scholarly journals Dynamic graphical models of molecular kinetics

2019 ◽  
Vol 116 (30) ◽  
pp. 15001-15006 ◽  
Author(s):  
Simon Olsson ◽  
Frank Noé
Keyword(s):  
Graphical Models ◽  
Molecular System ◽  
System Size ◽  
Metastable States ◽  
Dynamics Simulation ◽  
Global State ◽  
Markov State ◽  
Coupled Subsystems ◽  
State Models ◽  
Frustrated Systems

Most current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be represented by a single global state (e.g., a Markov state in a Markov state model [MSM]). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small- to medium-sized proteins. However, this approach breaks down in frustrated systems and in large protein assemblies, where the number of global metastable states may grow exponentially with the system size. To address this problem, we here introduce dynamic graphical models (DGMs) that describe molecules as assemblies of coupled subsystems, akin to how spins interact in the Ising model. The change of each subsystem state is only governed by the states of itself and its neighbors. DGMs require fewer parameters than MSMs or other global state models; in particular, we do not need to observe all global system configurations to characterize them. Therefore, DGMs can predict previously unobserved molecular configurations. As a proof of concept, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.

scholarly journals Dynamic Graphical Models of Molecular Kinetics

2018 ◽  
Author(s):  
Simon Olsson ◽  
Frank Noé
Keyword(s):  
Graphical Models ◽  
Molecular System ◽  
System Size ◽  
Ising Models ◽  
Metastable States ◽  
Dynamics Simulation ◽  
Global State ◽  
Stable States ◽  
Markov State ◽  
State Models

AbstractMost current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be characterized by a single global state, e.g., a Markov State in a Markov State Model (MSM). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small to medium-sized proteins. However this approach breaks down in frustrated systems and in large protein assemblies, where the number of global meta-stable states may grow exponentially with the system size. Here, we introduce Dynamic Graphical Models (DGMs), which build upon the idea of Ising models, and describe molecules as assemblies of coupled subsystems. The switching of each sub-system state is only governed by the states of itself and its neighbors. DGMs need many fewer parameters than MSMs or other global-state models, in particular we do not need to observe all global system configurations to estimate them. Therefore, DGMs can predict new, previously unobserved, molecular configurations. Here, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.

scholarly journals Independent Markov Decomposition: Towards modeling kinetics of biomolecular complexes

2021 ◽  
Author(s):  
Tim Hempel ◽  
Mauricio J. del Razo ◽  
Christopher T. Lee ◽  
Bryn C. Taylor ◽  
Rommie E. Amaro ◽  
...  
Keyword(s):  
Cell Biology ◽  
Molecular System ◽  
Biological Systems ◽  
Global State ◽  
Global System ◽  
Markov State ◽  
Markov State Models ◽  
Weakly Coupled ◽  
System States ◽  
State Models

In order to advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) and Markov state models (MSMs) have enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increase exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called Independent Markov Decomposition (IMD) that leverages weak coupling between subsystems in order to compute a global kinetic model without requiring to sample all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.Significance StatementMolecular simulations of proteins are often interpreted using Markov state models (MSMs), in which each protein configuration is assigned to a global state. As we explore larger and more complex biological systems, the size of this global state space will face a combinatorial explosion, rendering it impossible to gather sufficient sampling data. In this work, we introduce an approach to decompose a system of interest into separable subsystems. We show that MSMs built for each subsystem can be later coupled to reproduce the behaviors of the global system. To aid in the choice of decomposition we also describe a score to quantify its goodness. This decomposition strategy has the promise to enable robust modeling of complex biomolecular systems.

scholarly journals Reconciling simulated ensembles of apomyoglobin with experimental HDX data using Bayesian inference and multi-ensemble Markov State Models

2019 ◽  
Author(s):  
Hongbin Wan ◽  
Yunhui Ge ◽  
Asghar Razavi ◽  
Vincent A. Voelz
Keyword(s):  
Molecular Dynamics ◽  
Bayesian Inference ◽  
Conformational Dynamics ◽  
Molecular Simulations ◽  
Dynamics Simulation ◽  
Trajectory Data ◽  
Protection Factor ◽  
Markov State ◽  
Markov State Models ◽  
State Models

AbstractHydrogen/deuterium exchange (HDX) is a powerful technique to investigate protein conformational dynamics at amino acid resolution. Because HDX provides a measurement of solvent exposure of backbone hydrogens, ensemble-averaged over potentially slow kinetic processes, it has been challenging to use HDX protection factors to refine structural ensembles obtained from molecular dynamics simulations. This entails two dual challenges: (1) identifying structural observables that best correlate with backbone amide protection from exchange, and (2) restraining these observables in molecular simulations to model ensembles consistent with experimental measurements. Here, we make significant progress on both fronts. First, we describe an improved predictor of HDX protection factors from structural observables in simulated ensembles, parameterized from ultra-long molecular dynamics simulation trajectory data, with a Bayesian inference approach used to retain the full posterior distribution of model parameters.We next present a new method for obtaining simulated ensembles in agreement with experimental HDX protection factors, in which molecular simulations are performed at various temperatures and restraint biases, and used to construct multi-ensemble Markov State Models (MSMs). Finally, the BICePs algorithm (Bayesian Inference of Conformational Populations) is then used with our HDX protection factor predictor to infer which thermodynamic ensemble agrees best with experiment, and estimate populations of each conformational state in the MSM. To illustrate the approach, we use a combination of HDX protection factor restraints and chemical shift restraints to model the conformational ensemble of apomyoglobin at pH 6. The resulting ensemble agrees well with experiment, and gives insight into the all-atom structure of disordered helices F and H in the absence of heme.Graphical TOC Entry

scholarly journals Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

2021 ◽  
Vol 118 (31) ◽  
pp. e2105230118
Author(s):  
Tim Hempel ◽  
Mauricio J. del Razo ◽  
Christopher T. Lee ◽  
Bryn C. Taylor ◽  
Rommie E. Amaro ◽  
...  
Keyword(s):  
Cell Biology ◽  
Molecular System ◽  
Md Simulations ◽  
Weakly Coupled ◽  
Coupled Subsystems ◽  
Biomolecular Complexes ◽  
System States ◽  
State Models ◽  
Long Timescales ◽  
Kinetics Of

To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

Molecular Dynamics Simulation Of A Cyclic Siloxane Based Liquid Crystalline Material

1993 ◽  
Vol 328 ◽  
Author(s):  
Soumya S. Patnaik ◽  
Ruth Pachter ◽  
Steve Plimpton ◽  
W. WADE ADAMS
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Liquid Crystalline ◽  
Molecular System ◽  
Orientational Order ◽  
System Size ◽  
Dynamics Simulation ◽  
Cyclic Siloxane ◽  
Structural Anisotropy ◽  
Principal Axes

ABSTRACTWe have used molecular dynamics (MD) to study the room temperature bulk phase behavior of a cyclic siloxane with a pentamethylcyclosiloxane core and biphenyl-4-allyloxybenzoate Mesogens (BCS). This Material exhibits thermotropic liquid crystalline behavior above 120 °C. Bonded and non-bonded interactions were considered and a Molecular Mechanics force field was used to model the structural anisotropy of the siloxane Molecules. Molecular clusters with and without periodic boundary conditions (pbc) were studied to investigate the effect of the finite system size on the time evolution of the molecular structure. The precise nature of the boundary conditions was found to be significant and simulations that exclude pbc were better able to model the molecular system. It was found that molecular shapes associated with low energy conformations were not cylindrically symmetric but more splayed like. An approximate measure of the shape of the mesogens was obtained by describing ellipsoids around the Mesogens, and estimating the molecular length, breadth, and width from the principal axes of the ellipsoids. The orientational order was then calculated by defining the molecular axis to be along the major principal axis.

Development of the ChIMES Force Field for Reactive Molecular Systems: Carbon Monoxide at Extreme Conditions

2019 ◽  
Author(s):  
Rebecca Lindsey ◽  
Nir Goldman ◽  
Laurence E. Fried ◽  
Sorin Bastea
Keyword(s):  
Carbon Monoxide ◽  
Molecular System ◽  
Interaction Model ◽  
System Size ◽  
Single Atom ◽  
Reactive System ◽  
Extreme Conditions ◽  
Ambient Conditions ◽  
Molecular Systems ◽  
Three Body

<p>The interatomic Chebyshev Interaction Model for Efficient Simulation (ChIMES) is based on linear combinations of Chebyshev polynomials describing explicit two- and three-body interactions. Recently, the ChIMES model has been developed and applied to a molten metallic system of a single atom type (carbon), as well as a non-reactive molecular system of two atom types at ambient conditions (water). Here, we continue application of ChIMES to increasingly complex problems through extension to a reactive system. Specifically, we develop a ChIMES model for carbon monoxide under extreme conditions, with built-in transferability to nearby state points. We demonstrate that the resulting model recovers much of the accuracy of DFT while exhibiting a 10<sup>4</sup>increase in efficiency, linear system size scalability and the ability to overcome the significant system size effects exhibited by DFT.</p>

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