Related papers: Cell migration: Beyond Brownian motion
Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined…
In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
An analysis on the discrete versus continuous views of kinetics of macromolecules is presented. It is shown that the discrete approach traditional to biochemistry is insufficient for understanding the dynamics of protein molecules in…
We provide a detailed description of all possible Feller processes on infinite} star graphs with finite number of edges, processes that while away from the graph's center behave like a one-dimensional Brownian motion. The description can be…
Cell crawling is critical to biological development, homeostasis and disease. In many cases, cell trajectories are quasi-random-walk. In vitro assays on flat surfaces often described such quasi-random-walk cell trajectories as…
T cells undergo large shape changes (morphodynamics) when migrating. While progress has been made elucidating the molecular basis of cell migration, statistical characterization of morphodynamics and migration has been limited, particularly…
Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…
The crossover between dispersion patterns has been frequently observed in various systems. Inspired by the pathway-based kinetic model for E. coli chemotaxis that accounts for the intracellular adaptation process and noise, we propose a…
Mesenchymal motion describes the movement of cells in biological tissues formed by fiber networks. An important example is the migration of tumor cells through collagen networks during the process of metastasis formation. We investigate the…
Since the classical work of L\'evy, it is known that the local time of Brownian motion can be characterized through the limit of level crossings. While subsequent extensions of this characterization have primarily focused on Markovian or…
Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational…
The cytoskeleton in eukaryotic cells plays several crucial roles. In terms of intracellular transport, motor proteins use the cytoskeletal filaments as a backbone along which they can actively transport biological cargos such as vesicles…
Most microorganisms regulate their cell size. We review here some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics they generate. We review the…
Living cells exhibit multi-mode transport that switches between an active, self-propelled motion and a seemingly passive, random motion. Cellular decision-making over transport mode switching is a stochastic process that depends on the…
A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using piecewise diffusion Markov processes (PDifMPs) at the cellular level, we derive an equation for the…
The first arrivals among $N$ Brownian particles is ubiquitous in the life sciences, as it often trigger cellular processes from the molecular level. We study here the case where stochastic particles, which represent molecules, proteins or…
We address the problem of proteasomal protein translocation and introduce a new stochastic model of the proteasomal digestion (cleavage) of proteins. In this model we account for the protein translocation and the positioning of cleavage…