Special Issue "Computation in Molecular Modeling"

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Chemistry".

Deadline for manuscript submissions: closed (7 January 2018)

Special Issue Editors

Guest Editor
Prof. Dr. Luigi Delle Site

Freie Universitat Berlin, Institute of Mathematics, Berlin, Germany
Website | E-Mail
Interests: theoretical and mathematical physics of molecular simulation
Guest Editor
Prof. Dr. Christof Schuette

Freie Universitat Berlin, Department of Mathematics and Computer Science, Berlin; Zuse Institute Berlin (ZIB), Germany
Website | E-Mail
Interests: numerical analysis; scientific computing; biocomputing

Special Issue Information

Dear Colleagues,

Molecular modeling is becoming a truly interdisciplinary subject; physical principles formalized in rigorous mathematical frameworks rationalize chemical models; in turn they lead to computational tools of simulation and analysis of complex molecular systems that directly relate to experiments. The subsequent possibility of designing in silico systems with properties on demand, paves the way for tremendous discoveries, e.g., new drugs and materials, to cite a few. In this perspective, the intention of this Special Issue is to collect ideas from mathematicians, physicists and chemists where the subject of molecular modeling can be viewed from different points of view with a reciprocal gain in knowledge and potential future synergies. The topics of interest include (but are not restricted to):

- Quantum molecular models and simulation
-Classical atomistic and coarse-grained simulation
-Markov state model
-Rare events
-Non-equilibrium molecular simulation

Prof. Dr. Luigi Delle Site
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. Computation is an international peer-reviewed open access quarterly 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 350 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.

Keywords

  • Quantum Models
  • Classical Atomistic Models
  • Coarse-Grained Models
  • Molecular Simulation
  • Markov State Models
  • Rare Events
  • Non Equilibrium

Published Papers (11 papers)

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Research

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Open AccessArticle Singularly Perturbed Forward-Backward Stochastic Differential Equations: Application to the Optimal Control of Bilinear Systems
Computation 2018, 6(3), 41; https://doi.org/10.3390/computation6030041
Received: 12 February 2018 / Revised: 22 June 2018 / Accepted: 27 June 2018 / Published: 28 June 2018
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Abstract
We study linear-quadratic stochastic optimal control problems with bilinear state dependence where the underlying stochastic differential equation (SDE) has multiscale features. We show that, in the same way in which the underlying dynamics can be well approximated by a reduced-order dynamics in the
[...] Read more.
We study linear-quadratic stochastic optimal control problems with bilinear state dependence where the underlying stochastic differential equation (SDE) has multiscale features. We show that, in the same way in which the underlying dynamics can be well approximated by a reduced-order dynamics in the scale separation limit (using classical homogenization results), the associated optimal expected cost converges to an effective optimal cost in the scale separation limit. This entails that we can approximate the stochastic optimal control for the whole system by a reduced-order stochastic optimal control, which is easier to compute because of the lower dimensionality of the problem. The approach uses an equivalent formulation of the Hamilton-Jacobi-Bellman (HJB) equation, in terms of forward-backward SDEs (FBSDEs). We exploit the efficient solvability of FBSDEs via a least squares Monte Carlo algorithm and show its applicability by a suitable numerical example. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle An Energy Landscape Treatment of Decoy Selection in Template-Free Protein Structure Prediction
Computation 2018, 6(2), 39; https://doi.org/10.3390/computation6020039
Received: 22 April 2018 / Revised: 11 June 2018 / Accepted: 14 June 2018 / Published: 19 June 2018
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Abstract
The energy landscape, which organizes microstates by energies, has shed light on many cellular processes governed by dynamic biological macromolecules leveraging their structural dynamics to regulate interactions with molecular partners. In particular, the protein energy landscape has been central to understanding the relationship
[...] Read more.
The energy landscape, which organizes microstates by energies, has shed light on many cellular processes governed by dynamic biological macromolecules leveraging their structural dynamics to regulate interactions with molecular partners. In particular, the protein energy landscape has been central to understanding the relationship between protein structure, dynamics, and function. The landscape view, however, remains underutilized in an important problem in protein modeling, decoy selection in template-free protein structure prediction. Given the amino-acid sequence of a protein, template-free methods compute thousands of structures, known as decoys, as part of an optimization process that seeks minima of an energy function. Selecting biologically-active/native structures from the computed decoys remains challenging. Research has shown that energy is an unreliable indicator of nativeness. In this paper, we advocate that, while comparison of energies is not informative for structures that already populate minima of an energy function, the landscape view exposes the overall organization of generated decoys. As we demonstrate, such organization highlights macrostates that contain native decoys. We present two different computational approaches to extracting such organization and demonstrate through the presented findings that a landscape-driven treatment is promising in furthering research on decoy selection. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle Testing Convergence of Different Free-Energy Methods in a Simple Analytical System with Hidden Barriers
Computation 2018, 6(2), 27; https://doi.org/10.3390/computation6020027
Received: 24 January 2018 / Revised: 26 February 2018 / Accepted: 19 March 2018 / Published: 21 March 2018
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Abstract
In this work, we study the influence of hidden barriers on the convergence behavior of three free-energy calculation methods: well-tempered metadynamics (WTMD), adaptive-biasing forces (ABF), and on-the-fly parameterization (OTFP). We construct a simple two-dimensional potential-energy surfaces (PES) that allows for an exact analytical
[...] Read more.
In this work, we study the influence of hidden barriers on the convergence behavior of three free-energy calculation methods: well-tempered metadynamics (WTMD), adaptive-biasing forces (ABF), and on-the-fly parameterization (OTFP). We construct a simple two-dimensional potential-energy surfaces (PES) that allows for an exact analytical result for the free-energy in any one-dimensional order parameter. Then we chose different CV definitions and PES parameters to create three different systems with increasing sampling challenges. We find that all three methods are not greatly affected by the hidden-barriers in the simplest case considered. The adaptive sampling methods show faster sampling while the auxiliary high-friction requirement of OTFP makes it slower for this case. However, a slight change in the CV definition has a strong impact in the ABF and WTMD performance, illustrating the importance of choosing suitable collective variables. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle Ionic Liquids Treated within the Grand Canonical Adaptive Resolution Molecular Dynamics Technique
Computation 2018, 6(1), 23; https://doi.org/10.3390/computation6010023
Received: 19 January 2018 / Revised: 6 February 2018 / Accepted: 23 February 2018 / Published: 28 February 2018
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Abstract
We use the Grand Canonical Adaptive Resolution Molecular Dynamics Technique (GC-AdResS) to examine the essential degrees of freedom necessary for reproducing the structural properties of the imidazolium class of ionic liquids. In this technique, the atomistic details are treated as an open sub-region
[...] Read more.
We use the Grand Canonical Adaptive Resolution Molecular Dynamics Technique (GC-AdResS) to examine the essential degrees of freedom necessary for reproducing the structural properties of the imidazolium class of ionic liquids. In this technique, the atomistic details are treated as an open sub-region of the system while the surrounding environment is modelled as a generic coarse-grained model. We systematically characterize the spatial quantities such as intramolecular, intermolecular radial distribution functions, other structural and orientational properties of ILs. The spatial quantities computed in an open sub-region of the system are in excellent agreement with the equivalent quantities calculated in a full atomistic simulation, suggesting that the atomistic degrees of freedom outside the sub-region are negligible. The size of the sub-region considered in this study is 2 nm, which is essentially the size of a few ions. Insight from the study suggests that a higher degree of spatial locality seems to play a crucial role in characterizing the properties of imidazolium based ionic liquids. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics
Computation 2018, 6(1), 22; https://doi.org/10.3390/computation6010022
Received: 12 January 2018 / Revised: 15 February 2018 / Accepted: 23 February 2018 / Published: 26 February 2018
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Abstract
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us noticing it,
[...] Read more.
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us noticing it, due to insufficient observations; and it even might be a system failing to admit an equilibrium distribution at all. We review some of the approaches that model the effective statistical behavior of equilibrium and non-equilibrium dynamical systems, and show that both cases can be considered under the unified framework of optimal low-rank approximation of so-called transfer operators. Particular attention is given to the connection between these methods, Markov state models, and the concept of metastability, further to the estimation of such reduced order models from finite simulation data. All these topics bear an important role in, e.g., molecular dynamics, where Markov state models are often and successfully utilized, and which is the main motivating application in this paper. We illustrate our considerations by numerical examples. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle The Role of Conformational Entropy in the Determination of Structural-Kinetic Relationships for Helix-Coil Transitions
Computation 2018, 6(1), 21; https://doi.org/10.3390/computation6010021
Received: 21 December 2017 / Revised: 13 February 2018 / Accepted: 16 February 2018 / Published: 26 February 2018
Cited by 1 | PDF Full-text (1081 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Coarse-grained molecular simulation models can provide significant insight into the complex behavior of protein systems, but suffer from an inherently distorted description of dynamical properties. We recently demonstrated that, for a heptapeptide of alanine residues, the structural and kinetic properties of a simulation
[...] Read more.
Coarse-grained molecular simulation models can provide significant insight into the complex behavior of protein systems, but suffer from an inherently distorted description of dynamical properties. We recently demonstrated that, for a heptapeptide of alanine residues, the structural and kinetic properties of a simulation model are linked in a rather simple way, given a certain level of physics present in the model. In this work, we extend these findings to a longer peptide, for which the representation of configuration space in terms of a full enumeration of sequences of helical/coil states along the peptide backbone is impractical. We verify the structural-kinetic relationships by scanning the parameter space of a simple native-biased model and then employ a distinct transferable model to validate and generalize the conclusions. Our results further demonstrate the validity of the previous findings, while clarifying the role of conformational entropy in the determination of the structural-kinetic relationships. More specifically, while the global, long timescale kinetic properties of a particular class of models with varying energetic parameters but approximately fixed conformational entropy are determined by the overarching structural features of the ensemble, a shift in these kinetic observables occurs for models with a distinct representation of steric interactions. At the same time, the relationship between structure and more local, faster kinetic properties is not affected by varying the conformational entropy of the model. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle Implications of PCCA+ in Molecular Simulation
Computation 2018, 6(1), 20; https://doi.org/10.3390/computation6010020
Received: 8 January 2018 / Revised: 16 February 2018 / Accepted: 16 February 2018 / Published: 19 February 2018
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Abstract
Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., ‘bound’ vs. ‘unbound’), although the process itself takes place in a continuous space. In
[...] Read more.
Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., ‘bound’ vs. ‘unbound’), although the process itself takes place in a continuous space. In this context, the formula χ = X A connects the micro-dynamics of the molecular system to its macro-dynamics. χ can be understood as a clustering of micro-states of a molecular system into a few macro-states. X is a basis of an invariant subspace of a transfer operator describing the micro-dynamics of the system. The formula claims that there is an unknown linear relation A between these two objects. With the aid of this formula we can understand rebinding effects, the electron flux in pericyclic reactions, and systematic changes of binding rates in kinetic ITC experiments. We can also analyze sequential spectroscopy experiments and rare event systems more easily. This article provides an explanation of the formula and an overview of some of its consequences. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle Multiresolution Modeling of Semidilute Polymer Solutions: Coarse-Graining Using Wavelet-Accelerated Monte Carlo
Computation 2017, 5(4), 44; https://doi.org/10.3390/computation5040044
Received: 21 August 2017 / Revised: 20 September 2017 / Accepted: 25 September 2017 / Published: 28 September 2017
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Abstract
We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations.
[...] Read more.
We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations. Previously, it was applied to simulations examining the structure of individual polymer chains in solution using up to four levels of coarse-graining (Ismail et al., J. Chem. Phys., 2005, 122, 234901 and Ismail et al., J. Chem. Phys., 2005, 122, 234902), recovering the correct scaling behavior in the coarse-grained representation. In the present work, we extend this method to the study of polymer solutions, deriving the bonded and non-bonded potentials between coarse-grained superatoms from the single chain statistics. A universal scaling function is obtained, which does not require recalculation of the potentials as the scale of the system is changed. To model semi-dilute polymer solutions, we assume the intermolecular potential between the coarse-grained beads to be equal to the non-bonded potential, which is a reasonable approximation in the case of semidilute systems. Thus, a minimal input of microscopic data is required for simulating the systems at the mesoscopic scale. We show that coarse-grained polymer solutions can reproduce results obtained from the more detailed atomistic system without a significant loss of accuracy. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Review

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Open AccessFeature PaperReview Using the Maximum Entropy Principle to Combine Simulations and Solution Experiments
Computation 2018, 6(1), 15; https://doi.org/10.3390/computation6010015
Received: 15 January 2018 / Revised: 31 January 2018 / Accepted: 1 February 2018 / Published: 6 February 2018
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Abstract
Molecular dynamics (MD) simulations allow the investigation of the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with
[...] Read more.
Molecular dynamics (MD) simulations allow the investigation of the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with experimental data obtained from ensemble measurements. We review here the approaches that can be used to combine MD and experiment under the guidance of the maximum entropy principle. We mostly focus on methods based on Lagrangian multipliers, either implemented as reweighting of existing simulations or through an on-the-fly optimization. We discuss how errors in the experimental data can be modeled and accounted for. Finally, we use simple model systems to illustrate the typical difficulties arising when applying these methods. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessFeature PaperReview Holonomic Constraints: A Case for Statistical Mechanics of Non-Hamiltonian Systems
Computation 2018, 6(1), 11; https://doi.org/10.3390/computation6010011
Received: 8 January 2018 / Revised: 25 January 2018 / Accepted: 25 January 2018 / Published: 1 February 2018
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Abstract
A dynamical system submitted to holonomic constraints is Hamiltonian only if considered in the reduced phase space of its generalized coordinates and momenta, which need to be defined ad hoc in each particular case. However, specially in molecular simulations, where the number of
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A dynamical system submitted to holonomic constraints is Hamiltonian only if considered in the reduced phase space of its generalized coordinates and momenta, which need to be defined ad hoc in each particular case. However, specially in molecular simulations, where the number of degrees of freedom is exceedingly high, the representation in generalized coordinates is completely unsuitable, although conceptually unavoidable, to provide a rigorous description of its evolution and statistical properties. In this paper, we first review the state of the art of the numerical approach that defines the way to conserve exactly the constraint conditions (by an algorithm universally known as SHAKE) and permits integrating the equations of motion directly in the phase space of the natural Cartesian coordinates and momenta of the system. We then discuss in detail SHAKE numerical implementations in the notable cases of Verlet and velocity-Verlet algorithms. After discussing in the same framework how constraints modify the properties of the equilibrium ensemble, we show how, at the price of moving to a dynamical system no more (directly) Hamiltonian, it is possible to provide a direct interpretation of the dynamical system and so derive its Statistical Mechanics both at equilibrium and in non-equilibrium conditions. To achieve that, we generalize the statistical treatment to systems no longer conserving the phase space volume (equivalently, we introduce a non-Euclidean invariant measure in phase space) and derive a generalized Liouville equation describing the ensemble even out of equilibrium. As a result, we can extend the response theory of Kubo (linear and nonlinear) to systems subjected to constraints. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
Open AccessReview Molecular Dynamics Simulation of High Density DNA Arrays
Received: 15 December 2017 / Revised: 4 January 2018 / Accepted: 5 January 2018 / Published: 8 January 2018
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Abstract
Densely packed DNA arrays exhibit hexagonal and orthorhombic local packings, as well as a weakly first order transition between them. While we have some understanding of the interactions between DNA molecules in aqueous ionic solutions, the structural details of its ordered phases and
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Densely packed DNA arrays exhibit hexagonal and orthorhombic local packings, as well as a weakly first order transition between them. While we have some understanding of the interactions between DNA molecules in aqueous ionic solutions, the structural details of its ordered phases and the mechanism governing the respective phase transitions between them remains less well understood. Since at high DNA densities, i.e., small interaxial spacings, one can neither neglect the atomic details of the interacting macromolecular surfaces nor the atomic details of the intervening ionic solution, the atomistic resolution is a sine qua non to properly describe and analyze the interactions between DNA molecules. In fact, in order to properly understand the details of the observed osmotic equation of state, one needs to implement multiple levels of organization, spanning the range from the molecular order of DNA itself, the possible ordering of counterions, and then all the way to the induced molecular ordering of the aqueous solvent, all coupled together by electrostatic, steric, thermal and direct hydrogen-bonding interactions. Multiscale simulations therefore appear as singularly suited to connect the microscopic details of this system with its macroscopic thermodynamic behavior. We review the details of the simulation of dense atomistically resolved DNA arrays with different packing symmetries and the ensuing osmotic equation of state obtained by enclosing a DNA array in a monovalent salt and multivalent (spermidine) counterions within a solvent permeable membrane, mimicking the behavior of DNA arrays subjected to external osmotic stress. By varying the DNA density, the local packing symmetry, and the counterion type, we are able to analyze the osmotic equation of state together with the full structural characterization of the DNA subphase, the counterion distribution and the solvent structural order in terms of its different order parameters and consequently identify the most important contribution to the DNA-DNA interactions at high DNA densities. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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