José García de la Torre

Calculation of Hydrodynamic Properties of Globular Proteins from Their Atomic-Level Structure

The solution properties, including hydrodynamic quantities and the radius of gyration, of globular proteins are calculated from their detailed, atomic-level structure, using bead-modeling methodologies described in our previous article (, Biophys. J. 76:3044-3057). We review how this goal has been pursued by other authors in the past. Our procedure starts from a list of atomic coordinates, from which we build a primary hydrodynamic model by replacing nonhydrogen atoms with spherical elements of some fixed radius. The resulting particle, consisting of overlapping spheres, is in turn represented by a shell model treated as described in our previous work. We have applied this procedure to a set of 13 proteins. For each protein, the atomic element radius is adjusted, to fit all of the hydrodynamic properties, taking values close to 3 A, with deviations that fall within the error of experimental data. Some differences are found in the atomic element radius found for each protein, which can be explained in terms of protein hydration. A computational shortcut makes the procedure feasible, even in personal computers. All of the model-building and calculations are carried out with a HYDROPRO public-domain computer program.

Comparison of theories for the translational and rotational diffusion coefficients of rod‐like macromolecules. Application to short DNA fragments

Two theories relating the translational and rotational diffusion coefficients Dt and Dr of a rod‐like macromolecule to its length and diameter, proposed by Broersma [J. Chem. Phys. 74, 6989 (1981)], and Tirado and Garcia de la Torre [J. Chem. Phys. 71, 2581 (1979); 73, 1986 (1980)] are shown to predict different values of the coefficients for a particle of given dimensions. Next, we use the two theories to analyze existing experimental data of sedimentation coefficients s and translational and rotational diffusion coefficients of short DNA fragments, and obtain values of the hydrated diameter of DNA d which is treated as an adjustable parameter. The results are compared with the expected value, d≂26A. This comparison favors clearly the Tirado–Garcia de la Torre theory in the case of Dt and s. For Dr, and using a rise per base pair r=3.4 A, this theory gives best agreement for all the data examined, while when r=3.3 A, the agreement depends on the source of data.

The Conformation of Serum Albumin in Solution: A Combined Phosphorescence Depolarization-Hydrodynamic Modeling Study

There is a striking disparity between the heart-shaped structure of human serum albumin (HSA) observed in single crystals and the elongated ellipsoid model used for decades to interpret the protein solution hydrodynamics at neutral pH. These two contrasting views could be reconciled if the protein were flexible enough to change its conformation in solution from that found in the crystal. To investigate this possibility we recorded the rotational motions in real time of an erythrosin-bovine serum albumin complex (Er-BSA) over an extended time range, using phosphorescence depolarization techniques. These measurements are consistent with the absence of independent motions of large protein segments in solution, in the time range from nanoseconds to fractions of milliseconds, and give a single rotational correlation time phi(BSA, 1 cP, 20 degrees C) = 40 +/- 2 ns. In addition, we report a detailed analysis of the protein hydrodynamics based on two bead-modeling methods. In the first, BSA was modeled as a triangular prismatic shell with optimized dimensions of 84 x 84 x 84 x 31.5 A, whereas in the second, the atomic-level structure of HSA obtained from crystallographic data was used to build a much more refined rough-shell model. In both cases, the predicted and experimental rotational diffusion rate and other hydrodynamic parameters were in good agreement. Therefore, the overall conformation in neutral solution of BSA, as of HSA, should be rigid, in the sense indicated above, and very similar to the heart-shaped structure observed in HSA crystals.

Hydrodynamic Properties of Rigid Particles: Comparison of Different Modeling and Computational Procedures

The hydrodynamic properties of rigid particles are calculated from models composed of spherical elements (beads) using theories developed by Kirkwood, Bloomfield, and their coworkers. Bead models have usually been built in such a way that the beads fill the volume occupied by the particles. Sometimes the beads are few and of varying sizes (bead models in the strict sense), and other times there are many small beads (filling models). Because hydrodynamic friction takes place at the molecular surface, another possibility is to use shell models, as originally proposed by Bloomfield. In this work, we have developed procedures to build models of the various kinds, and we describe the theory and methods for calculating their hydrodynamic properties, including approximate methods that may be needed to treat models with a very large number of elements. By combining the various possibilities of model building and hydrodynamic calculation, several strategies can be designed. We have made a quantitative comparison of the performance of the various strategies by applying them to some test cases, for which the properties are known a priori. We provide guidelines and computational tools for bead modeling.

Brownian Dynamics Simulation of Rigid Particles of Arbitrary Shape in External Fields

We have developed a Brownian dynamics simulation algorithm to generate Brownian trajectories of an isolated, rigid particle of arbitrary shape in the presence of electric fields or any other external agents. Starting from the generalized diffusion tensor, which can be calculated with the existing HYDRO software, the new program BROWNRIG (including a case-specific subprogram for the external agent) carries out a simulation that is analyzed later to extract the observable dynamic properties. We provide a variety of examples of utilization of this method, which serve as tests of its performance, and also illustrate its applicability. Examples include free diffusion, transport in an electric field, and diffusion in a restricting environment.

The molecular weight distribution and conformation of citrus pectins in solution studied by hydrodynamics

Abstract The molecular weight distribution of a citrus pectin has been analysed by a combined approach using gel-permeation chromatography with low-speed sedimentation equilibrium. (1) A pectin preparation from citrus fruit was fractionated on Sepharose CL-2B/Sepharose CL-4B. (2) Weight average molecular weights of the fractions were determined by low speed sedimentation equilibrium in multichannel cells. (3) An absolute calibration for the column for this material was thereby defined. (4) The (lognormal) molecular weight distribution thus obtained is consistent with a weight average of (90000±10000) g/mol, obtained separately on unfractionated material, and consistent with a distribution obtained on the same material but using light scattering as the molecular weight probe. The conformation of the pectin fractions in solution was studied in terms of: (1) the Wales-Van Holde parameter, k s [η] ; (2) Mark-Houwink-Kuhn-Sakurada plots of sedimentation coefficient and intrinsic viscosity data versus molecular weight; (3) rod models and (4) worm-like-coil models. The sedimentation data is consistent with a rod model (or a worm-like-coil with a large persistence length) with mass per unit length ∼ 430 g mol−1 nm−1. The intrinsic viscosity data is also consistent with a rod model but shows some anomalous features which may be suggestive of worm-like-coil behaviour at higher molecular weight, although it is not possible to fit this data with a realistic value of the mass per unit length.

Effects from bead size and hydrodynamic interactions on the translational and rotational coefficients of macromolecular bead models

In this work, we analyze a deficiency of the currently used form of the Kirkwood–Riseman (KR) theory for macromolecular bead models in regard to the finite size of the beads and illustrate the importance of a more complete description of hydrodynamic interactions. We consider several exact or very accurate theories for two‐bead models and compare their results with different KR‐based methods. One of them is the substitution technique in which the beads are substituted by a cubic array of smaller spheres. Its disadvantage is an increase in computer requirements. A novel result of our work is a very simple correction for the KR rotational coefficients intended to correct, in part, the failure originated by size effects. The comparison of the various approaches has been made for two specific cases, the rigid dumbbell and prolate ellipsoids, for which rigorous results are available. We show that the performance of the substitution technique is excellent, and that our correction improves in many cases the KR r...

Calculation of hydrodynamic properties of macromolecular bead models with overlapping spheres.

Abstract For the calculation of hydrodynamic properties of rigid macromolecules using bead modelling, models with overlapping beads of different sizes are used in some applications. The hydrodynamic interaction tensor between unequal overlapping beads is unknown, and an oversimplified treatment with the Oseen tensor may introduce important errors. Here we discuss some aspects of the overlapping problem, and explore an ad hoc form of the interaction tensor, proposed by Zipper and Durchschlag. We carry out a systematic numerical study of the hydrodynamic properties of a two-spheres model, showing how the Zipper-Durchschlag correction removes efficiently the numerical instabilities, and predicts the correct limits.

A Multiscale Scheme for the Simulation of Conformational and Solution Properties of Different Dendrimer Molecules

We propose a multiscale protocol for the simulation of conformation and dynamics of dendrimer molecules in dilute solution. Conformational properties (radius of gyration, mass distribution, and scattering intensities) and overall hydrodynamic properties (translational diffusion and intrinsic viscosity) are predicted by means of a very simple coarse-grained bead-and-spring model, whose parameters are not adjusted against experimental properties, but rather they are obtained from previous, atomic-level simulations which are also quite simple, performed with small fragments and Langevin dynamics simulation. The scheme is described and applied systematically to four different dendrimer molecules with up to seven generations. The predictive capability of this scheme is tested by comparison with experimental data. It is found that the predicted geometric and hydrodynamic radii of the dendrimer molecules are in agreement (typical error is about 4%) with a large set experimental values of the four dendrimers with various numbers of generations. Agreement with some X-ray scattering experimental intensities also confirms the good prediction of the internal structure. This scheme is easily extendable to study more complex molecules (e.g., functionalized dendrimers) and to simulate internal dynamics.

Molecular Flexibility of Methylcelluloses of Differing Degree of Substitution by Combined Sedimentation and Viscosity Analysis

The flexibility/rigidity of methylcelluloses (MCs) plays an important part in their structure-function relationship and therefore on their commercial applications in the food and biomedical industries. In the present study, two MCs of low degree of substitution (DS) 1.09 and 1.32 and four of high DS (1.80, 1.86, 1.88 and 1.93) were characterised in distilled water in terms of intrinsic viscosity [h]; sedimentation coefficient (s020,w) and weight average molar mass (Mw). Solution conformation and flexibility were estimated qualitatively using conformation zoning and quantitatively (persistence length Lp) using the new combined global method. Sedimentation conformation zoning showed an extended coil (Type C) conformation and the global method applied to each MC sample yielded persistence lengths all within the range Lp(1/4)12-17 nm (for a fixed mass per unit length) with no evidence of any significant change in flexibility with DS.