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author = {Towns, John and Cockerill, Timothy and Dahan, Maytal and Foster, Ian and Gaither, Kelly and Grimshaw, Andrew and Hazlewood, Victor and Lathrop, Scott and Lifka, Dave and Peterson, Gregory D. and Roskies, Ralph and Scott, J. Ray and Wilkens-Diehr, Nancy},
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doi = {10.1109/MCSE.2014.80},
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issn = {1521-9615},
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journal = {Comput. Sci. Eng.},
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number = {5},
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pages = {62--74},
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title = {{XSEDE: Accelerating Scientific Discovery}},
author = {Kirchmair, Johannes and G{\"{o}}ller, Andreas H. and Lang, Dieter and Kunze, Jens and Testa, Bernard and Wilson, Ian D and Glen, Robert C and Schneider, Gisbert},
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doi = {10.1038/nrd4581},
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issn = {1474-1776},
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journal = {Nat. Rev. Drug Discov.},
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number = {6},
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pages = {387--404},
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publisher = {Nature Publishing Group},
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title = {{Predicting drug metabolism: experiment and/or computation?}},
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url = {http://dx.doi.org/10.1038/nrd4581},
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volume = {14},
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year = {2015}
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}
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@article{Sresht2017,
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author = {Sresht, Vishnu and Lewandowski, Eric P. and Blankschtein, Daniel and Jusuf, Arben},
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doi = {10.1021/acs.langmuir.7b01073},
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journal = {Langmuir},
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pages = {8319−8329},
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title = {{Combined Molecular Dynamics Simulation–Molecular-Thermodynamic Theory Framework for Predicting Surface Tensions}},
Copy file name to clipboardExpand all lines: paper/basic_training.tex
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\author[1]{Efrem Braun}
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\author[2]{Justin Gilmer}
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\author[3]{Heather Mayes}
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\author[3]{Heather B. Mayes}
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\author[4]{David L. Mobley}
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\author[5]{Jacob I. Monroe}
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\author[6]{Samarjeet Prasad}
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%\author[2*]{Firstname Surname}
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\affil[1]{University of California, Berkeley}
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\affil[2]{Vanderbilt University}
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\affil[3]{University of Michigan}
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\affil[3]{University of Michigan, Ann Arbor}
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\affil[4]{University of California, Irvine}
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\affil[5]{University of California, Santa Barbara}
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\affil[6]{National Institutes of Health}
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\label{sec:intro}
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Molecular simulation techniques play a very important role in our quest to understand and predict the properties, structure, and function of molecular systems, and are a key tool as we seek to enable predictive molecular design.
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Simulation methods are extremely useful for studying the structure and dynamics of complex systems that are too complicated for pen and paper theory and helping interpret experimental data in terms of molecular motions, as well as (increasingly) for quantitative prediction of properties of use in molecular design and other applications.
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Simulation methods are extremely useful for studying the structure and dynamics of complex systems that are too complicated for pen and paper theory and helping interpret experimental data in terms of molecular motions, as well as (increasingly) for quantitative prediction of properties of use in molecular design and other applications~\cite{Nussinov2014,Towns2014,Kirchmair2015,Sresht2017,Bottaro2018}.
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The basic idea of any molecular simulation method is quite simple; a particle-based description of the system under investigation is constructed and then the system is propagated by either deterministic or probabilistic rules to generate a trajectory describing its evolution over the course of the simulation.
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The basic idea of any molecular simulation method is straightforward; a particle-based description of the system under investigation is constructed and then the system is propagated by either deterministic or probabilistic rules to generate a trajectory describing its evolution over the course of the simulation~\cite{Frenkel:2001:,2001Leach}.
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Relevant properties can be calculated for each ``snapshot'' (a stored configuration of the system, also called a ``frame'') and averaged over the the entire trajectory to compute estimates of desired properties.
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Depending on how the system is propagated, molecular simulation methods can be divided into two main categories: Molecular Dynamics (MD) and Monte Carlo (MC).
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With MD methods, the equation of motion is numerically integrated and a dynamical trajectory of the system is generated.
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With MD methods, the equations of motion are numerically integrated to generate a dynamical trajectory of the system.
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MD simulations can be used for investigating structural, dynamic, and thermodynamic properties of the system.
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With MC methods, probabilistic rules are used to generate a new configuration from the present configuration and this process is repeated to generate a sequence of states that can be used to calculate structural and thermodynamic properties but not dynamical properties; indeed, MC simulations lack any concept of time.
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Thus, the ``dynamics'' produced by an MC method are not the temporal dynamics of the system.
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Thus, the ``dynamics'' produced by an MC method are not the temporal dynamics of the system, but the ensemble of configurations that reflect those that could be dynamically sampled.
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This foundational document will focus on the concepts needed to carry out correct MD simulations that utilize good practices.
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Many, but not all, of the concepts here are also useful for MC simulations and apply there as well, but MC as a whole needs its own document.
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Many, but not all, of the concepts here are also useful for MC simulations and apply there as well. However, there are a sufficient number of key differences, which are outside the scope of this current document.
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Either method can be carried out with different underlying physical theories to describe the particle-based model of the system under investigation.
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If a quantum mechanics (QM) description of matter is used, electrons are explicitly represented in the model and interaction energy is calculated by solving the electronic structure of the molecules in the system with no (or few) empirical parameters, but with various approximations to the physics for tractability.
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In a classical description, the molecules are represented by particles representing atoms or groups of atoms. Each atom may be assigned an electric charge and a potential energy function with a large number of empirical parameters (fitted to experiment, QM, or other data) is used to calculate non-bonded as well bonded interactions.
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Classical simulations are much faster than quantum simulations, making them the methods of choice for vast majority of molecular simulation studies on biomolecular systems in the condensed phase.
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If a quantum mechanics (QM) description of matter is used, electrons are explicitly represented in the model and interaction energy is calculated by solving the electronic structure of the molecules in the system with no (or few) empirical parameters, but with various approximations to the physics for tractability.
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In a molecular mechanics (MM) description, the molecules are represented by particles representing atoms or groups of atoms. Each atom may be assigned an electric charge and a potential energy function with a large number of empirical parameters (fitted to experiment, QM, or other data) used to calculate non-bonded and bonded interactions. Unless otherwise specified, MD simulations employ MM force fields, which calculate the forces that determine the system dynamics.
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MM simulations are much faster than quantum simulations, making them the methods of choice for vast majority of molecular simulation studies on biomolecular systems in the condensed phase.
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%\todo[inline, color={red!20}]{Put in a few-sentence discussion re the size \& timescales of systems and the appropriate method; perhaps like the images often in papers; what are typical sizes and timescales that are tractable? This of course changes with time, but this is a living document so we're good. Also add in general, that the topology does not change--most FF do not allow chemical reactions}
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Speed is a particular concern when describing condensed phase systems, as we are often interested in the properties of molecules (even biomacromolecules) in solution, meaning that systems will consist of thousands to hundreds of thousands or millions of atoms.
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The key dynamical concept to understand is embodied in the twin characteristics of timescales and rates.
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The two are literally reciprocals of one another.
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In Fig.\ \ref{landscapes}(a), assume you have started an MD simulation in basin A.
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The trajectory is likely to remain in that basin for a period of time -- the “dwell” timescale -- which increases exponentially with the barrier height according to the (reciprocal) Arrhenius factor as $\exp[(U^\ddagger - U_A)/k_B T]$; barriers many times the thermal energy $k_BT$ imply long dwells.
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The trajectory is likely to remain in that basin for a period of time -- the ``dwell'' timescale -- which increases exponentially with the barrier height according to the (reciprocal) Arrhenius factor as $\exp[(U^\ddagger - U_A)/k_B T]$; barriers many times the thermal energy $k_BT$ imply long dwells.
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The rate $k_{AB}$, which is the transition probability per unit time, exhibits reciprocal behavior -- i.e., $k_{AB} \sim\exp[-(U^\ddagger - U_A)/k_B T]$ according to the traditional Arrhenius factor.
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Note that all transitions occur in a random, \emph{stochastic} fashion and are not predictable except in terms of average behavior.
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More detailed discussions of rate constants can be found in numerous textbooks (e.g.,~\cite{DillBook, Zuckerman:2010:}).
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Books which we recommend as particularly helpful in this area include:
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\begin{itemize}
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\item Reif's ``Fundamentals of Statistical and Thermal Physics''~\ref{Reif:2008:}
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\item Reif's ``Fundamentals of Statistical and Thermal Physics''~\ref{Reif:2009:}
\item Dill and Bromberg's ``Molecular Driving Forces''~\cite{DillBook}
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\item Hill's ``Statistical Mechanics: Principles and Selected Applications''~\cite{Hill:1987:}
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\item Production
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\end{enumerate}
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Additional explanations of these steps along with procedural details specific to a given simulation package and application may be found in a variety of tutorials\citep{LemkulTutorials,AmberBeginner}.
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Additional explanations of these steps along with procedural details specific to a given simulation package and application may be found in a variety of tutorials~\cite{LemkulTutorials,AmberBeginner}.
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It should be noted that these steps may be difficult to unambiguously differentiate and define in some cases.
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Additionally, it is assumed that prior to performing any of these steps, an appropriate amount of deliberation has been devoted to clearly defining the system and determining the appropriate simulation techniques.
This is accomplished by modifying the force calculation with the form $F = F_{interaction} + F_{constraint}$, where $F_{interaction}$ is the standard interactions calculated during the course of the simulation and $F_{constraint}$ is a Lagrange multiplier that keeps the kinetic energy constant.
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The reasoning for the naming of this thermostat is due to its use of the Gaussian principle of least constraint to determine the smallest perturbative forces needed to maintain the instantaneous temperature\cite{thermostatAlgorithms2005}.
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Clearly, this thermostat does not sample the canonical distribution; it instead samples the isokinetic (constant kinetic energy) ensemble.
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However, the isokinetic ensemble samples the same configurational phase space as the canonical ensemble, so position-dependent (structural) equilibrium properties can be obtained equivalently with either ensemble\cite{Minary:2003:JChemPhys:Algorithms}.
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However, the isokinetic ensemble samples the same configurational phase space as the canonical ensemble, so position-dependent (structural) equilibrium properties can be obtained equivalently with either ensemble\cite{Minary:2003:JChemPhysAlgorithms}.
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However, velocity-dependent (dynamical) properties will not be equivalent between the ensembles.
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This thermostat is generally only used in certain advanced applications\cite{Minary:2002:JChemPhysAlgorithms}.
The simple velocity rescaling thermostat is one of the easiest thermostats to implement; however, this thermostat is also one of the most non-physical thermostats.
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This thermostat relies on rescaling the momenta of the particles such that the simulation's instantaneous temperature exactly matches the target temperature\cite{thermostatAlgorithms2005}.
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Similarly to the Gaussian thermosat, simple velocity rescaling aims to sample the isokinetic ensemble rather than the canonical ensemble.
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However, it has been shown that the sample velocity rescaling fails to properly sample the isokinetic ensemble except in the limit of extremely small timesteps\cite{Braun:2018:arXiv:Anomalous}.
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Its usage can lead to simulation artifacts, so it is not recommended\cite{Harvey:1998:JCompChem,Braun:2018:arXiv:Anomalous}.
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However, it has been shown that the sample velocity rescaling fails to properly sample the isokinetic ensemble except in the limit of extremely small timesteps\cite{Braun:2018}.
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Its usage can lead to simulation artifacts, so it is not recommended\cite{Harvey:1998:JCompChem,Braun:2018}.
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\item\textbf{Berendsen}
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The Berendsen\cite{berendsen1984molecular} thermostat (also known as the weak coupling thermostat) is similar to the simple velocity rescaling thermostat, but instead of rescaling velocities completely and abruptly to the target kinetic energy, it includes a relaxation term to allow the system to more slowly approach the target.
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Although the Berendsen thermostat allows for temperature fluctuations, it samples neither the canonical distribution nor the isokinetic distribution.
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Its usage can lead to simulation artifacts, so it is not recommended\cite{Harvey:1998:JCompChem,Braun:2018:arXiv}.
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Its usage can lead to simulation artifacts, so it is not recommended\cite{Harvey:1998:JCompChem,Braun:2018}.
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\item\textbf{Bussi-Donadio-Parrinello (Canonical Sampling through Velocity Rescaling)}
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