MULTIHYDRO and MONTEHYDRO: conformational search and Monte Carlo calculation of solution properties of rigid or flexible bead models

A computer program, MULTIHYDRO, has been constructed for the calculation of hydrodynamic coefficients and other solution properties of multiple possible conformations of a bead model. With minimal additional programming to describe the model under study, this program interfaces efficiently with HYDRO for the calculation of solution properties, including hydrodynamic coefficients, radius of gyration, covolume, etc. A useful application is the conformation search of rigid macromolecules, because many possible conformations can be evaluated in a single run of the program. In this paper we also pay attention to the properties of flexible macromolecules, in the so-called Monte Carlo rigid-body approximation, which is virtually exact for the simpler solution properties. The theoretical aspects of the procedure are described, and we show how MULTIHYDRO can be employed for this calculation. However, for flexible molecules, a more general simulation scheme is importance-sampling Monte Carlo generation. We describe how this procedure is implemented in another computer program, MONTEHYDRO. Examples of the usage of these tools are provided.     

SOLPRO: theory and computer program for the prediction of SOLution PROperties of rigid macromolecules and bioparticles

Single-valued hydrodynamic coefficients of a rigid particle can be calculated from existing theories and computer programs for either bead models or ellipsoids. Starting from these coefficients, we review the procedures for the calculation of complex solution properties depending on rotational diffusion, such as the decays of electric birefringence and fluorescence anisotropy. We also describe the calculation of the scattering form factor of bead models. The hydrodynamic coefficients and solution properties can be combined to give universal, shape-dependent functions, which were initially intended for ellipsoidal particles, and are extended here for the most general case. We have implemented all these developments in a new computer program, SOLPRO, for calculation of SOLution PROperties, which can be linked to existing software for bead models or ellipsoids. Accepted: 1 November 1996     

Hydrodynamic properties of rigid macromolecules composed of ellipsoidal and cylindrical subunits.

A procedure is devised for the calculation of hydrodynamic properties of rigid macromolecules composed subunits that are modeled as ellipsoids of revolution and cylinders. Owing to the axial symmetry of these shapes, smooth shell models can be constructured for the subunit structure. The bead shell model so constructed is employed for the calculation of the properties. A computer program, HYDROSUB, has been written implementing both the model building and the hydrodynamic calculation. A detailed example of the use of this methodology is presented for the case of the solution properties of the human antibody molecule immunoglobulin G3 (IgG3). Finally, hints are given on other uses and applications of the procedure.     

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.     

Building hydrodynamic bead-shell models for rigid bioparticles of arbitrary shape.

The calculation of hydrodynamic and other solution properties of rigid macromolecules, using bead-shell model methodologies, requires the specification of the macromolecular shape in a format that can be interfaced with existing programs for hydrodynamic computations. Here, a procedure is presented for such a structural specification that is applicable to arbitrarily shaped particles. A computer program (MAKEPIXB), in which the user inserts the code needed to determine the structure, produces an structural file that is interpreted by another program (HYDROPIX) which is in charge of the computation of properties. As simple and yet illustrative examples we consider two cases: (1) dimeric structures composed of ellipsoidal subunits; and (2) toroidal structures, presenting simple equations that predict the properties of toroids with varying radial ratios.     

Calculation of NMR relaxation, covolume, and scattering-related properties of bead models using the SOLPRO computer program

The hydrodynamic properties of macromolecules and bioparticles, represented by bead models, can be calculated using methods implemented in the computer routine HYDRO. Recently, a new computer routine, SOLPRO, has been presented for the calculation of various SOLution PROperties. These include (1) time-dependent electro-optic and spectroscopic properties related to rotational diffusion, (2) non-dynamic properties like scattering curves, and (3) dimensionless quantities that combine two or more solution properties in a form which depends on the shape of the macromolecule but not on its size. In the present work we describe the inclusion of more of those types of properties in a new version of SOLPRO. Particularly, we describe the calculation of relaxation rates in nuclear magnetic resonance (NMR). For dipolar coupling, given the direction of the dipole the program calculates values of the spectral density, from which the NMR relaxation times can be obtained. We also consider scattering-related properties, namely the distribution of distances for the bead model, which is directly related to the angular dependence of scattered intensity, and the particle's longest distance. We have devised and programmed a procedure to calculate the covolume of the bead model, related to the second virial coefficient and, in general, to the concentration dependence of solution properties. Various shape-dependent dimensionless quantities involving the covolume are calculated. In this paper we also discuss some aspects, namely bead overlapping and hydration, that are not explicitely included in SOLPRO, but should be considered by the user. Received: 25 May 1998 / Revised version: 30 July 1998 / Accepted: 30 July 1998     

Calculation of the solution properties of flexible macromolecules: methods and applications

While the prediction of hydrodynamic properties of rigid particles is nowadays feasible using simple and efficient computer programs, the calculation of such properties and, in general, the dynamic behavior of flexible macromolecules has not reached a similar situation. Although the theories are available, usually the computational work is done using solutions specific for each problem. We intend to develop computer programs that would greatly facilitate the task of predicting solution behavior of flexible macromolecules. In this paper, we first present an overview of the two approaches that are most practical: the Monte Carlo rigid-body treatment, and the Brownian dynamics simulation technique. The Monte Carlo procedure is based on the calculation of properties for instantaneous conformations of the macromolecule that are regarded as if they were instantaneously rigid. We describe how a Monte Carlo program can be interfaced to the programs in the HYDRO suite for rigid particles, and provide an example of such calculation, for a hypothetical particle: a protein with two domains connected by a flexible linker. We also describe briefly the essentials of Brownian dynamics, and propose a general mechanical model that includes several kinds of intramolecular interactions, such as bending, internal rotation, excluded volume effects, etc. We provide an example of the application of this methodology to the dynamics of a semiflexible, wormlike DNA.     

Hydration from hydrodynamics. General considerations and applications of bead modelling to globular proteins.

The effect of hydration on hydrodynamic properties of globular proteins can be expressed in terms of two quantities: the delta (g/g) parameter and the thickness of the hydration layer. The two paradigms on hydration that originate these alternative measures are described and compared. For the numerical calculation of hydrodynamic properties, from which estimates of hydration can be made, we employ the bead modelling with atomic resolution implemented in programs HYDROPRO and HYDRONMR. As typical, average values, we find 0.3 g/g and a thickness of only approximately 1.2 A. However, noticeable differences in this parameter are found from one protein to another. We have made a numerical analysis, which leaves apart marginal influences of modelling imperfections by simulating properties of a spherical protein. This analysis confirms that the errors that one can attribute to the experimental quantities suffice to explain the observed fluctuations in the hydration parameters. However, for the main purpose of predicting protein solution properties, the above mentioned typical values may be safely used. Particularly for atomic bead modelling, a hydrodynamic radius of approximately 3.2 A yields predictions in very good agreement with experiments.     

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.     

A quasi-elastic light scattering study of smooth muscle myosin in the presence of ATP.

We have investigated the hydrodynamic properties of turkey gizzard smooth muscle myosin in solution using quasi-elastic light scattering (QELS). The effects of ionic strength (0.05-0.5 M KCl) and light chain phosphorylation on the conformational transition of myosin were examined in the presence of ATP at 20 degrees C. Cumulant analysis and light scattering models were used to describe the myosin system in solution. A nonlinear least squares fitting procedure was used to determine the model that best fits the data. The conformational transition of the myosin monomer from a folded form to an extended form was clearly demonstrated in a salt concentration range of 0.15-0.3 M KCl. Light chain phosphorylation regulates the transition and promotes unfolding of the myosin. These results agree with the findings obtained using sedimentation velocity and electron microscopy (Onishi and Wakabayashi, 1982; Trybus et al., 1982; Trybus and Lowey, 1984). In addition, we present evidence for polymeric myosin coexisting with the two monomeric myosin species over a salt concentration range from 0.05 to 0.5 M KCl. The size of the polymeric myosin varied with salt concentration. This observation supports the hypothesis that, in solution, a dynamic equilibrium exists between the two conformations of myosin monomer and filaments.     

Chromatin conformation: a systematic analysis of helical parameters from hydrodynamic data

Chromatin has a “bead-and-bridge” appearance when viewed by electron microscopy. We have used quasielastic light scattering and sedimentation velocity techniques to study the hydrodynamic properties of chicken erythrocyte chromatin multimers in an attempt to determine the superstructure in solution. The functional dependence of the friction factor on the number of core particles in the multimer was analyzed by the Garcia de la Torre-Bloomfield formalism for a rigid array of odd-sized beads. The hydrodynamic parameters of the monomeric and dimeric subunit components, i.e., bead size and separation, form the basis of a systematic determination of the superstructure. These calculations support a helical conformation for chromatin multimers containing up to twenty repeat units. It is also shown that an “equivalent” helix can be obtained if the bead separation distance is not constrained to that determined for the dimer.     

Construction of hydrodynamic bead models from high-resolution X-ray crystallographic or nuclear magnetic resonance data.

Computer software such as HYDRO, based upon a comprehensive body of theoretical work, permits the hydrodynamic modeling of macromolecules in solution, which are represented to the computer interface as an assembly of spheres. The uniqueness of any satisfactory resultant model is optimized by incorporating into the modeling procedure the maximal possible number of criteria to which the bead model must conform. An algorithm (AtoB, for atoms to beads) that permits the direct construction of bead models from high resolution x-ray crystallographic or nuclear magnetic resonance data has now been formulated and tested. Models so generated then act as informed starting estimates for the subsequent iterative modeling procedure, thereby hastening the convergence to reasonable representations of solution conformation. Successful application of this algorithm to several proteins shows that predictions of hydrodynamic parameters, including those concerning solvation, can be confirmed.     

Micro-video study of moving bacterial flagellar filaments. I. Passive rotation by hydrodynamic force in vitro.

Moving images of reconstituted single bacterial flagellar filaments in a dark-field microscope were recorded by an ultrasensitive video camera, and then transferred to 16 mm cinefilm for quantitative analysis of the dynamic properties of the filaments.Flagellar filaments are found to attach to a glass surface at only one end (the H -end). When attached helical filaments were subjected to viscous flow of methylcellulose solution, they rotated as a result of the hydrodynamic torque generated. Occasionally, two filaments associated into a bundle and rotated coordinately in the viscous flow, even though each filament was separately attached to the glass surface. In addition, we have observed partly rotating filaments which consisted of two portions, the rotating portion being connected end-to-end to the non-rotating portion.The magnitude of the hydrodynamic torque depended on the rotational friction which was determined by the manner of attachment. Based on hydrodynamic calculations, values of ?5 × 10^?12 and ?1 × 10^?13 dyne cm were obtained for the average torque for rotating filaments on glass and partly rotating filaments, respectively, in viscous fluid at a flow rate of 15 μm/s.     

Study of blood flow in microvessels using biospeckle dynamics

The hydrodynamic properties of the blood plasma flow in smallest microvessels have been investigated. It has been shown that velocity distribution in such flows essentially differs from the Poseuille flow. The interrelations between the optical parameters and hydrodynamic characteristics of blood microflow have been analyzed. A new method for in vivo measurement of blood plasma rate in small microvessels is proposed, which uses in vivo microscopy in combination with speckle microscopy.     

Global fit and structure optimization of flexible and rigid macromolecules and nanoparticles from analytical ultracentrifugation and other dilute solution properties

The calculation of hydrodynamic and other solution properties from structural information (size and shape or flexibility) of macromolecules and nanoparticles is feasible thanks to existing theories and computational tools. Here we review our recent advances in the inverse problem of extracting structural information from those properties. The concepts of equivalent radii and ratios of radii are particularly useful in global-fitting structural analysis, when one has to treat simultaneously with various properties, eventually for a series of samples. Based on the equivalent radii or their ratios, we define target functions that measure the adequacy of a given structure to fit a set of experimental properties. Structural determination is carried out by minimization of those target functions. We review a variety of examples. Some of them refer to the simple, yet important models like ellipsoids, cylinders and wormlike chains, whose structure is determined by optimization of the model parameters. In other, more complex cases, properties are calculated with computational tools like programs in the HYDRO suite. We have devised other tools to make the structure optimization from the results of those calculations in a quite direct, simple and systematic manner.     

The two coiled coils in the isolated rod domain of the intermediate filament protein desmin are staggered. A hydrodynamic analysis of tetramers and dimers

Desmin protofilaments and the proteolytically derived alpha-helical rod domain have been characterized by high-resolution gel permeation chromatography (GPC) using columns calibrated for the determination of viscosity radii. Additional characterization by chemical cross-linking and the determination of sedimentation values allowed the calculation of the molecular dimensions of the molecular species isolated. In dilute buffers GPC separated desmin rod preparations into two complexes: a dimer species (single coiled coil) with a length of 50 +/- 5 nm and a tetramer species (two coiled coils) with a length of 65 +/- 5 nm. Thus the two coiled coils in the tetramer are staggered by approximately 15 nm. The hydrodynamically derived lengths of the rod dimer and tetramer are supported by electron microscopy after metal shadowing. The hydrodynamic properties of desmin protofilaments follow that of the rod tetramer. The data on the hydrodynamic analysis of the rod tetramer of desmin in solution are in full agreement with the structural information recently deduced from paracrystals of the rod of glial fibrillary acid protein [Stewart, M., Quinlan, R.A. & Moir, R.D. (1989) J. Cell Biol. 109, 225-234]. Our results explain the inhomogeneity of molecules encountered in previous electron microscopical analyses.     

Estimation of the shape and size of fribrinogen in solution from its hydrodynamic properties using theories for bead models and cylinders

The translational and rotational diffusion coefficients and the intrinsic viscosity of fibrinogen in solution are used to estimate its size, shape and hydration. Experimental data of the three hydrodynamic properties taken from the literature are compared with theoretical predictions for several molecular geometries that have been observed by electron microscopy. Modern theories for the hydrodynamics of bead models and cylindrical particles are employed in the calculations. The discrepancy between experimental results and theoretical predictions for spherical particles rules out the dodecahedral model and indicates that fibrinogen is elongated. The Hall-Slayter nodular model and its refinements perform better but still underestimate the size of the hydrated molecule. The best agreement between theoretical and experimental values is found for a cylindrical particle with length and diameter of about 48 and 6.8 nm, respectively. The hydration is calculated to be 3 g water/g protein. We speculate that, to accommodate such a large amount of water, fibrinogen in solution should be appreciably hydrated.     

Further evidence for a flexible and highly expanded spheroidal model for mucus glycoproteins in solution.

The flexible and greatly expanded roughly spherical model for mucus glycoproteins proposed earlier, on the basis of hydrodynamic and n.m.r. data, is supported by new hydrodynamic results on a bronchial glycoprotein from a cystic-fibrosis patient. Furthermore, images from electron microscopy of this molecule and a lower-molecular-weight mucus glycoprotein (which closely resembles a glycopolypeptide) appear to be at least consistent with this model.