128 research outputs found
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.Comment: Main Text (25 pages, 7 figures) with supporting material (12 pages, 9
figures, 2 tables
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.Comment: 4.1 pages; 3 figure
Soft Spheres Make More Mesophases
We use both mean-field methods and numerical simulation to study the phase
diagram of classical particles interacting with a hard-core and repulsive, soft
shoulder. Despite the purely repulsive interaction, this system displays a
remarkable array of aggregate phases arising from the competition between the
hard-core and shoulder length scales. In the limit of large shoulder width to
core size, we argue that this phase diagram has a number of universal features,
and classify the set of repulsive shoulders that lead to aggregation at high
density. Surprisingly, the phase sequence and aggregate size adjusts so as to
keep almost constant inter-aggregate separation.Comment: 4 pages, 2 included figure
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.Comment: 10 pages, 7 figure
A Geometric Theory of Diblock Copolymer Phases
We analyze the energetics of sphere-like micellar phases in diblock
copolymers in terms of well-studied, geometric quantities for their lattices.
We argue that the A15 lattice with Pm3n symmetry should be favored as the
blocks become more symmetric and corroborate this through a self-consistent
field theory. Because phases with columnar or bicontinuous topologies
intervene, the A15 phase, though metastable, is not an equilibrium phase of
symmetric diblocks. We investigate the phase diagram of branched diblocks and
find thatthe A15 phase is stable.Comment: 4 pages, RevTeX, 3 eps figures include
Braided Bundles and Compact Coils: The Structure and Thermodynamics of Hexagonally-Packed, Chiral Filament Assemblies
Molecular chirality frustrates the two-dimensional assembly of filamentous
molecules, a fact that reflects the generic impossibility of imposing a global
twisting of layered materials. We explore the consequences of this frustration
for hexagonally-ordered assemblies of chiral filaments that are {\it finite} in
lateral dimension. Specifically, we employ a continuum-elastic description of
cylindrical bundles of filaments, allowing us to consider the most general
resistance to and preference for chiral ordering of the assembly. We explore
two distinct mechanisms by which chirality at the molecular scale of the
filament frustrates the assembly into aggregates. In the first, chiral
interactions between filaments impart an overall twisting of filaments around
the central axis of the bundle. In the second, we consider filaments that are
inherently helical in structure, imparting a writhing geometry to the central
axis. For both mechanisms, we find that a thermodynamically-stable state of
dispersed bundles of {\it finite} width appears close to, but below, the point
of bulk filament condensation. The range of thermodynamic stability of
dispersed bundles is sensitive only to the elastic cost and preference for
chiral filament packing. The self-limited assembly of chiral filaments has
particular implications for a large class of biological molecules -- DNA,
filamentous proteins, viruses, bacterial flagella -- which are universally
chiral and are observed to form compact bundles under a broad range of
conditions.Comment: 15 pages, 8 figure
Interfaces in Diblocks: A Study of Miktoarm Star Copolymers
We study AB miktoarm star block copolymers in the strong segregation
limit, focussing on the role that the AB interface plays in determining the
phase behavior. We develop an extension of the kinked-path approach which
allows us to explore the energetic dependence on interfacial shape. We consider
a one-parameter family of interfaces to study the columnar to lamellar
transition in asymmetric stars. We compare with recent experimental results. We
discuss the stability of the A15 lattice of sphere-like micelles in the context
of interfacial energy minimization. We corroborate our theory by implementing a
numerically exact self-consistent field theory to probe the phase diagram and
the shape of the AB interface.Comment: 12 pages, 11 included figure
Possible origins of macroscopic left-right asymmetry in organisms
I consider the microscopic mechanisms by which a particular left-right (L/R)
asymmetry is generated at the organism level from the microscopic handedness of
cytoskeletal molecules. In light of a fundamental symmetry principle, the
typical pattern-formation mechanisms of diffusion plus regulation cannot
implement the "right-hand rule"; at the microscopic level, the cell's
cytoskeleton of chiral filaments seems always to be involved, usually in
collective states driven by polymerization forces or molecular motors. It seems
particularly easy for handedness to emerge in a shear or rotation in the
background of an effectively two-dimensional system, such as the cell membrane
or a layer of cells, as this requires no pre-existing axis apart from the layer
normal. I detail a scenario involving actin/myosin layers in snails and in C.
elegans, and also one about the microtubule layer in plant cells. I also survey
the other examples that I am aware of, such as the emergence of handedness such
as the emergence of handedness in neurons, in eukaryote cell motility, and in
non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue.
Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in
Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec
Flexible prey handling, preference and a novel capture technique in invasive, sub-adult Chinese mitten crabs
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