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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 applicat
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 stoc
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
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,
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 ster