Characterization of the overall and internal dynamics of short oligonucleotides by depolarized dynamic light scattering and NMR relaxation measurements

The dynamics of three synthetic oligonucleotides d(CG)4, d(CG)6, and d(CGCGTTGTTCGCG) of different length and shape were studied in solution by depolarized dynamic light scattering (DDLS) and time-resolved nuclear Overhauser effect cross-relaxation measurements. For cylindrically symmetric molecules the DDLS spectrum is dominated by the rotation of the main symmetry axis of the cylinder. The experimental correlation times describe the rotation of the oligonucleotides under hydrodynamic stick boundary conditions. It is shown that the hydrodynamic theory of Tirado and Garcia de la Torre gives good predictions of the rotational diffusion coefficients of cylindrically symmetric molecules of the small axial ratios studied here. These relations are used to calculate the solution dimensions of the DNA fragments from measured correlation times. The hydrodynamic diameter of the octamer and dodecamer is 20.5 +/- 1.0 A, assuming a rise per base of 3.4 A. The tridecamer, d(CGCGTTGTTCGCG), adopts a hairpin structure with nearly spherical dimensions and a diameter of 23.0 +/- 2.0 A. The DDLS relaxation measurements provide a powerful method for distinguishing between different conformations of the oligonucleotides (e.g., DNA double-helix versus hairpin structure). Furthermore, the rotational correlation times are a very sensitive probe of the length of different fragments. The NMR results reflect the anisotropic motion of the molecules as well as the amount of local internal motion present. The experimental correlation time from NMR is determined by the rotation of both the short and long axes of the oligonucleotide.(ABSTRACT TRUNCATED AT 250 WORDS)     

A unified picture of protein hydration: prediction of hydrodynamic properties from known structures.

Hydration is essential for the structural and functional integrity of globular proteins. How much hydration water is required for that integrity? A number of techniques such as X-ray diffraction, nuclear magnetic resonance (NMR) spectroscopy, calorimetry, infrared spectroscopy, and molecular dynamics (MD) simulations indicate that the hydration level is 0.3-0.5 g of water per gram of protein for medium sized proteins. Hydrodynamic properties, when accounted for by modeling proteins as ellipsoids, appear to give a wide range of hydration levels. In this paper we describe an alternative numerical technique for hydrodynamic calculations that takes account of the detailed protein structures. This is made possible by relating hydrodynamic properties (translational and rotational diffusion constants and intrinsic viscosity) to electrostatic properties (capacitance and polarizability). We show that the use of detailed protein structures in predicting hydrodynamic properties leads to hydration levels in agreement with other techniques. A unified picture of protein hydration emerges. There are preferred hydration sites around a protein surface. These sites are occupied nearly all the time, but by different water molecules at different times. Thus, though a given water molecule may have a very short residence time (approximately 100-500 ps from NMR spectroscopy and MD simulations) in a particular site, the site appears fully occupied in experiments in which time-averaged properties are measured.     

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.     

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.     

Simulation of the conformation and dynamics of a double-helical model for DNA

We propose a partially flexible, double-helical model for describing the conformational and dynamic properties of DNA. In this model, each nucleotide is represented by one element (bead), and the known geometrical features of the double helix are incorporated in the equilibrium conformation. Each bead is connected to a few neighbor beads in both strands by means of stiff springs that maintain the connectivity but still allow for some extent of flexibility and internal motion. We have used Brownian dynamics simulation to sample the conformational space and monitor the overall and internal dynamics of short DNA pieces, with up to 20 basepairs. From Brownian trajectories, we calculate the dimensions of the helix and estimate its persistence length. We obtain translational diffusion coefficient and various rotational relaxation times, including both overall rotation and internal motion. Although we have not carried out a detailed parameterization of the model, the calculated properties agree rather well with experimental data available for those oligomers.     

Modeling the hydration of proteins: prediction of structural and hydrodynamic parameters from X-ray diffraction and scattering data

The implications of protein-water interactions are of importance for understanding the solution behavior of proteins and for analyzing the fine structure of proteins in aqueous solution. Starting from the atomic coordinates, by bead modeling the scattering and hydrodynamic properties of proteins can be predicted reliably (Debye modeling, program HYDRO). By advanced modeling techniques the hydration can be taken into account appropriately: by some kind of rescaling procedures, by modeling a water shell, by iterative comparisons to experimental scattering curves (ab initio modeling) or by special hydration algorithms. In the latter case, the surface topography of proteins is visualized in terms of dot surface points, and the normal vectors to these points are used to construct starting points for placing water molecules in definite positions on the protein envelope. Bead modeling may then be used for shaping the individual atomic or amino acid residues and also for individual water molecules. Among the tuning parameters, the choice of the scaling factor for amino acid hydration and of the molecular volume of bound water turned out to be crucial. The number and position of bound water molecules created by our hydration modeling program HYDCRYST were compared with those derived from X-ray crystallography, and the capability to predict hydration, structural and hydrodynamic parameters (hydrated volume, radius of gyration, translational diffusion and sedimentation coefficients) was compared with the findings generated by the water-shell approach CRYSOL. If the atomic coordinates are unknown, ab initio modeling approaches based on experimental scattering curves can provide model structures for hydrodynamic predictions.     

Solution structure of biopolymers: a new method of constructing a bead model

We propose a new, automated method of converting crystallographic data into a bead model used for the calculations of hydrodynamic properties of rigid macromolecules. Two types of molecules are considered: nucleic acids and small proteins. A bead model of short DNA fragments has been constructed in which each nucleotide is represented by two identical, partially overlapping spheres: one for the base and one for the sugar and phosphate group. The optimum radius sigma = 5.0 A was chosen on the basis of a comparison of the calculated translational diffusion coefficients (D(T)) and the rotational relaxation times (tau(R)) with the corresponding experimental data for B-DNA fragments of 8, 12, and 20 basepairs. This value was assumed for the calculation D(T) and tau(R) of tRNA(Phe). Better agreement with the experimental data was achieved for slightly larger sigma = 5.7 A. A similar procedure was applied to small proteins. Bead models were constructed such that each amino acid was represented by a single sphere or a pair of identical, partially overlapping spheres, depending on the amino acid's size. Experimental data of D(T) of small proteins were used to establish the optimum value of sigma = 4.5 A for amino acids. The lack of experimental data on tau(R) for proteins restricted the tests to the translational diffusion properties.     

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     

Hydrodynamic properties of a double-helical model for DNA.

The translational and rotational diffusion coefficients of very short DNA fragments have been calculated using a double-helical bead model in which each nucleotide is represented by one bead. The radius of the helix is regarded as an adjustable parameter. The translational coefficient and the perpendicular rotation coefficient agree very well with experimental values for oligonuclotides with 8, 12, and 20 base pairs, for a single value of the helical radius of about 10 A. We have also calculated a nuclear magnetic resonance relaxation time in which the coefficient for rotation about the main axis is involved. As found previously with cylindrical models, the results deviate from experimental values, indicating that the internal motion of the bases has a remarkable amplitude. An attempt to quantify the extent of internal motions is presented.     

Calculation of translational friction and intrinsic viscosity. II. Application to globular proteins.

The translational friction coefficients and intrinsic viscosities of four proteins (ribonuclease A, lysozyme, myoglobin, and chymotrypsinogen A) are calculated using atomic-level structural details. Inclusion of a 0.9-A-thick hydration shell allows calculated results for both hydrodynamic properties of each protein to reproduce experimental data. The use of detailed protein structures is made possible by relating translational friction and intrinsic viscosity to capacitance and polarizability, which can be calculated easily. The 0.9-A hydration shell corresponds to a hydration level of 0.3-0.4 g water/g protein. Hydration levels within this narrow range are also found by a number of other techniques such as nuclear magnetic resonance spectroscopy, infrared spectroscopy, calorimetry, and computer simulation. The use of detailed protein structures in predicting hydrodynamic properties thus allows hydrodynamic measurement to join the other techniques in leading to a unified picture of protein hydration. In contrast, earlier interpretations of hydrodynamic data based on modeling proteins as ellipsoids gave hydration levels that varied widely from protein to protein and thus challenged the existence of a unified picture of protein hydration.     

Protein effective rotational correlation times from translational self-diffusion coefficients measured by PFG-NMR

Molecular rotational correlation times are of interest for many studies carried out in solution, including characterization of biomolecular structure and interactions. Here we have evaluated the estimates of protein effective rotational correlation times from their translational self-diffusion coefficients measured by pulsed-field gradient NMR against correlation times determined from both collective and residue-specific (15)N relaxation analyses and those derived from 3D structure-based hydrodynamic calculations. The results show that, provided the protein diffusive behavior is coherent with the Debye-Stokes-Einstein model, translational diffusion coefficients provide rapid estimates with reasonable accuracy of their effective rotational correlation times. Effective rotational correlation times estimated from translational diffusion coefficients may be particularly beneficial in cases where i) isotopically labelled material is not available, ii) collective backbone (15)N relaxation rates are difficult to interpret because of the presence of flexible termini or loops, or iii) a full relaxation analysis is practically difficult because of limited sensitivity owing to low protein concentration, high molecular mass or low temperatures.     

Behavior of supercoiled DNA.

We study DNA supercoiling in a quantitative fashion by micromanipulating single linear DNA molecules with a magnetic field gradient. By anchoring one end of the DNA to multiple sites on a magnetic bead and the other end to multiple sites on a glass surface, we were able to exert torsional control on the DNA. A rotating magnetic field was used to induce rotation of the magnetic bead, and reversibly over- and underwind the molecule. The magnetic field was also used to increase or decrease the stretching force exerted by the magnetic bead on the DNA. The molecule's degree of supercoiling could therefore be quantitatively controlled and monitored, and tethered-particle motion analysis allowed us to measure the stretching force acting on the DNA. Experimental results indicate that this is a very powerful technique for measuring forces at the picoscale. We studied the effect of stretching forces ranging from 0.01 pN to 100 pN on supercoiled DNA (-0.1 < sigma < 0.2) in a variety of ionic conditions. Other effects, such as stretching-relaxing hysteresis and the braiding of two DNA molecules, are discussed.     

Conformational studies of antisense DNA by PFG NMR

Pulsed field gradient diffusion constant measurements were used to resolve the ambiguity in determining the conformational states of single-stranded DNA dodecanucleotides (d1s, d4s and d5s). For d1s and d5s, because of the spectral symmetry conventional NMR analyses cannot differentiate whether they are hairpins or homo-duplexes. However, the diffusion constants of these sequences at 300 K are 1.4 times greater than those of the comparison complementary duplexes. This result agrees well with what is expected for D_hairpin>/D_duplex based on classic liquid-phase translational diffusion models and the Einstein–Stokes equation, confirming that d1s and d5s form hairpins. d4s did not show a structured spectral pattern, but its diffusion constant measurement suggests that this sequence may not be a random coil. The DNA sequences studied contain chemically modified backbone linkages and are potential antisense agents for gene regulation. The knowledge of their diffusion constants, in combination with conventional NMR analysis and other biophysical spectroscopic measurements, provides new insights into the relationships of chemical structure and conformational preference of antisense oligonucleotides and their analogs.     

Translational diffusion and intrinsic viscosity of globular proteins. Theoretical predictions using hydrated hydrodynamic models. Application to BPTI.

In this paper, we present a way to make hydrodynamic models of globular proteins, including the hydration shell associated with them in aqueous solutions. Theoretical calculations using these models are made in order to determine the hydrodynamic properties of these proteins, employing rigorous and approximate methods of calculation. These will be applied to the bovine pancreatic trypsin inhibitor, BPTI. Several hydrodynamic models are constructed: the A-model for the unhydrated protein BPTI and a set of H-models for hydrated protein with different hydration degrees. Theoretical results for the translational diffusion coefficient Dt and the intrinsic viscosity [eta] are obtained from different models. From the analysis of the A-model and hydrodynamic properties, there is not a clear assignation of an ellipsoidal shape to this protein molecule. An amount of approximately 0.5 g H2O/g protein could be assigned to the BPTI.     

Transport properties and hydrodynamic centers of rigid macromolecules with arbitrary shapes

A general formalism, which includes translation–rotation coupling, is proposed for calculating translational and rotational transport properties, as well as intrinsic viscosities, of rigid macromolecules with an arbitrary shape. This formalism is based on Brenner's theory of translational–rotational dynamics and on methods for the calculation of hydrodynamic properties that have been already presented, and can be regarded as a generalization of the one proposed by Nakajima and Wada. The calculated transport properties depend on the origin as predicted by Brenner's theory, but in a disagreement with him, the center of resistance and the center of diffusion do not coincide. As one can define several hydrodynamic centers, which in practice turn out to be located at different points, the influence of the choice of the center on the calculated transport properties is discussed. An analysis of the translation–rotation coupling effects in translational diffusion reveals that they arise exclusively from hydrodynamic interactions and are rather small in some cases of interest. Finally, we present a study of the rotational diffusion of rigid bent rods with a fixed length-to-diameter ratio. The diffusion coefficients obtained can be useful to estimate changes with respect to a straight rod.     

Hydration of short DNA, RNA and 2'-OMe oligonucleotides determined by osmotic stressing

Studies on hydration are important for better understanding of structure and function of nucleic acids. We compared the hydration of self-complementary DNA, RNA and 2′-O-methyl (2′-OMe) oligonucleotides GCGAAUUCGC, (UA)₆ and (CG)₃ using the osmotic stressing method. The number of water molecules released upon melting of oligonucleotide duplexes, Δn_W, was calculated from the dependence of melting temperature on water activity and the enthalpy, both measured with UV thermal melting experiments. The water activity was changed by addition of ethylene glycol, glycerol and acetamide as small organic co-solutes. The Δn_W was 3–4 for RNA duplexes and 2–3 for DNA and 2′-OMe duplexes. Thus, the RNA duplexes were hydrated more than the DNA and the 2′-OMe oligonucleotide duplexes by approximately one to two water molecules depending on the sequence. Consistent with previous studies, GC base pairs were hydrated more than AU pairs in RNA, whereas in DNA and 2′-OMe oligonucleotides the difference in hydration between these two base pairs was relatively small. Our data suggest that the better hydration of RNA contributes to the increased enthalpic stability of RNA duplexes compared with DNA duplexes.     

Structure of the Tet repressor and Tet repressor-operator complexes in solution from electrooptical measurements and hydrodynamic simulations

The Tet repressor protein and tet operator DNA fragments and their complexes have been analyzed by electrooptical procedures. The protein shows a positive linear dichroism at 280 nm, a negative linear dichroism at 248 nm, and a strong permanent dipole moment of 3.5 X 10(-27) C m, which is independent of the salt concentration within experimental accuracy. Its rotation time constant of 40 ns indicates an elongated structure, which is consistent with a prolate ellipsoid of 100 A for the long axis and 40 A for the short axis. The time constant can also be fitted by a cylinder of length 78 A and diameter 37 A, which is consistent with nuclease protection data reported on repressor-operator complexes, if the cylinder axis is aligned parallel to the DNA axis. Addition of tetracycline induces changes of the limit dichroism but very little change of the rotation time constant. The rotation time constants observed for the operator DNA fragments show some deviations from the values expected from their contour length; however, these deviations remain relatively small. Formation of repressor-operator complexes leads to some increase of the DNA rotation time constants. Simulations by bead models demonstrate that these time constants can be explained without any major change of the hydrodynamic dimension of the components. The data for the complexes are fitted by bead models with smooth bending of the DNA corresponding to a radius of curvature of 500 A, but at the given accuracy, we cannot rule out that the DNA in the complex remains straight or is bent to a smaller radius of approximately 400 A. Thus, binding of the Tet repressor, which is a helix-turn-helix protein as judged from its sequence, to its operator seems to induce minor bending but does not induce strong bending of the DNA double helix.     

Solution properties of γ‐crystallins: Hydration of fish and mammal γ‐crystallins

Lens γ crystallins are found at the highest protein concentration of any tissue, ranging from 300 mg/mL in some mammals to over 1000 mg/mL in fish. Such high concentrations are necessary for the refraction of light, but impose extreme requirements for protein stability and solubility. γ‐crystallins, small stable monomeric proteins, are particularly associated with the lowest hydration regions of the lens. Here, we examine the solvation of selected γ‐crystallins from mammals (human γD and mouse γS) and fish (zebrafish γM2b and γM7). The thermodynamic water binding coefficient B₁ could be probed by sucrose expulsion, and the hydrodynamic hydration shell of tightly bound water was probed by translational diffusion and structure‐based hydrodynamic boundary element modeling. While the amount of tightly bound water of human γD was consistent with that of average proteins, the water binding of mouse γS was found to be relatively low. γM2b and γM7 crystallins were found to exhibit extremely low degrees hydration, consistent with their role in the fish lens. γM crystallins have a very high methionine content, in some species up to 15%. Structure‐based modeling of hydration in γM7 crystallin suggests low hydration is associated with the large number of surface methionine residues, likely in adaptation to the extremely high concentration and low hydration environment in fish lenses. Overall, the degree of hydration appears to balance stability and tissue density requirements required to produce and maintain the optical properties of the lens in different vertebrate species.