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Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them po…

Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on experimental…

Protein folding is an important problem in structural biology with significant medical implications, particularly for misfolding disorders like Alzheimer’s disease. Solving the folding problem will ultimately require a combination of theory and experiment, with theoretical models providing a comprehensive view of folding and experiments grounding these models …

Protein folding is a classic grand challenge that is relevant to numerous human diseases, such as protein misfolding diseases like Alzheimer’s disease. Solving the folding problem will ultimately require a combination of theory, simulation, and experiment, with theory and simulation providing an atomically detailed picture of both the thermodynamics and …

We present a simple model of protein folding dynamics that captures key qualitative elements recently seen in all-atom simulations. The goals of this theory are to serve as a simple formalism for gaining deeper insight into the physical properties seen in detailed simulations as well as to serve as a model to easily compare why these simulations suggest a diff…

As the fastest folding protein, the villin headpiece (HP35) serves as an important bridge between simulation and experimental studies of protein folding. Despite the simplicity of this system, experiments continue to reveal a number of surprises, including structure in the unfolded state and complex equilibrium dynamics near the native state. Using 2.5 ms of m…

Two strategies have been recently employed to push molecular simulation to long, biologically relevant time scales: projection-based analysis of results from specialized hardware producing a small number of ultralong trajectories and the statistical interpretation of massive parallel sampling performed with Markov state models (MSMs). Here, we assess the MSM a…

As the resolution of experiments to measure folding kinetics continues to improve, it has become imperative to avoid bias that may come with fitting data to a predetermined mechanistic model. Toward this end, we present a rate spectrum approach to analyze timescales present in kinetic data. Computing rate spectra of noisy time series data via numerical discret…

Markov state models (MSMs) have proven themselves to be effective statistical and quantitative models for understanding protein folding dynamics. As stochastic networks, MSMs allow for descriptions of parallel folding pathways and facilitate quantitative comparison to experiments conducted at the ensemble level. While this complex network structure is advantag…

Markov state models (MSMs) have proven to be useful tools in simulating large and slowly-relaxing biological systems like proteins. MSMs model proteins through dynamics on a discrete-state energy landscape, allowing molecules to effectively sample large regions of phase space. In this work, we use aspects of MSMs to ask: is protein folding mechanistically robu…