A data-driven alternative to the fractional Fokker–Planck equation

Anomalous diffusion processes are ubiquitous in biology and arise in the transport of proteins, vesicles and other particles. Such anomalously diffusive behavior is attributed to a number of factors within the cell including heterogeneous environments, active transport processes and local trapping/binding. There are a number of microscopic principles?such as power law jump size and/or waiting time distributions?from which the fractional Fokker?Planck equation (FFPE) can be derived and used to provide mechanistic insight into the origins of anomalous diffusion. On the other hand, it is fair to ask if other microscopic principles could also have given rise to the evolution of an observed density profile that appears to be well fit by an FFPE. Here we discuss another possible mechanistic alternative that can give rise to densities like those generated by FFPEs. Rather than to fit a density (or concentration profile) using a solution to the spatial FFPE, we reconstruct the profile generated by an FFPE using a regular FPE with a spatial and time-dependent force. We focus on the special case of the spatial FFPE for superdiffusive processes. This special case is relevant to, for example, active transport in a biological context. We devise a prescription for extracting such forces on synthetically generated data and provide an interpretation to the forces extracted. In particular, the time-dependence of forces could tell us about ATP depletion or changes in the cell's metabolic activity. Modeling anomalous behavior with normal diffusion driven by these effective forces yields an alternative mechanistic picture that, ultimately, could help motivate future experiments

From the volcano effect to banding: a minimal model for bacterial behavioral transitions near chemoattractant sources

Sharp chemoattractant (CA) gradient variations near food sources may give rise to dramatic behavioral changes of bacteria neighboring these sources. For instance, marine bacteria exhibiting run-reverse motility are known to form distinct bands around patches (large sources) of chemoattractant such as nutrient-soaked beads while run-and-tumble bacteria have been predicted to exhibit a 'volcano effect' (spherical shell-shaped density) around a small (point) source of food. Here we provide the first minimal model of banding for run-reverse bacteria and show that, while banding and the volcano effect may appear superficially similar, they are different physical effects manifested under different source emission rate (and thus effective source size). More specifically, while the volcano effect is known to arise around point sources from a bacterium's temporal differentiation of signal (and corresponding finite integration time), this effect alone is insufficient to account for banding around larger patches as bacteria would otherwise cluster around the patch without forming bands at some fixed radial distance. In particular, our model demonstrates that banding emerges from the interplay of run-reverse motility and saturation of the bacterium's chemoreceptors to CA molecules and our model furthermore predicts that run-reverse bacteria susceptible to banding behavior should also exhibit a volcano effect around sources with smaller emission rates

Inferring models of bacterial dynamics toward point sources

Experiments have shown that bacteria can be sensitive to small variations in chemoattractant (CA) concentrations. Motivated by these findings, our focus here is on a regime rarely studied in experiments: bacteria tracking point CA sources (such as food patches or even prey). In tracking point sources, the CA detected by bacteria may show very large spatiotemporal fluctuations which vary with distance from the source. We present a general statistical model to describe how bacteria locate point sources of food on the basis of stochastic event detection, rather than CA gradient information. We show how all model parameters can be directly inferred from single cell tracking data even in the limit of high detection noise. Once parameterized, our model recapitulates bacterial behavior around point sources such as the "volcano effect". In addition, while the search by bacteria for point sources such as prey may appear random, our model identifies key statistical signatures of a targeted search for a point source given any arbitrary source configuration

Role of fluctuations and defects in select condensed matter problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2008.Page 122 blank. Vita.Includes bibliographical references.Defects and fluctuations dominate both static and dynamical properties of systems in the condensed phase. In this work, we focus on three such examples. Firstly, we model the effect of proton fluctuations on the rate of electron transfer in the condensed phase through an electron donor-acceptor assembly linked via an H-bonding bridge. The model suggests that it is possible for the electron transfer rate through a deuterated H-bonding assembly to exceed the rate through a protonated H-bonding bridge at low temperature, consistent with experimental findings. Next, we consider the convergence properties of Jarzynski's non-equilibrium work relation. This relation expresses the free energy change of a system, onto which finite-time work is done, as an ensemble average over all possible trajectories of the system. We quantify the regime of applicability of this equality by considering the role of rare fluctuations which dominate the work average of entropy generating processes. Lastly, we consider fluorophore lifetime variations arising when single molecules are placed near non-planar metallic surfaces. We compute the exact first order self-fields of vertical dipoles located above locally curved perfectly conducting surfaces by invoking a small slope phase perturbation technique. The results suggest that smooth perturbations lead to deviations from the image theory results extensively used to interpret the experimentally observed single molecule lifetime changes.by Steve Pressé.Ph.D