Related papers: Cell migration: Beyond Brownian motion
This manuscript provides an in-depth exploration of Brownian Motion, a fundamental stochastic process in probability theory for Biostatisticians. It begins with foundational definitions and properties, including the construction of Brownian…
Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We extend a model for the morphology and dynamics of a crawling eukaryotic cell to describe cells on micropatterned substrates. This model couples cell morphology, adhesion, and cytoskeletal flow in response to active stresses induced by…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
Hematopoietic stem cells in mammals are known to reside mostly in the bone marrow, but also transitively passage in small numbers in the blood. Experimental findings have suggested that they exist in a dynamic equilibrium, continuously…
The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do…
This is a short review of two common approximations in stochastic chemical and biochemical kinetics. It will appear as Chapter 6 in the book "Quantitative Biology: Theory, Computational Methods and Examples of Models" edited by Brian…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor…
Many fundamental cellular processes involve small numbers of molecules. When numbers are small, fluctuations dominate, and stochastic models, which account for these fluctuations, are required. In this chapter, we describe minimal…
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
DNA migration in topologically structured microchannels with periodic cavities is investigated experimentally and with Brownian dynamics simulations of a simple bead-spring model. The results are in very good agreement with one another. In…
Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal…
We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a…