Estimating friction coefficients of mixed globular/chain molecules, such as protein/DNA complexes

A simple biophysical model emulates budding yeast chromosome condensation

Mitotic chromosomes were one of the first cell biological structures to be described, yet their molecular architecture remains poorly understood. We have devised a simple biophysical model of a 300 kb-long nucleosome chain, the size of a budding yeast chromosome, constrained by interactions between binding sites of the chromosomal condensin complex, a key component of interphase and mitotic chromosomes. Comparisons of computational and experimental (4C) interaction maps, and other biophysical features, allow us to predict a mode of condensin action. Stochastic condensin-mediated pairwise interactions along the nucleosome chain generate native-like chromosome features and recapitulate chromosome compaction and individualization during mitotic condensation. Higher order interactions between condensin binding sites explain the data less well. Our results suggest that basic assumptions about chromatin behavior go a long way to explain chromosome architecture and are able to generate a molecular model of what the inside of a chromosome is likely to look like.

A molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman's Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor.

An empirical relationship between rotational correlation time and solvent accessible surface area

Structure-dynamics interrelationships are important in understanding protein function. We have explored the empirical relationship between rotational correlation times (tau(c) and the solvent accessible surface areas (SASA) of 75 proteins with known structures. The theoretical correlation between SASA and tau(c) through the equation SASA = K(r)tau(c) ((2/3)) is also considered. SASA was determined from the structure, tau(c) (calc) was determined from diffusion tensor calculations, and tau(c) (expt) was determined from NMR backbone(13) C or (15)N relaxation rate measurements. The theoretical and experimental values of tau(c) correlate with SASA with regression analyses values of K(r) as 1696 and 1896 m(2)s(-(2/3)), respectively, and with corresponding correlation coefficients of 0.92 and 0.70.

A pulsed field gradient NMR study of the aggregation and hydration of parvalbumin

Pulsed field gradient NMR is a convenient alternative to traditional methods for measuring diffusion of biological macromolecules. In the present study, pulsed field gradient NMR was used to study the effects of calcium binding and hydration on carp parvalbumin. Carp parvalbumin is known to undergo large changes in tertiary structure with calcium loading. The diffusion coefficient is a sensitive guide to changes in molecular shape and in the present study the large changes in tertiary structure were clearly reflected in the measured diffusion coefficient upon calcium loading. The (monomeric) calcium-loaded form had a diffusion coefficient of 1.4 x 10(-10) m(2) s(-1) at 298 K, which conforms with the structure being a nearly spherical prolate ellipsoid from X-ray studies. The calcium-free form had a significantly lower diffusion coefficient of 1.1 x 10(-10) m(2) s(-1). The simplest explanation consistent with the change in diffusion coefficient is that the parvalbumin molecules form dimers upon the removal of Ca(2+) at the protein concentration studied (1 mM).