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Special Issue "Understanding Molecular Dynamics via Stochastic Processes"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 30 September 2017

Special Issue Editors

Guest Editor
Prof. Dr. Giovanni Ciccotti

University of Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma, Italy
Website | E-Mail
Interests: methods in molecular dynamics simulation of systems of statistical mechanical interest; equilibrium and non equilibrium molecular dynamics; rare events; computer simulation of complex molecular systems
Guest Editor
Prof. Dr. Mauro Ferrario

University of Modena and Reggio Emilia, Via G. Campi 213/A, 41100 Modena Italy
Website | E-Mail
Interests: molecular dynamics simulation of condensed matter systems; solvation in h-bonded liquids; friction at the nanoscale
Guest Editor
Prof. Dr. Christof Schuette

Freie Universität Berlin, ZIB, Takustraße 7, 14195 Berlin, Germany
Website | E-Mail
Interests: rare events statistics in molecular dynamics; coarse graining in molecular dynamics; conformation dynamics

Special Issue Information

Dear Colleagues,

Contrary to what the name seems to suggest, Molecular Dynamics (MD) is not only about generating a dynamical trajectory of a system of molecules, but also, and foremost, about understanding the statistical properties of this trajectory. As a result, to make sense of this solution is to extract its main statistical features, which must be done within the probabilistic framework of Statistical Mechanics. Pushing this viewpoint one step further, an MD trajectory can be thought of not so much as a small piece of the actual trajectory of a realistic system of molecules, but rather as a sampling device for the statistical mechanics properties of this system.

When speaking about equilibrium quantities like free energy, etc., the probabilistic interpretation of an MD trajectory as a sampling device has long be recognized, and so has its computational advantages. One is that the numerical accuracy of an MD trajectory should be analyzed in terms of the statistics it produces rather than by pathwise comparison with an actual solution, which simplifies matters. A second advantage is that the sampling performances can be improved by fiddling with MD dynamics as long as this does not affect the statistical properties one is aiming at. This is why, for example, Monte Carlo is used as a perfectly valid alternative to MD to compute equilibrium quantities: from the present perspective, the two approaches are not so different in spirit.

Contrary to a widespread opinion in the community of practitioners, there is no reason to restrict this type of approach to the computation of the standard equilibrium quantities of Statistical Mechanics: the same philosophy in which MD is fully integrated within a probabilistic perspective can be applied to understand dynamical properties such as correlation functions, transport coefficients, pathways and rates of rare events, etc. In this context, also, identifying the right statistical quantities first, then using MD or whichever modification thereof to sample them can prove valuable. However, developing the right probabilistic framework for the study of dynamical phenomena, such as rare events, is a formidable challenge. This part of Statistical Mechanics is still much less developed. It also requires more sophisticated tools from Stochastic Processes Theory, for dynamical properties are multiple- rather than single-time statistical properties of the systems, i.e., one must deal with a stochastic process rather than with random variables. As a result the probability distributions relevant to dynamical phenomena are more complicated objects, often not even readily available. However, establishing what these distributions are and how to use MD as a tool to sample them efficiently is the right way to go. The steady growth in computing power as well as the development of various computational tricks may permit to generate ever longer trajectories in ever bigger systems; however bare trajectories have very little use without the right probabilistic framework to under- stand their meaning and looking at them in their gory details may even be more confusing than helpful.

It is in this spirit that, in this Special Issue, we would like to collect papers focusing, with a pedagogical aim, on the importance of stochastic process modeling, to understand and put on solid basis classical statistical mechanics and MD simulations, showing that not brute force MD but intelligent use of probability will give us the possibility to solve the most challenging problems when modeling physical, chemical and biological processes on all space and time scales. To comply with this goal we have invited a group of highly qualified researchers working along these lines to produce some useful glimpses of the ongoing process.

Planned Papers*

  • Ron Elber, Juan M. Bello-Rivas, Piao Ma, Alfredo Cardenas and Arman Fathizadeh, Calculating isocommittor surfaces as optimal reaction coordinates with milestoning
  • Anastasia S. Georgiou, Juan M. Bello-Rivas, C. William Gear, Hau-Tieng Wu, Eliodoro Chiavazzo and Ioannis G. Kevrekidis, An exploration algorithm for stochastic simulators driven by energy gradients
  • Wei Zhang and Christof Schütte, Reliable approximation of long relaxation timescales in molecular dynamics.
  • Carsten Hartmann, Susana Gomes and Grigorios A. Pavliotis, On the linear response of a system of infinitely many randomly perturbed oscillators
  • Josh Fass, Gavin E. Crooks, and John D. Chodera, Comparing the efficiencies of Langevin integrators, force splittings, and mass repartitioning schemes for biomolecular simulation
  • Carsten Hartmann, Christof Schütte and Wei Zhang, Variational characterisation of free energy: theory and algorithms
  • Mattias Sachs, Vincent Danos and Ben Leimkuhler, Adaptive Brownian Dynamics
  • Robert Jack, Geometrical properties of stochastic coarse-grained models of dynamical systems, and their implications for rare events.
  • Robert Skeel and Youhan Fang, Comparing samplers (and assessing samples)

[*The above list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review]

Prof. Dr. Giovanni Ciccotti
Prof. Dr. Mauro Ferrario
Prof. Dr. Christof Schuette
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

Open AccessArticle Ion Hopping and Constrained Li Diffusion Pathways in the Superionic State of Antifluorite Li2O
Entropy 2017, 19(5), 227; doi:10.3390/e19050227
Received: 21 March 2017 / Revised: 25 April 2017 / Accepted: 15 May 2017 / Published: 18 May 2017
PDF Full-text (2600 KB) | HTML Full-text | XML Full-text
Abstract
Li2O belongs to the family of antifluorites that show superionic behavior at high temperatures. While some of the superionic characteristics of Li2O are well-known, the mechanistic details of ionic conduction processes are somewhat nebulous. In this work, we first
[...] Read more.
Li2O belongs to the family of antifluorites that show superionic behavior at high temperatures. While some of the superionic characteristics of Li2O are well-known, the mechanistic details of ionic conduction processes are somewhat nebulous. In this work, we first establish an onset of superionic conduction that is emblematic of a gradual disordering process among the Li ions at a characteristic temperature Tα (~1000 K) using reported neutron diffraction data and atomistic simulations. In the superionic state, the Li ions are observed to portray dynamic disorder by hopping between the tetrahedral lattice sites. We then show that string-like ionic diffusion pathways are established among the Li ions in the superionic state. The diffusivity of these dynamical string-like structures, which have a finite lifetime, shows a remarkable correlation to the bulk diffusivity of the system. Full article
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
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Open AccessArticle Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with Milestoning
Entropy 2017, 19(5), 219; doi:10.3390/e19050219
Received: 17 February 2017 / Revised: 24 April 2017 / Accepted: 8 May 2017 / Published: 11 May 2017
PDF Full-text (2983 KB) | HTML Full-text | XML Full-text
Abstract
Reaction coordinates are vital tools for qualitative and quantitative analysis of molecular processes. They provide a simple picture of reaction progress and essential input for calculations of free energies and rates. Iso-committor surfaces are considered the optimal reaction coordinate. We present an algorithm
[...] Read more.
Reaction coordinates are vital tools for qualitative and quantitative analysis of molecular processes. They provide a simple picture of reaction progress and essential input for calculations of free energies and rates. Iso-committor surfaces are considered the optimal reaction coordinate. We present an algorithm to compute efficiently a sequence of isocommittor surfaces. These surfaces are considered an optimal reaction coordinate. The algorithm analyzes Milestoning results to determine the committor function. It requires only the transition probabilities between the milestones, and not transition times. We discuss the following numerical examples: (i) a transition in the Mueller potential; (ii) a conformational change of a solvated peptide; and (iii) cholesterol aggregation in membranes. Full article
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
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Figure 1

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