About MeI am a graduate student in the Physics department of the University of Illinois at Urbana-Champaign. I work with Prof. Nigel Goldenfeld at the Carl R. Woese Institute For Genomic Biology .
Research InterestMy research focuses on biological systems that have inherently non-equilibrium dynamics because their individual components constantly harness energy from their environment. Such systems, ranging in scale from bacterial colonies and actomyosin motility assays to giant flocks of birds and entire forests, exhibit varied collective behavior (flocking, swarming to locate nutrients, dynamic pattern formation), as well as phase-transitions from one behavioral regime to another. We are interested in understanding how noisy interactions among such individuals agents give rise to the observed macroscopic behavior in these systems, and what dictates transitions from one stable regime to another.
Active matter : Active matter consists of self-driven particles which convert stored energy into directed motion, keeping the system perpetually driven out of equilibrium. Interactions among such self-propelled particles give rise to novel collective behavior with no equilibrium analogue. Examples of such emergent collective phenomena can be found in a wide range of systems, both biological and synthetic, like bacterial colonies, motor protein-cytoskeletal filament assays, terrestrial, aerial and aquatic flocks and vibrated polar rods and disks. Among these, a class of collective phenomena that is of special interest to me is flocking - the collective migration of a very large number of active agents over length scales much larger than their individual sizes. Active systems undergo a transition from an isotropic phase (gas) in which all agents move randomly in every direction, to the flocking phase (liquid) with coordinated unidirectional motion, when the system's density is increased or the noise in alignment interactions decreased. This transition is discontinuous however, and there is always an intermediate regime of phase-coexistence. What microscopic interactions give rise to the flocking phase, that has long-range orientational order? A large class of mesoscopic and macroscopic flocking theories are coarse grained from microscopic models that feature binary interactions as the chief aligning mechanism between individual agents. However, while such theories seemingly predict the existence of polar-ordered phases with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. In order to resolve this paradox here we look at a simple 1D individual level model for flocking with probabilistic alignment interactions and self-propulsion, and look at both its exact simulation as well as its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless a skewed noise distribution is imposed upon it artificially. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density. Additionally, we discover that the intrinsic noise generated by the probabilistic individual level interactions gives rise to a new phase at low densities which shows noise-induced local orientational ordering, but no global polar order. This phase is mediated by binary interactions and has been observed in fish schools.
Another aspect of active systems that I am interested in is the emergence of macroscopic mechanical properties. From observations of bird flocks and fish schools, we know that such social agents frequently self-organize into compact objects with a well-defined boundary. If we consider all such collective systems as active materials, we may then ask whether they have emergent bulk and interfacial material properties such as elasticity and surface tension. Recent experimental evidence has revealed that certain fish schools can exhibit highly elastic behaviour and obey hooke’s law. Through our simple individual level model of self-propelled particles, we are investigating how such macroscopic material properties can emerge through noisy interactions among agents.
Ecology : Ecosystems, besides exhibiting standard fluctuations about their stable state, are often subjected to irreversible and often catastrophic phase transitions to an alternative unhealthy state. For example, coral reefs can be degraded by overgrowth of algae, shallow lakes may switch from clear to turbid due to eutrophication, and arid grasslands may revert to deserts due to overgrazing or reduced rainfall. Given the detrimental impact of such regime shifts on ecological and human socio-economic resources, there is an ever-increasing need for early warning signals that predict impending critical transitions. In analogy with our studies of active matter, we develop stochastic individual level descriptions for ecosystems on the verge of a critical transition to extinction, with the goal of identifying early warning signals. In particular, we focus on the important case of arid grasslands that undergo regime shifts to deserts. The question we are interested in answering is what happens close to extinction, where demographic stochasticity plays a vital role.
DNA Transcription : Transcription of DNA by RNA polymerases (RNAPs) as the first step to protein synthesis, has been the subject of extensive studies. It is well known that multiple co-transcribing RNAPs cooperatively increase their elongation rates, transcribing a gene much faster that a single RNAP would. Recent experiments demonstrate that the rate of transcription elongation is constant for a large range of promoter strengths and thus RNAP densities, in contrast to the predictions of existing models of transcription. Moreover, these experiments also show that environmentally induced promoter repression results in a long-distance antagonistic effect on already loaded RNAPs, decreasing their transcription elongation efficiency. What is the underlying mechanism for the emergence of cooperative or antagonistic dynamics from the interaction of individual RNAPs? We try to answer this question through a model of transcription where RNAP elongation is mechanically constrained by transcription induced DNA supercoiling. Accumulation of many positive supercoils in front and negative supercoils behind an RNAP slows it down due to torsional stress generated in the DNA. However, with multiple co-transcribing RNAPs, there can be cancellation of positive and negative supercoils between adjacent RNAPs, and this cooperative interaction increases local speeds and in turn, the average elongation rate.