Conformational Free-Energy Landscapes for a Peptide in Saline Environments

AbstractThe conformations that proteins adopt in solution are a function of both their primary structure and surrounding aqueous environment. Recent experimental and computational work on small peptides, e.g., polyK, polyE, and polyR, have highlighted an interesting and unusual behavior in the presence of aqueous ions such as ClO4−, Na+, and K+. Notwithstanding the aforementioned studies, as of this writing, the nature of the driving force induced by the presence of ions and its role on the conformational stability of peptides remains only partially understood. Molecular-dynamics simulations have been performed on the heptapeptide AEAAAEA in NaCl and KCl solutions at concentrations of 0.5, 1.0, and 2.0 M. Metadynamics in conjunction with a three-dimensional model reaction coordinate was used to sample the conformational space of the peptide. All simulations were run for 2 μs. Free-energy landscapes were computed over the model reaction coordinate for the peptide in each saline assay as well as in the absence of ions. Circular dichroism spectra were also calculated from each trajectory. In the presence of Na+ and K+ ions, no increase in helicity is observed with respect to the conformation in pure water

Tensor Embedding of the Fundamental Matrix

We revisit the bilinear matching constraint between two perspective views of a 3D scene. Our objective is to represent the constraint in the same manner and form as the trilinear constraint among three views. The motivation is to establish a common terminology that bridges between the fundamental matrix F (associated with the bilinear constraint) and the trifocal tensor T jk i (associated with the trilinearities). By achieving this goal we can unify both the properties and the techniques introduced in the past for working with multiple views for geometric applications. Doing that we introduce a 3 \Theta 3 \Theta 3 tensor F jk i , we call the bifocal tensor, that represents the bilinear constraint. The bifocal and trifocal tensors share the same form and share the same contraction properties. By close inspection of the contractions of the bifocal tensor into matrices we show that one can represent the family of rank-2 homography matrices by [ffi] \Theta F where ffi is a free vector. ..

High-Order Differential Geometry of Curves for Multiview Reconstruction and Matching

Abstract. The relationship between the orientation and curvature of projected curves and the orientation and curvature of the underlying space curve has been previously established. This has allowed a disambiguation of correspondences in two views and a transfer of these properties to a third view for confirmation. We propose that a higher-order intrinsic differential geometry attribute, namely, curvature derivative, is necessary to account for the range of variation of space curves and their projections. We derive relationships between curvature derivative in a projected view, and curvature derivative and torsion of the underlying space curve. Regardless of the point, tangent, and curvature, any pair of curvature derivatives are possible correspondences, but most would lead to very high torsion and curvature derivatives. We propose that the minimization of third order derivatives of the reconstruction, which combines torsion and curvature derivative of the space curve, regularizes the process of finding the correct correspondences.