Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure

Application of Spectral Remote Sensing for Agronomic Decisions

Remote sensing has provided valuable insights into agronomic management over the past 40 yr. The contributions of individuals to remote sensing methods have lead to understanding of how leaf reflectance and leaf emittance changes in response to leaf thickness, species, canopy shape, leaf age, nutrient status, and water status. Leaf chlorophyll and the preferential absorption at different wavelengths provides the basis for utilizing reflectance with either broad-band radiometers typical of current satellite platforms or hyperspectral sensors that measure reflectance at narrow wavebands. Understanding of leaf reflectance has lead to various vegetative indices for crop canopies to quantify various agronomic parameters, e.g., leaf area, crop cover, biomass, crop type, nutrient status, and yield. Emittance from crop canopies is a measure of leaf temperature and infrared thermometers have fostered crop stress indices currently used to quantify water requirements. These tools are being developed as we learn how to use the information provided in reflectance and emittance measurements with a range of sensors. Remote sensing continues to evolve as a valuable agronomic tool that provides information to scientists, consultants, and producers about the status of their crops. This area is still relatively new compared with other agronomic fields; however, the information content is providing valuable insights into improved management decisions. This article details the current status of our understanding of how reflectance and emittance have been used to quantitatively assess agronomic parameters and some of the challenges facing future generations of scientists seeking to further advance remote sensing for agronomic applications