Research in our group encompasses different areas of condensed matter theory, including the statistical mechanics
of complex fluids, polymer physics and stochastic processes. Over the last few years, in an effort to understand the role of noise on processes operating at the scale
of single molecules, our work has been concerned more specifically with the development of analytical models of fluctuating nanoscale systems. The following studies are
representative of the kind of work we have recently been doing on these systems:
The Stochastic Thermodynamics of Flow-Driven Polymers
The Jarzynski relation (and other variants of a broad class of statistical mechanical results known collectively as fluctuation theorems), have made it
possible, in the last few decades, to experimentally determine equilibrium thermodynamic parameters (such as the free energy) from measurements conducted under
arbitrary non-equilibrium conditions. This fact has recently been exploited by researchers to obtain the elastic properties of model DNA from simulations and
experiments of chain extension under elongational flow, bypassing the need to measure these properties mechanically using sophisticated optical trapping techniques.
Motivated by these observations, we have been investigating chain elasticity analytically, using the Jarzynski relation and a finitely extensible Rouse model within a
path integral formalism to calculate both the flow-induced free energy change between chain conformations of definite average end-to-end distance, as well as the force-
extension curves that are obtained from it. This work has led to interesting theoretical predictions about the statistics of the work performed by single polymers
during flow-induced stretching, the role of confinement on the microscopic details of the chain’s coil-stretch transition, and the nature of the order parameter
fluctuations in the vicinity of this transition. We are currently applying our formalism to the study of fluctuation relations in other model flow-driven systems.
Brownian Motion under Dynamic Disorder
In complex cellular environments it is often possible for a particle to both execute a simple random walk and be governed by a non-Gaussian distribution of
displacements. This behavior is now understood to originate in the modulation of the white noise that normally drives Brownian dynamics by a second stochastic process
with a finite relaxation time. We have been exploring this phenomenon of non-Gaussian Brownian diffusion using path integral techniques, and have developed methods that
simplify and extend some of the approaches used to treat it earlier. Our work has also led to the identification of other stochastic processes – including dichotomous
white noise – that exhibit the same “anomalous” Brownian behavior, suggesting that the occurrence of such behavior may be more commonplace than assumed. We have also
recently found that the inclusion of memory effects in our model can account for an as yet unexplained but frequently observed aspect of non-Gaussian Brownian motion:
the non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. An interesting sidelight of this work is our finding that
stochastically modulated Brownian motion can also serve as a model of target location on fluctuating DNA by binding proteins. Other extensions of the formalism –
especially as they relate to stochastic phenomena inside living cells – are currently under investigation.