Hydrodynamic properties of macromolecular complexes. IV. Intrinsic viscosity theory, with applications to once-broken rods and multisubunit proteins

GRPY: An Accurate Bead Method for Calculation of Hydrodynamic Properties of Rigid Biomacromolecules

Two main problems that arise in the context of hydrodynamic bead modeling are an inaccurate treatment of bead overlaps and the necessity of using volume corrections when calculating intrinsic viscosity. We present a formalism based on the generalized Rotne-Prager-Yamakawa approximation that successfully addresses both of these issues. The generalized Rotne-Prager-Yamakawa method is shown to be highly effective for the calculation of transport properties of rigid biomolecules represented as assemblies of spherical beads of different sizes, both overlapping and nonoverlapping. We test the method on simple molecular shapes as well as real protein structures and compare its performance with other computational approaches.

High-precision tracking of brownian boomerang colloidal particles confined in quasi two dimensions

In this article, we present a high-precision image-processing algorithm for tracking the translational and rotational Brownian motion of boomerang-shaped colloidal particles confined in quasi-two-dimensional geometry. By measuring mean square displacements of an immobilized particle, we demonstrate that the positional and angular precision of our imaging and image-processing system can achieve 13 nm and 0.004 rad, respectively. By analyzing computer-simulated images, we demonstrate that the positional and angular accuracies of our image-processing algorithm can achieve 32 nm and 0.006 rad. Because of zero correlations between the displacements in neighboring time intervals, trajectories of different videos of the same particle can be merged into a very long time trajectory, allowing for long-time averaging of different physical variables. We apply this image-processing algorithm to measure the diffusion coefficients of boomerang particles of three different apex angles and discuss the angle dependence of these diffusion coefficients.

Rotational Brownian dynamics of semiflexible broken rods

Using the Brownian dynamics simulation technique, we study the rotational dynamics of a semiflexible broken rod. We employ a suitable bead model with stiff springs between beads and strong forces opposing to bending, except at the joint where flexibility is variable. We consider mostly broken rods with equal arms. From the simulated Brownian trajectories we obtain the correlation function for the second order Legendre polynomial of the reorientational angle of the end-to-end vector and of the arm vector. These correlation functions are closely related to fluorescence anisotropy decay and electric birefringence decay, respectively. In the first case, the relaxation time for a completely flexible rod agrees with the Harvey-Wegener theory, and in the second, the longest relaxation time agrees well with that obtained from the rigid-body treatment over the whole range of flexibility. Furthermore, we discuss the relative importance of flexibility in both types of decay. Finally, we present results for a case with unequal arms, confirming the validity of the Harvey-Wegener theory and the rigid-body treatment.

Brownian motion of boomerang colloidal particles

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Triple-helix DNA structural studies using a Love wave acoustic biosensor

The development of sensors for detecting the conformation of surface-attached molecules is an emerging field with significance in the pharmaceutical industry and in drug design. In this work, triplex-forming oligos (TFOs), a separate class of non-natural DNA bending agents that can affect the mechanical properties of DNA through the formation of triple-helical structures of specific conformation and/or flexibility, are used as a model system in combination with an acoustic biosensor to determine molecular geometrical features. In practice, the degree of bending of a specific DNA target caused by a particular TFO was evaluated by measuring the ratio of acoustic energy change over phase change observed during the binding of pre-formed triplex DNA molecules to the device surface. The DNA bending angle derived via acoustic measurements is in excellent agreement with previously reported values using molecular biology techniques. The reported acoustic technique appears quite appealing for the biophysical study of DNA molecules providing rapid qualitative and quantitative information, at the same time holding promise to be developed as a high-throughput method for the evaluation of DNA conformational changes.

Intrinsic viscosity of bead models for macromolecules and nanoparticles

The calculation of the intrinsic viscosity by means of classical treatments of bead models, typically composed of a number of identical beads, presents some problems when applied to models where the beads are unequal and their number is not very large. A correction to this problem was proposed 10 years ago (García de la Torre and Carrasco in Eur Biophys J 27:549-557, 1998). This so-called volume correction, which consisted of adding a term proportional to the volume of the model, was proved to be rigorous in physico-mathematical terms, and produced improved results in some circumstances, but not always. Recently, the volume correction is being reconsidered so that with some deduced or empirical modifications, it can allow for safer predictions of the intrinsic viscosity. This paper contributes a discussion and further improvements of that correction for the intrinsic viscosity.

Quantitative determination of size and shape of surface-bound DNA using an acoustic wave sensor

DNA bending plays a significant role in many biological processes, such as gene regulation, DNA replication, and chromosomal packing. Understanding how such processes take place and how they can, in turn, be regulated by artificial agents for individual oriented therapies is of importance to both biology and medicine. In this work, we describe the application of an acoustic wave device for characterizing the conformation of DNA molecules tethered to the device surface via a biotin-neutravidin interaction. The acoustic energy dissipation per unit mass observed upon DNA binding is directly related to DNA intrinsic viscosity, providing quantitative information on the size and shape of the tethered molecules. The validity of the above approach was verified by showing that the predesigned geometries of model double-stranded and triple-helix DNA molecules could be quantitatively distinguished: the resolution of the acoustic measurements is sufficient to allow discrimination between same size DNA carrying a bent at different positions along the chain. Furthermore, the significance of this analysis to the study of biologically relevant systems is shown during the evaluation of DNA conformational change upon protein (histone) binding.

Numerical path integration technique for the calculation of transport properties of proteins

We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are O(m(3)) where m is the number of finite elements. The new technique, a numerical path integration method, has computation times that are only O(m). We have applied the technique to approximately 1000 different protein structures. The computed translational diffusivities and intrinsic viscosities are, to lowest order, proportional respectively to N(-1/3)(R) and N(0)(R), where N(R) is the number of amino acid residues in the protein. Our calculations also show some correlation with the shape of the molecule, as represented by the ratio m(2)/m(3), where m(2) and m(3) are, respectively, the middle and the smallest of the three principal moments of inertia. Comparisons with a number of experimental results are also performed, with results generally consistent to within experimental error.

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.

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.

Bead modeling using HYDRO and SOLPRO of the conformation of multisubunit proteins: sunflower and rape-seed 11S globulins

Oil seed globulins from sunflower and rape seed are multi-subunit, oligomeric proteins whose native 11S form is a hexamer. In this work we try to determine the spatial structure in which the six subunits of 11S globulin are arranged. Experimental values of solution properties, including radius of gyration, sedimentation and diffusion coefficients and intrinsic viscosity, are compared with theoretical predictions for hexamers of various geometries. Bead model calculations of solution properties are carried out using the HYDRO and SOLPRO computer programs. A most compact shape, the regular octahedron, is the hexameric structure that fits best the experimental values.

On the hydrodynamic analysis of macromolecular conformation

Hydrodynamics provides a powerful complementary role to the traditional "high resolution" techniques for the investigation of macromolecular conformation, especially in dilute solution, conditions which are generally inaccessible to other structural techniques. This paper describes the state of art of hydrodynamic representations for macromolecular conformation, in terms of (1) simple but straightforward ellipsoid of revolution modelling; (2) general triaxial ellipsoid modelling; (3) hydrodynamic bead modelling; (4) the ability, especially for polydisperse macromolecular systems, to distinguish between various conformation types; (5) analysis of macromolecular flexibility.

Secondary conformational polymorphism of nucleic acids as a possible functional link between cellular parameters and DNA packaging processes

Circular dichroism and electron microscopy studies of various in vitro DNA packaging systems indicate that all the factors which induce and modulate the secondary conformation of DNA molecules are capable of eliciting nucleic acids condensation processes into tight, highly ordered tertiary structures as well as altering the extent of order and compactness within the resulting species. Specifically, such factors include the ionic strength, the presence of particular dehydrating agents and polyamines, as well as the pH values. It is proposed that slight alterations of these parameters induce the formation of short non-B-DNA segments that propagate as a perturbation along the B-DNA double helix. The structural fluctuations of the dsDNA molecules that result from the conformational discontinuities formed at the junction sites between the B motif and the conformationally altered segments alter the elastic response of the nucleic acids and facilitate cooperative condensation processes. Moreover, the type and frequency of the structurally modified clusters interspersed within the B conformation and determined by the environmental parameters are shown to provide a means for continuous regulation of the extent and mode of DNA packaging. The ionic strength and hydrophobic environment in the close vicinity of the DNA molecules are controlled and modulated in vivo by DNA-binding proteins such as histones and protamines; similarly, pH values and polyamine concentrations are constantly regulated in living systems. It is suggested, therefore, that the secondary structural polymorphism which characterizes the DNA molecules might display a regulatory role by acting as a functional link between cellular parameters and the extent, mode, and timing of nucleic acid packaging processes.

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.

Surface-induced aggregation of type I procollagen

We have examined the state of aggregation of type I procollagen in the concentration range 5 to 800 micrograms/ml. Electron microscopy typically indicates a high proportion of aggregated material (greater than 50%), when a range of preparative techniques are used. Aggregates of in-register molecules (segment-long-spacing-like aggregates) are frequently observed, often with units of in-register molecules connected via the C-terminal propeptides. In contrast, studies using gel-filtration chromatography and density-gradient ultracentrifugation demonstrate only limited aggregation in solution (less than 5%) even at 800 micrograms/ml. The aggregated material is mainly dimeric and probably not segment-long-spacing-like. We conclude that aggregation of procollagen is strongly favoured by adsorption to a surface when samples are prepared for electron microscopy. The possible relevance of these observations to the fate of procollagen secreted by cells in vivo is discussed.

Milk proteins: physicochemical and functional properties

Because of the growing trend toward widespread use of protein ingredients in food formulation and fabrication, an understanding of the relationships between the physical properties of proteins and their behavior in food systems is desirable. A range of milk-derived protein preparations, i.e., dry milk, milk proteins, caseins, whey proteins, and lactalbumin, are used in a range of food products for their specific functional attributes. In this paper some of the apparent relationships between the properties of the protein components and specific functional properties are discussed. Thus, the roles of milk proteins in determining some important physical characteristics (i.e. color, bulk density, sinkability, dispersibility) of milk powders and their involvement in a range of functional properties (water holding, solubility, rheological behavior, gelation, film formation, emulsification, and foaming) are reviewed. Because of the various methods and conditions used in determining functional properties and the variability in composition of preparations it is difficult to compare data and/or reconcile differences in published information. The desirability of developing standard methods is emphasized.

Transport properties of rigid, symmetrical oligomeric structures composed of prolate, ellipsoidal subunits

We have calculated translational and rotational diffusion coefficients and intrinsic viscosities of oligomeric structures composed of n identical subunits having a prolate ellipsoidal shape with axial ratio p. Results are presented for p = 1-6 for a variety of structures with n = 1-6. We compare our results with those obtained by a different modeling procedure, proposed by other workers, in which the monomeric subunit is represented as a string of touching, colinear spheres. If n and an estimate of p are known, the structure of the oligomer can be. in most cases, unambiguously determined by comparison of the experimental oligomer-to-monomer ratios of a given property with the numerical results of this work. As examples of the applicability of our results, we examine the relationship between structure and properties for neurophysin. bovine serum albumin, hemoglobin and phycocyanin.

Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications

Among the Various methods for characterizing macromolecules in solution, hydrodynamic techniques play a major role. Since the advent of the ultracentrifuge and the development of viscometric apparatus, sedimentation coefficients and intrinsic viscosities have been extensively used to learn about the size and shape of synthetic and biological polymers. More recently, refined techniques such as quasielastic light scattering, transient electric birefringence and fluorescence anisotropy decay have made it possible to obtain in a simple and rapid way quantitative information of high precision on the translational and rotational brownian dynamics of dissolved macromolecules.

Conformation of myosin in dilute solution as estimated from hydrodynamic properties

On the basis of the current knowledge of the structure and dimensions of myosin and its parts, we analyze available data on hydrodynamic properties (translational diffusion, rotational diffusion, and intrinsic viscosity) for comparison with values calculated for models with varying geometry. Special attention is paid to detecting flexibility effects in those properties. After obtaining a plausible model for subfragment S-1, we concentrate on the conformation of the rodlike parts of myosin. Although uncertainties in the experimental values do not allow a rigorous, quantitative analysis, we show how hydrodynamic data provide evidence for the flexibility of the rod at the joint of subfragment S-2 and light meromyosin.