Constructing Markov State Models to elucidate the functional conformational changes of complex biomolecules

Abstract

The function of complex biomolecular machines relies heavily on their conformational changes. Investigating these functional conformational changes is therefore essential for understanding the corresponding biological processes and promoting bioengineering applications and rational drug design. Constructing Markov State Models (MSMs) based on large-scale molecular dynamics simulations has emerged as a powerful approach to model functional conformational changes of the biomolecular system with sufficient resolution in both time and space. However, the rapid development of theory and algorithms for constructing MSMs has made it difficult for nonexperts to understand and apply the MSM framework, necessitating a comprehensive guidance toward its theory and practical usage. In this study, we introduce the MSM theory of conformational dynamics based on the projection operator scheme. We further propose a general protocol of constructing MSM to investigate functional conformational changes, which integrates the state-of-the-art techniques for building and optimizing initial pathways, performing adaptive sampling and constructing MSMs. We anticipate this protocol to be widely applied and useful in guiding nonexperts to study the functional conformational changes of large biomolecular systems via the MSM framework. We also discuss the current limitations of MSMs and some alternative methods to alleviate them.

A DNA-origami nuclear pore mimic reveals nuclear entry mechanisms of HIV-1 capsid

“…NUP153 was found to be mostly unstructured during the simulations ( Figure S3A), except for a short α-helix at the C-terminus (residue 1470 to 1475) that appeared temporarily ( Figure S3C and Movie S1). The interaction between NUP153 1451-1475 and hexamer-2 appeared to be dynamic, rapidly transitioning between bound and unbound states as analyzed by the Markov state model (Chodera and Noe, 2014;Husic and Pande, 2018a;Wang et al, 2018b) ( Figure S3). The NUP153 C-terminal tail formed high occupancy contacts with polar CA residues in different states (Table S1) whereby in the last state the RRR motif inserted deeply into the tri-hexamer interface, surrounded by negatively charged glutamate residues from 4 different CA monomers (Figure 2E, bottom).…”

“…Markov state models (MSMs) have been widely applied to study the conformational dynamics of biomolecules (Chodera and Noé, 2014;Husic and Pande, 2018b;Wang et al, 2018a). To identify the important metastable states of NUP153CTD in the MD simulation, Markov state models were constructed and validated in the PyEMMA 2.5.7 package (Scherer et al, 2015).…”

Identifying mechanistically distinct pathways in kinetic transition networks

“…A notable class of transition networks is Markov state models 12,13,106,107 (MSMs), networks parameterised by a transition matrix determined from many short simulation trajectories. MSMs have been used extensively to study biomolecular conformational transitions, 13,[107][108][109] and are amenable to analysis by transition path theory [110][111][112] to calculate important dynamical quantities such as reactive fluxes. Stochastic network models are also of fundamental importance in many other domains, such as in systems biology, 113,114 and in studies of epidemic spread 115 and finance.…”

Computational structure‐based drug design: Predicting target flexibility

“…In fact, atomistic simulations can be used for estimating both absolute and relative binding free energies ( G s) (Shirts, ). Absolute G s can be calculated by applying “end‐point” methods, where receptor and ligand are only simulated in isolation or in closed complex, such as Molecular Mechanics Poisson‐Boltzmann Surface Area (MMPB(SA)) and Molecular Mechanics Generalized Born Surface Area (MMGB(SA)) (Wang et al, ; Wang, Cao, Zhu, & Huang, ), or they can be calculated based on reproducing the whole binding event, such as those that apply Markov State Models (MSMs, Plattner & Noé, ). In the former methods, flexibility is explored partially, as the intermediate states of recognition are neglected, while the latter exhaustively explore how the conformational landscape of target and ligand vary all along binding, opening up a way to study association mechanisms and kinetics.…”