Related papers: Cross-diffusion induced patterns for a single-step…
Chemical reactions are usually studied under the assumption that both substrates and catalysts are well mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in…
In this work we investigate the convergence to equilibrium for mass action reaction-diffusion systems which model irreversible enzyme reactions. Using the standard entropy method in this situation is not feasible as the irreversibility of…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
A comparison is made between conventional Michaelis-Menten kinetics and two models that take into account the duration of the conformational changes that take place at the molecular level during the catalytic cycle of a monomer. The models…
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics…
Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion…
Positive feedback regulation is ubiquitous in cell signaling networks, often leading to binary outcomes in response to graded stimuli. However, the role of such feedbacks in clustering, and in spatial spreading of activated molecules, has…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
The enzyme turnover rate is a fundamental parameter in enzyme kinetics, reflecting the catalytic efficiency of enzymes. However, enzyme turnover rates remain scarce across most organisms due to the high cost and complexity of experimental…
We present a rigorous mathematical approach of two species channel transport within the framework of stochastic thermodynamics, which explains the impact of interparticle in-channel interactions. Different from mean field approaches, the…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…
Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
We investigate the transport of a single excitation through a chain of weakly coupled subunits. At both ends the chain is exposed to baths which are incorporated by means of a master equation in Lindblad form. This master equation is solved…
Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105…