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In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell…

The investigation of collective behaviour in dense assemblies of self-propelled active particles has been motivated by a wide range of biological phenomena. Of particular interest are dynamical transitions of cellular and sub-cellular…

We consider a coupled bulk/surface model for advection and diffusion of interacting chemical species in biological cells. Specifically, we consider a signalling protein that can exist in both a cytosolic and a membrane-bound state, along…

Transport of molecules across membrane channels is investigated theoretically using exactly solvable discrete stochastic site-binding models. It is shown that the interaction potential between molecules and the channel has a strong effect…

In cell membranes, proteins and lipids diffuse in a highly crowded and heterogeneous landscape, where aggregates and dense domains of proteins or lipids obstruct the path of diffusing molecules. In general, hindered motion gives rise to…

A fundamental question in biology is to understand how patterns and shapes emerge from the collective interplay of large numbers of cells. Cells forming two-dimensional epithelial tissues behave as active materials that undergo remodeling…

Cells are strongly out-of-equilibrium systems driven by continuous energy supply. They carry out many vital functions requiring active transport of various ingredients and organelles, some being small, others being large. The cytoskeleton,…

Many bacteria use rotating helical flagellar filaments to swim. The filaments undergo polymorphic transformations in which the helical pitch and radius change abruptly. These transformations arise in response to mechanical loading, changes…

The dynamics of a folded protein is studied in water and glycerol at a series of temperatures below and above their respective dynamical transition. The system is modeled in two distinct states whereby the protein is decoupled from the bulk…

Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in…

Regulation to a well-defined target state is a fundamental requirement for achieving reliable functionality in living systems and maintaining specific non-equilibrium states. The control of certain properties and functionalities of systems…

Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network…

The cell cycle is a tightly controlled process, yet its underlying genetic network shows marked differences across species. Which of the associated structural features follow solely from the ability to impose the appropriate gene expression…

Various molecules exclusively accumulate at the front or back of migrating eukaryotic cells in response to a shallow gradient of extracellular signals. Directional sensing and signal amplification highlight the essential properties in the…

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…

Molecular transport maintains cellular structures and functions. For example, lipid and protein diffusion sculpts the dynamic shapes and structures on the cell membrane that perform essential cellular functions, such as cell signaling.…

In processes such as embryo shaping, wound healing, and malignant cell invasion, epithelial cells transition between dispersed phases, where the cells move independently, and condensed phases, where they aggregate and deform to close gaps,…

We propose an active Cahn-Hilliard theory for the dynamics of a new type of phase transition where the driving force is not the direct interactions between the two separating components, but their active sorting by a third polar species.…

Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…

We propose a novel mechanism of cell motility, which relies on the coupling of actin polymerization at the cell membrane to geometric confinement. We consider a polymerizing viscoelastic cytoskeletal gel confined in a narrow channel, and…