Publications by authors named "Michael F Hagan"

76 Publications

Active liquid crystals powered by force-sensing DNA-motor clusters.

Proc Natl Acad Sci U S A 2021 Jul;118(30)

Department of Physics, University of California, Santa Barbara, CA 93106;

Cytoskeletal active nematics exhibit striking nonequilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order. The properties of the DNA linker enable the design of force-sensing clusters. When the load across the linker exceeds a critical threshold, the clusters fall apart, ceasing to generate active stresses and slowing the system dynamics. Fluorescence readout reveals the fraction of bound clusters that generate interfilament sliding. In turn, this yields the average load experienced by the kinesin motors as they step along the microtubules. DNA-motor clusters provide a foundation for understanding the molecular mechanism by which nanoscale molecular motors collectively generate mesoscopic active stresses, which in turn power macroscale nonequilibrium dynamics of active nematics.
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http://dx.doi.org/10.1073/pnas.2102873118DOI Listing
July 2021

Avidity and surface mobility in multivalent ligand-receptor binding.

Nanoscale 2021 Jul 14. Epub 2021 Jul 14.

Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.

Targeted drug delivery relies on two physical processes: the selective binding of a therapeutic particle to receptors on a specific cell membrane, followed by transport of the particle across the membrane. In this article, we address some of the challenges in controlling the thermodynamics and dynamics of these two processes by combining a simple experimental system with a statistical mechanical model. Specifically, we characterize and model multivalent ligand-receptor binding between colloidal particles and fluid lipid bilayers, as well as the surface mobility of membrane-bound particles. We show that the mobility of the receptors within the fluid membrane is key to both the thermodynamics and dynamics of binding. First, we find that the particle-membrane binding free energy-or avidity-is a strongly nonlinear function of the ligand-receptor affinity. We attribute the nonlinearity to a combination of multivalency and recruitment of fluid receptors to the binding site. Our results also suggest that partial wrapping of the bound particles by the membrane enhances avidity further. Second, we demonstrate that the lateral mobility of membrane-bound particles is also strongly influenced by the recruitment of receptors. Specifically, we find that the lateral diffusion coefficient of a membrane-bound particle is dominated by the hydrodynamic drag against the aggregate of receptors within the membrane. These results provide one of the first direct validations of the working theoretical framework for multivalent interactions. They also highlight that the fluidity and elasticity of the membrane are as important as the ligand-receptor affinity in determining the binding and transport of small particles attached to membranes.
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http://dx.doi.org/10.1039/d1nr02083hDOI Listing
July 2021

Programmable icosahedral shell system for virus trapping.

Nat Mater 2021 Jun 14. Epub 2021 Jun 14.

Department of Physics, Technical University of Munich, Munich, Germany.

Broad-spectrum antiviral platforms that can decrease or inhibit viral infection would alleviate many threats to global public health. Nonetheless, effective technologies of this kind are still not available. Here, we describe a programmable icosahedral canvas for the self-assembly of icosahedral shells that have viral trapping and antiviral properties. Programmable triangular building blocks constructed from DNA assemble with high yield into various shell objects with user-defined geometries and apertures. We have created shells with molecular masses ranging from 43 to 925 MDa (8 to 180 subunits) and with internal cavity diameters of up to 280 nm. The shell interior can be functionalized with virus-specific moieties in a modular fashion. We demonstrate this virus-trapping concept by engulfing hepatitis B virus core particles and adeno-associated viruses. We demonstrate the inhibition of hepatitis B virus core interactions with surfaces in vitro and the neutralization of infectious adeno-associated viruses exposed to human cells.
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http://dx.doi.org/10.1038/s41563-021-01020-4DOI Listing
June 2021

Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control.

ACS Nano 2021 03 8;15(3):4197-4212. Epub 2021 Mar 8.

Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States.

This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.
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http://dx.doi.org/10.1021/acsnano.0c05715DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8058603PMC
March 2021

Confinement-Induced Self-Pumping in 3D Active Fluids.

Phys Rev Lett 2020 Dec;125(26):268003

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.

Two dimensional active fluids display a transition from turbulent to coherent flow upon decreasing the size of the confining geometry. A recent experiment suggests that the behavior in three dimensions is remarkably different; emergent flows transition from turbulence to coherence upon increasing the confinement height to match the width. Using a simple hydrodynamic model of a suspension of extensile rodlike units, we provide the theoretical explanation for this puzzling behavior. Furthermore, using extensive numerical simulations supported by theoretical arguments, we map out the conditions that lead to coherent flows and elucidate the critical role played by the aspect ratio of the confining channel. The mechanism that we identify applies to a large class of symmetries and propulsion mechanisms, leading to a unified set of design principles for self-pumping 3D active fluids.
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http://dx.doi.org/10.1103/PhysRevLett.125.268003DOI Listing
December 2020

Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays.

Soft Matter 2021 Jan 8;17(4):1091-1104. Epub 2020 Dec 8.

Department of Physics, Indian Institute of Technology Bombay, Mumbai, India.

Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient - even in the absence of inter-filament hydrodynamic interactions - to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics - specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems.
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http://dx.doi.org/10.1039/d0sm01162bDOI Listing
January 2021

Machine learning forecasting of active nematics.

Soft Matter 2021 Jan 21;17(3):738-747. Epub 2020 Nov 21.

Computer Science, Brandeis University, USA.

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.
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http://dx.doi.org/10.1039/d0sm01316aDOI Listing
January 2021

Optimal Control of Active Nematics.

Phys Rev Lett 2020 Oct;125(17):178005

Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA.

In this work we present the first systematic framework to sculpt active nematic systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (i) applied vorticity and (ii) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological +1/2 defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate nontrivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter.
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http://dx.doi.org/10.1103/PhysRevLett.125.178005DOI Listing
October 2020

Two-step crystallization and solid-solid transitions in binary colloidal mixtures.

Proc Natl Acad Sci U S A 2020 11 29;117(45):27927-27933. Epub 2020 Oct 29.

Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453

Crystallization is fundamental to materials science and is central to a variety of applications, ranging from the fabrication of silicon wafers for microelectronics to the determination of protein structures. The basic picture is that a crystal nucleates from a homogeneous fluid by a spontaneous fluctuation that kicks the system over a single free-energy barrier. However, it is becoming apparent that nucleation is often more complicated than this simple picture and, instead, can proceed via multiple transformations of metastable structures along the pathway to the thermodynamic minimum. In this article, we observe, characterize, and model crystallization pathways using DNA-coated colloids. We use optical microscopy to investigate the crystallization of a binary colloidal mixture with single-particle resolution. We observe classical one-step pathways and nonclassical two-step pathways that proceed via a solid-solid transformation of a crystal intermediate. We also use enhanced sampling to compute the free-energy landscapes corresponding to our experiments and show that both one- and two-step pathways are driven by thermodynamics alone. Specifically, the two-step solid-solid transition is governed by a competition between two different crystal phases with free energies that depend on the crystal size. These results extend our understanding of available pathways to crystallization, by showing that size-dependent thermodynamic forces can produce pathways with multiple crystal phases that interconvert without free-energy barriers and could provide approaches to controlling the self-assembly of materials made from colloids.
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http://dx.doi.org/10.1073/pnas.2008561117DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7668103PMC
November 2020

All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes.

Sci Adv 2020 Jul 29;6(31):eaba2331. Epub 2020 Jul 29.

Department of Physics, Brandeis University, Waltham, MA 02454, USA.

Using theory and experiments, we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane. The midplane tilt at the interdomain edge forces splay, which, in turn, manifests as spontaneous edge curvature with energetics controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at interdomain edges explains a number of experimental observations, including annularly shaped long-rod domains, and a nonmonotonic dependence of edge twist on domain radius. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids gives rise to complex shapes of fluid domains, analogous to shape transitions in 3D fluid vesicles.
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http://dx.doi.org/10.1126/sciadv.aba2331DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7439760PMC
July 2020

Probing the Transition State in Enzyme Catalysis by High-Pressure NMR Dynamics.

Nat Catal 2019 Aug 24;2(8):726-734. Epub 2019 Jun 24.

Department of Biochemistry and Howard Hughes Medical Institute, Brandeis University, Waltham, Massachusetts 02452, United States.

Protein conformational changes are frequently essential for enzyme catalysis, and in several cases, shown to be the limiting factor for overall catalytic speed. However, a structural understanding of corresponding transition states, needed to rationalize the kinetics, remains obscure due to their fleeting nature. Here, we determine the transition-state ensemble of the rate-limiting conformational transition in the enzyme adenylate kinase, by a synergistic approach between experimental high-pressure NMR relaxation during catalysis and molecular dynamics simulations. By comparing homologous kinases evolved under ambient or high pressure in the deep-sea, we detail transition state ensembles that differ in solvation as directly measured by the pressure dependence of catalysis. Capturing transition-state ensembles begins to complete the catalytic energy landscape that is generally characterized by structures of all intermediates and frequencies of transitions among them.
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http://dx.doi.org/10.1038/s41929-019-0307-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7063682PMC
August 2019

Topological structure and dynamics of three-dimensional active nematics.

Science 2020 03;367(6482):1120-1124

Department of Physics, Brandeis University, Waltham, MA 02453, USA.

Topological structures are effective descriptors of the nonequilibrium dynamics of diverse many-body systems. For example, motile, point-like topological defects capture the salient features of two-dimensional active liquid crystals composed of energy-consuming anisotropic units. We dispersed force-generating microtubule bundles in a passive colloidal liquid crystal to form a three-dimensional active nematic. Light-sheet microscopy revealed the temporal evolution of the millimeter-scale structure of these active nematics with single-bundle resolution. The primary topological excitations are extended, charge-neutral disclination loops that undergo complex dynamics and recombination events. Our work suggests a framework for analyzing the nonequilibrium dynamics of bulk anisotropic systems as diverse as driven complex fluids, active metamaterials, biological tissues, and collections of robots or organisms.
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http://dx.doi.org/10.1126/science.aaz4547DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7984424PMC
March 2020

Response of active Brownian particles to boundary driving.

Phys Rev E 2019 Oct;100(4-1):042610

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts, USA.

We computationally study the behavior of underdamped active Brownian particles in a sheared channel geometry. Due to their underdamped dynamics, the particles carry momentum a characteristic distance away from the boundary before it is dissipated into the substrate. We correlate this distance with the persistence of particle trajectories, determined jointly by their friction and self-propulsion. Within this characteristic length, we observe counterintuitive phenomena stemming from the interplay of activity, interparticle interactions, and the boundary driving. Depending on the values of friction and self-propulsion, interparticle interactions can either aid or hinder momentum transport. More dramatically, in certain cases we observe a flow reversal near the wall, which we correlate with an induced polarization of the particle self-propulsion directions. We rationalize these results in terms of a simple kinetic picture of particle trajectories.
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http://dx.doi.org/10.1103/PhysRevE.100.042610DOI Listing
October 2019

Nanoparticles binding to lipid membranes: from vesicle-based gels to vesicle tubulation and destruction.

Nanoscale 2019 Oct;11(39):18464-18474

Department of Physics, University of Massachusetts Amherst, USA.

While cells offer numerous inspiring examples in which membrane morphology and function are controlled by interactions with viruses or proteins, we still lack design principles for controlling membrane morphology in synthetic systems. With experiments and simulations, we show that spherical nanoparticles binding to lipid-bilayer membrane vesicles results in a remarkably rich set of collective morphologies that are controllable via the particle binding energy. We separately study cationic and anionic particles, where the adhesion is tuned by addition of oppositely charged lipids to the vesicles. When the binding energy is weak relative to a characteristic membrane-bending energy, vesicles adhere to one another and form a soft solid gel, a novel and useful platform for controlled release. With larger binding energy, a transition from partial to complete wrapping of the nanoparticles causes a remarkable vesicle destruction process culminating in rupture, nanoparticle-membrane tubules, and an apparent inversion of the vesicles. These findings help unify the diverse phenomena observed previously. They also open the door to a new class of vesicle-based, closed-cell gels that are more than 99% water and can encapsulate and release on demand, and show how to drive intentional membrane remodeling for shape-responsive systems.
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http://dx.doi.org/10.1039/c9nr06570aDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7155749PMC
October 2019

Structure, dynamics and phase behavior of short rod inclusions dissolved in a colloidal membrane.

Soft Matter 2019 Sep 22;15(35):7033-7042. Epub 2019 Aug 22.

Department of Physics, Brandeis University, Waltham, MA 02454, USA and Department of Physics, University of California, Santa Barbara, CA 93106, USA.

Inclusions dissolved in an anisotropic quasi-2D membrane acquire new types of interactions that can drive assembly of complex structures and patterns. We study colloidal membranes composed of a binary mixture of long and short rods, such that the length ratio of the long to short rods is approximately two. At very low volume fractions, short rods dissolve in the membrane of long rods by strongly anchoring to the membrane polymer interface. At higher fractions, the dissolved short rods phase separate from the background membrane, creating a composite structure comprised of bilayer droplets enriched in short rods that coexist with the background monolayer membrane. These results demonstrate that colloidal membranes serve as a versatile platform for assembly of soft materials, while simultaneously providing new insight into universal membrane-mediated interactions.
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http://dx.doi.org/10.1039/c9sm01064eDOI Listing
September 2019

Equation of state of colloidal membranes.

Soft Matter 2019 Aug;15(34):6791-6802

Department of Physics, Brandeis University, Waltham, MA 02454, USA.

In the presence of a non-adsorbing polymer, monodisperse rod-like colloids assemble into one-rod-length thick liquid-like monolayers, called colloidal membranes. The density of the rods within a colloidal membrane is determined by a balance between the osmotic pressure exerted by the enveloping polymer suspension and the repulsion between the colloidal rods. We developed a microfluidic device for continuously observing an isolated membrane while dynamically controlling the osmotic pressure of the polymer suspension. Using this technology we measured the membrane rod density over a range of osmotic pressures than is wider that what is accessible in equilibrium samples. With increasing density we observed a first-order phase transition, in which the in-plane membrane order transforms from a 2D fluid into a 2D solid. In the limit of low osmotic pressures, we measured the rate at which individual rods evaporate from the membrane. The developed microfluidic technique could have wide applicability for in situ investigation of various soft materials and how their properties depend on the solvent composition.
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http://dx.doi.org/10.1039/c9sm01054hDOI Listing
August 2019

Conformational switching of chiral colloidal rafts regulates raft-raft attractions and repulsions.

Proc Natl Acad Sci U S A 2019 08 18;116(32):15792-15801. Epub 2019 Jul 18.

Department of Physics, Brandeis University, Waltham, MA 02454;

Membrane-mediated particle interactions depend both on the properties of the particles themselves and the membrane environment in which they are suspended. Experiments have shown that chiral rod-like inclusions dissolved in a colloidal membrane of opposite handedness assemble into colloidal rafts, which are finite-sized reconfigurable droplets consisting of a large but precisely defined number of rods. We systematically tune the chirality of the background membrane and find that, in the achiral limit, colloidal rafts acquire complex structural properties and interactions. In particular, rafts can switch between 2 chiral states of opposite handedness, which alters the nature of the membrane-mediated raft-raft interactions. Rafts with the same chirality have long-ranged repulsions, while those with opposite chirality acquire attractions with a well-defined minimum. Both attractive and repulsive interactions are qualitatively explained by a continuum model that accounts for the coupling between the membrane thickness and the local tilt of the constituent rods. These switchable interactions enable assembly of colloidal rafts into intricate higher-order architectures, including stable tetrameric clusters and "ionic crystallites" of counter-twisting domains organized on a binary square lattice. Furthermore, the properties of individual rafts, such as their sizes, are controlled by their complexation with other rafts. The emergence of these complex behaviors can be rationalized purely in terms of generic couplings between compositional and orientational order of fluids of rod-like elements. Thus, the uncovered principles might have relevance for conventional lipid bilayers, in which the assembly of higher-order structures is also mediated by complex membrane-mediated interactions.
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http://dx.doi.org/10.1073/pnas.1900615116DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6689927PMC
August 2019

The interplay between activity and filament flexibility determines the emergent properties of active nematics.

Soft Matter 2018 Dec;15(1):94-101

Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.

Active nematics are microscopically driven liquid crystals that exhibit dynamical steady states characterized by the creation and annihilation of topological defects. Motivated by differences between previous simulations of active nematics based on rigid rods and experimental realizations based on semiflexible biopolymer filaments, we describe a large-scale simulation study of a particle-based computational model that explicitly incorporates filament semiflexibility. We find that energy injected into the system at the particle scale preferentially excites bend deformations, reducing the apparent filament bend modulus. The emergent characteristics of the active nematic depend on activity and flexibility only through this activity-renormalized bend 'modulus', demonstrating that apparent values of material parameters, such as the Frank 'constants', depend on activity. Thus, phenomenological parameters within continuum hydrodynamic descriptions of active nematics must account for this dependence. Further, we present a systematic way to estimate these parameters from observations of deformation fields and defect shapes in experimental or simulation data.
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http://dx.doi.org/10.1039/c8sm02202jDOI Listing
December 2018

The role of the encapsulated cargo in microcompartment assembly.

PLoS Comput Biol 2018 07 31;14(7):e1006351. Epub 2018 Jul 31.

Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America.

Bacterial microcompartments are large, roughly icosahedral shells that assemble around enzymes and reactants involved in certain metabolic pathways in bacteria. Motivated by microcompartment assembly, we use coarse-grained computational and theoretical modeling to study the factors that control the size and morphology of a protein shell assembling around hundreds to thousands of molecules. We perform dynamical simulations of shell assembly in the presence and absence of cargo over a range of interaction strengths, subunit and cargo stoichiometries, and the shell spontaneous curvature. Depending on these parameters, we find that the presence of a cargo can either increase or decrease the size of a shell relative to its intrinsic spontaneous curvature, as seen in recent experiments. These features are controlled by a balance of kinetic and thermodynamic effects, and the shell size is assembly pathway dependent. We discuss implications of these results for synthetic biology efforts to target new enzymes to microcompartment interiors.
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http://dx.doi.org/10.1371/journal.pcbi.1006351DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6086489PMC
July 2018

Self-assembly of convex particles on spherocylindrical surfaces.

Soft Matter 2018 Jul;14(28):5728-5740

Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA.

The precise control of assembly and packing of proteins and colloids on curved surfaces has fundamental implications in nanotechnology. In this paper, we describe dynamical simulations of the self-assembly of conical subunits around a spherocylindrical template, and a continuum theory for the bending energy of a triangular lattice with spontaneous curvature on a surface with arbitrary curvature. We find that assembly depends sensitively on mismatches between subunit spontaneous curvature and the mean curvature of the template, as well as anisotropic curvature of the template (mismatch between the two principal curvatures). Our simulations predict assembly morphologies that closely resemble those observed in experiments in which virus capsid proteins self-assemble around metal nanorods. Below a threshold curvature mismatch, our simulations identify a regime of optimal assembly leading to complete, symmetrical particles. Outside of this regime we observe defective particles, whose morphologies depend on the degree of curvature mismatch. To learn how assembly is affected by the nonuniform curvature of a spherocylinder, we also study the simpler cases of assembly around spherical and cylindrical cores. Our results show that both the intrinsic (Gaussian) and extrinsic (mean) curvatures of a template play significant roles in guiding the assembly of anisotropic subunits, providing a rich design space for the formation of nanoscale materials.
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http://dx.doi.org/10.1039/c8sm00129dDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6051892PMC
July 2018

Defects and Chirality in the Nanoparticle-Directed Assembly of Spherocylindrical Shells of Virus Coat Proteins.

ACS Nano 2018 06 25;12(6):5323-5332. Epub 2018 Apr 25.

Department of Chemistry , Indiana University , Bloomington , Indiana 47405 , United States.

Virus coat proteins of small isometric plant viruses readily assemble into symmetric, icosahedral cages encapsulating noncognate cargo, provided the cargo meets a minimal set of chemical and physical requirements. While this capability has been intensely explored for certain virus-enabled nanotechnologies, additional applications require lower symmetry than that of an icosahedron. Here, we show that the coat proteins of an icosahedral virus can efficiently assemble around metal nanorods into spherocylindrical closed shells with hexagonally close-packed bodies and icosahedral caps. Comparison of chiral angles and packing defects observed by in situ atomic force microscopy with those obtained from molecular dynamics models offers insight into the mechanism of growth, and the influence of stresses associated with intrinsic curvature and assembly pathways.
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http://dx.doi.org/10.1021/acsnano.8b00069DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6202266PMC
June 2018

Insensitivity of active nematic liquid crystal dynamics to topological constraints.

Phys Rev E 2018 Jan;97(1-1):012702

Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA.

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.
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http://dx.doi.org/10.1103/PhysRevE.97.012702DOI Listing
January 2018

Why Enveloped Viruses Need Cores-The Contribution of a Nucleocapsid Core to Viral Budding.

Biophys J 2018 02;114(3):619-630

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts. Electronic address:

During the lifecycle of many enveloped viruses, a nucleocapsid core buds through the cell membrane to acquire an outer envelope of lipid membrane and viral glycoproteins. However, the presence of a nucleocapsid core is not required for assembly of infectious particles. To determine the role of the nucleocapsid core, we develop a coarse-grained computational model with which we investigate budding dynamics as a function of glycoprotein and nucleocapsid interactions, as well as budding in the absence of a nucleocapsid. We find that there is a transition between glycoprotein-directed budding and nucleocapsid-directed budding that occurs above a threshold strength of nucleocapsid interactions. The simulations predict that glycoprotein-directed budding leads to significantly increased size polydispersity and particle polymorphism. This polydispersity can be explained by a theoretical model accounting for the competition between bending energy of the membrane and the glycoprotein shell. The simulations also show that the geometry of a budding particle leads to a barrier to subunit diffusion, which can result in a stalled, partially budded state. We present a phase diagram for this and other morphologies of budded particles. Comparison of these structures against experiments could establish bounds on whether budding is directed by glycoprotein or nucleocapsid interactions. Although our model is motivated by alphaviruses, we discuss implications of our results for other enveloped viruses.
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http://dx.doi.org/10.1016/j.bpj.2017.11.3782DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5985022PMC
February 2018

Theory of microphase separation in bidisperse chiral membranes.

Phys Rev E 2017 Jul 13;96(1-1):012704. Epub 2017 Jul 13.

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.

We present a Ginzburg-Landau theory of microphase separation in a bidisperse chiral membrane consisting of rods of opposite handedness. This model system undergoes a phase transition from an equilibrium state where the two components are completely phase separated to a state composed of microdomains of a finite size comparable to the twist penetration depth. Characterizing the phenomenology using linear stability analysis and numerical studies, we trace the origin of the discontinuous change in microdomain size that occurs during this phase transition to a competition between the cost of creating an interface and the gain in twist energy for small microdomains in which the twist penetrates deep into the center of the domain.
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http://dx.doi.org/10.1103/PhysRevE.96.012704DOI Listing
July 2017

Kinetic constraints on self-assembly into closed supramolecular structures.

Sci Rep 2017 09 25;7(1):12295. Epub 2017 Sep 25.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.

Many biological and synthetic systems exploit self-assembly to generate highly intricate closed supramolecular architectures, ranging from self-assembling cages to viral capsids. The fundamental design principles that control the structural determinants of the resulting assemblies are increasingly well-understood, but much less is known about the kinetics of such assembly phenomena and it remains a key challenge to elucidate how these systems can be engineered to assemble in an efficient manner and avoid kinetic trapping. We show here that simple scaling laws emerge from a set of kinetic equations describing the self-assembly of identical building blocks into closed supramolecular structures and that this scaling behavior provides general rules that determine efficient assembly in these systems. Using this framework, we uncover the existence of a narrow range of parameter space that supports efficient self-assembly and reveal that nature capitalizes on this behavior to direct the reliable assembly of viral capsids on biologically relevant timescales.
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http://dx.doi.org/10.1038/s41598-017-12528-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5613031PMC
September 2017

Equilibrium mappings in polar-isotropic confined active particles.

Eur Phys J E Soft Matter 2017 Jun 13;40(6):61. Epub 2017 Jun 13.

Martin Fisher School of Physics, Brandeis University, 02453, Waltham, MA, USA.

Despite their fundamentally nonequilibrium nature, the individual and collective behavior of active systems with polar propulsion and isotropic interactions (polar-isotropic active systems) are remarkably well captured by equilibrium mapping techniques. Here we examine two signatures of equilibrium systems --the existence of a local free energy function and the independence of the coarse-grained behavior on the details of the microscopic dynamics-- in polar-isotropic active particles confined by hard walls of arbitrary geometry at the one-particle level. We find that boundaries that possess concave regions make the density profile strongly dynamics-dependent and give it a nonlocal dependence on the geometry of the confining box. This in turn constrains the scope of equilibrium mapping techniques in polar-isotropic active systems.
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http://dx.doi.org/10.1140/epje/i2017-11551-3DOI Listing
June 2017

Gradation (approx. 10 size states) of synaptic strength by quantal addition of structural modules.

Philos Trans R Soc Lond B Biol Sci 2017 03;372(1715)

Department of Biology, Brandeis University, 415 South Street, Waltham, MA 02454, USA

Memory storage involves activity-dependent strengthening of synaptic transmission, a process termed long-term potentiation (LTP). The late phase of LTP is thought to encode long-term memory and involves structural processes that enlarge the synapse. Hence, understanding how synapse size is graded provides fundamental information about the information storage capability of synapses. Recent work using electron microscopy (EM) to quantify synapse dimensions has suggested that synapses may structurally encode as many as 26 functionally distinct states, which correspond to a series of proportionally spaced synapse sizes. Other recent evidence using super-resolution microscopy has revealed that synapses are composed of stereotyped nanoclusters of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors and scaffolding proteins; furthermore, synapse size varies linearly with the number of nanoclusters. Here we have sought to develop a model of synapse structure and growth that is consistent with both the EM and super-resolution data. We argue that synapses are composed of modules consisting of matrix material and potentially one nanocluster. LTP induction can add a trans-synaptic nanocluster to a module, thereby converting a silent module to an AMPA functional module. LTP can also add modules by a linear process, thereby producing an approximately 10-fold gradation in synapse size and strength.This article is part of the themed issue 'Integrating Hebbian and homeostatic plasticity'.
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http://dx.doi.org/10.1098/rstb.2016.0328DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5247597PMC
March 2017

Faceted particles formed by the frustrated packing of anisotropic colloids on curved surfaces.

Soft Matter 2016 Nov;12(44):8990-8998

Martin Fisher School of Physics, Brandeis University, Waltham, MA, USA.

We use computer simulations and simple theoretical models to analyze the morphologies that result when rod-like particles end-attach onto a curved surface, creating a finite-thickness monolayer aligned with the surface normal. This geometry leads to two forms of frustration, one associated with the incompatibility of hexagonal order on surfaces with Gaussian curvature, and the second reflecting the deformation of a layer with finite thickness on a surface with non-zero mean curvature. We show that the latter effect leads to a faceting mechanism. Above threshold values of inter-particle attraction strength and surface mean curvature, the adsorbed layer undergoes a transition from orientational disorder to an ordered state that is demarcated by reproducible patterns of line defects. The number of facets is controlled by the competition between line defect energy and intra-facet strain. Tuning control parameters thus leads to a rich variety of morphologies, including icosahedral particles and irregular polyhedra. In addition to suggesting a new strategy for the synthesis of aspherical particles with tunable symmetries, our results may shed light on recent experiments in which rod-like HIV GAG proteins assemble around nanoscale particles.
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http://dx.doi.org/10.1039/c6sm01498dDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5287255PMC
November 2016

Classical Nucleation Theory Description of Active Colloid Assembly.

Phys Rev Lett 2016 Sep 30;117(14):148002. Epub 2016 Sep 30.

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.

Nonaligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods and analytic theory to examine the kinetics of formation of the dense phase. Despite the intrinsically nonequilibrium nature of the phase transition, we show that the kinetics can be described using an approach analogous to equilibrium classical nucleation theory, governed by an effective free energy of cluster formation with identifiable bulk and surface terms. The theory captures the location of the binodal, nucleation rates as a function of supersaturation, and the cluster size distributions below the binodal, while discrepancies in the metastable region reveal additional physics about the early stages of active crystal formation. The success of the theory shows that a framework similar to equilibrium thermodynamics can be obtained directly from the microdynamics of an active system, and can be used to describe the kinetics of evolution toward nonequilibrium steady states.
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http://dx.doi.org/10.1103/PhysRevLett.117.148002DOI Listing
September 2016

The allosteric switching mechanism in bacteriophage MS2.

J Chem Phys 2016 Jul;145(3):035101

Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02474, USA.

We use all-atom simulations to elucidate the mechanisms underlying conformational switching and allostery within the coat protein of the bacteriophage MS2. Assembly of most icosahedral virus capsids requires that the capsid protein adopts different conformations at precise locations within the capsid. It has been shown that a 19 nucleotide stem loop (TR) from the MS2 genome acts as an allosteric effector, guiding conformational switching of the coat protein during capsid assembly. Since the principal conformational changes occur far from the TR binding site, it is important to understand the molecular mechanism underlying this allosteric communication. To this end, we use all-atom simulations with explicit water combined with a path sampling technique to sample the MS2 coat protein conformational transition, in the presence and absence of TR-binding. The calculations find that TR binding strongly alters the transition free energy profile, leading to a switch in the favored conformation. We discuss changes in molecular interactions responsible for this shift. We then identify networks of amino acids with correlated motions to reveal the mechanism by which effects of TR binding span the protein. We find that TR binding strongly affects residues located at the 5-fold and quasi-sixfold interfaces in the assembled capsid, suggesting a mechanism by which the TR binding could direct formation of the native capsid geometry. The analysis predicts amino acids whose substitution by mutagenesis could alter populations of the conformational substates or their transition rates.
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http://dx.doi.org/10.1063/1.4955187DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4947040PMC
July 2016