Rahul Marathe

Bacterial twitching motility is coordinated by a two-dimensional tug-of-war with directional memory

Type IV pili are ubiquitous bacterial motors that power surface motility. In peritrichously piliated species, it is unclear how multiple pili are coordinated to generate movement with directional persistence. Here we use a combined theoretical and experimental approach to test the hypothesis that multiple pili of Neisseria gonorrhoeae are coordinated through a tug-of-war. Based on force-dependent unbinding rates and pilus retraction speeds measured at the level of single pili, we build a tug-of-war model. Whereas the one-dimensional model robustly predicts persistent movement, the two-dimensional model requires a mechanism of directional memory provided by re-elongation of fully retracted pili and pilus bundling. Experimentally, we confirm memory in the form of bursts of pilus retractions. Bursts are seen even with bundling suppressed, indicating re-elongation from stable core complexes as the key mechanism of directional memory. Directional memory increases the surface range explored by motile bacteria and likely facilitates surface colonization.

Two simple models of classical heat pumps.

Motivated by recent studies of models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact solutions and unambiguous interpretation of results. We demonstrate that while both our models seem to be built on similar principles, one is able to function as a heat pump (or engine) while the other is not.

Driving particle current through narrow channels using a classical pump.

We study a symmetric exclusion process in which the hopping rates at two chosen adjacent sites vary periodically in time and have a relative phase difference. This mimics a colloidal suspension subjected to external time-dependent modulation of the local chemical potential. The two special sites act as a classical pump by generating an oscillatory current with a nonzero dc value whose direction depends on the applied phase difference. We analyze various features in this model through simulations and obtain an expression for the dc current via a novel perturbative treatment.

Deterministic and Stochastic Descriptions of Gene Expression Dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.

Modeling stochastic gene expression in growing cells

Gene expression is an inherently noisy process. Fluctuations arise at many points in the expression of a gene, as all the salient reactions such as transcription, translation, and mRNA degradation are stochastic processes. The fluctuations become important when the cellular copy numbers of the relevant molecules (mRNA or proteins) are low. For regulated genes, a computational complication arises from the fact that protein synthesis rates depend on the concentrations of the transcription factors that regulate the corresponding genes. Because of the growing cell volume, such rates are effectively time-dependent. We deal with the effects of volume growth computationally using a rather simple method: the growth of the cell volume is incorporated in our simulations by stochastically adding small volume elements to the cell volume. As an application of this method we study a gene circuit with positive autoregulation that exhibits bistability. We show how the region of bistability becomes diminished by increasing the effect of noise via a reduced copy number of the regulatory protein. Cell volume determines the region of bistability for different noise strengths. The method is general and can also be applied to other cases where synthesis rates of proteins are regulated and an appropriate analytical description is difficult to achieve.

Work distribution functions for hysteresis loops in a single-spin system

We compute the distribution of the work done in driving a single Ising spin with a time-dependent magnetic field. Using Glauber dynamics we perform Monte Carlo simulations to find the work distributions at different driving rates. We find that in general the work distributions are broad with a significant probability for processes with negative dissipated work. The special cases of slow and fast driving rates are studied analytically. We verify that various work fluctuation theorems corresponding to equilibrium initial states are satisfied while a steady state version is not.

Particle current in a symmetric exclusion process with time-dependent hopping rates

In a recent study (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases in inverse proportion with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.

Energy current magnification in coupled oscillator loops.

Motivated by studies on current magnification in quantum mesoscopic systems, we consider sound and heat transmission in classical models of oscillator chains. A loop of coupled oscillators is connected to two leads through which one can either transmit monochromatic waves or white-noise signal from heat baths. We look for the possibility of current magnification in this system due to some asymmetry introduced between the two arms in the loop. We find that current magnification is indeed obtained for particular frequency ranges. However, the integrated current shows the effect only in the presence of a pinning potential for the atoms in the leads. We also study the effect of anharmonicity on current magnification.

Sources of stochasticity in constitutive and autoregulated gene expression

Gene expression is inherently noisy as many steps in the read-out of the genetic information are stochastic. To disentangle the effect of different sources of stochasticity in such systems, we consider various models that describe some processes as stochastic and others as deterministic. We review earlier results for unregulated (constitutive) gene expression and present new results for a gene controlled by negative autoregulation with cell growth modeled by linear volume growth.

Two coupled, driven Ising spin systems working as an engine

Miniaturized heat engines constitute a fascinating field of current research. Many theoretical and experimental studies are being conducted that involve colloidal particles in harmonic traps as well as bacterial baths acting like thermal baths. These systems are micron-sized and are subjected to large thermal fluctuations. Hence, for these systems average thermodynamic quantities, such as work done, heat exchanged, and efficiency, lose meaning unless otherwise supported by their full probability distributions. Earlier studies on microengines are concerned with applying Carnot or Stirling engine protocols to miniaturized systems, where system undergoes typical two isothermal and two adiabatic changes. Unlike these models we study a prototype system of two classical Ising spins driven by time-dependent, phase-different, external magnetic fields. These spins are simultaneously in contact with two heat reservoirs at different temperatures for the full duration of the driving protocol. Performance of the model as an engine or a refrigerator depends only on a single parameter, namely the phase between two external drivings. We study this system in terms of fluctuations in efficiency and coefficient of performance (COP). We find full distributions of these quantities numerically and study the tails of these distributions. We also study reliability of the engine. We find the fluctuations dominate mean values of efficiency and COP, and their probability distributions are broad with power law tails.