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Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure…
Enzymes are on the front lines of evolution. All living organisms rely on highly efficient, specific enzymes for growth, sustenance, and reproduction; and many diseases are a consequence of a mutation on an enzyme that affects its catalytic…
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a…
We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferation mobile phase and a proliferating sedentary phase. Our model implements…
We review the models developed and techniques used in recent years to study the kinetics of phase ordering in a class of complex fluids, namely, ternary microemulsions and micellar solutions.
A recently experimentally observed biochemical "threshold filtering" mechanism by processes catalyzed by the enzyme malate dehydrogenase is explained in terms of a model that incorporates an unusual mechanism of inhibition of this enzyme…
We present a model for unicellular algal growth as motivated by several experiments implicating the importance of calcium ions and ``loosening'' enzymes in morphogenesis. A growing cell at rest in a diffusive calcium solution is viewed as…
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport…
Bacterial cellulose is an important class of biomaterials which can be grown in well-controlled laboratory and industrial conditions. The cellulose structure is affected by several biological, chemical and environmental factors, including…
The current global food system produces substantial waste and carbon emissions while exacerbating the effects of global hunger and protein deficiency. This study aims to address these challenges by exploring the use of lignocellulosic…
A number of swimming microorganisms such as ciliates ($\textit{Opalina}$) and multicellular colonies of flagellates ($\textit{Volvox}$) are approximately spherical in shape and swim using beating arrays of cilia or short flagella covering…
We propose a non-equilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, etc.) Our model becomes highly non-trivial, and different from the equilibrium…
Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go…
We present a simple model for bacteria like \emph{Escherichia coli} swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a…
We present a mathematical model based on a system of partial differential equations (PDEs) with cross-diffusion and reaction terms to describe ecological interactions between multiple bacterial species and substrates within microaggregates,…
In this paper we present a new model for single-celled, non-branching hypha tip growth. The growth mechanism of hypha cells consists of transport of cell wall building material to the cell wall and subsequent incorporation of this material…
A bacterial biofilm is an aggregate of micro-organisms growing fixed onto a solid surface, rather than floating freely in a liquid. Biofilms play a major role in various practical situations such as surgical infections and water treatment.…
In Part I of this article we have developed a novel mechanobiological model of a Tissue Engineering process that accounts for the mechanisms through which an isotropic or anisotropic adherence condition regulates the active functions of the…