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Register a new userTrapping in and escape from branched structures of neuronal dendrites
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We present a coarse-grained model for stochastic transport of noninteracting chemical signals inside neuronal dendrites and show how first-passage properties depend on the key structural factors affected by neurodegenerative disorders or aging: the extent of the tree, the topological bias induced by segmental decrease of dendrite diameter, and the trapping probabilities in biochemical cages and growth cones. We derive an exact expression for the distribution of first-passage times, which follows a universal exponential decay in the long-time limit. The asymptotic mean first-passage time exhibits a crossover from power-law to exponential scaling upon reducing the topological bias. We calibrate the coarse-grained model parameters and obtain the variation range of the mean first-passage time when the geometrical characteristics of the dendritic structure evolve during the course of aging or neurodegenerative disease progression (A few disorders are chosen and studied for which clear trends for the pathological changes of dendritic structure have been reported in the literature). We prove the validity of our analytical approach under realistic fluctuations of structural parameters, by comparing to the results of Monte Carlo simulations. Moreover, by constructing local structural irregularities, we analyze the resulting influence on transport of chemical signals and formation of heterogeneous density patterns. Since neural functions rely on chemical signal transmission to a large extent, our results open the possibility to establish a direct link between the disease progression and neural functions.
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We numerically investigate the escape kinetics of elliptic Janus particles from narrow two-dimensional cavities with reflecting walls. The self-propulsion velocity of the Janus particle is directed along either their major (prolate) or minor axis (oblate). We show that the mean exit time is very sensitive to the cavity geometry, particle shape and self-propulsion strength. The mean exit time is found to be a minimum when the self-propulsion length is equal to the cavity size. We also find the optimum mean escape time as a function of the self-propulsion velocity, translational diffusion, and particle shape. Thus, effective transport control mechanisms for Janus particles in a channel can be implemented.
Proteins form a very important class of polymers. In spite of major advances in the understanding of polymer science, the protein problem has remained largely unsolved. Here, we show that a polymer chain viewed as a tube not only captures the well-known characteristics of polymers and their phases but also provides a natural explanation for many of the key features of protein behavior. There are two natural length scales associated with a tube subject to compaction -- the thickness of the tube and the range of the attractive interactions. For short tubes, when these length scales become comparable, one obtains marginally compact structures, which are relatively few in number compared to those in the generic compact phase of polymers. The motifs associated with the structures in this new phase include helices, hairpins and sheets. We suggest that Nature has selected this phase for the structures of proteins because of its many advantages including the few candidate strucures, the ability to squeeze the water out from the hydrophobic core and the flexibility and versatility associated with being marginally compact. Our results provide a framework for understanding the common features of all proteins.
We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural scattering in terms of three equations expressing the sub-unit scattering. The structural scattering expressions allows a composite structures to be used as sub-units within the formalism itself. This allows the scattering expressions for complex hierarchical structures to be derived with great ease. The formalism is furthermore generic in the sense that the scattering due to structural connectivity is completely decoupled from internal structure of the sub-units. This allows sub-units to be replaced by more complex structures. We illustrate the physical interpretation of the formalism diagrammatically. By applying a self-consistency requirement we derive the pair distributions of an ideal flexible polymer sub-unit. We illustrate the formalism by deriving generic scattering expressions for branched structures such as stars, pom-poms, bottle-brushes, and dendrimers build out of asymmetric two-functional sub-units.
Actin cytoskeletal protrusions in crawling cells, or lamellipodia, exhibit various morphological properties such as two characteristic peaks in the distribution of filament orientation with respect to the leading edge. To understand these properties, using the dendritic nucleation model as a basis for cytoskeletal restructuring, a kinetic-population model with orientational-dependent branching (birth) and capping (death) is constructed and analyzed. Optimizing for growth yields a relation between the branch angle and filament orientation that explains the two characteristic peaks. The model also exhibits a subdominant population that allows for more accurate modeling of recent measurements of filamentous actin density along the leading edge of lamellipodia in keratocytes. Finally, we explore the relationship between orientational and spatial organization of filamentous actin in lamellipodia and address recent observations of a prevalence of overlapping filaments to branched filaments---a finding that is claimed to be in contradiction with the dendritic nucleation model.
By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $Delta_{TP}(t) sim t^{beta_{TP}}$ with $beta_{TP}<1$), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ($Delta_{TP}(t) sim t^{alpha_{TP}}$ with $alpha_{TP}>2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $alpha_{CC}$ exceeding unity. Most importantly, $alpha_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked.
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