Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how they interact with binding partners. However, it is unclear whether continuum methods can be used to quantitatively understand the energetics of membrane protein insertion and stability. Recent translation experiments suggest that the energy required to insert charged peptides into membranes is much smaller than predicted by present continuum theories. Atomistic simulations have pointed to bilayer inhomogeneity and membrane deformation around buried charged groups as two critical features that are neglected in simpler models. Here, we develop a fully continuum method that circumvents both of these shortcomings by using elasticity theory to determine the shape of the deformed membrane and then subsequently uses this shape to carry out continuum electrostatics calculations. Our method does an excellent job of quantitatively matching results from detailed molecular dynamics simulations at a tiny fraction of the computational cost. We expect that this method will be ideal for studying large membrane protein complexes.

The elasticity of α-helices is examined using equilibrium molecular-dynamics simulations. From the statistics of curvatures and twists, we compute the elastic moduli of several representative α-helices, both in the presence and absence of aqueous solvent. We discover that the bending modulus (persistence length) of the helices is independent of the amino-acid sequence, although helices in water are slightly softer than in vacuum. The response of the helices under the action of an external force is also computed and compared with continuum mechanics predictions. Within the time scale of our simulation, we show that the properties of α-helices are well reproduced by an elastic and isotropic rod. The persistence length (bending modulus) of most α-helices in water or vacuum is ≈100nm, roughly twice that of DNA.

We present the first results for masses of spin-$\frac{3}{2}$ N and $\Delta$ baryons in lattice QCD using fat-link irrelevant clover fermions. Spin-$\frac{3}{2}$ interpolating fields, providing overlap with both spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ states, are considered. In the isospin-$\frac{1}{2}$ sector we observe, after appropriate spin and parity projection, a strong signal for the $J^P={\frac{3}{2}}^{-}$ state together with a weak but discernible signal for the ${\frac{3}{2}}^{+}$ state with a mass splitting near that observed experimentally. We also find good agreement between the ${\frac{1}{2}}^{\pm }$ masses and earlier nucleon mass simulations with the standard spin-$\frac{1}{2}$ interpolating field. For the isospin-$\frac{3}{2}$ $\Delta$ states, clear mass splittings are observed between the various ${\frac{1}{2}}^{\pm }$ and ${\frac{3}{2}}^{\pm }$ channels, with the calculated level orderings in good agreement with those observed empirically.

We present a framework to compute the responses of hadron masses to the chemical potential in lattice QCD simulations. As a first trial, the screening mass of the pseudoscalar meson and its first and second responses are evaluated. We present results on a $16\times 8^2\times 4$ lattice with two flavors of staggered quarks below and above $T_c.$ The responses to both the isoscalar and isovector chemical potentials are obtained. They show different behavior in the low and the high temperature phases, which may be explained as a consequence of chiral symmetry breaking and restoration, respectively.