arXiv subjects

James P. Keener

Publications and source records attributed to James P. Keener.

6 recordsLinked to original sources

arXiv2026

The effect of predation on the dynamics of Chronic Wasting Disease in deer

Chronic Wasting Disease (CWD) is a neurological disease impacting deer, elk, moose, and other cervid populations and is caused by a misfolded protein known as a prion. CWD is difficult to control due to the persistence of prions in the environment. Prions can remain infectious for more than a decade and have been found in soil as well as other environmental vectors, such as ticks and plants. Here, we provide a bifurcation analysis of a simple mathematical model of CWD spread in a cervid population and use a modification of the Gillespie algorithm to explore if predators can be used as an ecological control strategy to limit the spread of the disease in several relevant scenarios. We then use several analytical probabilistic arguments to show that lowering the susceptible population is also beneficial to controlling CWD outbreaks. Finally, we consider a more complex model of CWD spread in a cervid population in which predators are assumed to be dynamic. Here, we find that, again, predators may be used to control CWD outbreaks, assuming they selectively prey upon infected cervids at a sufficiently high rate. From our analysis, we conclude that wolves may be used as an effective control strategy to limit the spread of CWD in cervid populations, and hunting or other means of lowering the susceptible population are beneficial to controlling CWD.

q-bio.PE↗

arXiv2018

Analysis of non-processive molecular motor transport using renewal reward theory

We propose and analyze a mathematical model of cargo transport by non-processive molecular motors. In our model, the motors change states by random discrete events (corresponding to stepping and binding/unbinding), while the cargo position follows a stochastic differential equation (SDE) that depends on the discrete states of the motors. The resulting system for the cargo position is consequently an SDE that randomly switches according to a Markov jump process governing motor dynamics. To study this system we (1) cast the cargo position in a renewal theory framework and generalize the renewal reward theorem and (2) decompose the continuous and discrete sources of stochasticity and exploit a resulting pair of disparate timescales. With these mathematical tools, we obtain explicit formulas for experimentally measurable quantities, such as cargo velocity and run length. Analyzing these formulas then yields some predictions regarding so-called non-processive clustering, the phenomenon that a single motor cannot transport cargo, but that two or more motors can. We find that having motor stepping, binding, and unbinding rates depend on the number of bound motors, due to geometric effects, is necessary and sufficient to explain recent experimental data on non-processive motors.

q-bio.SC↗

arXiv2018

Jump Locations of Jump-Diffusion Processes with State-Dependent Rates

We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump times. However, the state-dependence of the jump rate provides direct coupling between the diffusion and jump components, making disentangling the two to study individually difficult. We provide an iterative map formulation of the sequence of distributions of jump locations. Computation of these distributions allows for the extraction of the interjump time statistics. These quantities reveal a relationship between the long-time distribution of jump location and the stationary density of the full process. We provide a few examples to demonstrate the analytical and numerical tools stemming from the results proposed in the paper, including an application that shows a non-monotonic dependence on the strength of diffusion.

cond-mat.stat-mech↗

arXiv2018

Transport Facilitated by Rapid Binding to Elastic Tethers

Diffusion in cell biology is important and complicated. Diffusing particles must contend with a complex environment as they make their way through the cell. We analyze a particular type of complexity that arises when diffusing particles reversibly bind to elastically tethered binding partners. Using asymptotic analysis, we derive effective equations for the transport of both single and multiple particles in the presence of such elastic tethers. We show that for the case of linear elasticity and simple binding kinetics, the elastic tethers have a weak hindering effect on particle motion when only one particle is present, while, remarkably, strongly enhancing particle motion when multiple particles are present. We give a physical interpretation of this result that suggests a similar effect may be present in other biological settings.

q-bio.SC↗

arXiv2016

Bidirectionality From Cargo Thermal Fluctuations in Motor-Mediated Transport

Molecular motor proteins serve as an essential component of intracellular transport by generating forces to haul cargoes along cytoskeletal filaments. Two species of motors that are directed oppositely (e.g. kinesin, dynein) can be attached to the same cargo, which is known to produce bidirectional net motion. Although previous work focuses on the motor number as the driving noise source for switching, we propose an alternative mechanism: cargo diffusion. A mean-field mathematical model of mechanical interactions of two populations of molecular motors with cargo thermal fluctuations (diffusion) is presented to study this phenomenon. The delayed response of a motor to fluctuations in the cargo velocity is quantified, allowing for the reduction of the full model a single "characteristic distance", a proxy for the net force on the cargo. The system is then found to be metastable, with switching exclusively due to cargo diffusion between distinct directional transport states. The time to switch between these states is then investigated using a mean first passage time analysis. The switching time is found to be non-monotonic in the drag of the cargo, providing an experimental test of the theory.

q-bio.SC↗

arXiv2013

Breakdown of fast-slow analysis in an excitable system with channel noise

We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron, in which the noise originates from stochastic Sodium and Potassium ion channels opening and closing. One can analyze neural excitability in the deterministic model by using a separation of time scales involving a fast voltage variable and a slow recovery variable, which represents the fraction of open Potassium channels. In the stochastic setting, spontaneous excitation is initiated by ion channel noise. If the recovery variable is constant during initiation, the spontaneous activity rate can be calculated using Kramer's rate theory. The validity of this assumption in the stochastic model is examined using a systematic perturbation analysis. We find that in most physically relevant cases, this assumption breaks down, requiring an alternative to Kramers theory for excitable systems with one deterministic fixed point. We also show that an exit time problem can be formulated in an excitable system by considering maximum likelihood trajectories of the stochastic process.

q-bio.NC↗