Residence times of receptors in dendritic spines analyzed by simulations in empirical domains

Analysis of high-density superresolution imaging of receptors reveal the organization of dendrites at the nano-scale resolution. We present here simulations in empirical live cell images, which allows converting local information extracted from short range trajectories into simulations of long range trajectories. Based on these empirical simulations, we compute the residence time of an AMPA receptor (AMPAR) in dendritic spines that accounts for receptors local interactions and geometrical organization. We report here that depending on the type of the spine, the residence time varies from one to five minutes. Moreover, we show that there exists transient organized structures, previously described as potential wells that can regulate the trafficking of AMPARs to dendritic spines.Comment: 19 page

The auxiliary region method: A hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems

Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE and Brownian-based representations of reaction-diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based "auxiliary regions". We demonstrate that the hybrid method is able to simulate reaction-diffusion dynamics for a number of different test problems with high accuracy. Further, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including, filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.Comment: 29 pages, 14 figures, 2 table

Multi-level agent-based modeling - A literature survey

During last decade, multi-level agent-based modeling has received significant and dramatically increasing interest. In this article we present a comprehensive and structured review of literature on the subject. We present the main theoretical contributions and application domains of this concept, with an emphasis on social, flow, biological and biomedical models.Comment: v2. Ref 102 added. v3-4 Many refs and text added v5-6 bibliographic statistics updated. v7 Change of the name of the paper to reflect what it became, many refs and text added, bibliographic statistics update

Fundamental diagrams for kinetic equations of traffic flow

In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the so-called "spatially homogeneous problem" and, in the representative case of an exploratory model, we study the qualitative properties of its solutions for a generic number of discrete microstates. This includes, in particular, asymptotic trends and equilibria, whence fundamental diagrams originate.Comment: 14 page