Solvent interactions and protein dynamics in spin-labeled T4 lysozyme

Aspects of T4 lysozyme dynamics and solvent interaction are investigated using atomically detailed Molecular Dynamics (MD) simulations. Two spin-labeled mutants of T4 lysozyme are analyzed (T4L-N40C and T4L-K48C), which have been found from electronic paramagnetic resonance (EPR) experiments to exhibit different mobilities at the site of spin probe attachment (N- and C-terminus of helix B, respectively). Similarities and differences in solvent distribution and diffusion around the spin label, as well as around exposed and buried residues within the protein, are discussed. The purpose is to capture possible strong interactions between the spin label (ring) and solvent molecules, which may affect EPR lineshapes. The effect of backbone motions on the water density profiles is also investigated. The focus is on the domain closure associated with the T4 lysozyme hinge-bending motion, which is analyzed by Essential Dynamics (ED). The N-terminus of helix B is found to be a "hinge" residue, which explains the high degree of flexibility and motional freedom at this site.     

The Role of the Fast Motion of the Spin Label in the Interpretation of EPR Spectra for Spin-Labeled Macromolecules

Abstract

The spin label method was used to observe the nature of the fast motions of side chains in protein monocrystals. The EPR spectra of spin-labeled lysozyme monocrystals (with different orientations of the tetragonal protein crystal in relation to the direction of the magnetic field) were interpreted using the method of molecular dynamics (MD). Within the proposed simple model, MD calculations of the spin label motion trajectories are performed in a reasonable real time. The model regards the protein molecule as frozen as a whole and the spin labeled amino acid residue as unfrozen. To calculate the trajectories in vacuum, a model of spin-labeled lysozyme was assembled, and the parameters of the force fields were specified for atoms of the protein molecule, including the spin label. The calculations show that the protein environment sterically limits the area of the possible angular reorientations for the NO reporter group of the nitroxide (within the spin label), and this, in turn, affects the shape of the EPR spectrum. However, it turned out that the spread in the positions of the reporter group in the angle space strictly adheres to the Gaussian distribution. Using the coordinates of the spin label atoms obtained by the MD method within a selected time range and considering the distribution of the spin label states over the ensemble of spin-labeled macro- molecules in a crystal, the EPR spectra of spin-labeled lysozyme monocrystals were simulated. The resultant theoretical EPR spectra appeared to be similar to experimental ones.     

Structural origins of nitroxide side chain dynamics on membrane protein α-helical sites

Understanding the structure and dynamics of membrane proteins in their native, hydrophobic environment is important to understanding how these proteins function. EPR spectroscopy in combination with site-directed spin labeling (SDSL) can measure dynamics and structure of membrane proteins in their native lipid environment; however, until now the dynamics measured have been qualitative due to limited knowledge of the nitroxide spin label's intramolecular motion in the hydrophobic environment. Although several studies have elucidated the structural origins of EPR line shapes of water-soluble proteins, EPR spectra of nitroxide spin-labeled proteins in detergents or lipids have characteristic differences from their water-soluble counterparts, suggesting significant differences in the underlying molecular motion of the spin label between the two environments. To elucidate these differences, membrane-exposed α-helical sites of the leucine transporter, LeuT, from Aquifex aeolicus, were investigated using X-ray crystallography, mutational analysis, nitroxide side chain derivatives, and spectral simulations in order to obtain a motional model of the nitroxide. For each crystal structure, the nitroxide ring of a disulfide-linked spin label side chain (R1) is resolved and makes contacts with hydrophobic residues on the protein surface. The spin label at site I204 on LeuT makes a nontraditional hydrogen bond with the ortho-hydrogen on its nearest neighbor F208, whereas the spin label at site F177 makes multiple van der Waals contacts with a hydrophobic pocket formed with an adjacent helix. These results coupled with the spectral effect of mutating the i ± 3, 4 residues suggest that the spin label has a greater affinity for its local protein environment in the low dielectric than on a water-soluble protein surface. The simulations of the EPR spectra presented here suggest the spin label oscillates about the terminal bond nearest the ring while maintaining weak contact with the protein surface. Combined, the results provide a starting point for determining a motional model for R1 on membrane proteins, allowing quantification of nitroxide dynamics in the aliphatic environment of detergent and lipids. In addition, initial contributions to a rotamer library of R1 on membrane proteins are provided, which will assist in reliably modeling the R1 conformational space for pulsed dipolar EPR and NMR paramagnetic relaxation enhancement distance determination.     

Specific spin labelling of the sugar-H(+) symporter, GalP, in cell membranes of Escherichia coli: site mobility and overall rotational diffusion of the protein

The D-galactose-H(+) symport protein (GalP) of Escherichia coli is a homologue of the human glucose transport protein, GLUT1. After amplified expression of the GalP transporter in E. coli, other membrane proteins were prereacted with N-ethylmaleimide in the presence of excess D-galactose to protect GalP. Inner membranes were then specifically spin labelled on Cys(374) of GalP with 4-maleimide-2,2,6,6-tetramethylpiperidine-1-oxyl. The electron paramagnetic resonance (EPR) spectra are characteristic of a single labelling site in which the mobility of the spin label is very highly constrained. This is confirmed with other nitroxyl spin labels, which are derivatives of iodoacetamide and indanedione. Saturation transfer EPR spectra indicate that the overall rotation of the GalP protein in the membrane is slow at low temperatures (approx. 2 degrees C), but considerably more rapid and highly anisotropic at physiological temperatures. The rate of rotation about the membrane normal at 37 degrees C is consistent with predictions for a 12-transmembrane helix assembly that is less than closely packed.     

Specific spin labelling of the sugar-H+ symporter,GalP, in cell membranes of Escherichia coli: site mobility and overall rotational diffusion of the protein

The d-galactose-H⁺ symport protein (GalP) of Escherichia coli is a homologue of the human glucose transport protein, GLUT1. After amplified expression of the GalP transporter in E. coli, other membrane proteins were prereacted with N-ethylmaleimide in the presence of excess d-galactose to protect GalP. Inner membranes were then specifically spin labelled on Cys³⁷⁴ of GalP with 4-maleimide-2,2,6,6-tetramethylpiperidine-1-oxyl. The electron paramagnetic resonance (EPR) spectra are characteristic of a single labelling site in which the mobility of the spin label is very highly constrained. This is confirmed with other nitroxyl spin labels, which are derivatives of iodoacetamide and indanedione. Saturation transfer EPR spectra indicate that the overall rotation of the GalP protein in the membrane is slow at low temperatures (approx. 2°C), but considerably more rapid and highly anisotropic at physiological temperatures. The rate of rotation about the membrane normal at 37°C is consistent with predictions for a 12-transmembrane helix assembly that is less than closely packed.     

Saturation transfer EPR measurements of the rotational motion of a strongly immobilized ouabain spin label on renal Na, K-ATPase

The rotational motion of an ouabain spin label with sheep kidney Na,K-ATPase has been measured by electron paramagnetic resonance (EPR) and saturation transfer EPR (ST-EPR) measurements. Spin-labelled ouabain binds with high affinity to the Na,K-ATPase with concurrent inhibition of ATPase activity. Enzyme preparations retain 0.61 ± 0.1 mol of bound ouabain spin label per ATPase β dimer. The conventional EPR spectrum of the ouabain spin label bound to the ATPase consists almost entirely (> 99%) of a broad resonance which is characteristic of a strongly immobilized spin label. ST-EPR measurements of the spin labelled ATPase preparations yield effective correlation times for the bound labels of 209 ± 11 μs at 0°C and 44 ± 4 μs at 20°C. These rotational correlation times most likely represent the motion of the protein itself rather than the independent motion of mobile spin probes relative to a slower moving protein. Additional ST-EPR measurements with glutaraldehyde-crosslinked preparations indicated that the observed rotational correlation times predominantly represented the motion of entire Na,K-ATPase-containing membrane fragments, rather than the motion of individual monomeric or dimeric polypeptides within the membrane fragment. The strong immobilization of the ouabain spin label will make it an effective paramagnetic probe of the extracellular surface of the Na,K-ATPase for a variety of NMR and EPR investigations.     

Structure-function relationships in immobilized chymotrypsin catalysis

Specific activities and the amounts of active immobilized enzyme were determined for several different preparations of alpha-chymotrypsin immobilized on CNBr-activated Sepharose 4B. Electron paramagnetic resonance (EPR) spectroscopy of free and immobilized enzyme with a spin label coupled to the active site was used to probe the effects of different immobilization conditions on the immobilized enzyme active site configuration. Specific activity of active enzyme decreased and rotational correlation time of the spin label increased with increasing immobilized enzyme loading. Enzyme immobilized using an intermediate six-carbon spacer arm exhibited greater specific activity and spin label mobility than directly coupled enzyme. The observed activity changes due to immobilization were completely consistent with corresponding active site structure alterations revealed by EPR spectroscopy.     

Structure-function relationships in immobilized chymotrypsin catalysis

Specific activities and the amounts of active immobilized enzyme were determined for several different preparations of alpha-chymotrypsin immobilized on CNBr-activated Sepharose 4B. Electron paramagnetic resonance (EPR) spectroscopy of free and immobilized enzyme with a spin label coupled to the active site was used to probe the effects of different immobilization conditions on the immobilized enzyme active site configuration. Specific activity of active enzyme decreased and rotational correlation time of the spin label increased with increasing immobilized enzyme loading. Enzyme immobilized using an intermediate six-carbon spacer arm exhibited greater specific activity and spin label mobility than directly coupled enzyme. The observed activity changes due to immobilization were completely consistent with corresponding active site structure alterations revealed by EPR spectroscopy.     

The role of the fast motion of the spin label in the interpretation of EPR spectra for spin-labeled macromolecules

The spin label method was used to observe the nature of the fast motions of side chains in protein monocrystals. The EPR spectra of spin-labeled lysozyme monocrystals (with different orientations of the tetragonal protein crystal in relation to the direction of the magnetic field) were interpreted using the method of molecular dynamics (MD). Within the proposed simple model, MD calculations of the spin label motion trajectories are performed in a reasonable real time. The model regards the protein molecule as frozen as a whole and the spin-labeled amino acid residue as unfrozen. To calculate the trajectories in vacuum, a model of spin-labeled lysozyme was assembled, and the parameters of the force fields were specified for atoms of the protein molecule, including the spin label. The calculations show that the protein environment sterically limits the area of the possible angular reorientations for the NO reporter group of the nitroxide (within the spin label), and this, in turn, affects the shape of the EPR spectrum. However, it turned out that the spread in the positions of the reporter group in the angle space strictly adheres to the Gaussian distribution. Using the coordinates of the spin label atoms obtained by the MD method within a selected time range and considering the distribution of the spin label states over the ensemble of spin-labeled macromolecules in a crystal, the EPR spectra of spin-labeled lysozyme monocrystals were simulated. The resultant theoretical EPR spectra appeared to be similar to experimental ones.     

Investigation of Domain Motions in Bacteriophage T4 Lysozyme

Abstract

Hinge-bending in T4 lysozyme has been inferred from single amino acid mutant crystalline allomorphs by Matthews and coworkers. This raises an important question: are the different conformers in the unit cell artifacts of crystal packing forces, or do they represent different solution state structures? The objective of this theoretical study is to determine whether domain motions and hinge-bending could be simulated in T4 lysozyme using molecular dynamics. An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. Molecular dynamics calculations were computed using the Discover software package (Biosym Technologies). All hydrogen atoms were modeled explicitly with the inclusion of all 152 crystallographic waters at a temperature of 300 K. The native T4 lysozyme molecular dynamics simulation demonstrated hinge-bending in the protein. Relative domain motions between the N-terminal and C-terminal domains were evident. The enzyme hinge bending sites resulted from small changes in backbone atom conformations over several residues rather than rotation about a single bound. Two hinge loci were found in the simulation. One locus comprises residues 8–14 near the C-terminal of the A helix; the other site, residues 77–83 near the C-terminal of the C helix. Comparison of several snapshot structures from the dynamics trajectory clearly illustrates domain motions between the two lysozyme lobes. Time correlated atomic motions in the protein were analyzed using a dynamical cross-correlation map. We found a high degree of correlated atomic motions in each of the domains and, to a lesser extent, anticorrelated motions between the two domains. We also found that the hairpin loop in the N-terminal lobe (residues 19–24) acted as a mobile ‘flap’ and exhibited highly correlated dynamic motions across the cleft of the active site, especially with residue 142.     

Structural determinants of nitroxide motion in spin-labeled proteins: solvent-exposed sites in helix B of T4 lysozyme

Site-directed spin labeling provides a means for exploring structure and dynamics in proteins. To interpret the complex EPR spectra that often arise, it is necessary to characterize the rotamers of the spin-labeled side chain and the interactions they make with the local environment in proteins of known structure. For this purpose, crystal structures have been determined for T4 lysozyme bearing a nitroxide side chain (R1) at the solvent-exposed helical sites 41 and 44 in the B helix. These sites are of particular interest in that the corresponding EPR spectra reveal two dynamic states of R1, one of which is relatively immobilized suggesting interactions of the nitroxide with the environment. The crystal structures together with the effect of mutagenesis of nearest neighbors on the motion of R1 suggest intrahelical interactions of 41R1 with the i + 4 residue and of 44R1 with the i + 1 residue. Such interactions appear to be specific to particular rotamers of the R1 side chain.     

Electron spin-labelling of the EutC subunit in B12-dependent ethanolamine ammonia-lyase reveals dynamics and a two-state conformational equilibrium in the N-terminal,signal-sequence-associated domain

Abstract

The B₁₂ (adenosylcobalamin)-dependent ethanolamine ammonia-lyase (EAL) is a product of the ethanolamine utilisation (eut) gene cluster, that is involved in human gut microbiome homeostasis and in disease conditions caused by pathogenic strains of Salmonella and Escherichia coli. Toward elucidation of the molecular basis of EAL catalysis, and its intracellular trafficking and targeting to the Eut biomicrocompartment (BMC), we have applied electron spin-labelling and electron paramagnetic resonance spectroscopy to wild-type (wt) EAL from Salmonella typhimurium, by using the sulphydryl-specific, 4-maleimido-TEMPO (4MT) spin label. One cysteine residue per active site displays exceptional reactivity with 4MT. This site is identified as βC37 on the EutC subunit, by using 4MT-labeling of site-specific cysteine-to-alanine mutants, enzyme kinetics, and accessible surface area calculations. Electron paramagnetic resonance (EPR) spectra of 4MT-labelled wt EAL are collected over 200–265 K in frozen, polycrystalline water-only, and 1% v/v DMSO solvents. EPR simulations reveal two mobility components for each condition. Detectable spin probe reorientational motion of the two components occurs at 215 and 225 K with 1% v/v DMSO, relative to the water-only condition, consistent with formation of an aqueous-DMSO solvent mesodomain around EAL. Parallel trends in fast- and slow-reorientational correlation times and interconversion of the two populations with increasing temperature, indicate 4MT labelling of a single site (βC37). A two-state model is proposed, in which the fast and slow motional populations represent EAL-bound and free conformations of the EutC N-terminal domain. The approximately equal proportion of each state may represent a balance between EutC and EAL protein stability and efficient targeting to the BMC.     

Integrated analysis of the conformation of a protein-linked spin label by crystallography,EPR and NMR spectroscopy

Long-range structural information derived from paramagnetic relaxation enhancement observed in the presence of a paramagnetic nitroxide radical is highly useful for structural characterization of globular, modular and intrinsically disordered proteins, as well as protein–protein and protein-DNA complexes. Here we characterized the conformation of a spin-label attached to the homodimeric protein CylR2 using a combination of X-ray crystallography, electron paramagnetic resonance (EPR) and NMR spectroscopy. Close agreement was found between the conformation of the spin label observed in the crystal structure with interspin distances measured by EPR and signal broadening in NMR spectra, suggesting that the conformation seen in the crystal structure is also preferred in solution. In contrast, conformations of the spin label observed in crystal structures of T4 lysozyme are not in agreement with the paramagnetic relaxation enhancement observed for spin-labeled CylR2 in solution. Our data demonstrate that accurate positioning of the paramagnetic center is essential for high-resolution structure determination.     

Role of rapid movement of spin labels in interpreting EPR spectra for spin-labelled macromolecules

The method of spin labeling was used to monitor quick movements of side residues in protein monocrystals. The EPR spectra of monocrystals of spin-labeled lysozyme at different orientations of the tetrahonal crystal relative to the direction of the magnetic field were interpreted using the molecular dynamics method. A simple model was proposed, which enables one to calculate the trajectory of movements of the spin label by the molecular dynamic method over a relatively short period of time. The entire "frozen" protein molecule and a "defrozen" spin-labeled amino acid residue were considered in the framework of the model. To calculate the trajectories in vacuum, a model of spin-labeled lysozyme was constructed, and the parameters of force potentials for the atoms of the protein molecule and the spin label were specified. It follows from the calculations that the protein environment sterically hinders the range of eventual angular reorientations of the reporter NO-group of nitroxyl incorporated into the spin label, thereby affecting the shape of the EPR spectrum. However, the scatter in the positions of the reporter group in the angular space turned out to correspond to the Gauss distribution. Using the atomic coordinates of the spin label, obtained in a chosen time interval by the method of molecular dynamics, and taking into account the distribution of the states of the spin label in the ensemble of spin-labeled macromolecules in the crystal, we simulated the EPR spectra of monocrystals of spin-labeled lysozyme. The theoretical EPR spectra coincide well with the experimental.     

Simulation of nitroxide electron paramagnetic resonance spectra from brownian trajectories and molecular dynamics simulations

A simulated continuous wave electron paramagnetic resonance spectrum of a nitroxide spin label can be obtained from the Fourier transform of a free induction decay. It has been previously shown that the free induction decay can be calculated by solving the time-dependent stochastic Liouville equation for a set of Brownian trajectories defining the rotational dynamics of the label. In this work, a quaternion-based Monte Carlo algorithm has been developed to generate Brownian trajectories describing the global rotational diffusion of a spin-labeled protein. Also, molecular dynamics simulations of two spin-labeled mutants of T4 lysozyme, T4L F153R1, and T4L K65R1 have been used to generate trajectories describing the internal dynamics of the protein and the local dynamics of the spin-label side chain. Trajectories from the molecular dynamics simulations combined with trajectories describing the global rotational diffusion of the protein are used to account for all of the dynamics of a spin-labeled protein. Spectra calculated from these combined trajectories correspond well to the experimental spectra for the buried site T4L F153R1 and the helix surface site T4L K65R1. This work provides a framework to further explore the modeling of the dynamics of the spin-label side chain in the wide variety of labeling environments encountered in site-directed spin labeling studies.     

Synthesis of Duplex DNA Containing a Spin Labeled Analog of 2′ Deoxycytidine

Abstract

We report the chemical synthesis of phosphoramidite 8, containing a spin labeled analog of deoxycytidine, C?, and its incorporation into synthetic DNA. The EPR characteristics of the resulting DNAs indicated that the motion of the spin label was well-correlated with the uniform modes of the macromolecule, but that correlation of the spin label with internal motion was less effective than that achieved using a spin labeled quinolone, Q.     

Effect of various humidity on local dynamic structure of lysozyme in a spin-labeled tetragonal crystal

The dynamics of the side groups of amino acid residues and local conformational changes in the lysozyme molecule upon dehydration and rehydration of lysozyme crystals were studied by the methods of spin label, X-ray diffraction, and molecular dynamics. The His15 residue of lysozyme from chicken egg white was modified by spin label, and spin-labeled tetragonal crystals of the protein were grown. The spatial structure of the covalently bound spin label and its immediate surroundings in the lysozyme tetragonal crystal was determined. The conformation of a fragment of the lysozyme molecule with the spin label on His15, optimized by the method of molecular dynamics, closely agreed with X-ray data. It was found by the X-ray diffraction analysis that a decrease in relative humidity to 40% is accompanied by both a decrease in the unit cell volume by 27% and a change in the diffraction field of roentgenograms from 0.23 to 0.60 HM. The dehydration of spin-labeled lysozyme crystals leads to an anomalous widening of EPR peaks without changes in their position. The dehydration in the humidity range studied has a two-stage character. The decrease in humidity to 75% is accompanied by a sharp change in the parameters measured, and on further decrease in humidity to 40% they change insignificantly. The first stage is caused by the removal of the greater part of molecules of bulk water, and the second stage is due to the removal of the remaining bulk water and possible changes in the dynamics of weakly bound water molecules and their position. The simulation of experimental EPR spectra showed that the anomalous broadening of the spectrum upon dehydration is related to an increase in the dispersion of spin label orientations induced by changes in the network of hydrogen bonds generated by water molecules in the vicinity of the spin label and a possible turn (by no more than 5 degrees) of the entire protein molecule. After rehydration, the physical state of the lysozyme crystal did not return to the starting point.     

Algorithm for selection of optimized EPR distance restraints for de novo protein structure determination

A hybrid protein structure determination approach combining sparse Electron Paramagnetic Resonance (EPR) distance restraints and Rosetta de novo protein folding has been previously demonstrated to yield high quality models (Alexander et al. (2008)). However, widespread application of this methodology to proteins of unknown structures is hindered by the lack of a general strategy to place spin label pairs in the primary sequence. In this work, we report the development of an algorithm that optimally selects spin labeling positions for the purpose of distance measurements by EPR. For the α-helical subdomain of T4 lysozyme (T4L), simulated restraints that maximize sequence separation between the two spin labels while simultaneously ensuring pairwise connectivity of secondary structure elements yielded vastly improved models by Rosetta folding. 54% of all these models have the correct fold compared to only 21% and 8% correctly folded models when randomly placed restraints or no restraints are used, respectively. Moreover, the improvements in model quality require a limited number of optimized restraints, which is determined by the pairwise connectivities of T4L α-helices. The predicted improvement in Rosetta model quality was verified by experimental determination of distances between spin labels pairs selected by the algorithm. Overall, our results reinforce the rationale for the combined use of sparse EPR distance restraints and de novo folding. By alleviating the experimental bottleneck associated with restraint selection, this algorithm sets the stage for extending computational structure determination to larger, traditionally elusive protein topologies of critical structural and biochemical importance.     

Spin-labeling studies of the conformational changes in the vicinity of D36, D38, T46, and E161 of bacteriorhodopsin during the photocycle.

Electron paramagnetic resonance (EPR) spectroscopy of site-directed spin-labeled bacteriorhodopsin mutants is used to study structural changes during the photocycle. After exchange of the native amino acids D36 and D38 in the A-B loop, E161 in the E-F loop, and T46 in the putative proton channel by cysteines, these positions were modified by a methanethiosulfonate spin label. Time-resolved EPR spectroscopy reveals spectral changes during the photocycle for the mutants with spin labels attached to C36, C161, and C46. A comparison of the transient spectral amplitudes with simulated EPR difference spectra shows that the detected signals are due to changes in the spin label mobility and not to possible polarity changes in the vicinity of the attached spin label. The kinetic analysis of the EPR and the visible data with a global fitting procedure exhibits a structural rearrangement near position 161 in the E-F loop in the M state. The environmental changes at positions 36 and 46, however, occur during the M-to-N transition. All structural changes reverse with the recovery of the BR ground state. No structural changes are detected with a spin label attached to C38.     

Spin-Labeled Nucleotide Mobility in the Boundary of the EcoRI Endonuclease Binding Site

Abstract

A complex consisting of the EcoRI endonuclease site-specifically bound to spin-labeled DNA 26mers was prepared to provide a model system for studying possible conformational changes resulting from protein binding. EPR was used to monitor the mobility of the spin labels that were strategically placed in position 6, 9, or 11 with respect to the dyad axis of the 26mer. These positions are located within the flanking region on either side of the EcoRI hexamer binding site. This allows the monitoring of potential distal structural changes in the DNA helix caused by protein binding. The spectral line shapes indicate that the spin label closest to the EcoRI endonuclease binding site, i.e., in position 6, is most influenced by the binding event. The EPR data are analyzed according to a model that distinguishes between spectral effects due to a change in the hydrodynamic shape of the complex and those resulting from local variations in the spin-label mobility as characterized by a local order parameter S. S reflecting the motional restriction of the spin-labeled base is 0.20 ± 0.01 for all three oligomers as well as for the two complexes with the label in position 9 or 11, while the position 6 labeled complex yields S=0.25. To further evaluate the origin of the slightly larger EPR effect observed with position 6 labeled material, molecular dynamics (MD) simulations were used to explore the space accessible to the probes in positions 6, 9, and 11. MD results gave similar nitroxide trajectories for all three labeled 26mers in the absence or presence of EcoRI. Thus, the small position 6 effect is attributed to a structural distortion in the major groove of the DNA at this location possibly corresponding to a bend induced by protein binding. The observation that the spectral changes are small indicates the absence of any significant structural disruption being propagated along the helix as a result of protein binding. Also, the fact that the line shape of the 26mers did not change as expected from hydrodynamic theory in view of the significant increase in molecular volume upon protein binding suggests that there are additional relaxation processes involving the protein and nucleic acid.