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We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate…
Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to…
Network theorists have developed methods to characterize the complex interactions in natural phenomena. The structure of the network of interactions between proteins is important in the field of proteomics, and has been subject to intensive…
Cells contain multiple condensates which spontaneously form due to the heterotypic interactions between their components. Although the proteins and disordered region sequences that are responsible for condensate formation have been…
Multivalent particles have the ability to form multiple bonds to a substrate. Hence, a multivalent interaction can be strong, even if the individual bonds are weak. However, much more interestingly, multivalency greatly increases the…
The network paradigm is increasingly used to describe the dynamics of complex systems. Here we review the current results and propose future development areas in the assessment of perturbation waves, i.e. propagating structural changes in…
Proteins perform their functions usually by interacting with other proteins. Predicting which proteins interact is a fundamental problem. Experimental methods are slow, expensive, and have a high rate of error. Many computational methods…
The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I…
Including pairwise interactions between the predictors of a regression model can produce better predicting models. However, to fit such interaction models on typical data sets in biology and other fields can often require solving enormous…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
Complexes of physically interacting proteins constitute fundamental functional units responsible for driving biological processes within cells. A faithful reconstruction of the entire set of complexes is therefore essential to understand…
Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
Protein-protein interactions are fundamental to many biological processes. Experimental screens have identified tens of thousands of interactions and structural biology has provided detailed functional insight for select 3D protein…
Interacting-Particle Reaction Dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enable a wide range of…
We investigate proteins within heterogeneous cell membranes where non-equilibrium phenomena arises from spatial variations in concentration and temperature. We develop simulation methods building on non-equilibrium statistical mechanics to…
Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two…
The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k of other vertices…
Background: If biology is modular then clusters, or communities, of proteins derived using only protein interaction network structure should define protein modules with similar biological roles. We investigate the link between biological…