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Navigation of microorganisms is controlled by internal processes ultimately sensitive to mechanical or chemical signaling encountered along the path. In many natural environments, such as porous soils or physiological ducts, motile species…
This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where…
Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the…
Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
Classical descriptions of enzyme kinetics ignore the physical nature of the intracellular environment. Main implicit assumptions behind such approaches are that reactions occur in compartment volumes which are large enough so that molecular…
Active adaptive matter has attracted considerable interest due to its rich, largely unexplained dynamics and its relevance to a wide range of synthetic and biological materials. An important subclass of such systems consists of active…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
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…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
Intracellular components explore the cytoplasm via active motor-driven transport in conjunction with passive diffusion. We model the motion of organelles in narrow tubular cells using analytical techniques and numerical simulations to study…
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…
We introduce and analyze two general dynamical models for unidirectional movement of particles along a circular chain and an open chain of sites. The models include a soft version of the simple exclusion principle, that is, as the density…
Tracking of particles, be it a passive tracer or an actively moving bacterium in the growing bacterial colony, is a powerful technique to probe the physical properties of the environment of the particles. One of the most common measures of…
Granular materials are inherently out-of-equilibrium systems due to energy dissipation through inelastic collisions and friction. When driven by mechanical agitation such as vibration, they exhibit rich collective behaviors including…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…