Sergio R. Aragon

A precise boundary element method for macromolecular transport properties.

A very precise boundary element numerical solution of the exact formulation of the hydrodynamic resistance problem with stick boundary conditions is presented. BEST, the Fortran 77 program developed for this purpose, computes the full transport tensors in the center of resistance or the center of diffusion for an arbitrarily shaped rigid body, including rotation‐translation coupling. The input for this program is a triangulation of the solvent‐defined surface of the molecule of interest, given by Connollys MSROLL or other suitable triangulator. The triangulation is prepared for BEST by COALESCE, a program that allows user control over the quality and number of triangles to describe the surface. High numerical precision is assured by effectively exact integration of the Oseen tensor over triangular surface elements, and by scaling the hydrodynamic computation to the precise surface area of the molecule. Efficiency of computation is achieved by the use of public domain LAPACK routines that call BLAS Level 3 hardware‐optimized subroutines available for most processors. A protein computation can be done in less than 10 min of CPU time in a modern Pentium IV processor. The present work includes a complete analysis of the sources of error in the numerical work and techniques to eliminate these errors. The operation of BEST is illustrated with applications to ellipsoids of revolution, and Lysozyme, a small protein. The typical numerical accuracy achieved is 0.05% compared to analytical theory. The numerical precision for a protein is better than 1%, much better than experimental errors in these quantities, and more than 10 times better than traditional bead‐based methods.

Construction, MD Simulation, and Hydrodynamic Validation of an All-Atom Model of a Monoclonal IgG Antibody

At 150 kDa, antibodies of the IgG class are too large for their structure to be determined with current NMR methodologies. Because of hinge-region flexibility, it is difficult to obtain atomic-level structural information from the crystal, and questions regarding antibody structure and dynamics in solution remain unaddressed. Here we describe the construction of a model of a human IgG1 monoclonal antibody (trastuzumab) from the crystal structures of fragments. We use a combination of molecular-dynamics (MD) simulation, continuum hydrodynamics modeling, and experimental diffusion measurements to explore antibody behavior in aqueous solution. Hydrodynamic modeling provides a link between the atomic-level details of MD simulation and the size- and shape-dependent data provided by hydrodynamic measurements. Eight independent 40 ns MD trajectories were obtained with the AMBER program suite. The ensemble average of the computed transport properties over all of the MD trajectories agrees remarkably well with the value of the translational diffusion coefficient obtained with dynamic light scattering at 20 degrees C and 27 degrees C, and the intrinsic viscosity measured at 20 degrees C. Therefore, our MD results likely represent a realistic sampling of the conformational space that an antibody explores in aqueous solution.

RECENT ADVANCES IN MACROMOLECULAR HYDRODYNAMIC MODELING

The modern implementation of the boundary element method [23] 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 400kDa, have shown that a model using a 1.1Å 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 (about -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 10ns duration. We have also studied a 150kDa flexible monoclonal IgG antibody, Trastuzumab, with multiple independent trajectories encompassing over 320ns 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 1.1Å 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.

Orientational and Translational Dynamics of Polyether/Water Solutions

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments and pulsed field-gradient spin-echo NMR (PFGSE-NMR) experiments were performed to measure the rotational and translational diffusion constants of a polyether, tetraethylene glycol dimethyl ether (TEGDE), in binary mixtures with water over concentrations ranging from pure TEGDE to approaching infinite dilution. In addition, hydrodynamic calculations of the rotational and translational diffusion constants for several rigid TEGDE conformations in the neat liquid and in the infinitely dilute solution were performed to supplement the experimental data. The rotational relaxation data follow the Debye-Stokes-Einstein (DSE) equation within experimental error over the entire water concentration range. The agreement with the DSE equation indicates that there is no significant structural change of the polyether as the water content is changed. In contrast to the rotational dynamics, the translational diffusion data show a distinct deviation from Stokes-Einstein (SE) behavior. As the water content of the mixture is reduced, the translational diffusion rate decreases less rapidly than the increase in viscosity alone predicts until the water/TEGDE mole ratio of 7:1 is reached. Upon further reduction of water content, the translational diffusion tracks the viscosity. Comparison of the translational data with the rotational data and the hydrodynamic computations shows that the translational dynamics cannot be explained by a molecular shape change and that the low water fraction solutions are the ones that deviate from hydrodynamic behavior. A conjecture is presented as a possible explanation for the different behaviors of the rotational and translational dynamics.

Mie scattering from thin anisotropic spherical shells

Exact simple closed form solutions for the electromagnetic scattering problem for a thin spherical shell composed of radially oriented optically anisotropic scattering elements have been obtained. The solution is valid for arbitrary shell size and index of refraction, but is limited to the case of small shell thickness compared to the shell radius. Connections with the Rayleigh–Debye approximation are clearly established and the polarizability of the shell is given in terms of the dielectric constants. It is found that the Rayleigh–Debye approximation correctly computes the effect of the anisotropy in this case. These results are useful in the interpretation of light scattering experiments from phospholipid vesicle dispersions.

MIE SCATTERING FROM ANISOTROPIC THICK SPHERICAL SHELLS

A theory of the electromagnetic scattering from spherical shells composed of radially oriented optically anisotropic scattering elements is presented. The theory is valid for arbitrary shell size and index of refraction but is limited to moderate shell thickness compared to the shell radius. The theory includes the effect of the shell thickness to second order, thereby extending previous work by Lange and Aragon [J. Chem. Phys. 92, 4643, (1990)]. Exact closed form solutions could be obtained for some, but not all of the terms in the expansion. Extensive comparisons with exact numerical computations based on infinite series of non‐integral order Bessel functions are included, as well as comparisons with the exact closed form expressions of the first order theory. The relationship of the second order theory to the Rayleigh–Debye approximation is examined and it is shown that, in contrast to the first order case, there are Mie corrections to the effects of the optical anisotropy on the scattering amplitudes....

Elucidating molecular motion through structural and dynamic filters of energy-minimized conformer ensembles.

Complex RNA structures are constructed from helical segments connected by flexible loops that move spontaneously and in response to binding of small molecule ligands and proteins. Understanding the conformational variability of RNA requires the characterization of the coupled time evolution of interconnected flexible domains. To elucidate the collective molecular motions and explore the conformational landscape of the HIV-1 TAR RNA, we describe a new methodology that utilizes energy-minimized structures generated by the program “Fragment Assembly of RNA with Full-Atom Refinement (FARFAR)”. We apply structural filters in the form of experimental residual dipolar couplings (RDCs) to select a subset of discrete energy-minimized conformers and carry out principal component analyses (PCA) to corroborate the choice of the filtered subset. We use this subset of structures to calculate solution T1 and T1ρ relaxation times for 13C spins in multiple residues in different domains of the molecule using two simulation protocols that we previously published. We match the experimental T1 times to within 2% and the T1ρ times to within less than 10% for helical residues. These results introduce a protocol to construct viable dynamic trajectories for RNA molecules that accord well with experimental NMR data and support the notion that the motions of the helical portions of this small RNA can be described by a relatively small number of discrete conformations exchanging over time scales longer than 1 μs.

Accurate Hydrodynamic Modeling with the Boundary Element Method

The integral equations of hydrodynamics are presented for both stick and slip boundary conditions, and results of computations including rigid amino acids are used to obtain a new interpretation of the significance of the hydration parameter used in hydrodynamic modeling. The dynamics of the protein surface perturbs water at that boundary, giving rise to additional viscous energy dissipation which is mimicked by a uniform solvation of 1.1 A thick with stick boundary conditions. BEST (Aragon SR, J Comput Chem 25:1191–12055, 2004) has been used to study 49 different proteins, ranging in molecular weight from 9 to 400 kDa, and we have shown that a model using a 1.1 A thick hydration layer describes all protein transport properties very well. Molecular dynamics (MD) simulation has been used to investigate the origin of a handful of significant discrepancies in some multimeric proteins. 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 for small proteins 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.

Web-Based Hydrodynamics Computing

Proteins are long chains of amino acids that have a definite 3-d conformation and the shape of each protein is vital to its function. Since proteins are normally in solution, hydrodynamics (describes the movement of solvent around a protein as a function of shape and size of the molecule) can be used to probe the size and shape of proteins compared to those derived from X-ray crystallography. The computation chain needed for these hydrodynamics calculations consists of several separate programs by different authors on various platforms and often requires 3D visualizations of intermediate results. Due to the complexity, tools developed by a particular research group are not readily available for use by other groups, nor even by the non-experts within the same research group. To alleviate this situation, and to foment the easy and wide distribution of computational tools worldwide, we developed a web based interactive computational environment (WICE) including interactive 3D visualization that can be used with any web browser. Java based technologies were used to provide a platform neutral, user-friendly solution. Java Server Pages (JSP), Java Servlets, Java Beans, JOGL (Java bindings for OpenGL), and Java Web Start were used to create a solution that simplifies the computing chain for the user allowing the user to focus on their scientific research. WICE hides complexity from the user and provides robust and sophisticated visualization through a web browser.

Dynamics of wormlike chains: theory and computer simulations

The theory of the dynamics of wormlike chains based on the pure bending equation is reviewed. The normal mode solution obtained with the neglect of hydrodynamic interactions has been used to compute correlation functions for the forward depolarized dynamic light scattering, fluorescence polarization anisotropy, and the q dependent polarized dynamic light scattering of wormlike chains. The depolarized light scattering results are also applicable to the field free decay of the transient electric birefringence. Corrections to the relaxation rates due to hydrodynamic interactions are included. Extensive computer simulations based on Brownian dynamics for depolarized light scattering and fluorescence polarization anisotropy have been carried out with full and preaveraged hydrodynamic interaction, as a function of the ratio L/P of the contour length to persistence length of the chain. Flexibility was studied in the range 1 ≤ L/P ≤ 20 which spans relatively rigid to fairly flexible chains. The simulations are compared to theory in order to.study the validity of the assumptions used. It was found that the longest relaxation time observed in the simulations for all the experiments could be interpreted as the rotational diffusion of the chain, in agreement with the assumptions of the theory and the Yamakawa-Yoshisaki formulas for the rotational diffusion coefficient, even in the very flexible case. In the case of fluorescence, the data may show the presence of a small amount of coupling of flexing and rotation. The fast relaxation times in the rigid region are also in good agreement with theory, but the analysis of the data for greater flexibilities is not straightforward due to the resolution limitations of the exponential analysis programs and the large number of relaxations that contribute. The simulations show that, in general, the coupling between the degrees of freedom is small perhaps up to L/P ≤ 4, and is unknown beyond that. The difference between full and preaveraged hydrodynamic interactions was systematic but small.