Fast solver for diffusive transport times on dynamic intracellular networks

The transport of particles in cells is influenced by the properties of
intracellular networks they traverse while searching for localized target
regions or reaction partners. Moreover, given the rapid ...

From random walks on networks to nonlinear diffusion

Mathematical models of motility are often based on random-walk descriptions
of discrete individuals that can move according to certain rules. It is usually
the case that large masses concentrated in s ...

Quantifying biomolecular diffusion with a "spherical cow" model

The dynamics of biological polymers, including proteins, RNA, and DNA, occur
in very high-dimensional spaces. Many naturally-occurring polymers can navigate
a vast phase space and rapidly find their l ...

Arrival time for the fastest among $N$ switching stochastic particles

We study the first arrival time for the fastest among $N$ Brownian particles
that can switch between two states inside a finite interval. The switching is
modeled as a two-state Markov chain and parti ...

An equivalence framework for an age-structured multi-stage representation of the cell cycle

We develop theoretical equivalences between stochastic and deterministic
models for populations of individual cells stratified by age. Specifically, we
develop a hierarchical system of equations descr ...

Geometry adaptation of protrusion and polarity dynamics in confined cell migration

Cell migration in confining physiological environments relies on the
concerted dynamics of several cellular components, including protrusions,
adhesions with the environment, and the cell nucleus. How ...

Stochastic kinetic treatment of protein aggregation and the effects of macromolecular crowding

Investigation of protein self-assembly processes is important for the
understanding of the growth processes of functional proteins as well as
disease-causing amyloids. Inside cells, intrinsic molecula ...

Different anomalous diffusion regimes measured in the dynamics of tracer particles in actin networks

It was previously believed that diffusion of a tracer particle in a
viscoelastic material should be of the fractional Brownian motion (fBm) type.
This is due to the long-term memory in the response of ...

Learning the dynamics of cell-cell interactions in confined cell migration

The migratory dynamics of cells in physiological processes, ranging from
wound healing to cancer metastasis, rely on contact-mediated cell-cell
interactions. These interactions play a key role in shap ...

First Passage processes in cellular biology

Often sharp changes in cellular behavior are triggered by thresholded events,
i.e., by the attainment of a threshold value of a relevant cellular or
molecular dynamical variable. Since the governing v ...