Intrinsic Viscosity of Proteins and Platonic Solids by Boundary Element Methods

Abstract

The boundary element (BE) method is used to implement a very precise computation of the intrinsic viscosity for rigid molecules of arbitrary shape. The formulation, included in our program BEST, is tested against the analytical Simha formula for ellipsoids of revolution, and the results are essentially numerically exact. Previously unavailable, very precise results for a series of Platonic solids are also presented. The formulation includes the optional determination of the center of viscosity; however, for globular proteins, the difference compared to the computation based on the centroid is insignificant. The main application is to a series of 30 proteins ranging in molecular weight from 12 to 465 kD. The computation starts from the crystal structure as obtained from the Protein Data Bank, and a hydration thickness of 1.1 Å obtained in previous work with BEST was used. The results (extrapolated to an infinite number of triangular boundary elements) for the proteins are separated into two groups: monomeric and multimeric proteins. The agreement with experimental measurements of the intrinsic viscosity in the case of monomeric proteins is excellent and within experimental error of 5%, demonstrating that the solution and crystal structure are hydrodynamically equivalent. However, for some multimeric proteins, we observe strong systematic deviations around -20%, which we interpret as a systematic deviation of the solution structure from the crystal structure. A possible description of the structural change is deduced by using simple ellipsoid model parameters. A method to obtain intrinsic viscosity values for proteins to 1-2% accuracy (better than experimental error) on the basis of a single BE computation (avoiding the need for an extrapolation on the number of surface triangles) is also presented.

Lokale und globale Dynamik im ungeordneten Synuklein‐Protein

“…If we approximate that the R 2 is determined exclusively by J(0) and ignore the small contributions from higher frequency terms, then an intrinsic viscosity of 2.21-3.69 cm 3 /g (95% CI) would be required to explain the observed ratio of R 2 at two concentrations. The estimated value of intrinsic viscosity for α-synuclein is comparable to the intrinsic viscosities obtained for a broad range of proteins [18] . S12 Figure S7.…”

Computing translational diffusion and sedimentation coefficients: an evaluation of experimental data and programs

“…Most of these structures had already been utilised in previous studies by our groups (Brookes et al 2010a, b;Rai et al 2005) and had had missing atoms and/or residues modelled using WHATIF [ (Vriend 1990); http://swift.cmbi.ru.nl/servers/ html/index.html] and O (Jones et al 1991). The same procedures were applied, when necessary, to the additional proteins utilised in this study, all of which were taken from the list in Hahn and Aragon (2006). The presence of carbohydrate chains on the surface was limited to a single example (α-lactalbumin).…”

“…Of particular importance, the literature D t 0 (20,w) values considered were directly determined and not derived from s 0 (20,w) values, as was done in a number of cases in the comparisons reported by Hahn and Aragon (2006).…”

Newtonian Viscosity of Dilute, Semidilute, and Concentrated Polymer Solutions

“…Three general approaches have been described. One method models complex particles as an agglomeration of hydrodynamic point sources (the hydrodynamic bead model) [Garcia de la Torre et al, 2000], which interact via an Oseen-type hydrodynamic interaction; a second approach (the boundary element method) solves the Stokes integral equation for a particle whose surface is constructed from an array of flat polygons [Hahn and Aragon, 2006]; and a third method (numerical path integration method) is based on an analogy between hydrodynamics and electrostatics [Hahn et al, 2004]. The accuracy of each of the finite element methods increases as the number of finite elements, N, increases, but so does the computational time.…”

“…For dilute colloidal dispersions, the seminal work of Einstein and Simha has culminated in the development of numerical methods to compute the intrinsic viscosity of impermeable particles of irregular geometry as a tool for structural analysis [Garcia de la Torre et al, 2000;Hahn et al, 2004;Hahn and Aragon, 2006;Mansfield et al, 2007]. The effect of particle permeability can be incorporated via the Debye-Bueche-Brinkman theory [Veerapaneni and Wiesner, 1996;Zackrisson and Bergenholtz, 2003].…”