Metastability and Markov State Models in Molecular Dynamics
Metastability and Markov State Models in Molecular Dynamics

Author: Christof Schütte

Publisher: American Mathematical Soc.

Published: 2013-12-26

Total Pages: 141

ISBN-13: 0821843591

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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.

Machine Learning Meets Quantum Physics
Machine Learning Meets Quantum Physics

Author: Kristof T. Schütt

Publisher: Springer Nature

Published: 2020-06-03

Total Pages: 473

ISBN-13: 3030402452

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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.

An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation
An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation

Author: Gregory R. Bowman

Publisher: Springer Science & Business Media

Published: 2013-12-02

Total Pages: 148

ISBN-13: 9400776063

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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.

Stochastic Processes in Physics and Chemistry
Stochastic Processes in Physics and Chemistry

Author: N.G. Van Kampen

Publisher: Elsevier

Published: 1992-11-20

Total Pages: 482

ISBN-13: 0080571387

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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.

Stochastic Dynamics Out of Equilibrium
Stochastic Dynamics Out of Equilibrium

Author: Giambattista Giacomin

Publisher: Springer

Published: 2019-06-30

Total Pages: 654

ISBN-13: 3030150968

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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.

Multiple Time Scale Dynamics
Multiple Time Scale Dynamics

Author: Christian Kuehn

Publisher: Springer

Published: 2015-02-25

Total Pages: 816

ISBN-13: 3319123165

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This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.

Kinetic Phase Diagrams
Kinetic Phase Diagrams

Author: Zdeněk Chvoj

Publisher: Elsevier Publishing Company

Published: 1991

Total Pages: 640

ISBN-13:

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The present theoretical and experimental knowledge of the time evolution of a system during solidification, not only in equilibrium, but also in nonequilibrium conditions, is summarized in this book. Such knowledge is of fundamental importance for the determination of the constitution of materials or of the technological conditions necessary to prepare materials with a desired structure. Emphasizing the importance of kinetic phase diagrams, the authors focus the attention of the reader on the problems connected with nonequilibrium conditions, that are encountered during real phase transformations. A critical review of phenomenological and statistical theories of phase transformations and of mass and heat transport enables the reader to determine the range of applicability of concrete models for the description of the evolution of a given system. The book is supplemented with several less-known methods and results of phase characterization, including a detailed account of the Soviet school of T.A. Cherepanova which is not well known in the West. The text also covers the modern research area of glasses and their preparation.

Biomolecular Simulations in Structure-Based Drug Discovery
Biomolecular Simulations in Structure-Based Drug Discovery

Author: Francesco L. Gervasio

Publisher: John Wiley & Sons

Published: 2019-04-29

Total Pages: 368

ISBN-13: 3527342656

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A guide to applying the power of modern simulation tools to better drug design Biomolecular Simulations in Structure-based Drug Discovery offers an up-to-date and comprehensive review of modern simulation tools and their applications in real-life drug discovery, for better and quicker results in structure-based drug design. The authors describe common tools used in the biomolecular simulation of drugs and their targets and offer an analysis of the accuracy of the predictions. They also show how to integrate modeling with other experimental data. Filled with numerous case studies from different therapeutic fields, the book helps professionals to quickly adopt these new methods for their current projects. Experts from the pharmaceutical industry and academic institutions present real-life examples for important target classes such as GPCRs, ion channels and amyloids as well as for common challenges in structure-based drug discovery. Biomolecular Simulations in Structure-based Drug Discovery is an important resource that: -Contains a review of the current generation of biomolecular simulation tools that have the robustness and speed that allows them to be used as routine tools by non-specialists -Includes information on the novel methods and strategies for the modeling of drug-target interactions within the framework of real-life drug discovery and development -Offers numerous illustrative case studies from a wide-range of therapeutic fields -Presents an application-oriented reference that is ideal for those working in the various fields Written for medicinal chemists, professionals in the pharmaceutical industry, and pharmaceutical chemists, Biomolecular Simulations in Structure-based Drug Discovery is a comprehensive resource to modern simulation tools that complement and have the potential to complement or replace laboratory assays for better results in drug design.

The Theory of Critical Phenomena
The Theory of Critical Phenomena

Author: J. J. Binney

Publisher: Oxford University Press

Published: 1992-06-11

Total Pages: 477

ISBN-13: 0191660566

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The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.