Simple few-state models reveal hidden complexity in protein folding

Abstract

Markov state models constructed from molecular dynamics simulations have recently shown success at modeling protein folding kinetics. Here we introduce two methods, flux PCCA+ (FPCCA+) and sliding constraint rate estimation (SCRE), that allow accurate rate models from protein folding simulations. We apply these techniques to fourteen massive simulation datasets generated by Anton and Folding@home. Our protocol quantitatively identifies the suitability of describing each system using two-state kinetics and predicts experimentally detectable deviations from two-state behavior. An analysis of the villin headpiece and FiP35 WW domain detects multiple native substates that are consistent with experimental data. Applying the same protocol to GTT, NTL9, and protein G suggests that some beta containing proteins can form long-lived native-like states with small register shifts. Even the simplest protein systems show folding and functional dynamics involving three or more states. M ore than fifty years ago, Anfinsen (1) found that primary sequence encodes functional ribonuclease. Today, the process by which proteins self-assemble into their biologically-relevant states remains a key question in biophysics. A modern theory of protein folding must explain a variety of disparate experimental results. First, proteins can fold via a number of mechanisms, ranging from the simplest two-state model (2) to models with more complexity (3). Some proteins may not fold at all-recent work has shown that many eukaryotic proteins are either intrinsically disordered or fold only upon binding to their target (4). The misfolding and aggregation of other proteins have been associated with neurodegenerative disorders such as Alzheimer's disease (5). A "solution" to the protein folding problem must capture not only the folded and unfolded states but intermediate, disordered, and misfolded states as well.Kinetic models with two (2) or more (3, 6) states have been the dominant paradigm for understanding protein folding dynamics. This picture generalizes to an arbitrary number of states; the resulting dynamical model is known as the master equation (7). Recently, several labs (8-13) have used molecular dynamics simulations to parameterize discrete time master equations (also known as Markov state models) that describe the folding dynamics of proteins. Such procedures typically involve clustering the observed conformations to determine microstates, then counting transitions between microstates to estimate rates.Markov state model approaches have typically been limited by two issues. First, the models so constructed have involved hundreds or thousands of states, leading to difficulty making direct connections to experimentally-derived models of folding kinetics. To address this problem, we have developed flux PCCA+ (FPCCA+). Like its precursors PCCA and PCCA+ (14-16), FPCCA+ allows one to construct macrostate models that optimally capture the slow dynamics observed in a microstate model; the advantage of FPCCA+ is in its ability to ignore slow but ...

Identifying localized changes in large systems: Change-point detection for biomolecular simulations

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Quantitative comparison of alternative methods for coarse-graining biological networks

“…35 This flux will be low for poorly sampled transitions and higher for well-sampled transitions. BACE gives the highest fluxes (followed by PCCA), demonstrating that it identifies the most statistically reliable transitions.…”

Inclusion of persistence length-based secondary structure in replica field theoretic models of heteropolymer freezing

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“…With respect to protein folding, distributed computing networks like Folding@Home, and specialized supercomputing hardware like Anton, have pushed the boundaries of fully atomistic molecular dynamics (MD) simulations applied to protein folding systems. [10][11][12][13] The folding dynamics of numerous singledomain protein systems have now been elucidated, often near biological temperatures and in the presence of explicit solvent molecules. Using sophisticated statistical techniques like Markov state models (MSMs), protein simulations have been amassed to capture processes like folding and conformational change that occur on the order of tens of milliseconds in time scale.…”