Markov dynamic models for long-timescale protein motion

Molecular dynamics (MD) simulation is a well-established method for studying protein motion at the atomic scale. However, it is computationally intensive and generates massive amounts of data. One way of addressing the dual challenges of computation efficiency and data analysis is to construct simplified models of long-timescale protein motion from MD simulation data. In this direction, we propose to use Markov models with hidden states, in which the Markovian states represent potentially overlapping probabilistic distributions over protein conformations. We also propose a principled criterion for evaluating the quality of a model by its ability to predict long-timescale protein motions. Our method was tested on 2D synthetic energy landscapes and two extensively studied peptides, alanine dipeptide and the villin headpiece subdomain (HP-35 NleNle). One interesting finding is that although a widely accepted model of alanine dipeptide contains six states, a simpler model with only three states is equally good for predicting long-timescale motions. We also used the constructed Markov models to estimate important kinetic and dynamic quantities for protein folding, in particular, mean first-passage time. The results are consistent with available experimental measurements

Markov dynamic models for long-timescale protein motion

Ph.DDOCTOR OF PHILOSOPH

Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue.

The dynamics of the RNA polymerase II (Pol II) backtracking process is poorly understood. We built a Markov State Model from extensive molecular dynamics simulations to identify metastable intermediate states and the dynamics of backtracking at atomistic detail. Our results reveal that Pol II backtracking occurs in a stepwise mode where two intermediate states are involved. We find that the continuous bending motion of the Bridge helix (BH) serves as a critical checkpoint, using the highly conserved BH residue T831 as a sensing probe for the 3'-terminal base paring of RNA:DNA hybrid. If the base pair is mismatched, BH bending can promote the RNA 3'-end nucleotide into a frayed state that further leads to the backtracked state. These computational observations are validated by site-directed mutagenesis and transcript cleavage assays, and provide insights into the key factors that regulate the preferences of the backward translocation

Simulation of spontaneous G protein activation reveals a new intermediate driving GDP unbinding

Activation of heterotrimeric G proteins is a key step in many signaling cascades. However, a complete mechanism for this process, which requires allosteric communication between binding sites that are ~30 Å apart, remains elusive. We construct an atomically detailed model of G protein activation by combining three powerful computational methods: metadynamics, Markov state models (MSMs), and CARDS analysis of correlated motions. We uncover a mechanism that is consistent with a wide variety of structural and biochemical data. Surprisingly, the rate-limiting step for GDP release correlates with tilting rather than translation of the GPCR-binding helix 5. β-Strands 1 - 3 and helix 1 emerge as hubs in the allosteric network that links conformational changes in the GPCR-binding site to disordering of the distal nucleotide-binding site and consequent GDP release. Our approach and insights provide foundations for understanding disease-implicated G protein mutants, illuminating slow events in allosteric networks, and examining unbinding processes with slow off-rates

Diffusive hidden Markov model characterization of DNA looping dynamics in tethered particle experiments

In many biochemical processes, proteins bound to DNA at distant sites are brought into close proximity by loops in the underlying DNA. For example, the function of some gene-regulatory proteins depends on such DNA looping interactions. We present a new technique for characterizing the kinetics of loop formation in vitro, as observed using the tethered particle method, and apply it to experimental data on looping induced by lambda repressor. Our method uses a modified (diffusive) hidden Markov analysis that directly incorporates the Brownian motion of the observed tethered bead. We compare looping lifetimes found with our method (which we find are consistent over a range of sampling frequencies) to those obtained via the traditional threshold-crossing analysis (which can vary depending on how the raw data are filtered in the time domain). Our method does not involve any time filtering and can detect sudden changes in looping behavior. For example, we show how our method can identify transitions between long-lived, kinetically distinct states that would otherwise be difficult to discern

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported