Simulations Say Viral Genome Lengths are Optimal for Capsid Assembly

Viruses are infectious agents made up of proteins and a genome made of DNA or RNA. Upon infecting a host cell, viruses hijack the cell’s gene expression machinery and force it to produce copies of the viral genome and proteins, which then assemble into new viruses that can eventually infect other host cells. Because assembly is an essential step in the viral life cycle, understanding how this process occurs could significantly advance the fight against viral diseases.

In many viral families, a protein shell called a capsid forms around the viral genome during the assembly process. Capsids can also assemble around nucleic acids in solution, indicating that a host cell is not required for their formation. Since capsid proteins are positively charged, and nucleic acids are negatively charged, electrostatic interactions between the two are thought to be important in capsid assembly. Current questions of interest are how structural features of the viral genome affect assembly, and why the negative charge on viral genomes is actually far greater than the positive charge on capsids. These questions are difficult to address experimentally because most of the intermediates that form during virus assembly are too short-lived to be imaged.

Snapshots from a computer simulation in which model capsid subunits (blue) assemble around a linear, negatively charged polymer (red). Positive charges on the capsid proteins are shown in yellow.

In a new paper in eLife, Brandeis postdoc Jason Perlmutter, Physics grad student Cong Qiao, and Associate Professor Michael Hagan have used state of the art computational methods and advances in graphical processing units (on our High Performance Computing cluster) to produce the most realistic model of capsid assembly to date. They showed that the stability of the complex formed between the nucleic acid and the capsid depends on the length of the viral genome. Yield was highest for genomes within a certain range of lengths, and capsids that assembled around longer or shorter genomes tended to be malformed.

Perlmutter et al. also explored how structural features of the virus — including base-pairing between viral nucleic acids, and the size and charge of the capsid — determine the optimal length of the viral genome. When they included structural data from real viruses in their simulations and predicted the optimal lengths for the viral genome, the results were very similar to those seen in existing viruses. This indicates that the structure of the viral genome has been optimized to promote packaging into capsids. Understanding this relationship between structure and packaging will make it easier to develop antiviral agents that thwart or misdirect virus assembly, and could aid the redesign of viruses for use in gene therapy and drug delivery.

Perlmutter JD, Qiao C, Hagan MF. Viral genome structures are optimal for capsid assembly. eLife 2013;2:e00632

Easy Come, Easy Go

Whereas the diffusion of water molecules in the bulk liquid depends entirely on breaking hydrogen bonds, the diffusion of proton defects (i.e., an excess proton in acid or a proton deficit in base) is expedited by proton hopping across hydrogen bonds.  The details of this process are well understood in acid, and the process in base was believed to occur in analogous fashion. However, theoretical studies of hydroxide have given highly divergent predictions of solvation structures and diffusion rates, depending on the chosen recipe for such simulations: some predicted the traditionally expected solvation structures and some predicted the experimentally observed diffusion trends, but none do both. Now Seyit Kale, a graduate student in Prof. Judith Herzfeld’s group, has studied proton defects using the group’s recently developed LEWIS force field.^[1] The LEWIS simulations obtain the correct relative diffusion rates with hydroxide solvation structures that are analogous to those of hydronium,^[2] thereby supporting the traditional picture of the “proton hole”. The authors also catch and characterize proton transfer events, identifying similar “special pairs”^[3] as the intermediates in both cases (see figure).

[1]       S. Kale, J. Herzfeld, J. Chem. Phys. 2012, 136, 084109.
[2]       S. Kale, J. Herzfeld, Angew. Chem. Int. Edit. 2012 in press. DOI: 10.1002/anie.201203568.
[3]       O. Markovitch, H. Chen, S. Izvekov, F. Paesani, G. A. Voth, N. Agmon, J. Phys. Chem. B. 2008, 112, 9456-9466.

 

Why nanorods assemble

In a recent paper in Phys. Rev. E, Brandeis postdoc Yasheng Yang and Assistant Professor of Physics Michael Hagan developed a theory to describe the assembly behavior of colloidal rods (i.e. nanorods) in the presence of inert polymer (which induces attractions between the nanorods). The nanorods assemble into several kinds of structures, including colloidal membranes, which  are two dimensional membrane-like structures composed of a one rod-length thick monolayer of aligned rods.  The theory shows that colloidal membranes are stabilized against stacking on top of each other by an entropic force arising from protrusions of rods from the membranes and that there is a critical aspect ratio (rod length/rod diameter) below which membranes are never stable. Understanding the forces that stabilize colloidal membranes is of practical importance since these structures could enable the manufacture of inexpensive and easily scalable optoelectronic devices. This work was part of a collaboration with the experimental lab of Zvonimir Dogic at Brandeis, where colloidal membranes are developed and studied.

Yang YS, Hagan MF. Theoretical calculation of the phase behavior of colloidal membranes. Phys Rev E. 2011;84(5).

Escaping the Lattice

The next best thing to seeing real atoms is to mimic them in silico: we assign interactions between the atoms and then — pouf –They’re alive!

The number of particles in a visible sample is on the order of Avogadro’s constant, say ~10²³, whereas a fairly muscular computer can only follow ~10⁵-10⁷ atoms at a time. To compensate, computational scientists typically replicate their simulation boxes infinitely in space. This creates a quandary for calculating forces across replication boxes. The simplest option, which is to neglect forces beyond a chosen cut-off, suffices for many interactions, is too crude for the particularly long-range interactions that occur between charges. To accurately account for these interactions, it is customary to use a clever 90-year-old (!) technique, called the Ewald sum.(1)

The problem with the Ewald sum is that it requires imposing a long-range periodicity that is inappropriately short for macromolecules.(2) To avoid artifacts, a number of alternatives have been suggested. One intuitive approach, called “force shifting”, smooths the interaction energy and its first derivative (the force) at the chosen cutoff. However, this creates new artifacts (see figure) when particles have very large or varying charges, as in some ionic liquids. Brandeis scientists Seyit Kale and Judith Herzfeld, have found that this problem can be solved by also smoothing the second derivative of the interaction energy (the acceleration).(3)  This approach performs virtually as well as the Ewald sum in a new reactive force field that they have been developing (see figure).

The neighbor frequencies for bulk water calculated with force shifting at a cutoff of 9 Å (red) and 12 Å (magenta) versus with the authors’ new approach at a 9 Å cutoff (blue) and the Ewald sum (black). The blue and black curves are virtually the same while the red and magenta curves contain artifacts. The inset shows a representation of a water molecule from the force field that the authors are developing.

1. Ewald P (1921) The Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 369: 253-287.
2. Hunenberger PH, McCammon JA (1999) Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: A continuum electrostatics study. Biophys. Chem. 78: 69-88.
3. Kale S, Herzfeld J (2011) Pairwise Long-range Compensation for Strongly Ionic Systems. J. Chem. Theory Comput. 7: 3620-3624.

Lecture Series in Parallel Computing and CUDA-C

A new lecture series in practical aspects of Parallel Computing and CUDA-C will kick off on Tuesday, February 22nd. The series will run twice weekly, on Tuesdays and Fridays from 2:30-3:30 pm in Bassine 251, for a total of 12 lectures over six weeks. Lectures will be given by Gianluca Castellani, Ph.D. Research Computing Specialist and HPC Cluster Administrator (Volen Center, LTS, and Physics) and Francesco Pontiggia, Ph. D., Postdoctoral Fellow, (Volen Center and Biochemistry). The series is jointly sponsored by the Volen Center, MRSEC, Physics Dept., and Library and Technology Services.

Tentative Schdule

Lecture 1 :  Why Parallel Programming? Parallel Architectures and Programming Models.
Lecture 2 :  Parallelization Techniques
Lectures 3 – 4 : Programming in a Shared Memory Environment — Introduction to OpenMP
Lecture 5 : CUDA-C fundamentals. Compiler, kernels, host-device data transfer
Lecture 6 : Time execution tuning, catching error and hardware evaluation
Lectures 7 – 8 : GPU memory types
Lectures 9 – 11 : Distributed Memory — MPI Paradigm
Lecture 12 : Using High Performance Parallel Libraries : An Example — Parallel Matrix Inversion.

Notes and Examples will be posted on the HPCC Wiki

Chirality leads to self-limited self-assembly

Simple building blocks that self-assemble into ordered structures with controlled sizes are essential for nanomaterials applications, but what are the general design principles for molecules that undergo self-terminating self-assembly? The question is addressed in a recent paper in Physical Review Letters by Yasheng Yang, graduate student in Physics, working together with Profs. Meyer and Hagan,  The paper considers molecules that self assemble to form filamentous bundles, and shows that chirality, or asymmetry with respect to a molecule’s mirror image, can result in stable self-limited structures. Using modern computational techniques, the authors demonstrate that chirality frustrates long range order and thereby terminates assembly upon formation of regular self-limited bundles.  With strong interactions, however, the frustration is relieved by defects, which give rise to branched networks or irregular bundles.

Figure: (a) Snapshots of regular chiral bundles. Free energy calculations and dynamics demonstrate that the optimal diameter decreases with increasing chirality. (b) Branched bundles form with strong interactions

Simulating viral capsid assembly

Viral capsids assemble into complex structures with high fidelity, but also can adapt when given other nucleic acids cargoes to package. In a recent paper in Nano Letters, Brandeis physics grad student Oren Elrad and Professor Michael Hagan used computer simulations to investigate the mechanisms by which this occurs. These simulations were done on the Brandeis High Performance Computing cluster.