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.

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 Thermodynamics and kinetics of the amyloid-β peptide revealed by Markov state models based on MD data in agreement with experiment

2021 ◽  
Author(s):  
Arghadwip Paul ◽  
Suman Samantray ◽  
Marco Anteghini ◽  
Mohammed Khaled ◽  
Birgit Strodel
Keyword(s):  
Amyloid Β ◽  
Md Simulations ◽  
Amyloid Β Peptide ◽  
Intrinsically Disordered ◽  
Thermodynamics And Kinetics ◽  
Markov State ◽  
Markov State Models ◽  
State Models ◽  
Kinetics Of

The convergence of MD simulations is tested using varying measures for the intrinsically disordered amyloid-β peptide (Aβ). Markov state models show that 20–30 μs of MD is needed to reliably reproduce the thermodynamics and kinetics of Aβ.

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.

MasterMSM: A Package for Constructing Master Equation Models of Molecular Dynamics

2019 ◽  
Author(s):  
David De Sancho ◽  
Anne Aguirre
Keyword(s):  
Molecular Dynamics ◽  
Master Equation ◽  
Md Simulations ◽  
Distinctive Features ◽  
Markov State Models ◽  
Software Packages ◽  
Long Time ◽  
State Models ◽  
Definition Of ◽  
Kinetics Of

<div>Markov state models (MSMs) have become one of the most important techniques for understanding biomolecular transitions from classical molecular dynamics (MD) simulations. MSMs provide a systematized way of accessing the long time kinetics of the system of interest from the short-timescale microscopic transitions observed in simulation trajectories. At the same time, they provide a consistent description of the equilibrium and dynamical properties of the system of interest, and they are ideally suited for comparisons against experiment. A few software packages exist for building MSMs, which have been widely adopted. Here we introduce MasterMSM, a new Python package that uses the master equation formulation of MSMs and provides a number of new algorithms for building and analyzing these models. We demonstrate some of the most distinctive features of the package, including the estimation of rates, definition of core-sets for transition based assignment of states, the estimation of committors and fluxes, and the sensitivity analysis of the emerging networks. The package is available at https://github.com/daviddesancho/MasterMSM.</div>

scholarly journals Thermodynamics and kinetics of the amyloid-β peptide revealed by Markov state models based on MD data in agreement with experiment

2020 ◽  
Author(s):  
Arghadwip Paul ◽  
Suman Samantray ◽  
Marco Anteghini ◽  
Birgit Strodel
Keyword(s):  
Alzheimer’S Disease ◽  
Force Fields ◽  
Amyloid Β ◽  
Md Simulations ◽  
Amyloid Β Peptide ◽  
Thermodynamics And Kinetics ◽  
Markov State ◽  
Markov State Models ◽  
State Models ◽  
Kinetics Of

AbstractThe amlyoid-β peptide (Aβ) is closely linked to the development of Alzheimer’s disease. Molecular dynamics (MD) simulations have become an indispensable tool for studying the behavior of this peptide at the (sub)molecular level, thereby providing insight into the molecular basis of Alzheimer’s disease. General key aspects of MD simulations are the force field used for modeling the peptide or protein and its environment, which is important for accurate modeling of the system of interest, and the length of the simulations, which determines whether or not equilibrium is reached. In this study we address these points by analyzing 30-µs MD simulations acquired for Aβ40 using seven different force fields. We assess the convergence of these simulations based on the convergence of various structural properties and of NMR and fluorescence spectroscopic observables. Moreover, we calculate Markov state models for each of the seven MD simulations, which provide an unprecedented view of the thermodynamics and kinetics of the amyloid-β peptide. This further allows us to provide answers for pertinent questions, like: Which force fields are suitable for modeling Aβ? (a99SB-UCB and a99SB-ILDN/TIP4P-D); What does Aβ peptide really look like? (mostly extended and disordered) and; How long does it take MD simulations of Aβ to attain equilibrium? (20–30 µs). We believe the analyses presented in this study will provide a useful reference guide for important questions relating to the structure and dynamics of Aβin particular, and by extension other similar disordered peptides.

MasterMSM: A Package for Constructing Master Equation Models of Molecular Dynamics

2019 ◽  
Author(s):  
David De Sancho ◽  
Anne Aguirre
Keyword(s):  
Molecular Dynamics ◽  
Master Equation ◽  
Md Simulations ◽  
Distinctive Features ◽  
Markov State Models ◽  
Software Packages ◽  
Long Time ◽  
State Models ◽  
Definition Of ◽  
Kinetics Of

<div>Markov state models (MSMs) have become one of the most important techniques for understanding biomolecular transitions from classical molecular dynamics (MD) simulations. MSMs provide a systematized way of accessing the long time kinetics of the system of interest from the short-timescale microscopic transitions observed in simulation trajectories. At the same time, they provide a consistent description of the equilibrium and dynamical properties of the system of interest, and they are ideally suited for comparisons against experiment. A few software packages exist for building MSMs, which have been widely adopted. Here we introduce MasterMSM, a new Python package that uses the master equation formulation of MSMs and provides a number of new algorithms for building and analyzing these models. We demonstrate some of the most distinctive features of the package, including the estimation of rates, definition of core-sets for transition based assignment of states, the estimation of committors and fluxes, and the sensitivity analysis of the emerging networks. The package is available at https://github.com/daviddesancho/MasterMSM.</div>

scholarly journals Millisecond dynamics of BTK reveal kinome-wide conformational plasticity within the apo kinase domain

2017 ◽  
Author(s):  
Mohammad M. Sultan ◽  
Rajiah Aldrin Denny ◽  
Ray Unwalla ◽  
Frank Lovering ◽  
Vijay S. Pande
Keyword(s):  
Computational Cost ◽  
Md Simulations ◽  
Kinase Domain ◽  
Key Enzyme ◽  
Conformational Plasticity ◽  
Severe Immunodeficiency ◽  
Conformational Landscape ◽  
State Models ◽  
Kinetics Of ◽  
Aspartate Residue

AbstractBruton tyrosine kinase (BTK) is a key enzyme in B-cell development whose improper regulation causes severe immunodeficiency diseases. Design of selective BTK therapeutics would benefit from improved,in-silicostructural modeling of the kinase’s solution ensemble. However, this remains challenging due to the immense computational cost of sampling events on biological timescales. In this work, we combine multi-millisecond molecular dynamics (MD) simulations with Markov state models (MSMs) to report on the thermodynamics, kinetics, and accessible states of BTK’s kinase domain. Our conformational landscape links the active state to several inactive states, connected via a structurally diverse intermediate. Our calculations predict a kinome-wide conformational plasticity, and indicate the presence of several new potentially druggable BTK states. We further find that the population of these states and the kinetics of their inter-conversion are modulated by protonation of an aspartate residue, establishing the power of MD & MSMs in predicting effects of chemical perturbations.

Investigating the dynamic nature of the ABC transporters: ABCB1 and MsbA as examples for the potential synergies of MD theory and EPR applications

2015 ◽  
Vol 43 (5) ◽  
pp. 1023-1032 ◽  
Author(s):  
Thomas Stockner ◽  
Anna Mullen ◽  
Fraser MacMillan
Keyword(s):  
Crystal Structures ◽  
Conformational Changes ◽  
Abc Transporters ◽  
Epr Spectroscopy ◽  
Structural Information ◽  
Dynamic Properties ◽  
Molecular System ◽  
Synergistic Effects ◽  
Md Simulations ◽  
Substrate Spectrum

ABC transporters are primary active transporters found in all kingdoms of life. Human multidrug resistance transporter ABCB1, or P-glycoprotein, has an extremely broad substrate spectrum and confers resistance against chemotherapy drug treatment in cancer cells. The bacterial ABC transporter MsbA is a lipid A flippase and a homolog to the human ABCB1 transporter, with which it partially shares its substrate spectrum. Crystal structures of MsbA and ABCB1 have been solved in multiple conformations, providing a glimpse into the possible conformational changes the transporter could be going through during the transport cycle. Crystal structures are inherently static, while a dynamic picture of the transporter in motion is needed for a complete understanding of transporter function. Molecular dynamics (MD) simulations and electron paramagnetic resonance (EPR) spectroscopy can provide structural information on ABC transporters, but the strength of these two methods lies in the potential to characterise the dynamic regime of these transporters. Information from the two methods is quite complementary. MD simulations provide an all atom dynamic picture of the time evolution of the molecular system, though with a narrow time window. EPR spectroscopy can probe structural, environmental and dynamic properties of the transporter in several time regimes, but only through the attachment sites of an exogenous spin label. In this review the synergistic effects that can be achieved by combining the two methods are highlighted, and a brief methodological background is also presented.

THEORETICAL INVESTIGATIONS ON ELUCIDATING FUNDAMENTAL MECHANISMS OF CATALYSIS AND DYNAMICS INVOLVED IN TRANSCRIPTION BY RNA POLYMERASE

2013 ◽  
Vol 12 (08) ◽  
pp. 1341005 ◽  
Author(s):  
FÁTIMA PARDO-AVILA ◽  
LIN-TAI DA ◽  
YING WANG ◽  
XUHUI HUANG
Keyword(s):  
Rna Polymerase ◽  
Conformational Changes ◽  
Normal Mode Analysis ◽  
Md Simulations ◽  
Mode Analysis ◽  
Transcription Process ◽  
Nucleotide Addition ◽  
Theoretical Investigations ◽  
State Models ◽  
Elongation Process

RNA polymerase is the enzyme that synthesizes RNA during the transcription process. To understand its mechanism, structural studies have provided us pictures of the series of steps necessary to add a new nucleotide to the nascent RNA chain, the steps altogether known as the nucleotide addition cycle (NAC). However, these static snapshots do not provide dynamic information of these processes involved in NAC, such as the conformational changes of the protein and the atomistic details of the catalysis. Computational studies have made efforts to fill these knowledge gaps. In this review, we provide examples of different computational approaches that have improved our understanding of the transcription elongation process for RNA polymerase, such as normal mode analysis, molecular dynamic (MD) simulations, Markov state models (MSMs). We also point out some unsolved questions that could be addressed using computational tools in the future.

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