73 research outputs found
Nanoindentation of virus capsids in a molecular model
A molecular-level model is used to study the mechanical response of empty
cowpea chlorotic mottle virus (CCMV) and cowpea mosaic virus (CPMV) capsids.
The model is based on the native structure of the proteins that consitute the
capsids and is described in terms of the C-alpha atoms. Nanoindentation by a
large tip is modeled as compression between parallel plates. Plots of the
compressive force versus plate separation for CCMV are qualitatively consistent
with continuum models and experiments, showing an elastic region followed by an
irreversible drop in force. The mechanical response of CPMV has not been
studied, but the molecular model predicts an order of magnitude higher
stiffness and a much shorter elastic region than for CCMV. These large changes
result from small structural changes that increase the number of bonds by only
30% and would be difficult to capture in continuum models. Direct comparison of
local deformations in continuum and molecular models of CCMV shows that the
molecular model undergoes a gradual symmetry breaking rotation and accommodates
more strain near the walls than the continuum model. The irreversible drop in
force at small separations is associated with rupturing nearly all of the bonds
between capsid proteins in the molecular model while a buckling transition is
observed in continuum models.Comment: 18 figure
Nonlinear Finite Element Analysis of Nanoindentation of Viral Capsids
Recent Atomic Force Microscope (AFM) nanoindentation experiments measuring
mechanical response of the protein shells of viruses have provided a
quantitative description of their strength and elasticity. To better understand
and interpret these measurements, and to elucidate the underlying mechanisms,
this paper adopts a course-grained modeling approach within the framework of
three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic,
elastic, thick shell models are proposed for two capsids: the spherical Cowpea
Chlorotic Mottle Virus (CCMV), and the ellipsocylindrical bacteriophage . As analyzed by the finite element method, these models enable parametric
characterization of the effects of AFM tip geometry, capsid dimensions, and
capsid constitutive descriptions. The generally nonlinear force response of
capsids to indentation is shown to be insensitive to constitutive details, and
greatly influenced by geometry. Nonlinear stiffening and softening of the force
response is dependent on the AFM tip dimensions and shell thickness. Fits of
the models capture the roughly linear behavior observed in experimental
measurements and result in estimates of Young's moduli of 280--360 MPa
for CCMV and 4.5 GPa for .Comment: 24 pages, 10 figures, submitted to Biophysical Journa
Fluctuating shells under pressure
Thermal fluctuations strongly modify the large length-scale elastic behavior
of crosslinked membranes, giving rise to scale-dependent elastic moduli. While
thermal effects in flat membranes are well understood, many natural and
artificial microstructures are modeled as thin elastic {\it shells}. Shells are
distinguished from flat membranes by their nonzero curvature, which provides a
size-dependent coupling between the in-plane stretching modes and the
out-of-plane undulations. In addition, a shell can support a pressure
difference between its interior and exterior. Little is known about the effect
of thermal fluctuations on the elastic properties of shells. Here, we study the
statistical mechanics of shape fluctuations in a pressurized spherical shell
using perturbation theory and Monte Carlo computer simulations, explicitly
including the effects of curvature and an inward pressure. We predict novel
properties of fluctuating thin shells under point indentations and
pressure-induced deformations. The contribution due to thermal fluctuations
increases with increasing ratio of shell radius to thickness, and dominates the
response when the product of this ratio and the thermal energy becomes large
compared to the bending rigidity of the shell. Thermal effects are enhanced
when a large uniform inward pressure acts on the shell, and diverge as this
pressure approaches the classical buckling transition of the shell. Our results
are relevant for the elasticity and osmotic collapse of microcapsules.Comment: To appear in PNAS; accepted version including Supplementary
Informatio
Density waves theory of the capsid structure of small icosahedral viruses
We apply Landau theory of crystallization to explain and to classify the
capsid structures of small viruses with spherical topology and icosahedral
symmetry. We develop an explicit method which predicts the positions of centers
of mass for the proteins constituting viral capsid shell. Corresponding density
distribution function which generates the positions has universal form without
any fitting parameter. The theory describes in a uniform way both the
structures satisfying the well-known Caspar and Klug geometrical model for
capsid construction and those violating it. The quasiequivalence of protein
environments in viral capsid and peculiarities of the assembly thermodynamics
are also discussed.Comment: 8 pages, 3 figur
Mechanical properties of micro- and nanocapsules: Single-capsule measurements
AbstractCapsules of micron and sub-micron dimensions are abundant in nature in the form of bacterial or viral capsids and play an increasing role in modern technology for encapsulation and release of agents. The capsules' mechanical properties are of great importance in this context not only for stability but as well for transport properties in flow, rheology or adhesion. Thus, techniques that allow for single-capsule mechanical characterization have caught much attention recently and we summarize experimental developments in this field as well as theoretical background of capsule deformation with special attention to small deformation measurements. Deformation studies on polyelectrolyte multilayer capsules are introduced as a case study, since they can be tailored in their geometry and composition and are thus well-suited as a model system
Buckling instability of viral capsides
The crystallographic structure of spherical viruses is modeled using a multiscale approach combining a macroscopic Helfrich model for morphology evolution with a microscopic approximation of a classical density functional theory for the protein interactions. The derivation of the model is based on energy dissipation and conservation of protein number density. The resulting set of equations is solved within a diffuse domain approach using finite elements and shows buckling transitions of spherical into faceted viral shapes
Statistical mechanics of thin spherical shells
We explore how thermal fluctuations affect the mechanics of thin amorphous
spherical shells. In flat membranes with a shear modulus, thermal fluctuations
increase the bending rigidity and reduce the in-plane elastic moduli in a
scale-dependent fashion. This is still true for spherical shells. However, the
additional coupling between the shell curvature, the local in-plane stretching
modes and the local out-of-plane undulations, leads to novel phenomena. In
spherical shells thermal fluctuations produce a radius-dependent negative
effective surface tension, equivalent to applying an inward external pressure.
By adapting renormalization group calculations to allow for a spherical
background curvature, we show that while small spherical shells are stable,
sufficiently large shells are crushed by this thermally generated "pressure".
Such shells can be stabilized by an outward osmotic pressure, but the effective
shell size grows non-linearly with increasing outward pressure, with the same
universal power law exponent that characterizes the response of fluctuating
flat membranes to a uniform tension.Comment: 16 pages, 6 figure
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