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The cutting edge of research in chemical physics Each volume of the Advances in Chemical Physics series discusses aspects of the state of diverse subjects in chemical physics and related fields, with chapters written by top researchers in the field. Reviews published in Advances in Chemical Physics are typically longer than those published in journals, providing the space needed for readers to fully grasp the topic, including fundamentals, latest discoveries, applications, and emerging avenues of research. Volume 155 explores: * Modeling viral capsid assembly * Charges at aqueous interfaces, including the development of computational approaches in direct contact with the experiment * Theory and simulation advances in solute precipitate nucleation * A computational viewpoint of water in the liquid state * Construction of energy functions for lattice heteropolymer models, including efficient encodings for constraint satisfaction programming and quantum annealing Advances in Chemical Physics is ideal for introducing novices to topics in chemical physics and serves as the perfect supplement to any advanced graduate class devoted to its study. The series also provides the foundation needed for more experienced researchers to advance research studies.
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Cover
Editorial Board
Title Page
Copyright
Contributors to Volume 155
Preface to the Series
Chapter 1: Modeling Viral Capsid Assembly
I. Introduction
II. Thermodynamics of Capsid Assembly
III. Modeling Self-Assembly Dynamics and Kinetics of Empty Capsids
IV. Cargo-Containing Capsids
V. Outlook
References
Chapter 2: Charges at Aqueous Interfaces: Development of Computational Approaches in Direct Contact with Experiment
I. Introduction
II. Accounting for Polarizability Effects
III. Case Studies
IV. Outlook
References
Chapter 3: Solute Precipitate Nucleation: A Review of Theory and Simulation Advances
I. Introduction
II. Classical Nucleation Theory
III. Two-Step Nucleation Theory
IV. Simulation Challenges
V. Case Studies
VI. Closing Remarks
References
Chapter 4: Water in the Liquid State: A Computational Viewpoint
I. Introduction
II. Potential Energy Functions for Liquid Water
III. Multipoles
IV. The Water Molecule in the Pure Liquid
V. Liquid Water
VI. Aqueous Solutions
VII. Conclusions
References
Chapter 5: Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing
I. Introduction
II. The “Turn” Encoding of Self-Avoiding Walks
III. The “Diamond” Encoding of SAWs
IV. Pseudo-Boolean Function to W-SAT
V. W-SAT to Integer–Linear Programming
VI. Locality Reductions
VII. Quantum Realization
VIII. Conclusions
References
Author Index
Subject Index
End User License Agreement
Table I
Table I
Table II
Table III
Table IV
Table V
Table VI
Table VII
Table VIII
Table I
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Cover
Table of Contents
Preface to the Series
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Kurt Binder, Condensed Matter Theory Group, Institut Für Physik, Johannes Gutenberg-Universität, Mainz, Germany
William T. Coffey, Department of Electronic and Electrical Engineering, Printing House, Trinity College, Dublin, Ireland
Karl F. Freed, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA
Daan Frenkel, Department of Chemistry, Trinity College, University of Cambridge, Cambridge, UK
Pierre Gaspard, Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels, Belgium
Martin Gruebele, Departments of Physics and Chemistry, Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
Gerhard Hummer, Theoretical Biophysics Section, NIDDK-National Institutes of Health, Bethesda, Maryland, USA
Ronnie Kosloff, Department of Physical Chemistry, Institute of Chemistry and Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Israel
Ka Yee Lee, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA
Todd J. Martinez, Department of Chemistry, Photon Science, Stanford University, Stanford, California, USA
Shaul Mukamel, Department of Chemistry, School of Physical Sciences, University of California, Irvine, California, USA
Jose N. Onuchic, Department of Physics, Center for Theoretical Biological Physics, Rice University, Houston, Texas, USA
Stephen Quake, Department of Bioengineering, Stanford University, Palo Alto, California, USA
Mark Ratner, Department of Chemistry, Northwestern University, Evanston, Illinois, USA
David Reichman, Department of Chemistry, Columbia University, New York City, New York, USA
George Schatz, Department of Chemistry, Northwestern University, Evanston, Illinois, USA
Steven J. Sibener, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA
Andrei Tokmakoff, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA
Donald G. Truhlar, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, USA
John C. Tully, Department of Chemistry, Yale University, New Haven, Connecticut, USA
Volume 155
Edited by
Stuart A. Rice
Department of ChemistryandThe James Franck InstituteThe University of ChicagoChicago, Illinois
Aaron R. Dinner
Department of ChemistryandThe James Franck InstituteThe University of ChicagoChicago, Illinois
Copyright 2014 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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Library of Congress Catalog Number: 58-9935
ISBN: 978-1-118-75577-8
Vishal Agarwal, Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA
Alan Aspuru -Guzik, Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
Ryan Babbush, Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
Michael F. Hagan, Department of Physics, Brandeis University, MS057, Waltham, MA 02454, USA
Toshiko Ichiye, Department of Chemistry, Georgetown University, Washington, DC 20057-1227, USA
Pavel Jungwirth, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
William Macready, D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
Bryan O'Gorman, Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
Alejandro Perdomo -Ortiz, Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA; NASA Ames Quantum Laboratory, Ames Research Center, Moffett Field, CA 94035, USA
Baron Peters, Department of Chemical Engineering; Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106, USA
Frank Uhlig, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
Robert Vácha, National Centre for Biomolecular Research, Faculty of Science and CEITEC—Central European Institute of Technology, Masaryk University, Kamenice 5, 62500 Brno-Bohunice, Czech Republic
Advances in science often involve initial development of individual specialized fields of study within traditional disciplines followed by broadening and overlap, or even merging, of those specialized fields, leading to a blurring of the lines between traditional disciplines. The pace of that blurring has accelerated in the past few decades, and much of the important and exciting research carried out today seeks to synthesize elements from different fields of knowledge. Examples of such research areas include biophysics and studies of nanostructured materials. As the study of the forces that govern the structure and dynamics of molecular systems, chemical physics encompasses these and many other emerging research directions. Unfortunately, the flood of scientific literature has been accompanied by losses in the shared vocabulary and approaches of the traditional disciplines, and there is much pressure from scientific journals to be ever more concise in the descriptions of studies, to the point that much valuable experience, if recorded at all, is hidden in supplements and dissipated with time. These trends in science and publishing make this series, Advances in Chemical Physics, a much needed resource.
The Advances in Chemical Physics is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.
Stuart A. Rice
Aaron R. Dinner
Michael F. Hagan
Department of Physics, Brandeis University, MS057, Waltham, MA 02454, USA
Introduction
Virus Anatomies
Virus Assembly
Experiments That Characterize Capsid Assembly
Motivation for and Scope of Modeling
Thermodynamics of Capsid Assembly
Driving Forces
Law of Mass Action
Estimating Binding Energies from Experiments
Modeling Self-Assembly Dynamics and Kinetics of Empty Capsids
Timescales for Capsid Assembly
Scaling Estimates for Assembly Timescales
Lag Times
The Slow Approach to Equilibrium
Rate Equation Models for Capsid Assembly
Particle-Based Simulations of Capsid Assembly Dynamics
Conclusions from Assembly Dynamics Models
Differences Among Models
Higher
T
Numbers
Structural Stability of Different Capsid Geometries
Dynamics of Forming Icosahedral Geometries
Cargo-Containing Capsids
Structures
The Thermodynamics of Core-Controlled Assembly
Single-Stranded RNA Encapsidation
Dynamics of Assembly Around Cores
Outlook
References
The formation of a virus is a marvel of natural selection. A large number (60–10,000) of protein subunits and other components assemble into complete, reproducible structures, often with extreme fidelity, on a biologically relevant time scale. Viruses play a role in a significant portion of human diseases, as well as those of other animals, plants, and bacteria. Thus, it is of great interest to understand their formation process, with the goal of developing novel antivirus therapies that can block it, or alternatively to re-engineer viruses as drug delivery vehicles that can assemble around their cargo and disassemble to deliver it without requiring explicit external control. More fundamentally, learning the factors that make viral assembly so robust could advance the development of self-assembling nanostructured materials.
This chapter focuses on the use of theoretical and computational modeling to understand the viral assembly process. We begin with brief overviews of virus structure, assembly, and the experiments used to characterize the assembly process (Section I). We next perform an equilibrium analysis of the assembly of empty protein shells in Section II. In Section III, we then present a simple mathematical representation of the assembly process and its relevant timescales, followed by several types of modeling approaches that have been used to analyze and predict in vitro assembly kinetics. We then extend the equilibrium and dynamical approaches to consider the co-assembly of capsid proteins with RNA or other polyanionic cargoes in Section IV. Finally, we conclude with some of the important open questions and ways in which modeling can make a stronger connection with experiments.
In the interests of thoroughly examining the capsid assembly process, this chapter will not consider a number of interesting topics such as the structural dynamics of complete capsids (e.g., [1–4]), capsid swelling or maturation transitions (e.g., [5–13]), mechanical probing of assembled capsids (e.g., [10,14–24]), motor-driven packaging of double-stranded DNA (dsDNA) into assembled procapsids (e.g., [25–31], reviewed in Refs. [32–34]), or the conformations of dsDNA inside capsids (e.g., [35–37]).
Viruses consist of at least two types of components: the genome, which can be DNA or RNA and can be single or double stranded, and a protein shell called a capsid that surrounds and protects the fragile nucleic acid. Viruses vary widely in complexity, ranging from satellite tobacco mosaic virus (STMV), whose 1063-nucleotide genome encodes for two proteins including the capsid protein [38], to the giant Megavirus, with a 1,259,197 bp genome encoding for 1120 putative proteins [39], that is larger than some bacterial genomes and encased in two capsids and a lipid bilayer. Viruses such as Megavirus that acquire a lipid bilayer coating from the plasma membrane or an interior cell compartment of the host organism are known as “enveloped” viruses, whereas viruses such as STMV that present a naked protein exterior are termed “nonenveloped.” Since Harrison et al. achieved the first atomic-resolution structure of tomato bushy stunt virus (TBSV) in 1978 [40], structures of numerous virus capsids have been revealed to atomic resolution by X-ray crystallography and/or cryo-electron microscopy (cryo-EM) images. An extensive collection of virus structures can be found at the VIPERdb virus particle explorer web site () [41].
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