Modeling biological macromolecules in solution: 3. The Λ-R intersection method for triaxial ellipsoids

The general triaxial ellipsoid model for the gross conformation of macromolecules in solution represents a signficiant advance over the previously, almost ubiquitously used ellipsoid of revolution model. A new method is presented which involves the graphical intersection of two triaxial hydrodynamic functions (Λ and R) involving viscosity, sedimentation and fluorescence depolarization. The method is restricted to macromolecules asymmetric enough for the functions to be sufficiently sensitive but not so asymmetric for there to be problems of internal rotations between parts of the macromolecules. The method is illustrated by application to data for neurophysin II monomers and dimers.     

The ELLIPS suite of macromolecular conformation algorithms

This paper describes a series of four programmes for the PC based on ellipsoidal representations of macromolecular shape in solution using Universal shape functions. ELLIPS1 is based on simple ellipsoid of revolution models (where two of the three axes of the ellipsoid are fixed equal to each other). If the user types in a value for a shape function from sedimentation or other types of hydrodynamic measurement, it will return a value for the axial ratio of the ellipsoid. ELLIPS2 is based on the more general triaxial ellipsoid with the removal of the restriction of two equal axes. The user enters the three semi-axial dimensions of the molecule or the equivalent two axial ratios and ELLIPS2 returns the value of all the hydrodynamic shape functions. It also works of course for ellipsoids of revolution. ELLIPS3 and ELLIPS4 do the reverse of ELLIPS2, that is they both provide a method for the unique evaluation of the triaxial dimensions or axial ratios of a macromolecule (and without having to guess a value for the so-called „hydration”) after entering at least three pieces of hydrodynamic information: ELLIPS3 requires EITHER the intrinsic viscosity with the second virial coefficient (from sedimentation equilibrium, light scattering or osmometry) and the radius of gyration (from light or x-ray scattering) OR the intrinsic viscosity with the concentration dependence term for the sedimentation coefficient and the (harmonic mean) rotational relaxation time from fluorescence depolarisation measurements. ELLIPS4 evaluates the tri-axial shape of a macromolecule from electro-optic decay based Universal shape functions using another Universal shape function as a constraint in the extraction of the decay constants. Accepted: 1 November 1996     

Hydrodynamics of macromolecular complexes. II. Rotation

We have used the modified Oseen hydrodynamic interaction tensor along with iterative numerical solution of the coupled hydrodynamic interaction equations to calculate the rotational diffusion coefficients of macromolecular complexes composed of nonidentical spherical subunits. For the one structure, a prolate ellipsoid of revolution, for which exact solutions are available, a subunit model with the same length and volume gives asymptotic agreement with the Perrin equations. Other structures considered include plane polygonal rings, lollipops, and dumbbells.     

Challenges for the modern analytical ultracentrifuge analysis of polysaccharides

This article reviews some of the recent advances in analytical ultracentrifugation and how these advances have impacted--and can impact--on our understanding of the size, shape through conformation modelling, interactions and charge properties of polysaccharides in solution, particularly when used in combination with other solution techniques and also imaging techniques. Specifically we look at (1) polysaccharide polydispersity and simple shape analysis by sedimentation velocity, and in particular using new approaches such as SEDFIT analysis; (2) polysaccharide molecular-weight analysis by sedimentation equilibrium and MSTAR analysis and how this complements analysis of size exclusion chromatography coupled to multi-angle laser light scattering; (3) polysaccharide conformation analysis using traditional procedures such as the Wales-van Holde ratio, power law or 'scaling' relations, more specialised treatments for rigid cylindrical structures, semi-flexible chains and worm-like coils and complications through draining effects; (4) Analysis of polysaccharide interactions and in particular complex formation phenomena, focusing on interesting applications in the areas of mucoadhesion and sedimentation fingerprinting; and (5) the possibilities for macromolecular charge and charge screening measurement.     

A General Method for Modeling Macromolecular Shape in Solution: A Graphical (II-G) Intersection Procedure for Triaxial Ellipsoids

A general method for modeling macromolecular shape in solution is described involving measurements of viscosity, radius of gyration, and the second thermodynamic virial coefficient. The method, which should be relatively straightforward to apply, does not suffer from uniqueness problems, involves shape functions that are independent of hydration, and models the gross conformation of the macromolecule in solution as a general triaxial ellipsoid. The method is illustrated by application to myosin, and the relevance and applicability of ellipsoid modeling to biological structures is discussed.     

Prediction of protein conformation in water and on surfaces by Monte Carlo simulations using united-atom method

The united-atom method has been used to model an avian pancreatic polypeptide (APP) in water and the adsorption process of an albumin subdomain (AS) onto graphite surface to observe the capability of this lumped modelling approach to generate structures observed in protein data bank (PDB) and from atomistic modelling. The subdomain structure of a protein is simplified by the united-atom approximation where the side chains and peptide groups are represented by lumped spheres. The total potential energy of the adsorption process involves the interaction between these lumped spheres by means of virtual bond chain interaction and the interaction of the spheres with the graphite surface by means of Lennard-Jones potential. The protein/polypeptide structure has been perturbed by Monte Carlo with energy minimisation to obtain the global minimum. Results on the APP in water showed a near-to-experimental PDB conformation revealing the two α-helix structures of this small protein molecule with the root mean square deviation among carbon backbone atoms of 5.9 Å. Protein adsorption on biosurfaces has been made by modelling AS, which has 60 amino acids. The surface is graphite, which is characterised by its hydrophobicity. Graphite was chosen because of its widely used applications in certain implants that interact with blood. Our simulation results showed final conformation close to that obtained by atomistic modelling. It also proved that the whole pattern of intramolecular hydrogen bonds was distorted. The model also demonstrated the random conformation of the original α-helix secondary structures of AS consistent with experimental and atomistic results. While atomistic simulation works well for simulating individual small proteins, the united-atom model is more efficient when simulating macromolecular and multiple protein adsorption where time and limiting computer capacity are key factors.     

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.     

Properties of star-branched and linear chains in confined space. A Monte-Carlo study

We have studied the properties of simple models of linear and star-branched polymer chains confined in a slit formed by two parallel impenetrable walls. The polymer chains consisted of identical united atoms (homopolymers) and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain: linear and regular stars with three branches of equal length, were studied. The excluded volume was the only potential introduced into the model and thus the system was athermal. Monte-Carlo simulations with the sampling algorithm based on the chains local changes of conformation were carried out for chains with different lengths as well as for different distances between the confining surfaces. We found that the properties of model chains differ for both macromolecular architectures but a universal behavior for both kinds of chains was also found. Investigation of the frequency of chain-wall contacts shows that the ends of the chains are much more mobile than the rest of the chain, especially in the vicinity of the branching point in star polymers.Figure The scheme of a star-branched (left) and a linear (right) chain located between two parallel impenetrable surfaces.     

Structural properties of DNA:RNA duplexes containing 2'-O-methyl and 2'-S-methyl substitutions: a molecular dynamics investigation

The physical properties of a DNA:RNA hybrid sequence d(CCAACGTTGG)*(CCAACGUUGG) with modifications at the C2'-positions of the DNA strand by 2'-O-methyl (OMe) and 2'-S-methyl (SMe) groups are studied using computational techniques. Molecular dynamics simu-lations of SMe_DNA:RNA, OMe_DNA:RNA and standard DNA:RNA hybrids in explicit water indicate that the nature of the C2'-substituent has a significant influence on the macromolecular conformation. While the RNA strand in all duplexes maintains a strong preference for C3'-endo sugar puckering, the DNA strand shows considerable variation in this parameter depending on the nature of the C2'-substituent. In general, the preference for C3'-endo puckering follows the following trend: OMe_DNA>DNA>SMe_DNA. These results are further corroborated using ab initio methods. Both gas phase and implicit solvation calculations show the C2'-OMe group stabilizes the C3'-endo conformation while the less electronegative SMe group stabilizes the C2'-endo conformation when compared to the standard nucleoside. The macromolecular conformation of these nucleic acids also follows an analogous trend with the degree of A-form character decreasing as OMe_DNA:RNA>DNA:RNA>SMe_DNA:RNA. A structural analysis of these complexes is performed and compared with experimental melting point temper-atures to explain the structural basis to improved binding affinity across this series. Finally, a possible correlation between RNase H activity and conformational changes within the minor groove of these complexes is hypothesized.     

Macromolecular geometries determined with field-flow fractionation and their impact on the overlap concentration

In this paper we aim to understand the size/conformation relationship in waxy barley starch, a polydisperse and ultrahigh molar mass biomacromolecule. Characterizations are performed with asymmetrical flow field-flow fractionation (AsFlFFF). Furthermore, we study the effect of homogenization on the molar mass, rms radius (r rms) and hydrodynamic radius (r h). For the untreated sample, the macromolecules are elongated objects with low apparent density. As a result of homogenization, molar mass, and r rms decrease, while r h remains unaffected. The process also induces an increase, and scaling with size, of apparent density as well as changes in conformation, represented qualitatively by r rms/ r h. Finally, results from AsFlFFF are compared with viscosimetry and discussed in terms of concentration and close-packing in relation to macromolecular shape and conformation. Hence, the results show that AsFlFFF and our novel methodology enable the determination of several physical properties with high relevance for the solution behavior of polydisperse macromolecules.     

Modelling stereokinetic phenomena by a minimum relative motion assumption: the tilted disk, the ellipsoid and the tilted bar

The stereokinetic phenomena of the tilted disk and of the ellipsoid are visual illusions of depth elicited by a flat figure with elliptic contour rotating at uniform speed in the frontal plane of an observer. Strictly related to the appearance of the ellipsoid is the stereokinetic phenomenon of the tilted bar, elicited by a line segment of constant length rotating at uniform speed in the frontal plane. We present a mathematical model of these phenomena, based on an assumption of minimization by the Visual System of the differences between the lengths of the velocity vectors of the stimulus (minimum relative motion assumption): the "rigidity hypothesis" is able to explain the appearance of the tilted disk but not the appearance of the ellipsoid and of the tilted bar. The theoretical results obtained by our modelling are in good agreement with the experimental observations.     

Conformational and molecular interaction studies of glucagon-like peptide-2 with its N-terminal extracellular receptor domain

Glucagon-like peptide-2 (GLP-2) is a therapeutic target used in the treatment of short bowel syndrome. In this paper, we present the three dimensional solution structure of GLP-2 peptide determined using nuclear magnetic resonance (NMR) and molecular modelling. The GLP-2 adopts an α-helical conformation similar to that of secretin family of hormones. In order to understand the molecular details governing the ligand binding and receptor activation, macromolecular docking studies were performed between the N-terminal extracellular domain of GLP-2 receptor and the GLP-2 hormone using a data driven docking program.     

Reinvestigation of the shape and state of hydration of the skeletal myosin subfragment 1 monomer in solution

Hydrodynamic calculations lead to the conclusion that chymotryptic (or ethylenediaminetetraacetic acid) myosin S1 in solution (hydrated), at 1-5 degrees C, can be modeled as a prolate ellipsoid, with an axial ratio lying between p = 1.0 and 2.5 (major axis between 100.5 A, for p = 1.0, and 162.5 A, for p = 2.5). The degree of hydration is considerable (1.24 g/g for p = 2.5 and 2.02 g/g for p = 1.0). The dehydrated myosin head is pear-shaped under the electron microscope, and its narrowest part is located near the junction with the tail [Elliott, A., & Offer, G. (1978) J. Mol. Biol. 123, 505-519]. Mendelson & Kretzschmar [Mendelson, R. A., & Kretzschmar, K.M. (1980) Biochemistry 19, 4103-4108] have shown that the pear-shaped molecule does not predict the experimental X-ray scattering curve. Nor is this model able to predict the hydrodynamic values. The three-dimensional model for S1 used by Mendelson and Kretzschmar gives a rather good fit to the experimental X-ray scattering curve, but it does not predict the hydrodynamic values. In order to try to reconcile the three models and to fit the X-ray scattering curve and the hydrodynamic data, we suggest that, in solution, the S1 monomer has the shape of a prolate ellipsoid and that an inclusion of bound water exists at one extremity of the protein. The rest of bound water surrounds the protein. As first approximation, the dry protein and the hole are assumed to have the same shape as the hydrated molecule (prolate ellipsoid; p).(ABSTRACT TRUNCATED AT 250 WORDS)     

Novel size-independent modeling of the dilute solution conformation of the immunoglobulin IgG Fab' domain using SOLPRO and ELLIPS

The proliferation of hydrodynamic modeling strategies to represent the shape of quasirigid macromolecules in solution has been hampered by ambiguities caused by size. Universal shape parameters, independent of size, developed originally for ellipsoid modeling, are now available for modeling using the bead-shell approximation via the algorithm SOLPRO. This paper validates such a "size-independent" bead-shell approach by comparison with the exact hydrodynamics of 1) an ellipsoid of revolution and 2) a general triaxial ellipsoid (semiaxial ratios a/b, b/c) based on a fit using the routine ELLIPSE (. J. Mol. Graph. 1:30-38) to the chimeric (human/mouse) IgG Fab' B72.3; a similar fit is obtained for other Fabs. Size-independent application of the bead-shell approximation yields errors of only approximately 1% in frictional ratio based shape functions and approximately 3% in the radius of gyration. With the viscosity increment, errors have been reduced to approximately 3%, representing a significant improvement on earlier procedures. Combination of the Perrin frictional ratio function with the experimentally measured sedimentation coefficient for the same Fab' from B72.3 yields an estimate for the molecular hydration of the Fab' fragment of approximately (0.43 +/- 0.07) g/g. This value is compared to values obtained in a similar way for deoxyhemoglobin (0.44) and ribonuclease (0.27). The application of SOLPRO to the shape analysis of more complex macromolecules is indicated, and we encourage such size-independent strategies. The utility of modern sedimentation data analysis software such as SVEDBERG, DCDT, LAMM, and MSTAR is also clearly demonstrated.     

Conformational states of chromatin nu bodies induced by urea.

Monomer chromatin nu bodies (nu1) from chicken erythrocyte nuclei were exposed to 0-10 M urea plus 0.2 mM EDTA (PH 7). Alterations in nu1 conformation were examined using hydrodynamic methods (i.e., S, eta, and (formula: see text)), thermal denaturation, circular dichroism, reactivity of histone thiol groups to N-ethyl maleimide, and electron microscopy. The two domains of a nu body (i.e., the DNA-rich shell and the protein-rich core) aeared to respond differently to the destabilizing effects of increasing urea; DNA conformation and stability exhibited noncooperative changes; the core protein structure revealed cooperative destabilization between 4 and 7 M urea. Companion studies on the conformation of the inner histone "heterotypic tetramer" also revealed cooperative destabilization with increasing urea concentration.     

The use of analytical sedimentation velocity to extract thermodynamic linkage

For 25 years, the Gibbs Conference on Biothermodynamics has focused on the use of thermodynamics to extract information about the mechanism and regulation of biological processes. This includes the determination of equilibrium constants for macromolecular interactions by high precision physical measurements. These approaches further reveal thermodynamic linkages to ligand binding events. Analytical ultracentrifugation has been a fundamental technique in the determination of macromolecular reaction stoichiometry and energetics for 85 years. This approach is highly amenable to the extraction of thermodynamic couplings to small molecule binding in the overall reaction pathway. In the 1980s this approach was extended to the use of sedimentation velocity techniques, primarily by the analysis of tubulin-drug interactions by Na and Timasheff. This transport method necessarily incorporates the complexity of both hydrodynamic and thermodynamic nonideality. The advent of modern computational methods in the last 20 years has subsequently made the analysis of sedimentation velocity data for interacting systems more robust and rigorous. Here we review three examples where sedimentation velocity has been useful at extracting thermodynamic information about reaction stoichiometry and energetics. Approaches to extract linkage to small molecule binding and the influence of hydrodynamic nonideality are emphasized. These methods are shown to also apply to the collection of fluorescence data with the new Aviv FDS.     

Histone H1: Ultracentrifugation studies of the effects of ionic strength and denaturants on the solution conformation

The conformation of histone H1 has been examined under native and denaturing conditions in the absence of DNA or chromatin. Sedimentation coefficients were determined for Histone H1 in 0.1 m KCl and in 6 m guanidine hydrochloride solutions at pH 7.4. The influence of ionic strength on the conformation of histone H1 has been determined by measurement of the sedimentation coefficient in tetramethylammonium chloride solutions of up to 2.5 m and extrapolated to infinite ionic strength. Results from these experiments suggest that the native conformation of histone H1 is very asymmetric in shape. The molecule is best described as a prolate ellipsoid with axes of 312 Å (2a) and 16 Å (2b) in low ionic strength media and also as a prolate ellipsoid with axes of 202 Å (2a) and 20 Å (2b) at high ionic strength or when associated with polyanions, e.g., DNA. Denaturation of histone H1 by guanidine hydrochloride was found to be completely reversible. In 6 m guanidine hydrochloride, the H1 molecule collapses to a sphere but the original extended conformation of the protein is readily restored on dialysis. This suggests rigid conformational requirements for the H1 molecule as incorporated into chromatin. The shape and dimensions for the H1 molecule at high ionic strength are not sufficiently conclusive to locate H1 in the chromatin structure. It is proposed, however, that viable models for chromatin architecture must be consistent with the histone H1 solution dimensions obtained here.     

Contractility and conformation

Contractility in fibers can arise from changes of macromolecular conformation caused by changes in some thermodynamic variable such as temperature, pH, or solvent composition. Illustrations are given of contractile processes in fibers and of changes in macromolecular conformation in dilute solution. These may involve order-disorder transitions, e.g. of the type exhibited by the helix-coil transition. A statistical mechanical treatment of the helix-coil transition involves the assignment of statistical weights to various states and the proper counting of these statistical weights in the formation and evaluation of the partition function; the thermodynamic properties of the system are derivable from the partition function. The counting procedure involved in the consideration of the α-helix and random coil is described. In addition, the factors affecting the relative stabilities of various helical conformations are discussed. These considerations of macromolecular conformation provide a basis for discussing contractile mechanisms in which changes of conformation are involved.