The partitioning of lipids among different microenvironments in a bilayer is of considerable relevance to characterization of composition variations in biomembranes. Atomistic simulation has been ill-suited to model equilibrated lipid mixtures because the time required for diffusive exchange of lipids among microenvironments exceeds typical submicrosecond molecular dynamics trajectories. A method to facilitate local composition fluctuations, using Monte Carlo mutations to change lipid structures within the semigrand-canonical ensemble (at a fixed difference in component chemical potentials, Deltamu), was recently implemented to address this challenge. This technique was applied here to mixtures of dimyristoylphosphatidylcholine and a shorter-tail lipid, either symmetric (didecanoylphosphatidylcholine (DDPC)) or asymmetric (hexanoyl-myristoylphosphatidylcholine), arranged in two types of structure: bilayer ribbons and buckled bilayers. In ribbons, the shorter-tail component showed a clear enrichment at the highly curved rim, more so for hexanoyl-myristoylphosphatidylcholine than for DDPC. Results on buckled bilayers were variable. Overall, the DDPC content of buckled bilayers tended to exceed by several percent the DDPC content of flat ones simulated at the same Deltamu, but only for mixtures with low overall DDPC content. Within the buckled bilayer structure, no correlation could be resolved between the sign or magnitude of the local curvature of a leaflet and the mean local lipid composition. Results are discussed in terms of packing constraints, surface area/volume ratios, and curvature elasticity.
Protein similarity estimations can be achieved using reduced dimensional representations and we describe a new application for the generation of two-dimensional maps from the three-dimensional structure. The code for the dimensionality reduction is based on the concept of pseudo-random generation of two-dimensional coordinates and Monte Carlo-like acceptance criteria for the generated coordinates. A new method for calculating protein similarity is developed by introducing a distance-dependent similarity field. Similarity of two proteins is derived from similarity field indices between amino acids based on various criteria such as hydrophobicity, residue replacement factors and conformational similarity, each showing a one factor Gaussian dependence. Results on comparisons of misfolded protein models with data sets of correctly folded structures show that discrimination between correctly folded and misfolded structures is possible. Tests were carried out on five different proteins, comparing a misfolded protein structure with members of the same topology, architecture, family and domain according to the CATH classification.
Data reduction techniques are now a vital part of numerical analysis and principal component analysis is often used to identify important molecular features from a set of descriptors. We now take a different approach and apply data reduction techniques directly to protein structure. With this we can reduce the three-dimensional structural data into two-dimensions while preserving the correct relationships. With two-dimensional representations, structural comparisons between proteins are accelerated significantly. This means that protein-protein similarity comparisons are now feasible on a large scale. We show how the approach can help to predict the function of kinase structures according to the Hanks' classification based on their structural similarity to different kinase classes.
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