No Arabic abstract
Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport phenomena. However, in general, the interplay between crowding and geometry in complex real-life environments is poorly understood. Existing analytical methodologies are not always readily extendable to heterogeneous environments: in these situations predictions of crowded transport behaviour within heterogeneous environments rely on computationally intensive mesh-based approaches. Here, we take a different approach by employing networked representations of complex environments to provide an efficient framework within which the interactions between networked geometry and crowding can be explored. We demonstrate how the framework can be used to: extract detailed information at the level of the whole population or an individual within it; identify the topological features of environments that enable accurate prediction of transport phenomena; and, provide insights into the design of optimal environments.
We present a stochastic approach for ion transport at the mesoscopic level. The description takes into account the self-consistent electric field generated by the fixed and mobile charges as well as the discrete nature of these latter. As an application we study the noise in the ion transport process, including the effect of the displacement current generated by the fluctuating electric field. The fluctuation theorem is shown to hold for the electric current with and without the displacement current.
Signal transduction in biological cells is effected by signaling pathways that typically include multiple feedback loops. Here we analyze information transfer through a prototypical signaling module with biochemical feedback. The module switches stochastically between an inactive and active state; the input to the module governs the activation rate while the output (i.e., the product concentration) perturbs the inactivation rate. Using a novel perturbative approach, we compute the rate with which information about the input is gained from observation of the output. We obtain an explicit analytical result valid to first order in feedback strength and to second order in the strength of input. The total information gained during an extended time interval is found to depend on the feedback strength only through the total number of activation/inactivation events.
A transition rate model of cargo transport by $N$ molecular motors is proposed. Under the assumption of steady state, the force-velocity curve of multi-motor system can be derived from the force-velocity curve of single motor. Our work shows, in the case of low load, the velocity of multi-motor system can decrease or increase with increasing motor number, which is dependent on the single motor force-velocity curve. And most commonly, the velocity decreases. This gives a possible explanation to some recent
The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target. However, the more relevant quantity in many systems is the time it takes the fastest searcher to find a target from a large group of searchers. This fastest FPT depends on extremely rare events and has a drastically faster timescale than the FPT of a given single searcher. In this work, we prove a simple explicit formula for every moment of the fastest FPT. The formula is remarkably universal, as it holds for $d$-dimensional diffusion processes (i) with general space-dependent diffusivities and force fields, (ii) on Riemannian manifolds, (iii) in the presence of reflecting obstacles, and (iv) with partially absorbing targets. Our results rigorously confirm, generalize, correct, and unify various conjectures and heuristics about the fastest FPT.
Axonal growth and guidance at the ventral floor plate is here followed $textit{in vivo}$ in real time at high resolution by light-sheet microscopy along several hundred micrometers of the zebrafish spinal cord. The recordings show the strikingly stereotyped spatio-temporal control that governs midline crossing. Commissural axons are observed crossing the ventral floor plate midline perpendicularly at about 20 microns/h, in a manner dependent on the Robo3 receptor and with a growth rate minimum around the midline, confirming previous observations. At guidance points, commissural axons are seen to decrease their growth rate and growth cones increase in size. Commissural filopodia appear to interact with the nascent neural network, and thereby trigger immediate plastic and reversible sinusoidal-shaped bending movements of neighboring commissural shafts. Ipsilateral axons extend concurrently, but straight and without bends, at three to six times higher growth rates than commissurals, indicating they project their path on a substrate-bound surface rather than relying on diffusible guidance cues. Growing axons appeared to be under stretch, an observation that is of relevance for tension-based models of cortical morphogenesis. The textit{in vivo} observations provide for a discussion of the current distinction between substrate-bound and diffusible guidance cues. The study applies the transparent zebrafish model that provides an experimental model system to explore further the cellular, molecular and physical mechanisms involved during axonal growth, guidance and midline crossing through a combination of $textit{in vitro}$ and $textit{in vivo}$ approaches.