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We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
Network inference approaches are widely used to shed light on regulatory interplay between molecular players such as genes and proteins. Biochemical processes underlying networks of interest (e.g. gene regulatory or protein signalling…
Point-proton density distributions are deduced for 130 stable nuclei from $^{7}\mathrm{Li}$ to $^{232}\mathrm{Th}$ from nuclear charge densities determined in elastic electron scattering. There are 171 cases are presented in model-dependent…
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are…
The biological function of protein assemblies was conventionally equated with a unique three-dimensional protein structure and protein-specific interactions. However, in the past 20 years it was found that some assemblies contain long…
Proteins fold using a two-state or multi-state kinetic mechanisms, but up to now there isn't a first-principle model to explain this different behaviour. We exploit the network properties of protein structures by introducing novel…
Processes that proceed reliably from a variety of initial conditions to a unique final form, regardless of moderately changing conditions, are of obvious importance in biophysics. Protein folding is a case in point. We show that the action…
An activator-inhibitor-substrate model of side-branching used in the context of pulmonary vascular and lung development is considered on the supposition that spatially localized concentrations of the activator trigger local side-branching.…
We investigate a zero-range process where the underlying one-particle stationary distribution has multifractality. The multiparticle stationary probability measure can be written in a factorized form. If the number of the particles is…
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule…
The methylation of DNA regulates gene expression. On cell division the methylation state of the DNA is typically inherited from parent to daughter cells. While the chemical bond between the methyl group and the DNA is very strong, changes…
Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. To date, many theories for the prevalence of two-state kinetics have been…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…
We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed…
We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state…
We adopt the point of view that analysis of the stability of the protein folding process is central to understanding the underlying physics of folding. Stability of the folding process means that many perturbations do not disrupt the…
This paper investigates the stochastic fluctuations of the number of copies of a given protein in a cell. This problem has already been addressed in the past and closed-form expressions of the mean and variance have been obtained for a…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each…