In 2002, Thomas Simonson, Georgios Archontis and I published an article entitled, ‘Free Energy Simulations Come of Age: Protein-Ligand Recognition’.[Citation1]) ‘Coming of Age’, of course, means different things in different contexts. We meant that it was possible to do free energy simulations that gave meaningful results for ligand binding. Over the intervening 13 years, developments have taken place that have made possible significantly improved free energy simulations. Moreover, they have become more widely used, if for no other reason, than for the imprimatur from the 2013 Nobel Prize in Chemistry.[Citation2]
Computers of significantly increased power have played an essential role in the improvements. Interestingly, 2015 is the 50th anniversary of Moore’s Law,[Citation3] which stated that computers double in speed every years based on data for only four years. When asked about the Law this year, Moore said that he thought the doubling in speed might continue for 10 years. His focus was on the transitory industry, and it amazed him that the Law seemed to be still valid today. In a recent paper, Michele Vendruscolo and Christopher Dobson [Citation4] described a Moore’s-like Law for biomolecular simulations, which stated that their speed appeared to double every year. Given that, the computer power accessible to free energy simulations today is nearly 10,000 times greater than that in 2002. Now that microseconds, and even millisecond, simulations are becoming relatively routine, clear improvements in the statistical precision of free energy simulations are possible. Most of the papers in the special issue take advantage of this aspect, but it is not their focus. Instead, the papers are primarily concerned with developments in free energy methodology and its applications.
What has been included in the issue represents only a small, but interesting selection, from the field of free energy simulations that is continuing its phenomenal growth. My comments in this preface are made to aid the reader in choosing the papers of particular interest to him or her; they should not imply that I approve of or agree with everything that is presented.
There are two complementary reviews that provide an overview of the present state of free energy simulations. The one by Yinglong Miao and J. Andrew McCammon reviews the problems of obtaining sampling of the configuration space to obtain sufficiently accurate and precise results and the range of methods that are in use to try to overcome this problem. The fact that there are so many methods still being employed is indicative of the fact that the problem has not been solved, even with the long simulations that are now possible. The review by X. Lu, D. Fang, Y. Okamoto, V. Ovchinnikov and Q. Cui is concerned with QM/MM free energy simulations, which face even greater challenges in obtaining accurate results because of the higher computational cost of the QM portion. The review focuses on recent developments that are giving improved free energy values, though problems still remain.
The paper by Cheng Zhang, Chun-Liang Loi and B. Montgomery Pettitt complements the review of Miao and McCammon by focusing on the widely used weighted histogram method (WHAM). It describes a direct inversion approach to solving the WHAM equation, which is illustrated with several applications, including a study of the convergence of the total potential energy distribution of a small protein, the villin headpiece, in aqueous solution.
Thomas Simonson and Benoit Roux review methods for calculating the contribution of electrostatic interactions to the free energy. They point out certain subtleties hidden in the methods currently in use with periodic boundary conditions, and describe approaches that, if employed correctly, give meaningful results for the electrostatic free energy.
A didactic review of models for recovering the free energy landscape of conformational transitions from single-molecule pulling experiments is presented by Gaurav Arya. It is a unified treatment, including the classical Bell and Kramers theories, as well as the important contributions of Dudko, Hummer and Szabo in this area. The recent treatments of stiffness and ‘handles’ in single-molecule force spectroscopy are also described. The paper ends with a brief description of the role of molecular and Brownian dynamics in this area.
Stephen Williams focuses on the difficult problem of computing the rate at which rare events occur under non-equilibrium conditions that cannot be treated by classical transition state theory and describes some of its modern implementations. He then develops a new formalism to attack this problem, as exemplified by the mobility across the liquid–liquid interfaces of two immiscible liquids and presents the results obtained with molecular dynamic simulations for such a system.
The paper by Jamie Parkinson, Gabriel Lau and Ian Ford is also concerned with the simulation of a non-equilibrium system by molecular dynamics. Specifically, they consider the calculation of the free energy of formation of clusters of sulphuric acid and water molecules in a molecular vapour by guided disassembly trajectories analyzed with the Jarzynski relation. The paper is written very clearly so that it can serve as a useful introduction to this rather complicated field.
Lamberto Rondoni and Antonella Verderosa provide a pedagogical review of approaches to understand the relation between macroscopic irreversibility and microscopic reversibility, a subject of long-standing interest in statistical physics. They emphasise the use of fluctuation relations in obtaining insights into this question and discuss the role of non-equilibrium molecular dynamics to elucidate small system properties, though no simulations are reported.
The interesting paper by Pierre Ronceray and Peter Harrowell is somewhat of an ‘outlier’ in this special issue since it is not concerned with molecular dynamics simulations and their applications. What it does do is to describe formalism for the free energy of a liquid state in terms of a set of favoured local structures and their interactions using a high-temperature expansion for the system. A comparison of the present method with Monte Carlo estimates of the freezing point of model systems is encouraging since it shows quite good agreement.
Chemistry Department, Harvard University, USA
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References
- Simonson T, Archontis G, Karplus M. Free energy simulations come of age: Protein-ligand recognition. Acc. Chem. Res. 2002;35:430–437.10.1021/ar010030m
- Karplus M. Development of multiscale models for complex chemical systems: from H+H2 to biomolecules (Nobel Lecture). Angew. Chem. Int. Ed. 2014;53:2–16.
- Moore GM. Electronics. 1965;114–1178.
- Vendruscolo M, Dobson CM. Curr. Biol. 2010;21:R68–R70.