Magnetic relaxation analysis of dynamic processes in macromolecules in the pico- to microsecond range.

A formalism based on the theory of Markov processes and suitable for the analysis of multiple internal motions in macromolecules is presented. Computer calculations of specific motional models for (13)C nuclear magnetic resonance (NMR) relaxation, treated as special cases of the proposed formalism, demonstrate the potential of this approach for discriminating between different motional models on the basis of NMR relaxation data.     

A theoretical study of rotational diffusion models for rod-shaped viruses. The influence of motion on 31P nuclear magnetic resonance lineshapes and transversal relaxation.

Information about the interaction between nucleic acids and coat proteins in intact virus particles may be obtained by studying the restricted backbone dynamics of the incapsulated nucleic acids using 31P nuclear magnetic resonance (NMR) spectroscopy. In this article, simulations are carried out to investigate how reorientation of a rod-shaped virus particle as a whole and isolated nucleic acid motions within the virion influence the 31P NMR lineshape and transversal relaxation dominated by the phosphorus chemical shift anisotropy. Two opposite cases are considered on a theoretical level. First, isotropic rotational diffusion is used as a model for mobile nucleic acids that are loosely or partially bound to the protein coat. The effect of this type of diffusion on lineshape and transversal relaxation is calculated by solving the stochastic Liouville equation by an expansion in spherical functions. Next, uniaxial rotational diffusion is assumed to represent the mobility of phosphorus in a virion that rotates as a rigid rod about its length axis. This type of diffusion is approximated by an exchange process among discrete sites. As turns out from these simulations, the amplitude and the frequency of the motion can only be unequivocally determined from experimental data by a combined analysis of the lineshape and the transversal relaxation. In the fast motional region both the isotropic and the uniaxial diffusion model predict the same transversal relaxation as the Redfield theory. For very slow motion, transversal relaxation resembles the nonexponential relaxation as observed for water molecules undergoing translational diffusion in a magnetic field gradient. In this frequency region T2e is inversely proportional to the cube root of the diffusion coefficient. In addition to the isotropic and uniaxial diffusion models, a third model is presented, in which fast restricted nucleic acid backbone motions dominating the lineshape are superimposed on a slow rotation of the virion about its length axis, dominating transversal relaxation. In an accompanying article the models are applied to the 31P NMR results obtained for bacteriophage M13 and tobacco mosaic virus.     

Kinetics of the interaction between aspartic aminotransferase and anions.

The kinetics of the interaction between deionized supernatant aspartic aminotransferase and various anions (cacodylate, phosphate and chloride) were studied by the temperature-jump technique. The anion concentration in the range covered by our experiments does not affect the transamination rate. On the other hand the conformational transition, recently observed at the active site of the enzyme, is hindered by an excess of anions. A single relaxation effect was observed at the enzyme chromophore wavelength in systems containing the aldimine form of the enzyme and the above anions. It is shown that this effect corresponds to the protonation of the chromophore. The relaxation times were of about 10 mus with phosphate, 20-100 mus with cacodylate and 1-2 ms with chloride. The pH and concentration dependence of this effect were studied. The fits of experimental data to a rate equations for various models were tested by a chi2 analysis. The best fit was obtained with models where anions bind rapidly to a site close to the chromophore, so that the pK of the chromophore is affected by anions binding. The rate of the observed relaxation considerably increased when the anion has buffering capacities; this indicates, in the case of cacodylate and phosphate, that the acidic component of the buffer directly exchanges a proton with the enzyme chromophore.     

Proton magnetic relaxation of manganese (II) tetrakis(4-sulfophenyl)porphine ion in water.

Water proton nuclear magnetic spin-lattice relaxation rates are reported as a function of magnetic field strength for aqueous solutions of manganese tetrakis(4-sulfophenyl)porphine complexes. The manganese(III) complex displays relaxation that is remarkably independent of temperature at low magnetic field and a magnetic field dependence that is characteristic of the electron spin relaxation rates, making a contribution to the correlation time that dominates the electron-nuclear coupling. The manganese(II) complex is much more effective in relaxing water protons, but the usual models of first coordination sphere and outer-sphere relaxation fail to account for the magnitude and the magnetic field dependence of the relaxation rates. The data suggest that the delocalization of the electron density into the ligand system provides an increase in the effectiveness of what may be called the outer-sphere paths for water proton relaxation.     

A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in combination with fluid flow

Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.     

Analysis of 31P nuclear magnetic resonance lineshapes and transversal relaxation of bacteriophage M13 and tobacco mosaic virus.

The experimentally observed 31P lineshapes and transversal relaxation of 15% (wt/wt) M13, 30% M13, and 30% tobacco mosaic virus (TMV) are compared with lineshapes and relaxation curves that are simulated for various types of rotational diffusion using the models discussed previously (Magusin, P. C. M. M., and M. A. Hemminga. 1993. Biophys. J. 64:1851-1860). It is found that isotropic diffusion cannot explain the observed lineshape effects. A rigid rod diffusion model is only successful in describing the experimental data obtained for 15% M13. For 30% M13 the experimental lineshape and relaxation curve cannot be interpreted consistently and the TMV lineshape cannot even be simulated alone, indicating that the rigid rod diffusion model does not generally apply. A combined diffusion model with fast isolated motions of the encapsulated nucleic acid dominating the lineshape and a slow overall rotation of the virion as a whole, which mainly is reflected in the transversal relaxation, is able to provide a consistent picture for the 15 and 30% M13 samples, but not for TMV. Strongly improved lineshape fits for TMV are obtained assuming that there are three binding sites with different mobilities. The presence of three binding sites is consistent with previous models of TMV. The best lineshapes are simulated for a combination of one mobile and two static sites. Although less markedly, the assumption that two fractions of DNA with different mobilities exist within M13 also improves the simulated lineshapes. The possible existence of two 31P fractions in M13 sheds new light on the nonintegral ratio 2.4:1 between the number of nucleotides and protein coat subunits in the phage: 83% of the viral DNA is less mobile, suggesting that the binding of the DNA molecule to the protein coat actually occurs at the integral ratio of two nucleotides per protein subunit.     

Structure of a DNA intercalation complex as determined by NMR using a paramagnetic probe.

Longitudinal relaxation rates of the protons of the 3,8-dimethyl-N-methyl-phenanthrolinium (DMP) cation in solutions containing DNA are strongly affected by the addition of the paramagnetic manganese (II) ions due to the electron-nuclear dipolar interaction in the ternary Mn-DNA-DMP Complex. Two possible models for the DMP-DNA intercalation complex are examined and one of them is unequivocally discriminated on the basis of the proton relaxation data. It is concluded that in the intercalation complex the long axis of the DMP molecule is almost perpendicular to the hydrogen bonds of the DNA base-pairs.     

Electric and hydrodynamic properties of polypeptides in solution. 3. Aggregation of poly(L-glutamic acid) in aqueous methanol solvents studied by electric birefringence

The rise and decay of electric birefringence for poly(L -glutamic acid) (PLGA) in aqueous solvents containing 20 and 10 vol % methanol have been found to be unusual. The decay curves have been analyzed on the assumption that there exist two kinds of particles, namely, one (component I) with a shorter relaxation time exhibiting positive birefringence and the other (component II) with a longer relaxation time exhibiting negative birefringence at low fields. From the field strength dependence of the steadystate birefringence the permanent dipole moment, the anisotropy of electric polarizability, and the saturation value of birefringence have been determined for each component. Furthermore, from the relaxation time the length of component I and the diameter of component II have been computed on the models of cylindrical rod and oblate ellipsoid, respectively. The dipole moment, the anisotropy of electric polarizability, and the relaxation time of component II are much larger than those of component I. Both the anisotropy of electric polarizability and the optical anisotropy factor are positive in sign for component I and negative for component II. It is concluded that component I is the helical PLGA molecule itself and component II is the side-by-side (antiparallel) aggregate composed of many helical PLGA molecules. The optical anisotropy factor of each component has been discussed on the basis of Peterlin-Stuart theory.     

Association states of tubulin in the presence and absence of microtubule-associated proteins. Analysis by electric birefringence

Electric birefringence has been used to examine the states of association of tubulin in phosphocellulose-purified tubulin or depolymerized microtubule protein solutions at low temperature. In a high electric field (1000-4000 V/cm), tubulin could be orientated (owing to the existence of a permanent and/or induced dipole) and exhibited a positive birefringence (delta n), related to its intrinsic optical anisotropy. The analysis of the relaxation process (depending on hydrodynamic properties of molecules), by measurement of the time decay of delta n, revealed the existence of a multicomponent or polydisperse system, whatever the tubulin solution. Two relaxation times, representative of the smallest and the largest orientated species, were obtained by computer-fitting analysis. The mean values of relaxation time for phosphocellulose-purified tubulin were 0.8 and 8 microseconds. In microtubule protein solutions, large-sized macromolecular species with relaxation time up to 450 microseconds were detected. The largest species (relaxation times ranging from 50 to 450 microseconds) could be eliminated by centrifugation at 3000000 X g for 1 h. Addition of microtubule-associated protein to either pure tubulin or high-speed centrifuged microtubule protein led to a rapid formation of large species analogous to those present in microtubule protein. Molecular dimensions of the relaxing structures were estimated using simple hydrodynamic models and values of rotational diffusion constants calculated from the relaxation times, and compared to those of the structures described in the literature. In conclusion, we have found that (a) phosphocellulose-purified tubulin is not only composed of elementary species (dimers) but also contains tubulin-associated forms of limited size (up to 7-10 dimers), (b) depolymerized microtubule protein solutions contain ring oligomers and structures very much larger, the formation of which is dependent on the presence of microtubule-associated protein.     

Distance estimates from paramagnetic enhancements of nuclear relaxation in linear and flexible model peptides.

The distance dependence of electron-nuclear dipole-dipole coupling was tested using a series of poly-L-proline based peptides of different length. The poly-proline based peptides were synthesized with a nitroxide spin label on the N-terminus and a tryptophan on the C-terminus, and paramagnetic enhancements of nuclear spin-lattice relaxation rates were measured for the aromatic protons on the tryptophan as a function of the number of proline spacers in the sequence. As expected, paramagnetic enhancements decrease with distance, but the distances deduced from the NMR relaxation rates were shorter than expected for every peptide studied compared to a rigid linear poly-L-proline type II helix structure. Calculations of cross-relaxation rates indicate that this difference is not the result of spin-diffusion or the creation of a spin-temperature gradient in the proton spins caused by the nitroxide. Molecular dynamics simulations were used to estimate dynamically averaged value of (2). These weighted average distances were close to the experimentally determined distances, and suggest that molecular motion may account for differences between the rigid linear models and the distances implied by the NMR relaxation data. A poly-L-prolone peptide synthesized with a central glycine hinge showed dramatic relaxation rate enhancements compared to the peptide of the same length lacking the hinge. Molecular dynamics simulations for the hinged peptide support the notion that the NMR data is a representation of the weighted average distance, which in this case is much shorter than that expected for an extended conformation. These results demonstrate that intermoment distances based on NMR relaxation rates provide a sensitive indicator of intramolecular motions.     

A temperature-jump study of the reaction between azurin and cytochrome c-551 from Pseudomonas aeruginosa (Short Communication)

Temperature-jump studies on the electron-transfer reaction between azurin and cytochrome c-551 clearly reveal two chemical relaxations. The amplitudes of these relaxation processes have identical spectral distributions, but the relaxation times show different dependences on the reactant concentrations. These findings are discussed in terms of possible models.     

PMR relaxation times of micelles of the nonionic surfactant Triton X-100 and mixed micelles with phospholipids.

Previous pmr studies at 220 MHz have led to the suggestion that phosphatidylcholine and the nonionic surfactant Trition-X-100 form mixed micellar structures at high molar ratios of trition to phosphalipid. These mixed micelles provide one form of the phospholipid which the enzyme phospholipase A2 can utilize as substrate. Spin-lattice relaxation times (T1) and spin-spin relaxation times (T2) obtained from line widths for resolvable protons in Triton X-100 micelles and mixed micelles with egg phosphatidycholine and dipalmitoyl phosphatidylcholine are reported. They suggest that the structure of the mixed micelles is generally similar to that of pure Triton X-100 micelles. The T1 values for the phsopholipid in the mixed micelles are found to be similar to those reported for phospholipid in sonicated vesicle preparations which are used as membrane models, but the lines are somewhat sharper suggesting the possibility of less anisotropic motion in the mixed micelles than in the vesicles.     

Prediction of internal pressure profile of compression bandages using stress relaxation parameters

The efficacy of compression therapy using compression bandages is highly dependent on the level of compression applied and the sustenance of the pressure during the course of treatment. This study attempts to predict the pressure profile generated by compression bandages using constitutive equations describing relaxation behavior of viscoelastic materials. It is observed that this pressure profile is highly correlated with the stress relaxation behavior of the bandage. To model the pressure profile, the stress relaxation behavior of compression bandages was studied and modeled using three mechanical models: the Maxwell model, the standard linear solid model and the two-component Maxwell model with a nonlinear spring. It was observed that the models with more component values explained the experimental relaxation curves better. The parameters used for modelling relaxation behavior were used to describe the pressure profile, which is significantly dependent on the longitudinal stress relaxation behavior of the bandage, using the modified Laplace's law equation. This approach thus helps in evaluating the bandage performance with time during compression therapy as novel wound care management.     

Determination of kinetic parameters from chemical relaxation data discrimination between coupled two-step binding reactions differing in stoichiometry

The chemical relaxation times of two different two-step equilibrium reactions, characterized by a 1:1 binding process followed by a subsequent rearrangement step and a stepwise 1:2 binding reaction, are analyzed for the purpose of qualitative model discrimination and quantitative determination of kinetic parameters. The equations describing the dependences of the two reciprocal relaxation times on suitable concentrations are given for both models in the general case as well as for four different limiting situations which are characterized by well separated relaxation times. The conditions corresponding to the limiting cases are expressed in terms of strong, weak and no coupling between the two partial equilibrium steps involved in both models. The coupling strength depends on the rate constants as well as on the total concentrations of the reactants. Criteria to discriminate between these two reaction models under defined limiting conditions are developed. In the general case, the product of both reciprocal relaxation times can be used to distinguish both models. If only one relaxation time can be resolved experimentally, it is possible under conditions described to determine only a reduced set of individual rate constants for most of the limiting cases considered. If both relaxation times are observed, all rate constants are determinable in the general case as well as in most of the limiting cases discussed.     

Relaxation dynamics of the gel to liquid-crystalline transition of phosphatidylcholine bilayers. Effects of chainlength and vesicle size.

The relaxation kinetics of the gel to liquid-crystalline transition of five phosphatidylcholine (DC14PC to DC18PC) bilayer dispersions have been investigated using volume perturbation calorimetry, a steady-state technique which subjects a sample to sinusoidal changes in volume. Temperature and pressure responses to the volume perturbation are measured to monitor the relaxation to a new equilibrium position. The amplitude demodulation and phase shift of these observables are analyzed with respect to the perturbation frequency to yield relaxation times and amplitudes. In the limit of low perturbation frequency, the temperature and pressure responses are proportional to the equilibrium excess heat capacity and bulk modulus, respectively. At all temperatures, the thermal response data are consistent with a single primary relaxation process of the lipid. The less accurate bulk modulus data exhibit two relaxation times, but it is not clear whether they reflect lipid processes or are characteristic of the instrument. The observed thermal relaxation behavior of all multilamellar vesicles are quantitatively similar. The relaxation times vary from approximately 50 ms to 4 s, with a pronounced maximum at a temperature just greater than Tm, the temperature of the excess heat capacity maximum. Large unilamellar vesicles also exhibit a single relaxation process, but without a pronounced maximum in the relaxation time. Their relaxation time is approximately 80 ms over most of the transition range.     

Interaction between hydroxystilbamidine and DNA. II. Temperature jump relaxation study. Dynamics of nucleic acids and polynucleotides.

A temperature-jump relaxation study of the interaction of hydroxystilbamidine with DNA and synthetic polynucleotides has been performed. Two concentration dependent relaxation times tau1 and tau2 have been observed in the submillisecond range when detecting relaxation effects by means of light absorption. The longer of these two times (tau1) is also observed when using "blue" or "red" fluorescence detection. In the longer time scale the "red" fluorescence shows no other relaxation but the blue fluorescence shows two additional relaxation processes (tau3 and tau4) which correspond to an increase of fluorescence with temperature and which are independent of concentration. The experimental results clearly indicate that tau1 and tau2 are associated with the binding of the dye to strong and weak binding sites, respectively. A kinetic model is given to explain the results. It allows the determination of the four rate constants for the two binding reactions and yields equilibrium association constants in good agreement with those obtained from stoichiometric studies. The study of the effect of temperature, nature of the polymer, ionic strength and fraction of bound dye on tau3 and tau4 indicates that the dye acts only as a "blue" fluorescence probe of some processes involving the DNA or polynucleotide alone. These processes appear to be related with the dynamic structure of the polymers.     

On Fr?hlich's coherent effects in biological systems: influence of carriers and high order dissipative effects.

Following Fr?hlich we consider a system that models a biological one, for example, a long chain of proteins possessing polar modes of vibration and where energy is pumped through metabolic processes. We consider the effect produced by free electrons that are usually present as hole carriers in proteins with electron-donor molecules. A theory of relaxation based on the non-equilibrium statistical operator method is used in the derivation of the kinetic equations to introduce non-linearities due to interactions of the polar vibrations with the carriers and with a thermal bath. These non-linearities arising from high order relaxation processes lead to the emergence of the Fr?hlich effect in the polar modes, i.e. the occurrence of a (non-equilibrium) Bose-Einstein-like condensation. It points to an instability of the system that seems to be followed by a morphological transformation in the form of a spatially ordered dissipative structure.     

Pregnancy-induced alterations of vascular function in mouse mesenteric and uterine arteries

Normal pregnancy involves dramatic changes to maternal vascular function, while abnormal vascular adaptations may contribute to pregnancy-associated diseases such as preeclampsia. Many genetic mouse models have recently emerged to study vascular pathologies of pregnancy. However, vascular adaptations to pregnancy in normal mice are not fully understood. Thus, we studied changes in vascular reactivity during normal mouse pregnancy. We hypothesized that pregnant mice will have enhanced endothelial-dependent vasodilation compared with nonpregnant mice, via an enhancement of the nitric oxide synthase (NOS) prostaglandin H synthase (PGHS), and other endothelial-derived hyperpolarizing pathways. Late pregnant (Day 17-18) C57BL/6J mice (n = 10) were compared with nonpregnant mice (n = 7). Uterine and mesenteric arteries were mounted on a wire myograph system and assessed for endothelium-dependent (methacholine) and -independent (sodium nitroprusside; SNP) relaxation responses. Endothelial-dependent relaxation was enhanced in pregnant uterine and mesenteric arteries, which was blunted after the addition of inhibitors of the PGHS or NOS pathways. In nonpregnant mice, these pathways had no effect in modulating relaxation in uterine arteries, whereas vasodilation in mesenteric arteries was reduced only by NOS inhibition. Both uterine and mesenteric vessels had nonnitric oxide- and nonprostaglandin-mediated relaxation, but this relaxation was not enhanced during pregnancy. Endothelial-independent relaxation was also enhanced in pregnant uterine but not mesenteric arteries. Our data indicate that uterine and mesenteric arteries from pregnant mice have enhanced vasodilation. Understanding vascular adaptations to normal mouse pregnancy is crucial for interpreting changes that may occur in genetic mouse models.     

How the All-Atom Simulation and the Ising-Based Theory Reconcilewith Each Other on the Helix-Coil Transition

In this report, we addressed a somewhat basic question about how the twoextreme models, the all-atom model and the Ising-based model, can beconsistent with each other regarding the polypeptide helix-coil transition.Comparisons of several physical properties were made between the resultsof the all-atom simulations and those of the Ising-based theories. Fromthe equilibrium point of view, the two models were found to exhibit aqualitatively similar trend, which is significant considering the extremedifference in precision between the two models. On the other hand, fromthe kinetic viewpoint, there appeared a difference in relaxation behaviorbetween the two models; i.e., so-called stretched exponential relaxationwas observed in the all-atom simulation whereas the kinetic Ising modelshowed simple exponential relaxation. A plausible source of the observeddifference is briefly discussed.