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Exchange of biochemical substances is essential way in establishing communication between bacterial cells. It is noticeable that all phases of the process are heavily influenced by perturbations of either internal or external parameters.…
We derive stability conditions of Asymmetric Nuclear Matter ($ANM$) and discuss the relation to mechanical and chemical instabilities of general two-component systems. We show that the chemical instability may appear as an instability of…
Many processes in biology, from the regulation of gene expression in bacteria to memory in the brain, involve switches constructed from networks of biochemical reactions. Crucial molecules are present in small numbers, raising questions…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
The discerning behavior of living systems relies on accurate interactions selected from the lot of molecular collisions occurring in the cell. To ensure the reliability of interactions, binding partners are classically envisioned as finely…
Microbial communities routinely have several alternative stable states observed for the same environmental parameters. Sudden and irreversible transitions between these states make external manipulation of these systems more complicated. To…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
Multivalent associative proteins with strong complementary interactions play a crucial role in phase separation of intracellular liquid condensates. We study the internal dynamics of such "bond-network" condensates comprised of two…
A basic problem in the science of realistic granular matter is the plethora of heuristic models of the stress field in the absence of a first-principles theory. Such a theory is formulated here, based on the idea that static granular…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
Living systems, particularly multicellular systems, often seem hopelessly complex. But recent studies have suggested that beneath this complexity, there may be unifying quantitative principles that we are only now starting to unravel. All…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an…
Biomolecules composed of a limited set of chemical building blocks can co-localize into distinct, spatially segregated compartments known as biomolecular condensates. While many condensates are known to form spontaneously via phase…
Analytical stability calculation is done to prove stability properties for systems with parameters that do not have explicit values. For systems with three components, the usual method of finding the characteristic polynomial as the…
The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the…
Understanding the (de)mixing behavior of multicomponent lipid bilayers is an important step towards unraveling the nature of spatial composition heterogeneities in cellular membranes and their role in biological function. We use…
Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…