Here I summarize a few of the areas I worked on over the past several years, along with links to some related publications.
The Role of Nucleic Acids in Viral Assembly
We developed a coarse grained computational model for virus capsid assembly around RNA. Model predictions for RNA lengths that optimize capsid thermostability nearly quantitatively agreed with viral genome lengths for seven viruses [1a]. This result demonstrates that viral nucleic acid structures are evolutionarily constrained by their influence on capsid thermostability, in addition to the fitness of the genes they encode. Predicted assembly failures around non-optimal RNA lengths were confirmed by experiment. Our simulations demonstrated that capsid assembly around RNA proceeds through two classes of pathways [1b]. Extending our model to incorporate sequence-specific capsid protein-RNA interactions (packaging signals) demonstrated a mechanism of selective assembly around the viral genomic RNA [1c]. In direct collaborations with experimentalists, we investigated the effect of genome stiffness on the stability of an assembled HBV capsid [1d] and compared theoretical predictions to in vivo experiments on the amount of RNA packaged in virions whose charge was altered by mutagenesis [1e]. For a broader context of this work, and an overall review of modeling capsid assembly, please see these review articles [1f,1g].
Bacterial Microcompartment Assembly
Bacterial microcompartments (BMCs) are icosahedral protein-based organelles found in bacteria that assemble around a dense complex of enzymes and reactants involved in certain metabolic pathways. The best-known example of a BMC is the carboxysome, which enables carbon fixation in photosynthetic bacteria. Understanding the mechanisms that control BMC formation is a central unanswered question in cell biology. My group developed a computational model for BMC assembly , which demonstrated that BMCs can assemble by two pathways, in which the enzyme cargo undergoes liquid-liquid phase separation either prior to or during shell assembly. The model also identified factors that determine how many enzymes encapsulated. Thus, in addition to elucidating how native BMCs assemble, the model can help to redesign them as customizable organelles that assemble around a programmable set of enzymes, introducing capabilities such as biofuel production into new organisms.
Non-equilibrium Self-organization in Active Matter
Active matter describes systems whose constituent elements consume energy to drive motion or generate internal stresses. Examples include flocks or herds of animals, components of the cellular cytoskeleton, and collections of synthetic self-propelled colloids. By developing minimal models for these systems, my group is studying the relationship between molecular-scale energy dissipation (e.g. by molecular motors) and macroscale collective behaviors, such as those responsible for the capabilities of living organisms. Some examples of our work follow, categorized by the class of system studied:
a. Active Filaments
We have found that mixtures of active and equilibrium rods spontaneously demix [3a] and filaments constructed from motile particles exhibit flagella-like beating [3b]. L. Giomi with Mahadevan, B. Chakraborty and me analyzed a continuum theoretical of active nematics [3c], which laid the context for thinking theoretically about the widely studied experimental active nematics model system, the suspension of microtubules propelled by molecular motors developed by Dogic. Through collaborative modeling (my group) and experiments (Dogic) on the microtubule system we discovered a novel phase of matter, in which motile topological defects self-organize into higher-order structures with long-range orientational order [3d]. This discovery generalizes the concept of defect-ordered phases to non-equilibrium systems.
b. Self-propelled Spheres.
As a minimal model active system, I worked with Aparna Baskaran to model the behavior of self-propelled repulsive, non-aligning spheres. This model was motivated by experiments on self-propelled Janus particles (which undergo directed motion due to catalytic activity which occurs on one side of the particle). Computer simulations showed that self-propelled repulsive, non-aligning spheres undergo phase separation between a dilute gas and a new form of matter, an active crystal [3e]. This nonequilibrium phase transition demonstrates all the hallmarks of its equilibrium analog, including a critical point. We developed a kinetic model that explains the mechanism driving phase separation [3f], and showed that phase separation dynamics could be analyzed by an analog to classical nucleation theory [3e]. Further work describing self-propelled spheres with attractive interactions showed that their phase separation is reentrant as a function of activity [3f].
c. Boundaries in Active Materials
Despite the necessity of having boundaries in any real-world device, their effects on an active systems are incompletely understood. Yaouen Fily, Aparna Baskaran and I developed a general theory relating boundary geometry to the density distribution of self-propelled spheres [3h-3k]. The theory and numerical simulations demonstrate that the boundary shape dramatically affects the active fluid's dynamics and thermomechanical properties in certain limits. In particular, active particles are confined to the boundary, with a density that is inversely proportional to, and a pressure that decays exponentially with, the local Gaussian curvature of the boundary. The theory enables designing a box shape that yields any desired density distribution on the boundary.
My group has studied the assembly of colloids into biomimetic structures such as filamentous bundles or membranes, focusing on mechanisms that force assembly to self-terminate in one or more dimensions. I combined theory and computation with experiments performed by Z. Dogic (Brandeis) to characterize colloidal membranes (macroscopic monolayer membranes comprised of colloidal rods [4a]. We demonstrated a novel mechanism that stabilizes monolayers, in which protrusions of rods within the monolayer entropically limit growth in the direction perpendicular to the membrane. Subsequently, work with Dogic, Baskaran, and Chakraborty demonstrated that phase separation in 2D is qualitatively different from that in 3D. For example, chirality can drive equilibrium micro-phase separation into monodisperse, finite-size, self-healing domains [4b,4c].
We also studied rod-like particles end-attaching onto a curved surface, creating a finite-thickness monolayer aligned with the surface normal [4d]. This geometry leads to two forms of frustration, one associated with the incompatibility of hexagonal order on surfaces with Gaussian (intrinsic) curvature, and the second reflecting the deformation of a layer with finite thickness on a surface with non-zero mean (extrinsic) curvature. We found latter effect drives a novel faceting mechanism, which leads to a rich variety of morphologies.
1a. “Viral genome structures are optimal for capsid assembly”, Perlmutter, JD; Qiao, C; Hagan, MF. eLife (eLife 2013; 2:e00632).
1b. “Pathways for virus assembly around nucleic acids”, Perlmutter, JD, Perkett, MR; Hagan, MF. J. Mol. Biol., 426, 3148–3165; arXiv:1405.3310 (2014).
1c. “The role of packaging sites in efficient and specific virus assembly”, Perlmutter, JD; Hagan, MF. J. Mol. Biol., 427, 2451–2467 (2015). doi:10.1016/j.jmb.2015.05.008
1d. “Differential assembly of Hepatitis B Virus core protein on single- and double-stranded nucleic acid suggests the dsDNA-filled core is springloaded”, Dhason, MS; Wang, JC; Hagan, MF; Zlotnick, A. Virology, 430, 20-29 (2012).
1e. “An Examination of the Electrostatic Interactions between the N-Terminal Tail of the Coat Protein and RNA in Brome Mosaic Virus”, Ni, P; Wang, Z; Ma, X; Das, NC; Sokol, P; Chiu, W; Dragnea, B; Hagan, MF*; Kao, CC. J. Mol. Biol., 419, 284-300 (2012).
1f. “Modeling Viral Capsid Assembly”, Hagan, MF. Adv. Chem. Phys., 155, Ch 1; (2014) arXiv:1301.1657.
2. “Many-molecule encapsulation by an icosahedral shell”, Perlmutter JD; Mohajerani, F; Hagan, MF. eLife 5, e14078 (2016); Watch the movies.
3a. “Spontaneous Segregation of Self-Propelled Particles with Different Motilities”, McCandlish, SR; Baskaran, A; Hagan, MF. Soft Matter, 8, 2527 (2012). arXiv:1110.2479.
3b. “Flagellar dynamics of a connected chain of active, Brownian particles”, Chelakkot, R; Gopinath, A; Mahadevan, L*; Hagan, MF*. J. R. Soc. Interface, 11, 20130884 (2014). YouTube Videos: Periodic beating, Non periodic buckling, Rotational motion, Beating of long filament. doi:10.1098/rsif.2013.0884
3c. “Banding, excitability and chaos in active nematic suspensions”, Giomi L; Mahadevan L; Chakraborty, B; Hagan, MF. Nonlinearity, 25, 2245-2269 (2012). arXiv:1110.4338
3d. “Orientational order of motile defects in active nematics”, DeCamp, SJ; Redner, G; Baskaran, A; Hagan, MF*; Dogic, Z*. Nature Mater., 14, 1110–1115 (2015).
3e. “Structure and Dynamics of a Phase-Separating Active Colloidal Fluid”, Redner, G; Hagan, MF*; Baskaran, A*. Phys. Rev. Lett. 110, 055701, arXiv:1207.1737 (2013).
3f. “A classical nucleation theory description of active colloid assembly”, Redner, GS; Wagner, CG; Baskaran, A; Hagan, MF. Phys. Rev. Lett., 117, 148002, arXiv:1603.01362, (2016).
3g. “Reentrant Phase Behavior in Active Colloids with Attraction”, Redner, G; Baskaran, A; Hagan, MF. Phys. Rev. E, 88, 012305 arXiv:1303.3195 (2013).
3h. “Dynamics of Self-Propelled Particles Under Strong Confinement”, Fily, Y; Baskaran, A; Hagan, MF. Soft Matter, 10, 5609-5617; arXiv:1402.5583 (2014).
3i. “Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary”, Fily, Y; Baskaran, A; Hagan, MF. Phys. Rev. E, 91, 012125, arXiv:1410.5151.
3j. “Active Particles on Curved Surfaces”, Fily, Y; Baskaran, A; Hagan, MF. arXiv:1601.00324 (submitted).
3k. “Equilibrium mappings in polar-isotropic confined active particles”, Fily, Y; Baskaran, A; Hagan, MF. Eur. Phys. J. E 40, 61. doi:10.1140/epje/i2017-11551-3, arXiv:1612.08719 (2017).
4a. “Self-assembly of 2D membranes from mixtures of hard rods and depleting polymers”, Yang Y; Barry E; Dogic Z; Hagan, MF. Soft Matter, 8, 707 (2012) arXiv:1103.2760
4b. “Hierarchical organization of chiral rafts in colloidal membranes”, Sharma, P; Ward, AR; Gibaud, T; Hagan, MF; Dogic, Z. Nature, 513, 77-80 (2014).
4c. “Theory of microphase separation in bidisperse chiral membranes”, Sakhardande, R; Stanojeviea, S; Baskaran, A; Hagan, MF; Chakraborty, B. Phys. Rev. E 96, 012704, arXiv:1604.03012 (2017).
4d. “Faceted particles formed by the frustrated packing of anisotropic colloids on curved surfaces”, Yu, N; Ghosh, A; Hagan, MF. Soft Matter, 12, 8990 (2016), [cover article]. [DOI:10.1039/C6SM01498D]
“Aligned Arrays of Nanorods, and Methods of Making and Using Them”, Barry, E; Dogic, Z; Hagan, MF; Yang, Y; Perlman, D. (patent pending.)