Related papers: Phase Transition Analysis of the Dynamic Instabili…
We generalize the Dogterom-Leibler model for microtubule dynamics [DL] to the case where the rates of elongation as well as the lifetimes of the elongating and shortening phases are a function of GTP-tubulin concentration. We study also the…
Dynamic instability of microtubules is considered using frameworks of non-linear thermodynamics and non-equilibrium reaction-diffusion systems. Stochastic assembly/disassembly phases in the polymerization dynamics of microtubules are…
Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very…
A novel theoretical model of dynamic instability of a system of linear (1D) microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of…
Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in…
In this paper, we introduce a novel approach to study reaction-diffusion systems -- dynamic transition theory approach developed in Ma and Wang 2015. This approach generalizes Turing's classical result (linear stability analysis) on pattern…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
A simple stochastic model which describes microtubule dynamics and explicitly takes into account the relevant biochemical processes is presented. The model incorporates binding and unbinding of monomers and random phosphate release inside…
The reliability of any day-to-day material is critically dictated by its properties. One factor which governs the behaviour of a material, under a given condition, is the microstructure. Despite the absence of any phase transformation, a…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
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 general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Microtubule dynamic instability allows search and capture of kinetochores during spindle formation, an important process for accurate chromosome segregation during cell division. Recent work has found that microtubule rotational diffusion…
Experiments have not only revealed the remarkably long lifetime of nanobubbles, but also demonstrated the diffusive instability of bubbles above micrometers, thus a full-scale physical understanding on the stability of bubbles is in urgent…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
In this article, we study the mixing properties of metastable diffusion processes which possess a Gibbs invariant distribution. For systems with multiple stable equilibria, so-called metastable transitions between these equilibria are…