TRANSITION PATH SAMPLING: Throwing Ropes Over Rough Mountain Passes, in the Dark
01 Jan 2002-Annual Review of Physical Chemistry (Annual Reviews 4139 El Camino Way, P.O. Box 10139, Palo Alto, CA 94303-0139, USA)-Vol. 53, Iss: 1, pp 291-318
TL;DR: This article reviews the concepts and methods of transition path sampling, which allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states.
Abstract: This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states. Based upon a statistical mechanics of trajectory space, they provide a perspective with which time dependent phenomena, even for systems driven far from equilibrium, can be examined with the same types of importance sampling tools that in the past have been applied so successfully to static equilibrium properties.
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TL;DR: An overview of the CHARMM program as it exists today is provided with an emphasis on developments since the publication of the original CHARMM article in 1983.
Abstract: CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.
7,035 citations
TL;DR: To model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region and an MM treatment for the surroundings, enabling the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.
Abstract: Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.
2,172 citations
1,800 citations
TL;DR: The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
Abstract: The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.
1,695 citations
Cites background from "TRANSITION PATH SAMPLING: Throwing ..."
...It is of central importance in the medical sciences, and also has a rich mathematical structure; see Borcea (2002) and Uhlmann (2009) for reviews. Inverse problems for the heat equation, the subject of Section 3.5, are widely studied. See, for example, the cited literature in Beck, Blackwell and Clair (2005) and Engl et al. (1996). An early formulation of this problem in a Bayesian framework appears in Franklin (1970). We study applications to fluid dynamics in Section 3.6: the subject known as data assimilation. Kalnay (2003) and Bennett (2002) survey inverse problems in fluid mechanics from the perspective of weather prediction and oceanography respectively; see also Apte, Jones, Stuart and Voss (2008b), Lorenc (1986), Ide, Kuznetsov and Jones (2002), Kuznetsov, Ide and Jones (2003), Nichols (2003a) and Nodet (2006) for representative examples, some closely related to the specific model problems that we study in this article....
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...It is of central importance in the medical sciences, and also has a rich mathematical structure; see Borcea (2002) and Uhlmann (2009) for reviews. Inverse problems for the heat equation, the subject of Section 3.5, are widely studied. See, for example, the cited literature in Beck, Blackwell and Clair (2005) and Engl et al....
[...]
...It is of central importance in the medical sciences, and also has a rich mathematical structure; see Borcea (2002) and Uhlmann (2009) for reviews. Inverse problems for the heat equation, the subject of Section 3.5, are widely studied. See, for example, the cited literature in Beck, Blackwell and Clair (2005) and Engl et al. (1996). An early formulation of this problem in a Bayesian framework appears in Franklin (1970). We study applications to fluid dynamics in Section 3....
[...]
...It is of central importance in the medical sciences, and also has a rich mathematical structure; see Borcea (2002) and Uhlmann (2009) for reviews. Inverse problems for the heat equation, the subject of Section 3.5, are widely studied. See, for example, the cited literature in Beck, Blackwell and Clair (2005) and Engl et al. (1996). An early formulation of this problem in a Bayesian framework appears in Franklin (1970)....
[...]
...It is of central importance in the medical sciences, and also has a rich mathematical structure; see Borcea (2002) and Uhlmann (2009) for reviews....
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TL;DR: This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool, and covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role.
Abstract: The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations.
Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time.
Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function.
This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized.
1.1. Historical Background
MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics.
As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today.
The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly.
The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1.
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Figure 1
Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.
999 citations
References
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Abstract: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.
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TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Abstract: Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.
13,652 citations
TL;DR: In this article, a unified scheme combining molecular dynamics and density-functional theory is presented, which makes possible the simulation of both covalently bonded and metallic systems and permits the application of density functional theory to much larger systems than previously feasible.
Abstract: We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework.
8,852 citations
Book•
01 Jan 2001
TL;DR: In this paper, the physics behind molecular simulation for materials science is explained, and the implementation of simulation methods is illustrated in pseudocodes and their practical use in the case studies used in the text.
Abstract: From the Publisher:
This book explains the physics behind the "recipes" of molecular simulation for materials science. Computer simulators are continuously confronted with questions concerning the choice of a particular technique for a given application. Since a wide variety of computational tools exists, the choice of technique requires a good understanding of the basic principles. More importantly, such understanding may greatly improve the efficiency of a simulation program. The implementation of simulation methods is illustrated in pseudocodes and their practical use in the case studies used in the text. Examples are included that highlight current applications, and the codes of the case studies are available on the World Wide Web. No prior knowledge of computer simulation is assumed.
6,901 citations
6,232 citations