Motion of kinesin in a viscoelastic medium

Approximate Solutions of a General Stochastic Velocity-Jump Model Subject to Discrete-Time Noisy Observations

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion observed. In this paper, we aim to describe the solutions of velocity-jump models for single-agent motion in one spatial dimension, characterised by successive Markovian transitions within a finite network of n states, each with a specified velocity and a fixed rate of switching to every other state. In particular, we focus on obtaining the solutions of the model subject to noisy, discrete-time, observations, with no direct access to the agent state. The lack of direct observation of the hidden state makes the problem of finding the exact distributions generally intractable. Therefore, we derive a series of approximations for the data distributions. We verify the accuracy of these approximations by comparing them to the empirical distributions generated through simulations of four example model structures. These comparisons confirm that the approximations are accurate given sufficiently infrequent state switching relative to the imaging frequency. The approximate distributions computed can be used to obtain fast forwards predictions, to give guidelines on experimental design, and as likelihoods for inference and model selection.

A Semi-Markov Approach to Study a Group of Kinesin Motors

We propose a general mathematical and computational approach to study cellular transport driven by a group of kinesin motors. It is a framework for multi-scale modeling that integrates kinetic models of single kinesin motors, including detachment and reattachment events, to study group behaviors of several motors. By formulating the problem as a semi-Markov process and applying a central limit theorem, asymptotic velocity and diffusivity can be readily calculated, which offers considerable computational advantage over Monte Carlo simulations in tasks such as parameter sensitivity analysis and model selection. We demonstrate the method with some examples. The importance of incorporating the intrinsic microscopic-level dynamics of individual motors is illustrated by showing how changes at the microscopic level propagate to the motor-cargo complex at a mesoscopic level. Particularly, we showcase an example in which changes in the second moment of single-motor characteristics gives rise to different first moment characteristics of the motor group.

Non-specific cargo-filament interactions slow down motor-driven transport

Active, motor-based cargo transport is important for many cellular functions and cellular development. However, the cell interior is complex and crowded and could have many weak, non-specific interactions with the cargo being transported. To understand how cargo-environment interactions will affect single motor cargo transport and multi-motor cargo transport, we use an artificial quantum dot cargo bound with few (~ 1) to many (~ 5-10) motors allowed to move in a dense microtubule network. We find that kinesin-driven quantum dot cargo is slower than single kinesin-1 motors. Excitingly, there is some recovery of the speed when multiple motors are attached to the cargo. To determine the possible mechanisms of both the slow down and recovery of speed, we have developed a computational model that explicitly incorporates multi-motor cargos interacting non-specifically with nearby microtubules, including, and predominantly with the microtubule on which the cargo is being transported. Our model has recovered the experimentally measured average cargo speed distribution for cargo-motor configurations with few and many motors, implying that numerous, weak, non-specific interactions can slow down cargo transport and multiple motors can reduce these interactions thereby increasing velocity.