arXiv subjects

Gregory M. Grason

Publications and source records attributed to Gregory M. Grason.

At least 73 records · Page 4Linked to original sources

arXiv2015

Measuring cohesion between macromolecular filaments, one pair at a time: Depletion-induced microtubule bundling

In presence of non-adsorbing polymers, colloidal particles experience ubiquitous attractive interactions induced by depletion forces. Here, we measure the depletion interaction between a pair of microtubule filaments using a method that combines single filament imaging with optical trapping. By quantifying the dependence of filament cohesion on both polymer concentration and solution ionic strength, we demonstrate that the minimal model of depletion, based on the Asakura-Oosawa theory, fails to quantitatively describe the experimental data. By measuring the cohesion strength in two- and three- filament bundles we verify pairwise additivity of depletion interactions for the specific experimental conditions. The described experimental technique can be used to measure pairwise interactions between various biological or synthetic filaments and complements information extracted from bulk osmotic stress experiments.

physics.bio-ph↗

arXiv2015

Geometry and Optimal Packing of Twisted Columns and Filaments

This review presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing non-trivial textures, focusing in particular on the common motifs of twisted and toroidal structures. The mathematical framework is presented that relates spacing between line-like, filamentous elements to their backbone orientations, highlighting the explicit connection between the inter-filament {\it metric} properties and the geometry of non-Euclidean surfaces. The consequences of the hidden connection between packing in twisted filament bundles and packing on positively curved surfaces, like the Thomson problem, are demonstrated for the defect-riddled ground states of physical models of twisted filament bundles. The connection between the "ideal" geometry of {\it fibrations} of curved three-dimensional space, including the Hopf fibration, and the non-Euclidean constraints of filament packing in twisted and toroidal bundles is presented, with a focus on the broader dependence of metric geometry on the simultaneous twisting and folded of multi-filament bundles.

cond-mat.soft↗

arXiv2014

Geometry of flexible filament cohesion: Better contact through twist?

Cohesive interactions between filamentous molecules have broad implications for a range of biological and synthetic materials. While long-standing theoretical approaches have addressed the problem of inter-filament forces from the limit of infinitely rigid rods, the ability of flexible filaments to deform intra-filament shape in response to changes in inter-filament geometry has a profound affect on the nature of cohesive interactions. In this paper, we study two theoretical models of inter-filament cohesion in the opposite limit, in which filaments are sufficiently flexible to maintain cohesive contact along their contours, and address, in particular, the role played by helical-interfilament geometry in defining interactions. Specifically, we study models of featureless, tubular filaments interacting via 1) pair-wise Lennard-Jones (LJ) interactions between surface elements and 2) depletion-induced filament binding stabilized by electrostatic surface repulsion. Analysis of these models reveals a universal preference for cohesive filament interactions for non-zero helical skew, and further, that in the asymptotic limit of vanishing interaction range relative to filament diameter, the skew-dependence of cohesion approaches a geometrically defined limit described purely by the close-packing geometry of twisted tubular filaments. We further analyze non-universal features of the skew-dependence of cohesion at small-twist for both potentials, and argue that in the LJ model the pair-wise surface attraction generically destabilizes parallel filaments, while in the second model, pair-wise electrostatic repulsion in combination with non-pairwise additivity of depletion leads to a meta-stable parallel state.

cond-mat.soft↗

arXiv2013

Emergent structure of multi-dislocation ground states in curved crystals

We study the structural features and underlying principles of multi-dislocation ground states of a crystalline spherical cap. In the continuum limit where the ratio of crystal size to lattice spacing $W/a$ diverges, dislocations proliferate and ground states approach a characteristic sequence of structures composed of radial grain boundaries ("neutral scars"), extending radially from the boundary and terminating in the bulk. Employing a combination of numerical simulations and asymptotic analysis of continuum elasticity theory, we prove that an energetic hierarchy gives rise to a structural hierarchy, whereby dislocation number and scar number diverge as $a/W \to 0$ while scar length and dislocation number per scar become {\it independent} of lattice spacing. We characterize a secondary transition occurring as scar length grows, where the $n$-fold scar symmetry is broken and ground states are characterized by polydisperse, forked-scar morphologies.

cond-mat.soft↗

arXiv2013

Tensorial conservation law for nematic polymers

We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that respective order parameters satisfy fundamentally distinct constraints. Being necessarily scalar in its form, the tensorial conservation law is obtained straightforwardly from the gradients of the polymer nematic tensor field and connects the spatial variation of this tensor field with density variations. We analyze the differences between the polar and the tensorial forms of the conservation law, present some explicit orientational fields that satisfy this new constraint and discuss the role of singular "hairpins", which do not affect local quadrupolar order of polymer nematics, but nevertheless influence its gradients.

cond-mat.soft↗

arXiv2013

Topological Defects, Surface Geometry and Cohesive Energy of Twisted Filament Bundles

Cohesive assemblies of filaments are a common structural motif found in diverse contexts, ranging from biological materials such as fibrous proteins, to artificial materials such as carbon nanotube ropes and micropatterned filament arrays. In this paper, we analyze the complex dependence of cohesive energy on twist, a key structural parameter of both self-assembled and fabricated filament bundles. Based on the analysis of simulated ground states of cohesive bundles, we show that the non-linear influence of twist derives from two distinct geometric features of twisted bundles: (i) the geometrical frustration of inter-filament packing in the bundle cross-section; and (ii) the evolution of the surface geometry of bundles with twist, which dictates the cohesive cost of non-contacting filaments at the surface. Packing frustration in the bundle core gives rise to the appearance of a universal sequence of topological defects, excess 5-fold disclinations, with increasing twist, while the evolution of filament contact at the surface of the bundle generically favors twisted geometries for sufficiently long filaments. Our analysis of both continuum and discrete models of filament bundles shows that, even in the absence of external torque or intrinsic chirality, cohesive energy universally favors twisted ground states above a critical (length/radius) aspect ratio and below a critical filament stiffness threshold.

cond-mat.soft↗

arXiv2013

Frustration and Packing in Curved-Filament Assemblies: From Isometric to Isomorphic Bundles

Densely-packed bundles of biological filaments (filamentous proteins) are common and critical structural elements in range of biological materials. While most bundles form from intrinsically straight filaments, there are notable examples of protein filaments possessing a natural, or intrinsic, curvature, such as the helical bacterial flagellum. We study the non-linear interplay between thermodynamic preference for dense and regular inter-filament packing and the mechanical preference for uniform filament shape in bundles of helically-curved filaments. Geometric constraints in bundles make perfect inter-filament (constant spacing, or isometric) packing incompatible with perfect intra-filament (constant shape, or isomorphic) packing. As a consequence, we predict that bundle packing exhibits a strong sensitivity to bundle size, evolving from the isometric packing at small radii to an isomorphic packing at large radii. The nature of the transition between these extremal states depends on thermodynamic costs of packing distortion, with packing in elastically-constrained bundles evolving smoothly with size, while packing in osmotically-compressed bundles may exhibit a singular transition from the isometric packing at a finite bundle radius. We consider the equilibrium assembly of bundles in a saturated solution of filaments and show that mechanical cost of isomorphic packing leads to self-limited equilibrium bundle diameters, whose size and range of thermodynamic stability depend both on condensation mechanism, as well as the helical geometry of filaments.

cond-mat.soft↗

arXiv2012

Chirality in Block Copolymer Melts: Mesoscopic Helicity from Inter-Segment Twist

We study the effects of chirality at the segment scale on the thermodynamics of block copolymer melts using self consistent field theory. In linear diblock melts where segments of one block prefer a twisted, or cholesteric, texture, we show that melt assembly is critically sensitive to the ratio of random coil size to the preferred pitch of cholesteric twist. For weakly-chiral melts (large pitch), mesophases remain achiral, while below a critical value of pitch, two mesocopically chiral phases are stable: an undulated lamellar phase; and a phase of hexagonally-ordered helices. We show that the non-linear sensitivity of meso-scale chiral order to preferred pitch derives specifically from the geometric and thermodynamic coupling of the helical mesodomain shape to the twisted packing of chiral segments within the core, giving rise to a second-order cylinder-to-helix transition.

cond-mat.soft↗

arXiv2012

Conformational Collapse of Surface-Bound Helical Filaments

Chiral polymers are ubiquitous in nature and in the cellular context they are often found in association with membranes. Here we show that surface bound polymers with an intrinsic twist and anisotropic bending stiffness can exhibit a sharp continuous phase transition between states with very different effective persistence lengths as the binding affinity is increased. Above a critical value for the binding strength, determined solely by the torsional modulus and intrinsic twist rate, the filament can exist in a zero twist, surface bound state with a homogeneous stiffness. Below the critical binding strength, twist walls proliferate and function as weak or floppy joints that sharply reduce the effective persistence length that is measurable on long lengthscales. The existence of such dramatically different conformational states has implications for both biopolymer function {\it in vivo} and for experimental observations of such filaments {\it in vitro}.

cond-mat.soft↗

arXiv2011

Defects in Crystalline Packings of Twisted Filament Bundles: II. Dislocations and Grain Boundaries

Twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional organization of filaments in cross section and out-of-plane interfilament twist in bundles. Using non-linear continuum elasticity theory of columnar materials, we study the favorable coupling of twist-induced stresses to the presence of edge dislocations in the lattice packing of bundles, which leads to a restructuring of the ground-state order of these materials at intermediate twist. The stability of dislocations increases as both the degree of twist and lateral bundle size grow. We show that in ground states of large bundles, multiple dislocations pile up into linear arrays, radial grain boundaries, whose number and length grows with bundle twist, giving rise to a rich class of "polycrystalline" packings.

cond-mat.soft↗

arXiv2011

Defects in Crystalline Packings of Twisted Filament Bundles: I. Continuum Theory of Disclinations

We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the non-linear continuum elasticity theory of columnar materials. We show that twisted textures of filament backbones necessarily introduce stresses into the cross-sectional packing of bundles and that these stresses are formally equivalent to the geometrically-induced stresses generated in thin elastic sheets that are forced to adopt spherical curvature. As in the case of crystalline order on curved membranes, geometrically-induced stresses couple elastically to the presence of topological defects in the in-plane order. We derive the effective theory of multiple disclination defects in the cross section of bundle with a fixed twist and show that above a critical degree of twist, one or more 5-fold disclinations is favored in the elastic energy ground state. We study the structure and energetics of multi-disclination packings based on models of equilibrium and non-equilibrium cross-sectional order.

cond-mat.soft↗

arXiv2011

Frustrated order on extrinsic geometries

We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable and most important on surfaces of negative Gaussian curvature, where it leads to a complex ground state thermodynamics. We show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an "inside-outside" symmetry, defects are expelled altogether.

cond-mat.soft↗

arXiv2011

Filling the void in confined polymer nematics: phase transitions in a minimal model of dsDNA packing

Inspired to understand the complex spectrum of space-filling organizations the dsDNA genome within the capsid of bacterial viruses, we study a minimal, coarse-grained model of single chains densely-packed into a finite spherical volume. We build the three basic elements of the model--i) the absence of chain ends ii) the tendency of parallel-strand alignment and iii) a preference of uniform areal density of chain segments--into a polymer nematic theory for confined chains. Given the geometric constraints of the problem, we show that axially symmetric packings fall into one of three topologies: the coaxial spool; the simple solenoid; and the twisted-solenoid. Among these, only the twisted-solenoid fills the volume without the presence of line-like disclinations, or voids, and are therefore generically preferred in the incompressible limit. An analysis of the thermodynamics behavior of this simple model reveals a rich behavior, a generic sequence of phases from the empty state for small container sizes, to the coaxial spool configuration at intermediate sizes, ultimately giving way, via a second-order, symmetry-breaking transition, to the twisted-solenoid structure above a critical sphere size.

cond-mat.soft↗

arXiv2011

Theory of Crosslinked Bundles of Helical Filaments: Intrinsic Torques in Self-Limiting Biopolymer Assemblies

Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we study and analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the "grooves" of two neighboring filaments. We develop a coarse-grained model to investigate the interplay between the geometry of binding and mechanics of both linker and filament distortion, and we show that crosslinking in parallel bundles of helical filaments generates {\it intrinsic torques}, of the type that tend to wind bundle superhelically about its central axis. Crosslinking mediates a non-linear competition between the preference for bundle twist and the size-dependent mechanical cost of filament bending, which in turn gives rise to feedback between the global twist of self-assembled bundles and their lateral size. Finally, we demonstrate that above a critical density of bound crosslinkers, twisted bundles form with a thermodynamically preferred radius that, in turn, increases with a further increase in crosslinking bonds. We identify the {\it stiffness} of crosslinking bonds as a key parameter governing the sensitivity of bundle structure and assembly to the availability and affinity of crosslinkers.

cond-mat.soft↗

arXiv2010

Structural Reorganization of Parallel Actin Bundles by Crosslinking Proteins: Incommensurate States of Twist

We construct a coarse-grained model of parallel actin bundles crosslinked by compact, globular bundling proteins, such as fascin and espin, necessary components of filapodial and mechanosensory bundles. Consistent with structural observations of bundles, we find that the optimal geometry for crosslinking is overtwisted, requiring a coherent structural change of the helical geometry of the filaments. We study the linker-dependent thermodynamic transition of bundled actin filaments from their native state to the overtwisted state and map out the "twist-state'' phase diagram in terms of the availability as well as the flexibility of crosslinker proteins. We predict that the transition from the uncrosslinked to fully-crosslinked state is highly sensitive to linker flexibility: flexible crosslinking smoothly distorts the twist-state of bundled filaments, while rigidly crosslinked bundles undergo a phase transition, rapidly overtwisting filaments over a narrow range of free crosslinker concentrations. Additionally, we predict a rich spectrum of intermediate structures, composed of alternating domains of sparsely-bound (untwisted) and strongly-bound (overtwisted) filaments. This model reveals that subtle differences in crosslinking agents themselves modify not only the detailed structure of parallel actin bundles, but also the thermodynamic pathway by which they form.

cond-mat.soft↗

arXiv2010

Topological Defects in Twisted Bundles of Two-Dimensionally Ordered Filaments

Twisted assemblies of filaments in ropes, cables and bundles are essential structural elements in wide use in macroscopic materials as well as within the cells and tissues of living organisms. We develop the unique, non-linear elastic properties of twisted filament bundles that derive from generic properties of two-dimensional line-ordered materials. Continuum elasticity reveals a formal equivalence between the elastic stresses induced by bundle twist and those induced by the positive curvature in thin, elastic sheets. These geometrically-induced stresses can be screened by 5-fold disclination defects in lattice packing, and we predict a discrete spectrum elastic energy groundstates associated with integer numbers of disclinations in cylindrical bundles. Finally, we show that elastic-energy groundstates are extremely sensitive to defect position in the cross-section, with off-center disclinations driving the entire bundle to buckle, adopting globally writhing configurations.

cond-mat.soft↗

arXiv2009

Cooperativity and Frustration in Protein-Mediated Parallel Actin Bundles

We examine the mechanism of bundling of cytoskeletal actin filaments by two representative bundling proteins, fascin and espin. Small-angle X-ray studies show that increased binding from linkers drives a systematic \textit{overtwist} of actin filaments from their native state, which occurs in a linker-dependent fashion. Fascin bundles actin into a continuous spectrum of intermediate twist states, while espin only allows for untwisted actin filaments and fully-overtwisted bundles. Based on a coarse-grained, statistical model of protein binding, we show that the interplay between binding geometry and the intrinsic \textit{flexibility} of linkers mediates cooperative binding in the bundle. We attribute the respective continuous/discontinous bundling mechanisms of fascin/espin to differences in the stiffness of linker bonds themselves.

cond-mat.soft↗

arXiv2009

Mesophases of soft-sphere aggregates

Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a level surface analysis of the periodic structures of soft-sphere aggregates to study stable morphologies for all clustering potentials. We develop a systematic approach to the thermodynamics of mesophase assembly in the low-temperature, strong-segregation and predict a generic sequence of phases including lamella, hexagonal-columnar and body-center cubic phases, as well as the associated inverse structures. We discuss the finite-temperature corrections to strong segregation theory in terms of Sommerfeld-like expansion and how these corrections affect the thermodynamic stability of bicontinuous mesophase structures, such as gyroid. Finally, we explore the opposite limit of weakly-segregated particles, and predict the generic stability of a bicontinuous cluster morphology within the mean-field phase diagram.

cond-mat.soft↗