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Metastability And Markov State Models In Molecular Dynamics
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Book Synopsis Metastability and Markov State Models in Molecular Dynamics by : Christof Schütte
Download or read book Metastability and Markov State Models in Molecular Dynamics written by Christof Schütte and published by American Mathematical Soc.. This book was released on 2013-12-26 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a consequence, there is an increasing need for reduced models that describe the relevant dynamical properties while at the same time being less complex. In this book the authors exploit the existence of metastable sets for constructing such a reduced molecular dynamics model, the so-called Markov state model (MSM), with good approximation properties on the long timescales. With its many examples and illustrations, this book is addressed to graduate students, mathematicians, and practical computational scientists wanting an overview of the mathematical background for the ever-increasing research activity on how to construct MSMs for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Book Synopsis On Metastability and Markov State Models for Non-stationary Molecular Dynamics by : Péter Koltai
Download or read book On Metastability and Markov State Models for Non-stationary Molecular Dynamics written by Péter Koltai and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation by : Gregory R. Bowman
Download or read book An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation written by Gregory R. Bowman and published by Springer Science & Business Media. This book was released on 2013-12-02 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book volume is to explain the importance of Markov state models to molecular simulation, how they work, and how they can be applied to a range of problems. The Markov state model (MSM) approach aims to address two key challenges of molecular simulation: 1) How to reach long timescales using short simulations of detailed molecular models. 2) How to systematically gain insight from the resulting sea of data. MSMs do this by providing a compact representation of the vast conformational space available to biomolecules by decomposing it into states sets of rapidly interconverting conformations and the rates of transitioning between states. This kinetic definition allows one to easily vary the temporal and spatial resolution of an MSM from high-resolution models capable of quantitative agreement with (or prediction of) experiment to low-resolution models that facilitate understanding. Additionally, MSMs facilitate the calculation of quantities that are difficult to obtain from more direct MD analyses, such as the ensemble of transition pathways. This book introduces the mathematical foundations of Markov models, how they can be used to analyze simulations and drive efficient simulations, and some of the insights these models have yielded in a variety of applications of molecular simulation.
Book Synopsis Molecular Dynamics Simulation by : Giovanni Ciccotti
Download or read book Molecular Dynamics Simulation written by Giovanni Ciccotti and published by MDPI. This book was released on 2018-10-08 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Printed Edition of the Special Issue Published in Entropy
Book Synopsis Modulation of Protein Function by : Daniel E. Atkinson
Download or read book Modulation of Protein Function written by Daniel E. Atkinson and published by . This book was released on 1979 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Metastability written by Anton Bovier and published by Springer. This book was released on 2016-02-11 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.
Book Synopsis Stochastic Processes in Physics and Chemistry by : N.G. Van Kampen
Download or read book Stochastic Processes in Physics and Chemistry written by N.G. Van Kampen and published by Elsevier. This book was released on 1992-11-20 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.
Book Synopsis Machine Learning Meets Quantum Physics by : Kristof T. Schütt
Download or read book Machine Learning Meets Quantum Physics written by Kristof T. Schütt and published by Springer Nature. This book was released on 2020-06-03 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.
Book Synopsis Molecular Kinetics in Condensed Phases by : Ron Elber
Download or read book Molecular Kinetics in Condensed Phases written by Ron Elber and published by John Wiley & Sons. This book was released on 2020-02-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the theoretical and computational toolkits for the modern study of molecular kinetics in condensed phases Molecular Kinetics in Condensed Phases: Theory, Simulation and Analysis puts the focus on the theory, algorithms, simulations methods and analysis of molecular kinetics in condensed phases. The authors – noted experts on the topic – offer a detailed and thorough description of modern theories and simulation methods to model molecular events. They highlight the rigorous stochastic modelling of molecular processes and the use of mathematical models to reproduce experimental observations, such as rate coefficients, mean first passage times and transition path times. The book’s exploration of simulations examines atomically detailed modelling of molecules in action and the connections of these simulations to theory and experiment. The authors also explore the applications that range from simple intuitive examples of one- and two-dimensional systems to complex solvated macromolecules. This important book: Offers an introduction to the topic that combines theory, simulation and analysis Presents a guide written by authors that are well-known and highly regarded leaders in their fields Contains detailed examples and explanation of how to conduct computer simulations of kinetics. A detailed study of a two-dimensional system and of a solvated peptide are discussed. Discusses modern developments in the field and explains their connection to the more traditional concepts in chemical dynamics Written for students and academic researchers in the fields of chemical kinetics, chemistry, computational statistical mechanics, biophysics and computational biology, Molecular Kinetics in Condensed Phases is the authoritative guide to the theoretical and computational toolkits for the study of molecular kinetics in condensed phases.
Book Synopsis MARKOV STATE MODELS AND THEIR APPLICATIONS IN PROTEIN FOLDING SIMULATION, SMALL MOLECULE DESIGN, AND MEMBRANE PROTEIN MODELING by : Asghar Razavi Majarashin
Download or read book MARKOV STATE MODELS AND THEIR APPLICATIONS IN PROTEIN FOLDING SIMULATION, SMALL MOLECULE DESIGN, AND MEMBRANE PROTEIN MODELING written by Asghar Razavi Majarashin and published by . This book was released on 2015 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is focused on the application of Markov State Models on protein folding and designing of small drug-like molecules, as well as application of computational tools on the study of biological processes. The central focus of protein folding is to understand how proteins obtain their unique three-dimensional structure from their aminoacid sequences. The function of protein critically depends on its three- dimensional structure; hence, any internal (such as mutations) or external (such as high temperature) perturbation that obstructs three-dimensional structure of a protein will also interfere with its function. Many diseases are associated with inability of protein to form its unique structure. For example, sickle cell anemia is caused by a single mutation that changes glutamic acid to valine. Molecular dynamics (MD) simulations could be utilized to study protein folding and effects of perturbations on protein energy landscape; however, due to its inherent atomic resolution, MD simulations usually provide enormous amount of data even for small proteins. A thorough analysis and extraction of desired information from MD provided data could be extremely challenging and is well beyond human comprehension. Markov state models (MSMs) are proved to be apt for the analysis of large scale random processes and equilibrium conditions, hence it could be applied for protein folding studies. MSMs can be used to obtain long timescale information from short timescale simulations. In other words, the combination of many short simulations and MSMs is a powerful technique to study the folding mechanism of many proteins, even the ones with folding times over millisecond. This dissertation is centered on the use of MSMs and MD simulation in understanding protein folding and biological processes and is constructed as the following. The first chapter provides a brief introduction into MD simulation and the different techniques that could be used to facilitate simulations. Protein folding and its challenges are also discussed in chapter one. Finally, chapter one ends with describing MSMs and technical aspects of building them for protein folding studies. Chapter two is focused on using MD simulations and MSMs to design small protein like molecules to prevent biofilm propagation by disrupting its lifecycle. The biofilm lifecycle and strategy for its interruption is described first. Then, the designed molecules and their conformational sampling by MD simulations are explained. Next, the application of MSMs in obtaining and comparing equilibrium population of all designs are discussed. At the end of chapter two, the molecular descriptions of best designs are explained. Chapter three is focused on the effects of mutations on the energy landscape of a sixteen residue protein from c-terminal hairpin of protein G, GB1. Three mutations, tz4, tz5, and tz6 are discussed, and their folding rates and folding mechanisms are compared with wild-type GB1 using MSMs built from a significantly large MD simulation data set (aggregating over 9 millisecond). Finally, chapter four is focused on the application of MD simulations on understanding the selectivity of Na,K-ATPase, a biologically critical protein that transports sodium ions outside and potassium ions inside against their concentration gradient in almost all eukaryotic cells. Multiple MD approaches, including metadynamics and free energy perturbation methods are used to describe the origins of selectivity for Na,K-ATPase.
Book Synopsis Stochastic Dynamics Out of Equilibrium by : Giambattista Giacomin
Download or read book Stochastic Dynamics Out of Equilibrium written by Giambattista Giacomin and published by Springer. This book was released on 2019-06-30 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.
Book Synopsis Free Energy Computations by : Tony Lelivre
Download or read book Free Energy Computations written by Tony Lelivre and published by World Scientific. This book was released on 2010 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a general introduction to advanced computational methods for free energy calculations, from the systematic and rigorous point of view of applied mathematics. Free energy calculations in molecular dynamics have become an outstanding and increasingly broad computational field in physics, chemistry and molecular biology within the past few years, by making possible the analysis of complex molecular systems. This work proposes a new, general and rigorous presentation, intended both for practitioners interested in a mathematical treatment, and for applied mathematicians interested in molecular dynamics.
Book Synopsis Stochastic Dynamics in Computational Biology by : Stefanie Winkelmann
Download or read book Stochastic Dynamics in Computational Biology written by Stefanie Winkelmann and published by Springer Nature. This book was released on 2021-01-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.
Book Synopsis Markov State Models for Protein and RNA Folding by : Gregory Ross Bowman
Download or read book Markov State Models for Protein and RNA Folding written by Gregory Ross Bowman and published by Stanford University. This book was released on 2010 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the molecular bases of human health could greatly augment our ability to prevent and treat diseases. For example, a deeper understanding of protein folding would serve as a reference point for understanding, preventing, and reversing protein misfolding in diseases like Alzheimer's. Unfortunately, the small size and tremendous flexibility of proteins and other biomolecules make it difficult to simultaneously monitor their thermodynamics and kinetics with sufficient chemical detail. Atomistic Molecular Dynamics (MD) simulations can provide a solution to this problem in some cases; however, they are often too short to capture biologically relevant timescales with sufficient statistical accuracy. We have developed a number of methods to address these limitations. In particular, our work on Markov State Models (MSMs) now makes it possible to map out the conformational space of biomolecules by combining many short simulations into a single statistical model. Here we describe our use of MSMs to better understand protein and RNA folding. We chose to focus on these folding problems because of their relevance to misfolding diseases and the fact that any method capable of describing such drastic conformational changes should also be applicable to less dramatic but equally important structural rearrangements like allostery. One of the key insights from our folding simulations is that protein native states are kinetic hubs. That is, the unfolded ensemble is not one rapidly mixing set of conformations. Instead, there are many non-native states that can each interconvert more rapidly with the native state than with one another. In addition to these general observations, we also demonstrate how MSMs can be used to make predictions about the structural and kinetic properties of specific systems. Finally, we explain how MSMs and other enhanced sampling algorithms can be used to drive efficient sampling.
Book Synopsis Master Equation Models of Macromolecular Dynamics from Atomistic Simulation by : John D. Chodera
Download or read book Master Equation Models of Macromolecular Dynamics from Atomistic Simulation written by John D. Chodera and published by . This book was released on 2006 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is concerned with the construction, validation, and use of master equation models for the study of macromolecular conformational dynamics. The master equation formalism is a powerful tool for describing the dynamics of a system that can be characterized by a discrete-state, continuous-time Markov process. Once constructed from a large quantities of short trajectories, the evolution of experimentally measurable dynamical observables can be computed and compared with experiment. Additionally, information not yet directly accessible to experiment but which may be useful in aiding understanding or the generation of novel hypotheses, such as folding pathways, transiently populated conformations, and mean first passage times, can also be easily obtained. We demonstrate that a master equation model constructed from short trajectories can describe slow conformational dynamics for a solvated alanine peptide over long times, propose a number of tests to tell whether a model constructed from short trajectories will adequately describe dynamics over long times, and describe an algorithm for the automatic construction of these models from simulation data. While the focus here is on protein folding and dynamics, these techniques are very general, and can be broadly applied to problems in biomolecular dynamics.
Book Synopsis Mathematical Models in Developmental Biology by : Jerome K. Percus
Download or read book Mathematical Models in Developmental Biology written by Jerome K. Percus and published by American Mathematical Soc.. This book was released on 2015-06-19 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The path from relatively unstructured egg to full organism is one of the most fascinating trajectories in the biological sciences. Its complexity calls for a very high level of organization, with an array of subprocesses in constant communication with each other. These notes introduce an interleaved set of mathematical models representative of research in the last few decades, as well as the techniques that have been developed for their solution. Such models offer an effective way of incorporating reliable data in a concise form, provide an approach complementary to the techniques of molecular biology, and help to inform and direct future research. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Book Synopsis Experimental Algorithms by : Vincenzo Bonifaci
Download or read book Experimental Algorithms written by Vincenzo Bonifaci and published by Springer. This book was released on 2013-05-09 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Symposium on Experimental Algorithms, SEA 2013, held in Rome, Italy, in June 2013. The 32 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 73 submissions. The papers are organized in topical sections on transportation networks and graph algorithms, combinatorics and enumeration, data structures and compression, network partitioning and bioinformatics, mathematical programming, geometry and optimization, and scheduling and local search.
