The elastic properties of capsids of the cowpea chlorotic mottle virus have been examined at pH 4.8 by nanoindentation measurements with an atomic force microscope. Studies have been carried out on WT capsids, both empty and containing the RNA genome, and on full capsids of a salt-stable mutant and empty capsids of the subE mutant. Full capsids resisted indentation more than empty capsids, but all of the capsids were highly elastic. There was an initial reversible linear regime that persisted up to indentations varying between 20% and 30% of the diameter and applied forces of 0.6 -1.0 nN; it was followed by a steep drop in force that is associated with irreversible deformation. A single point mutation in the capsid protein increased the capsid stiffness. The experiments are compared with calculations by finite element analysis of the deformation of a homogeneous elastic thick shell. These calculations capture the features of the reversible indentation region and allow Young's moduli and relative strengths to be estimated for the empty capsids.atomic force microscopy ͉ cowpea chlorotic mottle virus ͉ finite element analysis ͉ biomechanics
The current rapid growth in the use of nanosized particles is fueled in part by our increased understanding of their physical properties and ability to manipulate them, which is essential for achieving optimal functionality. Here we report detailed quantitative measurements of the mechanical response of nanosized protein shells (viral capsids) to large-scale physical deformations and compare them with theoretical descriptions from continuum elastic modeling and molecular dynamics (MD). Specifically, we used nanoindentation by atomic force microscopy to investigate the complex elastic behavior of Hepatitis B virus capsids. These capsids are hollow, approximately 30 nm in diameter, and conform to icosahedral (5-3-2) symmetry. First we show that their indentation behavior, which is symmetry-axis-dependent, cannot be reproduced by a simple model based on Föppl-von Kármán thin-shell elasticity with the fivefold vertices acting as prestressed disclinations. However, we can properly describe the measured nonlinear elastic and orientation-dependent force response with a three-dimensional, topographically detailed, finite-element model. Next, we show that coarse-grained MD simulations also yield good agreement with our nanoindentation measurements, even without any fitting of force-field parameters in the MD model. This study demonstrates that the material properties of viral nanoparticles can be correctly described by both modeling approaches. At the same time, we show that even for large deformations, it suffices to approximate the mechanical behavior of nanosized viral shells with a continuum approach, and ignore specific molecular interactions. This experimental validation of continuum elastic theory provides an example of a situation in which rules of macroscopic physics can apply to nanoscale molecular assemblies.
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 . 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 particulars, and greatly influenced by geometric and kinematic details. 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 approximately 280-360 MPa for CCMV and approximately 4.5 GPa for phi29 .
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. Previous theoretical studies have shown that homogeneous changes in shell geometry can play a significant role in the mechanical response. This article develops a method for accurately capturing the heterogeneous geometry of a viral capsid and explores its effect on mechanical response with a nonlinear continuum elasticity model. Models of both native and swollen cowpea chlorotic mottle virus capsids are generated from x-ray crystal structures, and are used in finite element simulations of AFM indentation along two-, three-, and fivefold icosahedral symmetry orientations. The force response of the swollen capsid model is observed to be softer by roughly a factor of two, significantly more nonlinear, and more orientation-dependent than that of a native capsid with equivalent elastic moduli, demonstrating that capsid geometric heterogeneity can have significant effects on the global structural response.
Understanding causes of polar bear (Ursus maritimus) attacks on humans is critical to ensuring both human safety and polar bear conservation. Although considerable attention has been focused on understanding black (U. americanus) and grizzly (U. arctos) bear conflicts with humans, there have been few attempts to systematically collect, analyze, and interpret available information on human‐polar bear conflicts across their range. To help fill this knowledge gap, a database was developed (Polar Bear‐Human Information Management System [PBHIMS]) to facilitate the range‐wide collection and analysis of human‐polar bear conflict data. We populated the PBHIMS with data collected throughout the polar bear range, analyzed polar bear attacks on people, and found that reported attacks have been extremely rare. From 1870–2014, we documented 73 attacks by wild polar bears, distributed among the 5 polar bear Range States (Canada, Greenland, Norway, Russia, and United States), which resulted in 20 human fatalities and 63 human injuries. We found that nutritionally stressed adult male polar bears were the most likely to pose threats to human safety. Attacks by adult females were rare, and most were attributed to defense of cubs. We judged that bears acted as a predator in most attacks, and that nearly all attacks involved ≤2 people. Increased concern for both human and bear safety is warranted in light of predictions of increased numbers of nutritionally stressed bears spending longer amounts of time on land near people because of the loss of their sea ice habitat. Improved conflict investigation is needed to collect accurate and relevant data and communicate accurate bear safety messages and mitigation strategies to the public. With better information, people can take proactive measures in polar bear habitat to ensure their safety and prevent conflicts with polar bears. This work represents an important first step towards improving our understanding of factors influencing human‐polar bear conflicts. Continued collection and analysis of range‐wide data on interactions and conflicts will help increase human safety and ensure the conservation of polar bears for future generations. © 2017 The Wildlife Society.
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