Recent advances in macromolecular hydrodynamic modeling

Abstract

The modern implementation of the boundary element method (S.R. Aragon, J. Comput. Chem. 25(2004)1191–12055) has ushered unprecedented accuracy and precision for the solution of the Stokes equations of hydrodynamics with stick boundary conditions. This article begins by reviewing computations with the program BEST of smooth surface objects such as ellipsoids, the dumbbell, and cylinders that demonstrate that the numerical solution of the integral equation formulation of hydrodynamics yields very high precision and accuracy. When BEST is used for macromolecular computations, the limiting factor becomes the definition of the molecular hydrodynamic surface and the implied effective solvation of the molecular surface. Studies on 49 different proteins, ranging in molecular weight from 9 to over 400 kDa, have shown that a model using a 1.1 A thick hydration layer describes all protein transport properties very well for the overwhelming majority of them. In addition, this data implies that the crystal structure is an excellent representation of the average solution structure for most of them. In order to investigate the origin of a handful of significant discrepancies in some multimeric proteins (over −20% observed in the intrinsic viscosity), the technique of Molecular Dynamics simulation (MD) has been incorporated into the research program. A preliminary study of dimeric α-chymotrypsin using approximate implicit water MD is presented. In addition I describe the successful validation of modern protein force fields, ff03 and ff99SB, for the accurate computation of solution structure in explicit water simulation by comparison of trajectory ensemble average computed transport properties with experimental measurements. This work includes small proteins such as lysozyme, ribonuclease and ubiquitin using trajectories around 10 ns duration. We have also studied a 150 kDa flexible monoclonal IgG antibody, trastuzumab, with multiple independent trajectories encompassing over 320 ns of simulation. The close agreement within experimental error of the computed and measured properties allows us to conclude that MD does produce structures typical of those in solution, and that flexible molecules can be properly described using the method of ensemble averaging over a trajectory. We review similar work on the study of a transfer RNA molecule and DNA oligomers that demonstrate that within 3% a simple uniform hydration model 1.1 A thick provides agreement with experiment for these nucleic acids. In the case of linear oligomers, the precision can be improved close to 1% by a non-uniform hydration model that hydrates mainly in the DNA grooves, in agreement with high resolution x-ray diffraction. We conclude with a vista on planned improvements for the BEST program to decrease its memory requirements and increase its speed without sacrificing accuracy.

The Protein and Contrast Agent–Specific Influence of Pathological Plasma-Protein Concentration Levels on Contrast-Enhanced Magnetic Resonance Imaging

“…8,21 Because the IgG molecular mass (approximately 150 kDa) is approximately 3 times as large as that of albumin (67.5 kDa), 22 IgG could, in agreement with our results, be expected to exhibit larger effects on contrast-agent relaxivities than albumin under the assumption of a nonYspecific weak binding and an equal number of binding sites per protein mass. The effect size of a smaller protein could reach or even surpass that of a nonspecifically binding larger protein if it offered a particular contrast agent one or more tailored binding sites with optimally positioned protein functional groups that strongly increase either polar or nonYpolar attraction forces.…”

Introduction: Calculation of Hydrodynamic Parameters

“…Bead model coordinates are easily derived when (1) the model is based on atomic coordinates from a crystal or NMR structure (in which case the use of HYDROPRO ( (Ortega et al 2011b), below), US-SOMO ( (Brookes et al 2010a, b), below) or BEST ( (Aragon 2004;2011), below) is more appropriate) or (2) electron microscopy density maps (when HYDROMIC ((García de la Torre et al 2001), below) can be used) or (3) the particle can be reliably represented by a geometric shape which can, in turn, be defined by an equation and populated with spheres by HYDROPIX ((García de la Torre 2001a), below) or (4) AtoB (Byron 1997) is used to construct a bead model de novo (see, e.g., Byron (2008)). …”

“…For extremely large models, the computing time in US-SOMO can be reduced by using AtoB with a suitably large grid size to decrease the number of beads comprising a given model. BEST (BE modelling under stick boundary conditions) (Aragon 2004(Aragon , 2011) is conceptually similar to HYDROPRO in that the surface of the macromolecule is discretised, in order to facilitate the solution of the integral form of Eq. (9.8), not by dividing its volume into beads but instead by covering it with a patchwork of N very small triangles.…”

“…11) or the newer Zeno (Kang et al 2004) algorithm (Brookes and Rocco,Sect. 10.3) or (2) the BEST algorithm of Sergio Aragon (2004, 2011 where the theoretical basis for this approach is fully described). US-SOMO has, since its inception, developed to embrace the hugely complementary modelling possibilities afforded by smallangle X-ray and neutron scattering (SAXS and SANS, respectively); this is not covered in any detail by Brookes and Rocco in Chap.…”

“…Also can construct and compute HARPs for bead-per-atom/residue models BEST Aragon (2004, 2011 http://esmeralda.sfsu.edu/ Constructs triangular patchwork surface models from PDB files and computes HARPs for models of decreasing triangle size, extrapolating values to the case of infinitely small triangles to arrive at the final outputs (continued) …”