Related papers: A global convergence result for processive multisi…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
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…
Mechanical loading generally weakens adhesive structures and eventually leads to their rupture. However, biological systems can adapt to loads by strengthening adhesions, which is essential for maintaining the integrity of tissue and whole…
Multisite covalent modification of proteins is omnipresent in eukaryotic cells. A well-known example is the mitogen-activated protein kinase (MAPK) cascade, where in each layer of the cascade a protein is phosphorylated at two sites. It has…
We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product…
Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different…
Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Protein phosphorylation is a reversible post-translational modification commonly used by cell signaling networks to transmit information about the extracellular environment into intracellular organelles for the regulation of the activity…
The random arrest of the diffusion of a single particle and its return to its origin has served as the paradigmatic example of a large variety of processes undergoing stochastic resetting. While the implications and applications of…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
A variety of biomolecular systems rely on exploratory dynamics to reach target locations or states within a cell. Without a mechanism to remotely sense and move directly towards a target, the system must sample over many paths, often…
In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…
Robust oscillations play crucial roles in a wide variety of biological processes and are often generated by deterministic mechanisms. However, stochastic fluctuations often generate complex perturbations of these deterministic oscillations,…
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability,…
Counter-streaming systems are a canonical model for beam-plasma instabilities, such as the filamentation instability, which is critical in high energy density physics. However, scenarios involving intersecting fast electron beams break the…
Protein nanoclustering is a characteristic feature of their activated state and is essential for forming numerous subcellular structures. The formation of these nanoclusters is highly dependent on a series of post-translational…
This paper studies the dynamics of a network of diffusively-coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally…