Effects of cell geometry on reversible vesicular transport

Abstract

A major question in cell biology concerns the biophysical mechanism underlying delivery of newly synthesized macromolecules to specific targets within a cell. A recent modeling paper investigated this phenomenon in the context of vesicular delivery to en passant synapses in neurons (Bressloff and Levien 2015 Phys. Rev. Lett.). It was shown how reversibility in vesicular delivery to synapses could play a crucial role in achieving uniformity in the distribution of resources throughout an axon, which is consistent with experimental observations in C. elegans and Drosophila. In this work we generalize the previous model by investigating steady-state vesicular distributions on a Cayley tree, a disk, and a sphere. We show that for irreversible transport on a tree, branching increases the rate of decay of the steady-state distribution of vesicles. On the other hand, the steady-state profiles for reversible transport are similar to the 1D case. In the case of higher-dimensional geometries, we consider two distinct types of radially-symmetric microtubular network: (i) a continuum and (ii) a discrete set. In the continuum case, we model the motorcargo dynamics using a phenomenologically-based advection-diffusion equation in polar (2D) and spherical (3D) coordinates. On the other-hand, in the discrete case, we derive the population model from a stochastic model of a single motor switching between ballistic motion and diffusion. For all of the geometries we find that reversibility in vesicular delivery to target sites allows for a more uniform distribution of vesicles, provided that cargocarrying motors are not significantly slowed by their cargo. In each case we characterize the loss of uniformity as a function of the dispersion in velocities.

Diffusive transport in the presence of stochastically gated absorption

“…At the level of a single Brownian particle switching conformational states, one could extend the analysis in section II to a variety of trapping scenarios, including higher dimensional bounded domains with a distribution of static or dynamic traps within the domain or on the boundary of the domain. Indeed, we have previously shown how the notion of synaptic democracy extends to higher-dimensional domains with radial symmetry and reversible traps [25]. Generalizing the population level analysis of sections III and IV, however, requires a deeper understanding of possible mechanisms underlying the physical gating of trapping regions or inactivation domains, resulting in a common switching environment shared by all the particles.…”

“…Recently, we have shown how attenuation of the steady-state concentration can be mitigated by taking the absorption of particles to be reversible [22][23][24][25]. Although our mathematical analysis was motivated by experimental studies of intracellular transport in neurons [26,27], it reflects a general feature of diffusionabsorption processes: if absorption of particles is reversible then the particles absorbed close to the source are free to be re-released into the diffusing pool of particles for absorption at more distal regions.…”

Queuing model of axonal transport

“…For sufficiently small κ/v, the bulk concentration is approximately uniform but comes at the cost of a slow build up of resources within the synapses. One mechanism for generating a more uniform distribution of resources for relatively fast absorption is to allow for the reversible delivery of vesicles, which has been observed experimentally in C. elegans and Drosophila [69,38,39] and demonstrated theoretically using a generalized version of the population model (2.1) that keeps track of motor-complexes that are no longer carrying a vesicle [6,26]. More specifically, let c 1 (x, t) and c 0 (x, t) denote the density of motor-complexes with and without an attached vesicle, respectively, and denote the forward and backward rates for cargo delivery by κ ± .…”

Stochastic Hybrid Systems in Cellular Neuroscience

“…The hypothesized mechanism of synaptic democracy that combines bidirectional transport with reversible delivery of cargo to synaptic targets has recently been investigated in a series of modeling studies [ 13 , 16 , 20 , 78 ]. Consider a simple three-state transport model of a single motor-complex moving on a semiinfinite 1D track as shown in Fig.…”

“…For example, it can be extended to the case where each motor carries a vesicular aggregate rather than a single vesicle, assuming that only one vesicle can be exchanged with a target at any one time [ 13 ]. The effects of reversible vesicular delivery also persist when exclusion effects between between motor-cargo complexes are taken into account [ 16 ] and when higher-dimensional cell geometries are considered [ 78 ].…”