Research

Branching structures are ubiquitous in biological systems at a variety of scales, from cytoskeletal networks to plant roots. Here, we present an analytical study of deterministically elongating filaments that undergo stochastic branching in the absence of interactions. We calculate the length distributions of subpopulations of fixed and actively growing segments for tip bifurcations and side-branching processes. In the absence of side-branching, these subpopulations exhibit identical distributions. However, the inclusion of side-branching breaks this symmetry, producing distinct universality classes (functional forms) of length distributions depending on whether branching occurs on fixed and/or growing filaments. Furthermore, we find that the ratio of typical branch lengths of fixed and active filaments is confined to a finite interval when side branching acts on growing filaments. Thus, experimental measurements deviating from the predicted finite interval would suggest the involvement of branching mechanisms beyond those included in this model. All analytical results are verified by numerical simulations.

In a short-ranged equilibrium gas, boundary effects are sub-leading in the thermodynamic limit and have no influence on the macroscopic bulk properties of the system. In an active gas, by contrast, boundaries drive steady-state currents and long-range modulations of the density field throughout the bulk, while the gas exerts forces on the boundaries themselves. A generic boundary potential introduces additional length scales into the system, rendering both the modulations and these forces non-universal. Here we consider a 2D wedge, in which the persistence length is the only length scale, so that the density modulations and wall pressure decay as universal power laws fixed solely by the opening angle $\beta$.

When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. We present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations are distinct growth morphologies controlled by expansion rates, competitive abilities, or spatial anisotropy. In some cases the ability to expand in space may overcome reproductive advantage in colonizing new territory. When new traits appear with accumulating mutations, we find that variations in fitness in range expansion may be described by the Tracy-Widom distribution.

Glucose is the principal metabolic fuel for the energy needs of most cell types. Upon infection, cytokines secreted by the immune system regulate redistribution of glucose to meet new metabolic needs associated with clearing the pathogen. We develop a mathematical model to describe the dynamics of such adaptation of metabolic pathways mediated by the immune response and its impact on the ability to clear pathogen and restore health. We find that cytokine-regulated redistribution of glucose resources in different tissues is critical for an effective immune response to pathogen as strictly clamping plasma glucose levels to homeostatic levels results in an ineffective immune response. By studying the effects of various parameters in our model, we describe how aberrant regulation of adaptation mechanisms affect outcomes of infection. Too high a glucose consumption rate by innate immune cells to mediate functions results in failure to clear pathogen. Pathogens with a very high replication rate can be controlled to low levels, but at a very high metabolic cost. Too low a pathogen replication rate allows the pathogen to hide from the immune system and rebound to high levels at later times. Finally, the strength of the innate immune response must be regulated to not be too high, not only to limit immunopathogenesis, but also for mediating an effective adaptive immune response.