new density-based algorithm (ADHOC) for clustering vertices of a protein interaction network using a novel subgraph density measurement.</p> <p>Results</p> <p>By statistically evaluating several independent criteria, we found that ADHOC could significantly improve the outcome as compared with five previously reported density-dependent methods. We further applied ADHOC to investigate the hierarchical and overlapping modular structure in the yeast PPI network. Our method could effectively detect both protein modules and the overlaps between them, and thus greatly promote the precise prediction of protein functions. Moreover, by further assaying the intermodule layer of the yeast PPI network, we classified hubs into two types, module hubs and inter-module hubs. Each type presents distinct characteristics both in network topology and biological functions, which could conduce to the better understanding of relationship between network architecture and biological implications.</p> <p>Conclusions</p> <p>Our proposed algorithm based on the novel subgraph density measurement makes it possible to more precisely detect hierarchical and overlapping modular structures in protein interaction networks. In addition, our method also shows a strong robustness against the noise in network, which is quite critical for analyzing such a high noise network.</p

Robustness and modular design of the Drosophila segment polarity network

Biomolecular networks have to perform their functions robustly. A robust function may have preferences in the topological structures of the underlying network. We carried out an exhaustive computational analysis on network topologies in relation to a patterning function in Drosophila embryogenesis. We found that while the vast majority of topologies can either not perform the required function or only do so very fragilely, a small fraction of topologies emerges as particularly robust for the function. The topology adopted by Drosophila, that of the segment polarity network, is a top ranking one among all topologies with no direct autoregulation. Furthermore, we found that all robust topologies are modular--each being a combination of three kinds of modules. These modules can be traced back to three sub-functions of the patterning function and their combinations provide a combinatorial variability for the robust topologies. Our results suggest that the requirement of functional robustness drastically reduces the choices of viable topology to a limited set of modular combinations among which nature optimizes its choice under evolutionary and other biological constraints.Comment: Supplementary Information and Synopsis available at http://www.ucsf.edu/tanglab

Robustness and modular structure in networks

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a percolation problem [7-9] or by modeling cascading failures [10-12]. Many complex systems, from power grids and the Internet to the brain and society [13-15], can be modeled using modular networks comprised of small, densely connected groups of nodes [16, 17]. These modules often overlap, with network elements belonging to multiple modules [18, 19]. Yet existing work on robustness has not considered the role of overlapping, modular structure. Here we study the robustness of these systems to the failure of elements. We show analytically and empirically that it is possible for the modules themselves to become uncoupled or non-overlapping well before the network disintegrates. If overlapping modular organization plays a role in overall functionality, networks may be far more vulnerable than predicted by conventional percolation theory.Comment: 14 pages, 9 figure

Disordered proteins and network disorder in network descriptions of protein structure, dynamics and function. Hypotheses and a comprehensive review

During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here we review the links between disordered proteins and the associated networks, and describe the consequences of local, mesoscopic and global network disorder on changes in protein structure and dynamics. We introduce a new classification of protein networks into &#x2018;cumulus-type&#x2019;, i.e., those similar to puffy (white) clouds, and &#x2018;stratus-type&#x2019;, i.e., those similar to flat, dense (dark) low-lying clouds, and relate these network types to protein disorder dynamics and to differences in energy transmission processes. In the first class, there is limited overlap between the modules, which implies higher rigidity of the individual units; there the conformational changes can be described by an &#x2018;energy transfer&#x2019; mechanism. In the second class, the topology presents a compact structure with significant overlap between the modules; there the conformational changes can be described by &#x2018;multi-trajectories&#x2019;; that is, multiple highly populated pathways. We further propose that disordered protein regions evolved to help other protein segments reach &#x2018;rarely visited&#x2019; but functionally-related states. We also show the role of disorder in &#x2018;spatial games&#x2019; of amino acids; highlight the effects of intrinsically disordered proteins (IDPs) on cellular networks and list some possible studies linking protein disorder and protein structure networks

Spectral Analysis and the Dynamic Response of Complex Networks

The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network characteristics: random networks follow Wigner's semicircular law whereas scale-free networks exhibit a triangular distribution. In this paper we show that the spectral density of hierarchical networks follow a very different pattern, which can be used as a fingerprint of modularity. Of particular importance is the value $\rho(0)$, related to the homeostatic response of the network: it is maximum for random and scale free networks but very small for hierarchical modular networks. It is also large for an actual biological protein-protein interaction network, demonstrating that the current leading model for such networks is not adequate.Comment: 4 pages 14 figure

Complex networks vulnerability to module-based attacks

In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to efficiently break complex networks. The procedure first identifies the communities in which the network can be represented, then it deletes the nodes (edges) that connect different modules by its order in the betweenness centrality ranking list. We illustrate the method by applying it to various well known examples of social, infrastructure, and biological networks. We show that the proposed method always outperforms vertex (edge) attacks which are based on the ranking of node (edge) degree or centrality, with a huge gain in efficiency for some examples. Remarkably, for the US power grid, the present method breaks the original network of 4941 nodes to many fragments smaller than 197 nodes (4% of the original size) by removing mere 164 nodes (~3%) identified by the procedure. By comparison, any degree or centrality based procedure, deleting the same amount of nodes, removes only 22% of the original network, i.e. more than 3800 nodes continue to be connected after thatComment: 8 pages, 8 figure

Rigidity and flexibility of biological networks

The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is given. We also briefly discuss the network aspects of cytoskeletal tensegrity. Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks. Our summary raises the possibility that the concepts of flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl