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.

hagan-capsid-sim

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

More science

We’ve all been busy this spring writing grants and teaching courses and doing research and graduating(!), so lots of publications snuck by that we didn’t comment on. Here’s a few I think that might be interesting to our readers.

  • From Chris Miller‘s lab, bacterial antiporters do act as “virtual proton efflux pumps”:
  • nsrv2Are ninja stars responsible for controlling actin disassembly? Seems like the Goode lab might think so.
    • Chaudhry F, Breitsprecher D, Little K, Sharov G, Sokolova O, Goode BL. Srv2/cyclase-associated protein forms hexameric shurikens that directly catalyze actin filament severing by cofilin. Mol Biol Cell. 2013;24(1):31-41.
  • What do you get from statistical mechanics of self-propelled particles? The Hagan and Baskaran groups team up to find out.
  • From John Lisman and Ole Jensen (PhD ’98), thoughts about what the theta and gamma rhythms in the brain encode
  • From Mike Marr‘s lab, studeies using genome-wide nascent sequencing to understand how transcrption bursting is controlled in eukaryotic cells
  • From the Lau and Sengupta labs, RNAi pathways contribute to long term plasticity in worms that have gone through the Dauer stage
    • Hall SE, Chirn GW, Lau NC, Sengupta P. RNAi pathways contribute to developmental history-dependent phenotypic plasticity in C. elegans. RNA. 2013;19(3):306-19.
  • Can nanofibers selectively disrupt cancer cell types? Early results from Bing Xu‘s group.
    • Kuang Y, Xu B. Disruption of the Dynamics of Microtubules and Selective Inhibition of Glioblastoma Cells by Nanofibers of Small Hydrophobic Molecules. Angew Chem Int Ed Engl. 2013.

Baskaran Wins NSF-CAREER award to pursue research on active fluids

Dr. Aparna Baskaran of the Physics Department has been awarded the prestigious CAREER grant from the National Science Foundation that is a highly competitive development grant for early career tenure track faculty members. This grant will fund the research ongoing in Dr. Baskaran’s group on dynamics in active materials. Active materials are a novel class of complex fluids that are driven out of equilibrium at the level of individual entities. Examples of such systems include bacterial suspensions, cytoskeletal filaments interacting with motor proteins and inanimate systems such as self-propelled phoretic colloidal particles. The theoretical challenge in understanding these systems lies in the fact that, unlike traditional materials, we no longer have the scaffold of equilibrium on which to base the theoretical framework.  At the practical front, these materials exhibit novel properties not seen in regular materials.  Further, they form the physical framework of biological systems  in that regulatory mechanisms modulate the mechanical properties of this material in response to environmental stimuli.  Dr. Baskaran’s research in this field will be done in collaboration with the groups of Dr. Michael Hagan, Dr. Zvonimir Dogic and Dr. Bulbul Chakraborty. It will enhance and complement the MRSEC research activities in the active materials thrust.

Figure Caption : Videos of example systems for active materials. A) A fish school exhibiting complex collective swimming. B) Swarming at the edge of an E. Coli Bacterial Colony. C) Cytoplasmic streaming inside the yolk of a fertilized cell.

Six scientists secure fellowships

One current undergraduate, and five alumni, from the Brandeis Sciences were honored with offers of National Science Foundation Graduate Research Fellowships in 2012. The fellowships, which are awarded based on a national competition, provide three full years of support for Ph.D. research and are highly valued by students and institutions. These students are:

  • Samuel McCandlish ’12 (Physics) , a current student who did research with Michael Hagan and Aparna Baskaran, resulting in a paper “Spontaneous segregation of self-propelled particles with different motilities” in Soft Matter (as a junior). He then switched to work with Albion Lawrence for his senior thesis research. Sam will speak about “Bending and Breaking Time Contours: a World Line Approach to Quantum Field Theory” at the Berko Symposium on May 14.  Sam has been offered a couple of other fellowships as well, so he’ll have a nice choice to make. Sam will be heading to Stanford in the fall to continue his studies in theoretical physics.
  • Briana Abrahms ’08 (Physics). After graduating from Brandeis, Briana followed her interests in ecological and conversation issues, and  in Africa as a research assistant with the Botswana Predator Conservation Trust, Briana previously described some of her experiences here in “Three Leopards and a Shower“. Briana plans to pursue as Ph.D. in Ecology at UC Davis.
  • Sarah Robinson ’07 (Chemistry). Sarah did undergraduate research with Irving Epstein on “Pattern formation in a coupled layer reaction-diffusion system”. After graduating, Sarah spent time with the Peace Corps in Tanzania, returning to study Neurosciene at UCSF.
  • Si Hui Pan ’10 (Physics) participated in a summer REU program at Harvard, and continued doing her honors thesis in collaboration with the labs at Harvard. Her award is to study condensed matter physics at MIT.
  • Elizabeth Setren ’10 was a Mathematics and Economics double major who worked together with Donald Shepard (Heller School) on the cost of hunger in the US. She has worked as an Assistant Economist at the Federal Reserve Bank of New York and her award is to study Economics at Harvard.
  • Michael Ari Cohen ’01 (Psychology) worked as a technology specialist for several years before returning to academia as  PhD student in the Energy and Resources Group at UC Berkeley.

Congratulations to all the winners!

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).

Collective behaviors in active matter

Active matter is describes systems whose constituent elements consume energy and are thus out-of-equilibrium. Examples include flocks or herds of animals, collections of cells, and components of the cellular cytoskeleton. When these objects interact with each other, collective behavior can emerge that is unlike anything possible with an equilibrium system. The types of behaviors and the factors that control them however, remain incompletely understood. In a recent paper in Physical Review Letters, “Excitable patterns in active nematics“, Giomi and coworkers develop a continuum theoretical description motivated by recent experiments from the Dogic group at Brandeis in which microtubules (filamentous cytoskeletal molecules) and clusters of kinesin (a molecular motor) exhibit dramatic spatiotemporal fluctuations in density and alignment. Specifically, they consider a hydrodynamic description for density, flow, and nematic alignment. In contrast to previous theories of this type, the degree of nematic alignment is allowed to vary in space and time.  Remarkably, the theory predicts that the interplay between non-uniform nematic order, activity and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media and biological examples such as the cardiac cycle. At even higher activity the dynamics is chaotic and leads to large-scale swirling patterns which resemble those seen in recent experiments. An example of the flow pattern is shown below left, and the nematic order parameter, which describes the degree of alignment of the filaments, as shown for the same configuration below right. These predictions can be tested in future experiments on systems of microtubules and motor proteins.

The system behavior for an active nematic at high activity. (left) The velocity field (arrows) is superimposed on a plot of the concentration of active nematogens (green=large concentration, red=small concentration). (right) A plot of the nematic order parameter, S,  (blue=large S, brown=small S) is superimposed on a plot of the nematic director (arrows). The flow under high activity is characterized by large vortices that span lengths of the order of the system size and the director field is organized in grains.

 

Prolonging assembly through dissociation

Microtubules are semiflexible polymers that serve as structural components inside the eukaryotic cell and are involved in many cellular processes such as mitosis, cytokinesis, and vesicular transport. In order to perform these functions, microtubules continually rearrange through a process known as dynamic instability, in which they switch from a phase of slow elongation to rapid shortening (catastrophe), and from rapid shortening to growth (rescue). The basic self-assembly mechanism underlying this process, assembly mediated by nucleotide phosphate activity, is omnipresent in biological systems.  A recent paper, Prolonging assembly through dissociation: A self-assembly paradigm in microtubules ,  published in the May 3 issue of Physical Review E,  presents a new paradigm for such self-assembly in which increasing depolymerization rate can enhance assembly.  Such a scenario can occur only out of equilibrium. Brandeis Physics postdoc Sumedha, working with Chakraborty and Hagan, carried out theoretical analysis of a stochastic hydrolysis model to demonstrate the effect and predict features of growth fluctuations, which should be measurable in experiments that probe microtubule dynamics at the nanoscale.

Model for microtuble dynamics. All activity is assumed to occur at the right end of the microtubule (denoted as ">")

The essential features of the model that leads to the counterintuitive result of depolymerization helping assembly are (a) stochastic hydrolysis that allows GTP to transform into GDP  in any part of the microtubule, and (b) a much higher rate of GTP attachment if the end of the microtubule has a GTP-bound tubulin dimer, compared to a GDP-bound tubulin dimer.    Process (a) leads to islands of GTP-bound tubulins to be buried deep in the microtubule.   Depolymerization from the end reveals these islands and enhances assembly because of the biased attachment rate (b).  The simplicity of the model lent itself to analytical results for various aspects of the growth statistics in particular parameter regimes.   Simulations of the model supported these analytical results, and extended them to regimes where it was not possible to solve the model analytically.  The statistics of the growth fluctuations in this stochastic hydrolysis model are very different from “cap models” which do not have GTP remnants buried inside a growing microtubule.   Testing the predictions in experiments could, therefore, lead to a better understanding of the processes underlying dynamical instability in-vivo and in-vitro.   An interesting question to explore is whether the bias in the attachment rates is different under different conditions of microtubule growth.

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

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