Fluctuations in Mass-Action Equilibrium of Protein Binding Networks

We consider two types of fluctuations in the mass-action equilibrium in protein binding networks. The first type is driven by relatively slow changes in total concentrations (copy numbers) of interacting proteins. The second type, to which we refer to as spontaneous, is caused by quickly decaying thermodynamic deviations away from the equilibrium of the system. As such they are amenable to methods of equilibrium statistical mechanics used in our study. We investigate the effects of network connectivity on these fluctuations and compare them to their upper and lower bounds. The collective effects are shown to sometimes lead to large power-law distributed amplification of spontaneous fluctuations as compared to the expectation for isolated dimers. As a consequence of this, the strength of both types of fluctuations is positively correlated with the overall network connectivity of proteins forming the complex. On the other hand, the relative amplitude of fluctuations is negatively correlated with the abundance of the complex. Our general findings are illustrated using a real network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.Comment: 4 pages, 3 figure

Parameters of proteome evolution from histograms of amino-acid sequence identities of paralogous proteins

Background: The evolution of the full repertoire of proteins encoded in a given genome is mostly driven by gene duplications, deletions, and sequence modifications of existing proteins. Indirect information about relative rates and other intrinsic parameters of these three basic processes is contained in the proteome-wide distribution of sequence identities of pairs of paralogous proteins. Results: We introduce a simple mathematical framework based on a stochastic birth-and-death model that allows one to extract some of this information and apply it to the set of all pairs of paralogous proteins in H. pylori, E. coli, S. cerevisiae, C. elegans, D. melanogaster, and H. sapiens. It was found that the histogram of sequence identities p generated by an all-to-all alignment of all protein sequences encoded in a genome is well fitted with a power-law form ∼ p−γ with the value of the exponent γ around 4 for the majority of organisms used in this study. This implies that the intra-protein variability of substitution rates is best described by the Gamma-distribution with the exponent α ≈ 0.33. Different features of the shape of such histograms allow us to quantify the ratio between the genome-wide average deletion/duplication rates and the amino-acid substitution rate. 1 Conclusions: We separately measure the short-term (“raw”) duplication and deletion rates r ∗ dup, r ∗ del whic

Upstream plasticity and downstream robustness in evolution of molecular networks

BACKGROUND: Gene duplication followed by the functional divergence of the resulting pair of paralogous proteins is a major force shaping molecular networks in living organisms. Recent species-wide data for protein-protein interactions and transcriptional regulations allow us to assess the effect of gene duplication on robustness and plasticity of these molecular networks. RESULTS: We demonstrate that the transcriptional regulation of duplicated genes in baker's yeast Saccharomyces cerevisiae diverges fast so that on average they lose 3% of common transcription factors for every 1% divergence of their amino acid sequences. The set of protein-protein interaction partners of their protein products changes at a slower rate exhibiting a broad plateau for amino acid sequence similarity above 70%. The stability of functional roles of duplicated genes at such relatively low sequence similarity is further corroborated by their ability to substitute for each other in single gene knockout experiments in yeast and RNAi experiments in a nematode worm Caenorhabditis elegans. We also quantified the divergence rate of physical interaction neighborhoods of paralogous proteins in a bacterium Helicobacter pylori and a fly Drosophila melanogaster. However, in the absence of system-wide data on transcription factors' binding in these organisms we could not compare this rate to that of transcriptional regulation of duplicated genes. CONCLUSIONS: For all molecular networks studied in this work we found that even the most distantly related paralogous proteins with amino acid sequence identities around 20% on average have more similar positions within a network than a randomly selected pair of proteins. For yeast we also found that the upstream regulation of genes evolves more rapidly than downstream functions of their protein products. This is in accordance with a view which puts regulatory changes as one of the main driving forces of the evolution. In this context a very important open question is to what extent our results obtained for homologous genes within a single species (paralogs) carries over to homologous proteins in different species (orthologs)

Improved Reconstruction of In Silico Gene Regulatory Networks by Integrating Knockout and Perturbation Data

We performed computational reconstruction of the in silico gene regulatory networks in the DREAM3 Challenges. Our task was to learn the networks from two types of data, namely gene expression profiles in deletion strains (the ‘deletion data’) and time series trajectories of gene expression after some initial perturbation (the ‘perturbation data’). In the course of developing the prediction method, we observed that the two types of data contained different and complementary information about the underlying network. In particular, deletion data allow for the detection of direct regulatory activities with strong responses upon the deletion of the regulator while perturbation data provide richer information for the identification of weaker and more complex types of regulation. We applied different techniques to learn the regulation from the two types of data. For deletion data, we learned a noise model to distinguish real signals from random fluctuations using an iterative method. For perturbation data, we used differential equations to model the change of expression levels of a gene along the trajectories due to the regulation of other genes. We tried different models, and combined their predictions. The final predictions were obtained by merging the results from the two types of data. A comparison with the actual regulatory networks suggests that our approach is effective for networks with a range of different sizes. The success of the approach demonstrates the importance of integrating heterogeneous data in network reconstruction

An Approach for Determining and Measuring Network Hierarchy Applied to Comparing the Phosphorylome and the Regulome

Many biological networks naturally form a hierarchy with a preponderance of downward information flow. In this study, we define a score to quantify the degree of hierarchy in a network and develop a simulated-annealing algorithm to maximize the hierarchical score globally over a network. We apply our algorithm to determine the hierarchical structure of the phosphorylome in detail and investigate the correlation between its hierarchy and kinase properties. We also compare it to the regulatory network, finding that the phosphorylome is more hierarchical than the regulome

Detecting modules in multiplex networks – an application for integrating expression profiles across multiple species

Multiplex network, a set of networks linked through interconnected layers, is a useful mathematical framework for data integration. Here, we present a general method to detect modules in multiplex networks and apply it in a specific biological context: to simultaneously cluster the genome-wide expression profiles of C. elegans and D. melanogaster generated by the ENOCDE and modENCODE consortia. The method revealed modules that are fundamentally cross-species and can either be conserved or species-specific. In general, the method could be applied in various contexts like the integration of different social networks