Sensing and decision-making in random search

While microscopic organisms can use gradient-based search to locate resources, this strategy can be poorly suited to the sensory signals available to macroscopic organisms. We propose a framework that models search-decision making in cases where sensory signals are infrequent, subject to large fluctuations, and contain little directional information. Our approach simultaneously models an organism's intrinsic movement behavior (e.g. Levy walk) while allowing this behavior to be adjusted based on sensory data. We find that including even a simple model for signal response can dominate other features of random search and greatly improve search performance. In particular, we show that a lack of signal is not a lack of information. Searchers that receive no signal can quickly abandon target-poor regions. Such phenomena naturally give rise to the area-restricted search behavior exhibited by many searching organisms

A Stochastic Compartmental Model for Fast Axonal Transport

In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the smallest scale interactions, we can use recent microscopic experimental observations to infer all the parameters of the model. Then, using techniques from probability theory, we compute asymptotic limits of the stochastic behavior of individual motor-cargo complexes, while also characterizing both equilibrium and non-equilibrium ensemble behavior. We use these results in order to investigate three important biological questions: (1) How homogeneous are axons at stochastic equilibrium? (2) How quickly can axons return to stochastic equilibrium after large local perturbations? (3) How is our understanding of delivery time to a depleted target region changed by taking the whole cell point-of-view

Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing

We consider a simple model for the uctuating hydrodynamics of a exible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes uid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time uid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris chain argument. To this, we add the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the systems leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is an novel feature of this work

Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing

We consider a simple model for the fluctuating hydrodynamics of a flexible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes fluid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time fluid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris chain argument. In addition we allow the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the system leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is a novel feature of this work.Comment: A number of corrections and improvements. We thank the careful referee for useful suggestions and correction

Asymptotic Analysis of Microtubule-Based Transport by Multiple Identical Molecular Motors

We describe a system of stochastic differential equations (SDEs) which model the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment fits within a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. Through an asymptotic analysis of our system of SDEs, we develop a means for applying in vitro observations of the nonlinear response by motors to forces induced on the attached cargo to make analytical predictions for two parameter regimes that have thus far eluded direct experimental observation: 1) highly viscous in vivo transport and 2) dynamics when multiple identical motors are attached to the cargo and microtubule

Topological data analysis approaches to uncovering the timing of ring structure onset in filamentous networks

Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these data sets. Here we develop a TDA method to detect physical structures in a cell that persist over time. In most cells, protein filaments (actin) interact with motor proteins (myosins) and organize into polymer networks and higher-order structures. An example of these structures are ring channels that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. The interactions of actin with myosin can be challenging to investigate experimentally in living systems, given limitations in filament visualization \textit{in vivo}. We therefore use complex agent-based models that simulate mechanical and chemical interactions of polymer proteins in cells. To understand how filaments organize into structures, we propose a TDA method that assesses effective ring generation in data consisting of simulated actin filament positions through time. We analyze the topological structure of point clouds sampled along these actin filaments and propose an algorithm for connecting significant topological features in time. We introduce visualization tools that allow the detection of dynamic ring structure formation. This method provides a rigorous way to investigate how specific interactions and parameters may impact the timing of filamentous network organization.Comment: 20 pages, 9 figure