Complex Networks

Biomolecular networks

Mass-action equilibrium in protein binding networks

Complex biomolecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signaling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory network.  

Binding interactions between proteins form a weighted network in which individual edges are characterized by their binding strength (inverse dissociation constant) and individual protein-nodes – by their concentrations and subcellular localizations. However, the state-of-the-art high-throughput experimental techniques generate just a binary (yes or no) information about individual interactions. Therefore, most of the previous research concentrated just on topology of these networks, uncovering such general properties as a broad distribution of the number of binding partners of individual proteins, globally interconnected network architecture (the “small world” effect), a scarcity of direct interactions between highly connected hub-proteins, etc. We recently developed  a set of computational tools and analytical methods which allows one to go beyond purely topological studies of binding networks and efficiently calculate the mass-action equilibrium of protein concentrations and its response to systematic perturbations. 

Three views of a subset of 312 highly abundant nodes in yeast protein-binding network. (left panel) All binding links between these nodes. (middle panel) Binding links characterized by high concentration of heterodimers (>1,000 molecules per cell). (right panel) Concentration-coupled proteins A -> B with the property that a 2-fold increase in the total concentration of A reduces  the free concentration of its immediate binding partner B by 20% or more. Note that links roughly coincide with highly abundant dimers shown in the middle panel. Arrows reveal the preferential direction of propagation of perturbations (down the concentration gradient).

We are actively working to advance our understanding of biological effects of the mass-action equilibrium in protein binding networks by investigating 

Understanding the equilibrium and dynamical properties of protein binding networks, their response to large systematic perturbations and noise constitutes an important part of the system-level knowledge about an organism which could be further utilized in 

Degree-degree correlations and other non-random topological features 
of bio-molecular networks

For any complex network it is important to know which properties of such a network were designed (or evolved in case of living systems), and which arose by pure chance. To answer this question in our 2002 Science paper Kim Sneppen and myself proposed an algorithm measuring the correlation profile of a given complex network. This profile compares the number of edges between pairs of nodes with degrees (numbers of neighbors) K₀ and K₁ in a given complex network in question and its properly randomized version, and detects statistically significant deviations of one from another. 

We applied this algorithm to protein interaction and genetic regulatory networks in baker's yeast Saccharomyces cerevisiae.  It was found that links between highly connected proteins are systematically suppressed in favor of links between highly connected nodes and those of low connectivity. Such correlation pattern is beneficial for the cell since it decreases the likelihood of biologically undesirable cross talk and enhances the overall robustness of a network by localizing effects of deleterious perturbations.