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The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…
The main goal of Systems Biology research is to reconstruct biological networks for its topological analysis so that reconstructed networks can be used for the identification of various kinds of disease. The availability of high-throughput…
Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…
Identifying features of molecular regulatory networks is an important problem in systems biology. It has been shown that the combinatorial logic of such networks can be captured in many cases by special functions called nested canalyzing in…
The diverse, specialized genes in today's lifeforms evolved from a common core of ancient, elementary genes. However, these genes did not evolve individually: gene expression is controlled by a complex network of interactions, and…
Self-regulation of living tissue as an example of self-organization phenomena in hierarchical systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any…
The relationship between topology and network throughput of arbitrarily-connected mesh networks is studied. Taking into account nonlinear channel properties, it is shown that throughput decreases logarithmically with physical network size…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool…
The principles underlying protein folding remains one of Nature's puzzles with important practical consequences for Life. An approach that has gathered momentum since the late 1990's, looks at protein hetero-polymers and their folding…
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends…
We study how the dynamic equilibrium of the reversible protein-protein binding network in yeast Saccharomyces cerevisiae responds to large changes in abundances of individual proteins. The magnitude of shifts between free and bound…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approach to analyzing biological networks yields results that are…
Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions…
One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is…