Michael F. Hagan

Dynamic Pathways for Viral Capsid Assembly

We develop a class of models with which we simulate the assembly of particles into T1 capsidlike objects using Newtonian dynamics. By simulating assembly for many different values of system parameters, we vary the forces that drive assembly. For some ranges of parameters, assembly is facile; for others, assembly is dynamically frustrated by kinetic traps corresponding to malformed or incompletely formed capsids. Our simulations sample many independent trajectories at various capsomer concentrations, allowing for statistically meaningful conclusions. Depending on subunit (i.e., capsomer) geometries, successful assembly proceeds by several mechanisms involving binding of intermediates of various sizes. We discuss the relationship between these mechanisms and experimental evaluations of capsid assembly processes.

Sitting at the Edge: How Biomolecules use Hydrophobicity to Tune Their Interactions and Function

Water near extended hydrophobic surfaces is like that at a liquid-vapor interface, where fluctuations in water density are substantially enhanced compared to those in bulk water. Here we use molecular simulations with specialized sampling techniques to show that water density fluctuations are similarly enhanced, even near hydrophobic surfaces of complex biomolecules, situating them at the edge of a dewetting transition. Consequently, water near these surfaces is sensitive to subtle changes in surface conformation, topology, and chemistry, any of which can tip the balance toward or away from the wet state and thus significantly alter biomolecular interactions and function. Our work also resolves the long-standing puzzle of why some biological surfaces dewet and other seemingly similar surfaces do not.

Reconfigurable self-assembly through chiral control of interfacial tension

From determining the optical properties of simple molecular crystals to establishing the preferred handedness in highly complex vertebrates, molecular chirality profoundly influences the structural, mechanical and optical properties of both synthetic and biological matter on macroscopic length scales. In soft materials such as amphiphilic lipids and liquid crystals, the competition between local chiral interactions and global constraints imposed by the geometry of the self-assembled structures leads to frustration and the assembly of unique materials. An example of particular interest is smectic liquid crystals, where the two-dimensional layered geometry cannot support twist and chirality is consequently expelled to the edges in a manner analogous to the expulsion of a magnetic field from superconductors. Here we demonstrate a consequence of this geometric frustration that leads to a new design principle for the assembly of chiral molecules. Using a model system of colloidal membranes, we show that molecular chirality can control the interfacial tension, an important property of multi-component mixtures. This suggests an analogy between chiral twist, which is expelled to the edges of two-dimensional membranes, and amphiphilic surfactants, which are expelled to oil–water interfaces. As with surfactants, chiral control of interfacial tension drives the formation of many polymorphic assemblages such as twisted ribbons with linear and circular topologies, starfish membranes, and double and triple helices. Tuning molecular chirality in situ allows dynamical control of line tension, which powers polymorphic transitions between various chiral structures. These findings outline a general strategy for the assembly of reconfigurable chiral materials that can easily be moved, stretched, attached to one another and transformed between multiple conformational states, thus allowing precise assembly and nanosculpting of highly dynamical and designable materials with complex topologies.

Hybridization dynamics of surface immobilized DNA

We model the hybridization kinetics of surface attached DNA oligomers with solubilized targets. Using both master equation and rate equation formalisms, we show that, for surface coverages at which the surface immobilized molecules interact, barriers to penetration create a distribution of target molecule concentrations within the adsorbed layer. By approximately enumerating probe and target conformations, we estimate the probability of overlap between complementary probe and target regions as a function of probe density and chain length. In agreement with experiments, we find that as probe molecules interact more strongly, fewer nucleation sites become accessible and binding rates are diminished relative to those in solution. Nucleation sites near the grafted end of the probes are least accessible; thus targets which preferentially bind to this region show more drastic rate reductions than those that bind near the free end of the probe. The implications of these results for DNA-based biosensors are discussed.

Atomistic understanding of kinetic pathways for single base-pair binding and unbinding in DNA

We combine free-energy calculations and molecular dynamics to elucidate a mechanism for DNA base-pair binding and unbinding in atomic detail. Specifically, transition-path sampling is used to overcome computational limitations associated with conventional techniques to harvest many trajectories for the flipping of a terminal cytosine in a 3-bp oligomer in explicit water. Comparison with free-energy projections obtained with umbrella sampling reveals four coordinates that separate true dynamic transition states from stable reactant and product states. Unbinding proceeds via two qualitatively different pathways: one in which the flipping base breaks its intramolecular hydrogen bonds before it unstacks and another in which it ruptures both sets of interactions simultaneously. Both on- and off-pathway intermediates are observed. The relation of the results to coarse-grained models for DNA-based biosensors is discussed.

Mechanisms of Virus Assembly

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.

Encapsulation of a polymer by an icosahedral virus

The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.

Orientational order of motile defects in active nematics.

The study of liquid crystals at equilibrium has led to fundamental insights into the nature of ordered materials, as well as to practical applications such as display technologies. Active nematics are a fundamentally different class of liquid crystals, driven away from equilibrium by the autonomous motion of their constituent rod-like particles. This internally generated activity powers the continuous creation and annihilation of topological defects, which leads to complex streaming flows whose chaotic dynamics seem to destroy long-range order. Here, we study these dynamics in experimental and computational realizations of active nematics. By tracking thousands of defects over centimetre-scale distances in microtubule-based active nematics, we identify a non-equilibrium phase characterized by a system-spanning orientational order of defects. This emergent order persists over hours despite defect lifetimes of only seconds. Similar dynamical structures are observed in coarse-grained simulations, suggesting that defect-ordered phases are a generic feature of active nematics.

An Examination of the Electrostatic Interactions Between the N-Terminal Tail of the Brome Mosaic Virus Coat Protein and Encapsidated RNAs

The coat protein of positive-stranded RNA viruses often contains a positively charged tail that extends toward the center of the capsid and interacts with the viral genome. Electrostatic interaction between the tail and the RNA has been postulated as a major force in virus assembly and stabilization. The goal of this work is to examine the correlation between electrostatic interaction and amount of RNA packaged in the tripartite Brome Mosaic Virus (BMV). Nanoindentation experiment using atomic force microscopy showed that the stiffness of BMV virions with different RNAs varied by a range that is 10-fold higher than that would be predicted by electrostatics. BMV mutants with decreased positive charges encapsidated lower amounts of RNA while mutants with increased positive charges packaged additional RNAs up to ∼900 nt. However, the extra RNAs included truncated BMV RNAs, an additional copy of RNA4, potential cellular RNAs, or a combination of the three, indicating that change in the charge of the capsid could result in several different outcomes in RNA encapsidation. In addition, mutant with specific arginines changed to lysines in the capsid also exhibited defects in the specific encapsidation of BMV RNA4. The experimental results indicate that electrostatics is a major component in RNA encapsidation but was unable to account for all of the observed effects on RNA encapsidation. Thermodynamic modeling incorporating the electrostatics was able to predict the approximate length of the RNA to be encapsidated for the majority of mutant virions, but not for a mutant with extreme clustered positive charges. Cryo-electron microscopy of virions that encapsidated an additional copy of RNA4 revealed that, despite the increase in RNA encapsidated, the capsid structure was minimally changed. These results experimentally demonstrated the impact of electrostatics and additional restraints in the encapsidation of BMV RNAs, which could be applicable to other viruses.

Mechanisms of Size Control and Polymorphism in Viral Capsid Assembly

We simulate the assembly dynamics of icosahedral capsids from subunits that interconvert between different conformations (or quasi-equivalent states). The simulations identify mechanisms by which subunits form empty capsids with only one morphology but adaptively assemble into different icosahedral morphologies around nanoparticle cargoes with varying sizes, as seen in recent experiments with brome mosaic virus (BMV) capsid proteins. Adaptive cargo encapsidation requires moderate cargo-subunit interaction strengths; stronger interactions frustrate assembly by stabilizing intermediates with incommensurate curvature. We compare simulation results to experiments with cowpea chlorotic mottle virus empty capsids and BMV capsids assembled on functionalized nanoparticles and suggest new cargo encapsidation experiments. Finally, we find that both empty and templated capsids maintain the precise spatial ordering of subunit conformations seen in the crystal structure even if interactions that preserve this arrangement are favored by as little as the thermal energy, consistent with experimental observations that different subunit conformations are highly similar.