Queuing model of axonal transport

Deterministic principles underlying nicotinic receptor protein function

There are no available tools to verify whether current kinetic models correctly assume that the gating of ionotropic receptors is a stochastic process. Current models place no restrictions either on receptor conformational change rates or on the number of conformational states, making them insensitive to potential constraints imposed by deterministic principles. We formulate a new, deterministic model of receptor operation, providing a complete mathematical description and analyze the consequences of applying the model to the nicotinic receptor. In our model, the probability functions have narrowly defined forms with the number of parameters determined a priori. We redefine the origin of brief and long openings and introduce a state of partial desensitization. This model, in contrast to currently used kinetic models of nicotinic receptor, provides constant receptor affinity and enables the modulation of receptor activity without binding a modulator molecule.

Spectral theory of diffusion in partially absorbing media

A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator) for particle position X t and a Brownian functional U t that specifies the amount of time the particle is in contact with a reactive component M . Absorption occurs as soon as U t crosses a randomly distributed threshold (stopping time). Laplace transforming the propagator with respect to U t leads to a classical boundary value problem (BVP) in which the reactive component has a constant rate of absorption z , where z is the corresponding Laplace variable. Hence, a crucial step in the encounter-based approach is finding the inverse Laplace transform. In the case of a reactive boundary ∂ M , this can be achieved by solving a classical Robin BVP in terms of the spectral decomposition of a Dirichlet-to-Neumann (D-to-N) operator on ∂ M . In this paper, we develop the analogous construction in the case of a reactive substrate M . In particular, we show that the Laplace transformed propagator can be computed in terms of the spectral decomposition of a pair of D-to-N operators on ∂ M . However, inverting the Laplace transform with respect to z is considerably more involved. We illustrate the theory by considering the D-to-N operators for some simple geometries.

Superdiffusion in self-reinforcing run-and-tumble model with rests

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random-walk position, from which we obtain the second moment in the long-time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least 2/3 of the mean resting time for superdiffusion to be possible. Monte Carlo simulations validate this theoretical result. This work demonstrates the possibility of extending the telegrapher's (or Cattaneo) equation by adding self-reinforcing directionality so that superdiffusion occurs even when rests are introduced.