Inferring Network Mechanisms: The Drosophila melanogaster Protein Interaction Network

Naturally occurring networks exhibit quantitative features revealing underlying growth mechanisms. Numerous network mechanisms have recently been proposed to reproduce specific properties such as degree distributions or clustering coefficients. We present a method for inferring the mechanism most accurately capturing a given network topology, exploiting discriminative tools from machine learning. The Drosophila melanogaster protein network is confidently and robustly (to noise and training data subsampling) classified as a duplication-mutation-complementation network over preferential attachment, small-world, and other duplication-mutation mechanisms. Systematic classification, rather than statistical study of specific properties, provides a discriminative approach to understand the design of complex networks.Comment: 19 pages, 5 figure

Optimal signal processing in small stochastic biochemical networks

We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we may do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the "cross-talk" dilemma as well as the previously unexplained observation that transcription factors which undergo proteolysis are more likely to be auto-repressive.Comment: 41 pages 7 figures, 5 table

Information-theoretic approach to network modularity

Exploiting recent developments in information theory, we propose, illustrate, and validate a principled information-theoretic algorithm for module discovery and the resulting measure of network modularity. This measure is an order parameter (a dimensionless number between 0 and 1). Comparison is made with other approaches to module discovery and to quantifying network modularity (using Monte Carlo generated Erdös-like modular networks). Finally, the network information bottleneck (NIB) algorithm is applied to a number of real world networks, including the “social” network of coauthors at the 2004 APS March Meeting

Systematic identification of statistically significant network measures

We present a graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of “motif hubs” (multiple overlapping significant subgraphs), computational efficiency relative to subgraph census, and flexibility (the method is easily generalizable to weighted and signed graphs). The embedding space is based on scalars, functionals of the adjacency matrix representing the network. Scalars are global, involving all nodes; although they can be related to subgraph enumeration, there is not a one-to-one mapping between scalars and subgraphs. Improvements in network randomization and significance testing—we learn the distribution rather than assuming Gaussianity—are also presented. The resulting algorithm establishes a systematic approach to the identification of the most significant scalars and suggests machine-learning techniques for network classification

Discriminative Topological Features Reveal Biological Network Mechanisms

Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how well it reproduces a few key features of the real-world data, such as degree distributions, mean geodesic lengths, and clustering coefficients. Often pairs of models can reproduce these features with indistinguishable fidelity despite being generated by vastly different mechanisms. In such cases, these few target features are insufficient to distinguish which of the different models best describes real world networks of interest; moreover, it is not clear a priori that any of the presently-existing algorithms for network generation offers a predictive description of the networks inspiring them. To derive discriminative classifiers, we construct a mapping from the set of all graphs to a high-dimensional (in principle infinite-dimensional) ``word space.'' This map defines an input space for classification schemes which allow us for the first time to state unambiguously which models are most descriptive of the networks they purport to describe. Our training sets include networks generated from 17 models either drawn from the literature or introduced in this work, source code for which is freely available. We anticipate that this new approach to network analysis will be of broad impact to a number of communities.Comment: supplemental website: http://www.columbia.edu/itc/applied/wiggins/netclass

Towards the “Baby Connectome”: Mapping the Structural Connectivity of the Newborn Brain

Defining the structural and functional connectivity of the human brain (the human “connectome”) is a basic challenge in neuroscience. Recently, techniques for noninvasively characterizing structural connectivity networks in the adult brain have been developed using diffusion and high-resolution anatomic MRI. The purpose of this study was to establish a framework for assessing structural connectivity in the newborn brain at any stage of development and to show how network properties can be derived in a clinical cohort of six-month old infants sustaining perinatal hypoxic ischemic encephalopathy (HIE). Two different anatomically unconstrained parcellation schemes were proposed and the resulting network metrics were correlated with neurological outcome at 6 months. Elimination and correction of unreliable data, automated parcellation of the cortical surface, and assembling the large-scale baby connectome allowed an unbiased study of the network properties of the newborn brain using graph theoretic analysis. In the application to infants with HIE, a trend to declining brain network integration and segregation was observed with increasing neuromotor deficit scores