Transition paths are short events when a complex system, such as a biomolecule, crosses the free energy barrier separating its stable conformational basins (aka folded and unfolded states). When observed in single molecule experiments, such as those employing force spectroscopy or fluoresecence resonance energy transfer (FRET), transition paths offer insight into the dynamics and mechanism of biomolecular folding. Recent measurements of distributions of transition path durations in experiments and Molecular Dynamics (MD) simulations have revealed that the currently accepted model of one-dimensional diffusion over a potential energy surface is inadequate to describe all kinetic properties of folding reactions. Moreover, preliminary tests on reaction coordinate (such as inter-monomer distance) trajectories in simulations indicate significant non-Markovian or memory effects in dynamics, which simple diffusion can never capture.

My research attempts to develop a more general model that includes memory effects observed in folding reaction coordinates in MD simulations of biomolecules. We have previously shown how a Fractional Brownain Motion (FBM) model, characterized by a power-law time-dependent diffusion coefficient D(t), can successfully capture the shape of transition path time distribution in C-terminal domain of villin headpiece fragment (HP-35). Moreover, FBM performs better than one-dimensional diffusion to predict the shape of autocorrelation functions of reaction coordinates in a variety of proteins and polypeptides. Since the parameters of FBM are obtained directly from the short time-behavior of the reaction coordinate, it is a superior theory than diffusion, in which the diffusion coefficient is estimated by fitting.

However, the FBM equation is known to belong to a broader class of equations, which arise from the Generalized Langevin Equation (GLE). Unlike the FBM, which has a specific form of time-dependent diffusion coefficient, the GLE contains a memory kernel, which can be found directly from experimental/simulated trajectories. In a recent study, we have shown how to extract the memory kernel from slowly varying functions, such as the autocorrelation function, of the reaction coordinate. In addition, we have developed analytical theory to calculate transition path time distributions for an arbitrary memory kernel. As proof of concept, we have also shown that the GLE can successfully predict transition path time distributions and transition rates (or rates of biomolecular folding and unfolding) in a toy model of a Generalized Rouse chain, whose end-to-end distance undergoes transitions across a double-well potential, similar to those observed in single molecule experiments and simulations. 

1. Satija, R., & Makarov, D. E. (2019). Generalized Langevin Equation as a Model for Barrier Crossing Dynamics in Biomolecular Folding. The Journal of Physical Chemistry B.

2.Medina, E., Satija, R., & Makarov, D. E. (2018). Transition Path Times in Non-Markovian Activated Rate Processes. The Journal of Physical Chemistry B.

3.Padhi, A. K., Narain, P., Dave, U., Satija, R., Patir, A., & Gomes, J. (2018). Insights into the role of ribonuclease 4 polymorphisms in amyotrophic lateral sclerosis. Journal of Biomolecular Structure and Dynamics, 1-15.

4. Satija, R., Das, A., & Makarov, D. E. (2017). Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding. The Journal of chemical physics, 147(15), 152707.

5.Sen, S., Apurva, D., Satija, R., Siegal, D., & Murray, R. M. (2017). Design of a Toolbox of RNA Thermometers. ACS synthetic biology, 6(8), 1461-1470.

6. Avdoshenko, S. M., Das, A., Satija, R., Papoian, G. A., & Makarov, D. E. (2017). Theoretical and computational validation of the Kuhn barrier friction mechanism in unfolded proteins. Scientific Reports, 7(1), 269.

TA for-

CSE389D: Intro to Mathematical Modeling (Spring 2019)

CH353M: Thermodynamics for Life Scientists (Fall 2018)