Singular value decomposition of the radial distribution function for hard sphere and square well potentials

Models for randomly distributed nanoscopic domains on spherical vesicles

The existence of lipid domains in the plasma membrane of biological systems has proven controversial, primarily due to their nanoscopic size-a length scale difficult to interrogate with most commonly used experimental techniques. Scattering techniques have recently proven capable of studying nanoscopic lipid domains populating spherical vesicles. However, the development of analytical methods able of predicting and analyzing domain pair correlations from such experiments has not kept pace. Here, we developed models for the random distribution of monodisperse, circular nanoscopic domains averaged on the surface of a spherical vesicle. Specifically, the models take into account (i) intradomain correlations corresponding to form factors and interdomain correlations corresponding to pair distribution functions, and (ii) the analytical computation of interdomain correlations for cases of two and three domains on a spherical vesicle. In the case of more than three domains, these correlations are treated either by Monte Carlo simulations or by spherical analogs of the Ornstein-Zernike and Percus-Yevick (PY) equations. Importantly, the spherical analog of the PY equation works best in the case of nanoscopic size domains, a length scale that is mostly inaccessible by experimental approaches such as, for example, fluorescent techniques and optical microscopies. The analytical form factors and structure factors of nanoscopic domains populating a spherical vesicle provide a new and important framework for the quantitative analysis of experimental data from commonly studied phase-separated vesicles used in a wide range of biophysical studies.

Incorporation of Hard and Soft Protein-Protein Interactions into Models for Crowding Effects in Binary and Ternary Protein Mixtures. Comparison of Approximate Analytical Solutions with Numerical Simulation

In order to better understand how nonspecific interactions between solutes can modulate specific biochemical reactions taking place in complex media, we introduce a simplified model aimed at elucidating general principles. In this model, solutions containing two or three species of interacting globular proteins are modeled as a fluid of spherical particles interacting through square well potentials that qualitatively capture both steric hard core repulsion and longer-ranged attraction or repulsion. The excess chemical potential, or free energy of solvation, of each particle species is calculated as a function of species concentrations, particle radii, and square well interaction range and depth. The results of analytical models incorporating two-body and three-body interactions are compared with the estimates of free energy obtained via Widom insertion into simulated equilibrium square-well fluids. The analytical models agree well with results of numeric simulations carried out for a variety of model parameters and fluid compositions up to a total particle volume fraction of ca. 0.2.