Markov state models of biomolecular conformational dynamics

Chodera, John D.; Noé, Frank

doi:10.1016/j.sbi.2014.04.002

Cited by 693 publications

(736 citation statements)

References 77 publications

Supporting

Mentioning

731

Contrasting

Order By: Relevance

“…From the viewpoint of physics this additional assumption [4] means that these changes are explained through K different (unknown) configuration sets of the unresolved scales that give rise to the K different (unknown) causality vectors Λ i for the observed and analyzed scales. In a sense, [4] defines a decomposition of the whole configuration space of the system into K a priori unknown domains, each of which is defined by its unique causality relations for the resolved variables. Based only on the available observed time series for y t and x t 1 ; x t 2 ; .…”

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

“…From the machine-learning and probability theory perspectives, assumption [4] means that the true time-dependent parameters Λ(t) can be represented as a probabilistic mixture of K time-independent (or stationary) parameter vectors Λ i = ðλ ð1Þ i ; . .…”

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

“…; γ t K Þ (K is a priori unknown). I.e., with assumption [4] the nonstationarity of discrete state model [1] can be described and understood as a regimetransition process γ, switching between K different causality regimes, each one of them being described via a fixed causality vector Λ i . Setting K ≡ 1 is equivalent to the stationarity assumption of standard discrete state modeling mentioned above.…”

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

“…It can be demonstrated (detailed proof in SI Text) that based just on this assumption [4] and using the fact that the available data have a finite size (i.e., that N T < +∞), the original ill-posed problem [2,3] can be transformed to…”

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

See 3 more Smart Citations

On inference of causality for discrete state models in a multiscale context

Gerber

Horenko

2014

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Discrete state models are a common tool of modeling in many areas. E.g., Markov state models as a particular representative of this model family became one of the major instruments for analysis and understanding of processes in molecular dynamics (MD). Here we extend the scope of discrete state models to the case of systematically missing scales, resulting in a nonstationary and nonhomogeneous formulation of the inference problem. We demonstrate how the recently developed tools of nonstationary data analysis and information theory can be used to identify the simultaneously most optimal (in terms of describing the given data) and most simple (in terms of complexity and causality) discrete state models. We apply the resulting formalism to a problem from molecular dynamics and show how the results can be used to understand the spatial and temporal causality information beyond the usual assumptions. We demonstrate that the most optimal explanation for the appropriately discretized/ coarse-grained MD torsion angles data in a polypeptide is given by the causality that is localized both in time and in space, opening new possibilities for deploying percolation theory and stochastic subgridscale modeling approaches in the area of MD.multiscale systems | probabilistic networks | Granger causality | nonstationarity | regularization D iscrete state modeling is a powerful tool in many areas of science such as in computational biophysics [where it is mostly used in a form of Markov state models (1-4)], materials science [e.g., deployed in percolation theory and Ising models (5)], bioinformatics [e.g., as probabilistic Boolean models for analysis and control of complex biological networks (6)], and geosciences [e.g., used in the form of the generalized linear regression models (7)]. A central issue of discrete state modeling is the identification of an optimal model for the discrete quantity of interest y (e.g., being a Boolean variable or a probability measure) expressed as a function of other available discrete quantities x 1 , x 2 , . . . , x n (being also Boolean variables or probability measures) and of all other potentially relevant quantities u (being discrete and/or continuous variables). Inference of causality then implies identification of all x i that have a statistically significant impact on y and distinguishing them from all those x j that are insignificant for y. To give a concrete example, in the context of molecular dynamics variable y may describe a probability for a certain torsion angle (e.g., from the protein backbone) to be in one of the discrete conformational states; x 1 , x 2 , . . . , x n can be the values of probabilities for all torsion angles of this protein in previous times and variable u may represent all of the positions and velocities of individual atoms, simulation settings (e.g., temperature), and force-field and solvent properties, etc. Understanding the causality in this situation will mean, for example, identification of the memory depth (e.g., in the context of Markov state models, where...

show abstract

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

Section: Numerical Inference Of the Optimal Causalitymentioning

confidence: 99%

See 2 more Smart Citations

On inference of causality for discrete state models in a multiscale context

Gerber

Horenko

2014

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…MSMs allow more automated simulation analysis that relies less on human intuition, an advancement over previous techniques. MSMs have been used to make direct connections from simulations to experiments, such as ab initio structure prediction for the villin headpiece and characterization of its conformational dynamics [52][53][54] . The MSMbuilder 2.5 package 55 was used to construct a microstate model with 2,314 states.…”

Section: Methodsmentioning

confidence: 99%

A network of molecular switches controls the activation of the two-component response regulator NtrC

Vanatta

Shukla²,

Lawrenz

et al. 2015

Nat Commun

View full text Add to dashboard Cite

Recent successes in simulating protein structure and folding dynamics have demonstrated the power of molecular dynamics to predict the long timescale behaviour of proteins. Here, we extend and improve these methods to predict molecular switches that characterize conformational change pathways between the active and inactive state of nitrogen regulatory protein C (NtrC). By employing unbiased Markov state model-based molecular dynamics simulations, we construct a dynamic picture of the activation pathways of this key bacterial signalling protein that is consistent with experimental observations and predicts new mutants that could be used for validation of the mechanism. Moreover, these results suggest a novel mechanistic paradigm for conformational switching.

show abstract

Patterns that Persist

Tzelios¹,

Bishop²

2023

Conflicting Models for the Origin of Life

View full text Add to dashboard Cite

Markov state models of biomolecular conformational dynamics

Cited by 693 publications

References 77 publications

On inference of causality for discrete state models in a multiscale context

On inference of causality for discrete state models in a multiscale context

A network of molecular switches controls the activation of the two-component response regulator NtrC

Patterns that Persist

Contact Info

Product

Resources

About