Doctor of Philosophy

dissertationActive transport of cargoes is critical for cellular function. To accomplish this, networks of cytoskeletal filaments form highways along which small teams of mechanochemical enzymes (molecular motors) take steps to pull associated cargoes. The robustness of this transport system is juxtaposed by the stochasticity that exists at several spatial and temporal scales. For instance, individual motors stochastically step, bind, and unbind while the cargo undergoes nonnegligible thermal fluctuations. Experimental advances have produced rich quantitative measurements of each of these stochastic elements, but the interaction between them remains elusive. In this thesis, we explore the roles of stochasticity in motor-mediated transport with four specific projects at different scales. We first construct a mean-field model of a cargo transported by two teams of opposing motors. This system is known to display bidirectionality: switching between phases of transport in opposite directions. We hypothesize that thermal fluctuations of the cargo drive the switching. From our model, we predict how cargo size influences the switching time, an experimentally measurable quantity to verify the hypothesis. In the second work, we investigate the force dependence of motor stepping, formulated as a state-dependent jump-diffusion model. We prove general results regarding the computation of the statistics of this process. From this framework, we find that thermal fluctuations may provide a nonmonotonic influence on the stepping rate of motors. The remaining projects investigate the behavior of nonprocessive motors, which take few steps before detaching. In collaboration with experimentalists, we study seemingly diffusive data of motor-mediated transport. Using a jump-diffusion model, the active and passive portions of the diffusivity are disentangled, and curious higher order statistics are explained as a sampling issue. Lastly, we construct a model of cooperative transport by nonprocessive motors, which we study using reward-renewal theory. The theory provides predictions about measured quantities such as run length, which suggest that geometric effects have a large influence on the transport ability of these motors

Renewal reward perspective on linear switching diffusion systems

In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport, micro-organisms like bacteria, or animals moving within and responding to their environment. For example, in cells the movement of vesicles, organelles and other cargo are affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate the effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal-reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed framework are illustrated for case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of motor proteins.Comment: 35 pages, 6 figure

Fluctuations and uncertainty in stochastic models with persistent dynamics.

PhD Theses.We aim to explore the validity of recently proposed ‘thermodynamic uncertainty relations’ (universal entropic bounds on current fluctuations) in non-Markovian systems. First, we obtain a modified bound for the special case of a biased random walk model with one-step memory which resembles a variant of one-dimensional run-and-tumble motion widely used to model bacterial motility. The chief result of our work involves the extension of such modified bound for a general class of run-andtumble type processes. In particular, we derive a new bound based on the mathematical machinery of renewal-reward theory which can be extended to non-Markovian as well as Markovian systems. We illustrate our results for single-particle random walk models and an interactingparticle system with collective tumbles. For a broad parameter regime, our new bound is seen to provide a useful constraint even though its expression involves only run-statistics and the mean entropy associated with tumbles. Lastly, we also present a preliminary investigation of the validity of other universal relations such as infimum law and stoppingtime symmetry relation for entropy production and position variables in run-and-tumble-type processes