Structural studies of tailed spindle virus reveal a structural paradigm used in the assembly of spindle-shaped viruses.

The spindle-shaped virion morphology is common among archaeal viruses, where it is a defining characteristic of many viral families. However, structural heterogeneity intrinsic to spindle-shaped viruses has seriously hindered efforts to elucidate the molecular architecture of these lemon-shaped capsids. We have utilized a combination of cryo-electron microscopy and X-ray crystallography to study tailed spindle virus (ATSV).

Ground state instabilities of protein shells are eliminated by buckling.

We propose a hybrid discrete-continuum model to study the ground state of protein shells. The model allows for shape transformation of the shell and buckling transitions as well as the competition between states with different symmetries that characterize discrete particle models with radial pair potentials. Our main results are as follows.

Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response.

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model.

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart.

Bilayer-thickness-mediated interactions between integral membrane proteins.

Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compression and expansion of the bilayer hydrophobic core, membrane tension, and bilayer bending, resulting in biharmonic equilibrium equations describing the shape of lipid bilayers for a given set of bilayer-protein boundary conditions.

Nonuniform elastic properties of macromolecules and effect of prestrain on their continuum nature.

Many experimental and theoretical methods have been developed to calculate the coarse-grained continuum elastic properties of macromolecules. However, all of those methods assume uniform elastic properties. Following the continuum mechanics framework, we present a systematic way of calculating the nonuniform effective elastic properties from atomic thermal fluctuations obtained from molecular dynamics simulation at any coarse-grained scale using a potential of the mean-force approach.

Architecture and Function of Mechanosensitive Membrane Protein Lattices.

Experiments have revealed that membrane proteins can form two-dimensional clusters with regular translational and orientational protein arrangements, which may allow cells to modulate protein function. However, the physical mechanisms yielding supramolecular organization and collective function of membrane proteins remain largely unknown. Here we show that bilayer-mediated elastic interactions between membrane proteins can yield regular and distinctive lattice architectures of protein clusters, and may provide a link between lattice architecture and lattice function.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology.

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time.

Computational mechanics of viral capsids.

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics.

Mechanical collapse of confined fluid membrane vesicles.

Compact cylindrical and spherical invaginations are common structural motifs found in cellular and developmental biology. To understand the basic physical mechanisms that produce and maintain such structures, we present here a simple model of vesicles in confinement, in which mechanical equilibrium configurations are computed by energy minimization, balancing the effects of curvature elasticity, contact of the membrane with itself and the confining geometry, and adhesion. For cylindrical confinement, the shape equations are solved both analytically and numerically by finite element analysis.

Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology.

We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of 'lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs.

Microrheology of highly crosslinked microtubule networks is dominated by force-induced crosslinker unbinding.

We determine the time- and force-dependent viscoelastic responses of reconstituted networks of microtubules that have been strongly crosslinked by biotin-streptavidin bonds. To measure the microscale viscoelasticity of such networks, we use a magnetic tweezers device to apply localized forces. At short time scales, the networks respond nonlinearly to applied force, with stiffening at small forces, followed by a reduction in the stiffening response at high forces, which we attribute to the force-induced unbinding of crosslinks.

Linear invariant tensor interpolation applied to cardiac diffusion tensor MRI.

Purpose: Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape.

Methods: Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor.

Viral capsid equilibrium dynamics reveals nonuniform elastic properties.

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system.

Affine-nonaffine transition in networks of nematically ordered semiflexible polymers.

We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to nonaffine crossover controlled by the ratio of the filament length to the nonaffinity length. Deep in the nonaffine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear-response regime for highly ordered networks and a dependence of the shear modulus on shear direction at both small (linear) and finite (nonlinear) strains that is different from the affine prediction of orthotropic continuum linear elasticity. We show that these features can be understood in terms of a generalized floppy modes analysis of the nonaffine mechanics and a type of cooperative Euler buckling.

On the role of the filament length distribution in the mechanics of semiflexible networks.

This paper explores the effects of filament length polydispersity on the mechanical properties of semiflexible crosslinked polymer networks. Extending previous studies on monodisperse networks, we compute numerically the response of crosslinked networks of elastic filaments of bimodal and exponential length distributions. These polydisperse networks are subject to the same affine to nonaffine (A/NA) transition observed previously for monodisperse networks, wherein the decreases in either crosslink density or bending stiffness lead to a shift from affine, stretching-dominated deformations to nonaffine, bending-dominated deformations.

Morphology and interaction between lipid domains.

Cellular membranes are a heterogeneous mix of lipids, proteins and small molecules. Special groupings enriched in saturated lipids and cholesterol form liquid-ordered domains, known as "lipid rafts," thought to serve as platforms for signaling, trafficking and material transport throughout the secretory pathway. Questions remain as to how the cell maintains small fluid lipid domains, through time, on a length scale consistent with the fact that no large-scale phase separation is observed.

Mechanical stress analysis of a rigid inclusion in distensible material: a model of atherosclerotic calcification and plaque vulnerability.

The role of atherosclerotic calcification in plaque rupture remains controversial. In previous analyses using finite element model analysis, circumferential stress was reduced by the inclusion of a calcium deposit in a representative human anatomical configuration. However, a recent report, also using finite element analysis, suggests that microscopic calcium deposits increase plaque stress.

Membrane shape as a reporter for applied forces.

Recent advances have enabled 3-dimensional reconstructions of biological structures in vivo, ranging in size and complexity from single proteins to multicellular structures. In particular, tomography and confocal microscopy have been exploited to capture detailed 3-dimensional conformations of membranes in cellular processes ranging from viral budding and organelle maintenance to phagocytosis. Despite the wealth of membrane structures available, there is as yet no generic, quantitative method for their interpretation.

Influence of nonuniform geometry on nanoindentation of viral capsids.

A series of recent nanoindentation experiments on the protein shells (capsids) of viruses has established atomic force microscopy (AFM) as a useful framework for probing the mechanics of large protein assemblies. Specifically these experiments provide an opportunity to study the coupling of the global assembly response to local conformational changes. AFM experiments on cowpea chlorotic mottle virus, known to undergo a pH-controlled swelling conformational change, have revealed a pH-dependent mechanical response.

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 phi29 .

Failure of viral shells.

We report a combined theoretical and experimental study of the structural failure of viral shells under mechanical stress. We find that discontinuities in the force-indentation curve associated with failure should appear when the so-called Föppl-von Kármán (FvK) number exceeds a critical value. A nanoindentation study of a viral shell subject to a soft-mode instability, where the stiffness of the shell decreases with increasing pH, confirms the predicted onset of failure as a function of the FvK number.