Linear and non-linear pressure dependence of enzyme catalytic parameters

The pressure dependence of enzyme catalytic parameters allows volume changes associated with substrate binding and activation volumes for the chemical steps to be determined. Because catalytic constants are composite parameters, elementary volume change contributions can be calculated from the pressure differentiation of kinetic constants. Linear and non-linear pressure-dependence of single-step enzyme reactions and steady-state catalytic parameters can be observed. Non-linearity can be interpreted either in terms of interdependence between the pressure and other environmental parameters (i.e., temperature, solvent composition, pH), pressure-induced enzyme unfolding, compressibility changes and pressure-induced rate limiting changes. These different situations are illustrated with several examples.     

Dielectric relaxation and molecular motions in C14-lecithin-water systems

The dependence of the complex permittivity on the frequency has been measured between 10⁵ and 6 × 10¹⁰ Hz for aqueous solutions of dimyristoylphosphatidylcholine at several temperatures around the crystalline/liquid-crystalline phase transition temperature of the samples. To the observed data is fitted a sum of Cole-Cole functions and also a model relaxation function to yield various relaxation parameters. The variation of these parameters with temperature is discussed.A noteworthy result is that there exists a pronounced cooperativity effect in the diffusive motions of the phosphorylcholine groups at the bilayer surface and that the mobility of the cationic trimethylammonium head group is dramatically smaller than with lysolecithin micelles in aqueous solutions. As another remarkable result the hydration water relaxation time appears to be distinctly smaller than the reorientation time of the molecules in the pure solvent at the same temperature.     

Interactions of nucleic acid double helices induced by electric field pulses

Electric field pulses induce a substantial increase of the light scattering intensity of double-helical DNA. The relative change of light scattering and also the reciprocal relaxation time constants under electric field pulses increase with increasing nucleotide concentration. These observations, together with a large difference between dichroism orientation time constants and light scattering time constants under electric field pulses, demonstrate that the main part of the light scattering effect is due not to field-induced orientation but to interactions between DNA helices. From the concentration dependence of the light scattering time constants we obtain, according to an isodesmic reaction model, association rate constants in the range 3 × 10¹⁰ M^?1 helices s^?1 for DNA with approx. 300 base-pairs. These values are at the limit of a diffusion-controlled DNA association and do not show any dependence upon the field strength. The dissociation rate constants k_d decrease strongly with increasing field strength E and thus demonstrate that the interactions between the helices are induced by the electric field. This conclusion is consistent with independent measurements which do not reveal any DNA association at zero field strength. The observed linear relation between log(k_d) and E² suggests a field-induced reaction driven by dipole changes. According to this interpretation the change of dipole moment should be in the range of approx. 1400 debye. The dissociation rates for DNA helices with approx. 300 to approx. 800 base-pairs strongly increase with increasing sail concentration (measured in the range 1–5 mM ionic strength), whereas the association rate constants remain virtually unchanged. Measurements of the linear dichroism in the same range of DNA chain length demonstrate that for long field pulses of e.g., 40 μs, the amplitude approaches a maximum value and then decreases. The dichroism relaxation curves observed after long field pulses exhibit a component with a positive dichroism and an increased decay time. These observations suggest the formation of a DNA aggregate with an unusual arrangement of the bases.     

Kinetics of the helix-coil transition in DNA

The kinetics of the helix-coil transition have been investigated for T2 and T7 phage DNA in a formamide-water-salt mixed solvent using a slow temperature perturbation technique (applicable to kinetic processes with rate constants ? 3 min^?1). In this solvent degradation of the DNA is effectively suppressed. Complex kinetic curves are observed by absorbance and viscosity measurements for the response to denaturing perturbations in the transition region. Analysis of the decay curves indicates that the denaturation reaction in this time range can be treated as a first-order reaction with a variable first-order rate parameter, k, the derivative of the logarithm of the absorbance or viscosity change with respect to time. In the approach to denaturation equilibrium in the transition region, the rate parameter is determined only by the instantaneous extent of denaturation of the molecules. Near equilibrium, the rate parameter assumes a constant value characteristic of the equilibrium state. In this region, where the denaturation reaction proceeds as a simple first-order process, both the decay of absorbance (reflected local conformational change) and the decay of solution viscosity (reflecting macromolecular conformational change) are characterized by the same constant value of k. In 83% formamide, 0.3M Na⁺, the rate parameter k for T2 DNA decreases from an extrapolated value of 2.0 min^?1 at 0% denaturation to 0.11 min^?1 at 90% denaturation. Rate parameters determined for T7 DNA at the same counterion concentration and fraction of denaturation are approximately five times as large as those cited for T2 DNA, indicating an inverse proportionality of rate constant to molecular length. On the other hand, simple first-order kinetic responses with constant k are obtained for renaturing perturbations within the transition, indicating that the mechanism of rewinding differs, in most cases, from that of unwinding. Only in the limit of very small perturbations about a given equilibrium position are the rate constants k obtained from denaturing and renaturing perturbations equal. For perturbations of finite size, it appears possible that an intramolecular initiation or nucleation event may precede rewinding and limit the rate of this reaction. The rate parameters again are approximately inversely proportional to molecular weight. The one exception to the first-power dependence on molecular weight appears when temperature jumps are made upward into the post-transition region. Here the molecular-weight dependence is second power, but complications arising from the different strand-separation properties of T2 and T7 DNA's make interpretation difficult. The previously used model of friction-limited unwinding appears to fit all the observations except for the molecular-weight dependence.     

Site directed mutagenesis at position 193 of human trypsin 4 alters the rate of conformational change during activation: role of local internal viscosity in protein dynamics

Upon activation of trypsinogen four peptide segments flanked by hinge glycine residues undergo conformational changes. To test whether the degree of conformational freedom of hinge regions affects the rate of activation, we introduced amino acid side chains of different characters at one of the hinges (position 193) and studied their effects on the rate constant of the conformational change. This structural rearrangement leading to activation was triggered by a pH-jump and monitored by intrinsic fluorescence change in the stopped-flow apparatus. We found that an increase in the size of the side chain at position 193 is associated with the decrease of the reaction rate constant. To analyze the thermodynamics of the reaction, temperature dependence of the reaction rate constants was examined in a wide temperature range (5-60 degrees C) using a novel temperature-jump/stopped-flow apparatus developed in our laboratory. Our data show that the mutations do not affect the activation energy (the exponential term) of the reaction, but they significantly alter the preexponential term of the Arrhenius equation. The effect of solvent viscosity on the rate constants of the conformational change during activation of the wild type enzyme and its R193G and R193A mutants was determined and evaluated on the basis of Kramers' theory. Based on this we propose that the reaction rate of this conformational transition is regulated by the internal molecular friction, which can be specifically modulated by mutagenesis in the hinge region.     

Foreword

Rates of sulfate reduction in sediments of Long Island Sound have been determined, as a function of temperature, via the ³⁵S radiotracer method. Temperature dependence was measured either by following changes in rates in intact cores with seasonal changes in temperature, or by conducting laboratory experiments on homogenized sediments under controlled temperatures. At constant temperature, a large range of sulfate reduction rates were observed for the study sites. In both the intact cores and the laboratory experiments, sediments with lower rates of sulfate reduction exhibited a more pronounced temperature dependence. Apparent activation energies determined using the Arrhenius equation show a systematic trend with sulfate reduction rate when temperature was normalized. As the rate of sulfate reduction decreased, the apparent activation energy increased from 36 to 132 kJ/mole. Although this observation can be interpreted in a number of ways, it is suggested that susceptibility of organic matter to metabolic attack exerts an important control on the temperature dependence of sulfate reduction, as well as on the rate itself. Our findings indicate that the use of a constant temperature correction for estimating annual rates of sulfate reduction will be inaccurate.     

Temperature dependence and temperature compensation of kinetics of chemical oscillations; Belousov-Zhabotinskii reaction, glycolysis and circadian rhythms

Based on the distribution of activation energies around the experimental mean and averaging of rate constants we propose a theoretical scheme to examine the temperature dependence and temperature compensation of time periods of chemical oscillations. The critical finite width of the distribution is characteristic of endogeneous oscillations for compensating kinetics as observed in circadian oscillations, while the vanishing width corresponds to Arrhenius temperature dependent kinetics of non-endogeneous chemical oscillation in Belousov-Zhabotinskii reaction in a CSTR or glycolysis in cell-free yeast extracts. Our theoretical analysis is corroborated with experimental data.     

Structure and Dynamics of Double Helices in Solution: Modes of DNA Bending

Abstract

The long range structure of DNA restriction fragments has been analysed by electro-optical measurements. The overall rotation time constants observed in a low salt buffer with monovalent ions is shown to decrease upon addition of Mg²⁺ or spermine. Since the circular dichroism and also the limiting value of the linear dichroism remain almost constant under these conditions, the effect is attributed to a change of the long range structure. According to a weakly bending rod model, the persistence length decreases from about 600 Å in the absence of Mg²⁺ or spermine to about 350 Å in the presence of these ions. The persistence length measured in the presence of Mg²⁺ is almost independent of temperature in the range of 10 to 40 °C. The nature of DNA bending is analysed by measurements of bending amplitudes and time constants from dichroism decay curves. The observed absence of changes in the bending amplitudes upon addition of Mg²⁺ or spermine, even though addition induces changes of the persistence length by a factor of 2, is hardly consistent with simple thermal bending. The combined results, including the remarkably small temperature dependence of persistence length and bending amplitude, can be explained by the existence of two bending effects: inherent curvature of DNA dominates at low temperature, whereas thermal bending prevails at high temperature. Analysis of bending amplitudes from dichroism decay curves according to an arc model provides an approximate measure for the degree of bending in restriction fragments. The model is consistent with the observed chain length dependence of bending amplitudes and provides an approximate curvature corresponding to a radius of ab out400Å. Thus the curvature observed in restriction fragments is similar to that observed for high molecular DNA condensed into toroids by addition of ions like spermine.

Particularly strong bending of DNA is induced by [CO(NH₃)₆]³⁺, indicated by an apparent persistence length of 200 Å and an increased bending amplitude together with a reduced limit value of the linear dichroism. This effect is attributed to the high charge density of this ion and potential site binding.     

Ionic strength effects on macroion diffusion and excess light-scattering intensities of short DNA rods

Quasielastic and static light-scattering measurements were made on DNA isolated from chicken erythrocyte mononucleosomes as a function of ionic strength between 6 × 10^?4 and 1.0M. A transition from single-exponential autocorrelation functions to markedly non-single-exponential decays was observed around 10^?2M ionic strength and was accompanied by a large decrease in the excess light-scattering intensity. Autocorrelation functions recorded below 10^?2M salt were well fit by the sum of two exponential relaxation which differed by as much as 100-fold in time constants. Apparent diffusion coefficients for the fast and slow processes plateaued around 10^?3M with numerical values approximately 10-fold and 1/10, respectively, of the translational diffusion coefficient for mononucleosome DNA at high ionic strength. This behavior is similar to that observed with poly(L -lysine), for which the slow decay has been associated with a transition to an extraordinary phase. The strong and complex salt dependence observed here illustrates potential difficulties in deriving structural information from scattering by polyions at low ionic strength.     

Electrostatic changes in phosphorylase kinase induced by its obligatory allosteric activator Ca2+

Skeletal muscle phosphorylase kinase (PhK) is a 1.3-MDa hexadecameric complex that catalyzes the phosphorylation and activation of glycogen phosphorylase b. PhK has an absolute requirement for Ca(2+) ions, which couples the cascade activation of glycogenolysis with muscle contraction. Ca(2+) activates PhK by binding to its nondissociable calmodulin subunits; however, specific changes in the structure of the PhK complex associated with its activation by Ca(2+) have been poorly understood. We present herein the first comparative investigation of the physical characteristics of highly purified hexadecameric PhK in the absence and presence of Ca(2+) ions using a battery of biophysical probes as a function of temperature. Ca(2+)-induced differences in the tertiary and secondary structure of PhK measured by fluorescence, UV absorption, FTIR, and CD spectroscopies as low resolution probes of PhK's structure were subtle. In contrast, the surface electrostatic properties of solvent accessible charged and polar groups were altered upon the binding of Ca(2+) ions to PhK, which substantially affected both its diffusion rate and electrophoretic mobility, as measured by dynamic light scattering and zeta potential analyses, respectively. Overall, the observed physicochemical effects of Ca(2+) binding to PhK were numerous, including a decrease in its electrostatic surface charge that reduced particle mobility without inducing a large alteration in secondary structure content or hydrophobic tertiary interactions. Without exception, for all analyses in which the temperature was varied, the presence of Ca(2+) rendered the enzyme increasingly labile to thermal perturbation.     

Thermodynamic analysis of the lactose repressor-operator DNA interaction

Kinetic and equilibrium constants for lactose repressor-operator DNA interaction have been examined as a function of salt concentration, size and sequence context of the operator DNA, and temperature. Significant salt effects were observed on kinetic and equilibrium parameters for pLA 322-8, an operator-containing derivative of pBR 322, and pIQ, an operator and pseudooperator-containing derivative of pBR 322. The association rate constant and equilibrium constant for the 40 base pair operator fragment were also salt dependent. Data for all the DNAs were consistent with a sliding mechanism for repressor-operator association/dissociation [Berg, O. G., & Blomberg, C. (1978) Biophys. Chem. 8, 271-280]. Calculation of the number of ionic interactions based on salt dependence yielded a value of approximately 8 for repressor binding to pIQ and pLA 322-8 vs. approximately 6 for the repressor-40 base pair fragment. These data and the differences in binding parameters for the plasmids vs. the 40 base pair operator are consistent with the formation of an intramolecular ternary complex in the plasmid DNAs. Unusual biphasic temperature dependence was observed in the equilibrium and dissociation rate constants for pLA 322-8, pIQ, and the 40 base pair fragment. These observations coupled with a discontinuity found in the inducer association rate constant as a function of temperature suggest a structural change in the protein. The large positive entropy contributions associated with repressor binding to all the DNAs examined provide the significant driving force for the reaction and are consistent with involvement of ionic and apolar interactions in complex formation.     

Kinetic study on the molecular mechanism of light-driven inward proton transport by schizorhodopsins

Schizorhodopsins (SzRs) are light-driven inward proton pumping membrane proteins. A H⁺ is released to the cytoplasmic solvent from the chromophore, retinal Schiff base (RSB), after light absorption, and then another H⁺ is bound to the RSB at the end of photocyclic reaction. However, the mechanistic detail of H⁺ transfers in SzR is almost unknown. Here we studied the deuterium isotope effect and the temperature dependence of the reaction rate constants of elementary steps in the photocycles of SzRs. The former indicated that deprotonation and reprotonation of RSB is mainly accomplished by H⁺ hopping between heavy atoms with similar H⁺ affinity. Furthermore, the temperature dependence of the rate constants revealed that most of H⁺ transfer events have a high entropy barrier. In contrast, the activation enthalpy and entropy of extremely thermostable SzR (MsSzR) are significantly higher than other types of SzRs (SzR1 and MtSzR) suggesting that its highly thermostable structure is optimized with at the cost of slower reaction rates at ambient temperatures.     

Magnesium-DNA interactions from interpretation of 25Mg-nmr relaxation rates: Field and coion dependence

We have used ²⁵Mg-nmr to investigate the binding of magnesium ions to double-stranded DNA. We have measured line shapes for ²⁵Mg in the presence of monodisperse calf thymus DNA (160 base pairs; b.p.) (magnesium : phosphate = 2.0) at two different field strengths, 11.75 T and 7.05 T, and used the isotropic model of two-site exchange developed by Westlund and Wennerstrom to simultaneously fit the line shapes at both field strengths. This model does not reproduce the observed field dependence. This is in contrast to a previous study [E. Berggren, L. Nordenskiold, and W. H. Braunlin (1992), Biopolymers, Vol. 32, pp. 1339–1350] in which a similar model of isotropic two-site exchange qualitatively reproduced the temperature dependence of the line widths. Relaxation rates were also measured as a function of magnesium : phosphate ratio and colon type. These measurements were used to assess the sensitivity of magnesium relaxation measurements to small changes in DNA structure induced by changes in the solvent environment. The temperature dependence of the line shape varies with the type of coion (chloride or sulfate) present. This coion dependence of the line shape is consistent with the coion dependence of the aggregation midpoint temperature reported by Bloomfield and co-workers [O. A. Knoll, M. G. Fried, and V. A. Bloomfield (1988) in Structure and Expres-sion, Vol. 2, R. H. Sarma and M. H. Sarma, Eds., Adenine Press, New York] and attributed to a lyotropic effect. These results suggest that even at low magnesium : phosphate ratios, relaxation parameters are specific to each magnesium–coion–DNA system. © 1994 John Wiley & Sons, Inc.     

Kinetic Analysis of Oligo(C) Formation from the 5′-Monophosphorimidazolide of Cytidine with Pb(II) Ion Catalyst at 10–75°C

The temperature dependence of the rate constants for the formation of oligocytidylate (oligo(C)) from the 5′-monophosphorimidazolide of cytidine (ImpC) in the presence of Pb(II) ion catalyst has been investigated at 10–75°C. The rate constants for the formation of oligo(C) increased in the order of the formation of 2-mer < 3-mer ≤ 4-mer; this trend resembles the trend in the cases of the template-directed and the clay-catalyzed formations of oligonucleotides. While the rate constants of the formation of oligo(C) increased with increasing temperature, the yield of oligo(C) decreased with increasing temperature. This is due to the fact that the relative magnitude of the rate constants of the formation of 2-mer, 3-mer, and 4-mer to that of the hydrolysis of ImpC decreased with increasing temperature. This is probably due to the fact that association between ImpC with the elongating oligo(C) decreases with increasing temperature. The apparent activation energy was 61.9 ± 8.5 kJ mol⁻¹ for the formation of 2-mer, 49.3 ± 2.9 kJ mol⁻¹ for 3-mer, 51.8 kJ mol⁻¹ for 4-mer, and 66.8 ± 4.5 kJ mol⁻¹ for the hydrolysis of ImpC. The significance of the temperature dependence of the formation rate constants of the model prebiotic formation of RNA is discussed.     

Lipid fluidity directly modulates the overall protein rotational mobility of the Ca-ATPase in sarcoplasmic reticulum

We have developed a quantitative and relatively model-independent measure of lipid fluidity using EPR and have applied this method to compare the temperature dependence of lipid hydrocarbon chain fluidity, overall protein rotational mobility, and the calcium-dependent enzymatic activity of the Ca-ATPase in sarcoplasmic reticulum. We define membrane lipid fluidity to be T/eta, where eta is the viscosity of a long chain hydrocarbon reference solvent in which a fatty acid spin label gives the same EPR spectrum (quantitated by the order parameter S) as observed for the same probe in the membrane. This measure is independent of the reference solvent used as long as the spectral line shapes in the membrane and the solvent match precisely, indicating that the same type of anisotropic probe motion occurs in the two systems. We argue that this empirical measurement of fluidity, defined in analogy to the macroscopic fluidity (T/eta) of a bulk solvent, should be more directly related to protein rotational mobility (and thus to protein function) than are more conventional measures of fluidity, such as the rate or amplitude of rotational motion of the lipid hydrocarbon chains themselves. This new definition thus offers a fluidity measure that is more directly relevant to the protein's behavior. The direct relationship between this measure of membrane fluidity and protein rotational mobility is supported by measurements in sarcoplasmic reticulum. The overall rotational motion of the spin-labeled Ca-ATPase protein was measured by saturation-transfer EPR. The Arrhenius activation energy for protein rotational mobility (11-12 kcal/mol/degree) agrees well with the activation energy for lipid fluidity, if defined as in this study, but not if more conventional definitions of lipid fluidity are used. This agreement, which extends over the entire temperature range from 0 to 40 degrees C, suggests that protein mobility depends directly on lipid fluidity in this system, as predicted from hydrodynamic theory. The same activation energy is observed for the calcium-dependent ATPase activity under physiological conditions, suggesting that protein rotational mobility (dependent on lipid fluidity) is involved in the rate-limiting step of active calcium transport.     

Evidence for heterogeneity in DNA-associated solvent mobility from acridine phosphorescence spectra

The mobility of solvent associated with native DNA in comparison with that of the bulk solvent is monitored from the temperature-dependent red shift in the phosphorescence spectra of acridines bound to DNA and free in glycol–buffer mixtures. Over the temperature range for which the red shift occurs the phosphorescence decay changes with emission wavelength, indicating the time-dependent nature of the process. Moreover, at these temperatures, emission anisotropy measurements establish that motions of the dye itself are not involved. Correspondence between perturbations to the solvent that influence the temperature at which the red shift occurs for free acridine with those for the DNA-bound dye confirm that “bound solvent” is responsible for the spectral changes. For the DNA-bound acridines the extent of the red shift is smaller and the midpoint T_1/2 of the transition is warmer. The reduction in the red shift reveals that the bound dye is less exposed to solvent and varies as 9-aminoacridine < acridine orange ～ proflavin, i.e., 9-amino-acridine is less exposed to solvent. On the other hand, the warmer T_1/2 indicates that DNA-associated solvent is considerably less mobile than bulk solvent. T_1/2 varies for proflavin bound to DNA, poly[d(AT)], poly[d(GC)], and poly(dG): poly(dC), and for proflavin, acridine orange, and 9-aminoacrine bound to DNA. These observations suggest that there is a heterogeneity in the mobility of DNA-associated solvent.     

Temperature dependence of the barley root plasma membrane-bound Ca2+- and Mg2+-dependent ATPase

Arrhenius plots of the maximal velocities for the Ca²⁺-and Mg²⁺-dependent ATPase activities found in a plasma membrane-rich microsome fraction isolated from the roots of barley ( Hordeum vulgare L. cv. Conquest) were nonlinear. Arrhenius plot analyses using a relation which produced curvilinear Arrhenius plots accurately fit the data and allowed the calculation of the activation enthalpies and molar heat capacities of activation. The temperature dependence of the computed Km values for the Ca²⁺- and Mg²⁺-dependent ATPase activities was complex, with the highest enzyme-substrate affinities being obtained near the barley seedling growth temperature (16°C). Using electron paramagnetic resonance spectroscopy with amphiphilic cationic and anionic spin probes, it was possible to demonstrate that temperature changes and increasing Ca²⁺ concentrations could alter the mobility of the membrane lipid polar head groups. Inhibition of the ATPase activities by high levels of Ca²⁺ may result from a Ca2+-induced reduction in the lipid polar head group mobility. The possible role of lipid polar head group-protein interactions in the complex temperature dependence of the barley root ATPase kinetic constants is discussed.     

The temperature dependence of creatine kinase fluxes in the rat heart

A ³¹P nuclear magnetic resonance saturation transfer method was used to measure the temperature dependence of creatine kinase-catalysed fluxes in Langendorff-perfused rat hearts. A decrease in temperature from 37 to 4°C lowered the observed steady-state fluxes by about 80%. These data were used in conjunction with calculated changes in substrate concentrations with temperature to estimate the activation energy for creatine kinase in situ. The apparent activation energy of 42 kJ/mol agrees reasonably well with the range of literature values for the enzyme in vitro. This demonstrates that the reaction is not diffusion-limited in situ and that extraction and dilution of the enzyme for study in vitro does not alter fundamental kinetic properties of the enzyme exhibited in the intact tissue.     

Solvent accessibility in folded proteins. Studies of hydrogen exchange in trypsin.

In a native protein, the exchange of a peptide amide proton with solvent occurs by one of two pathways, either directly from the folded protein, or via unfolding, exchange taking place from the unfolded protein. From the thermal unfolding rate constants, the contribution of unfolding to the over-all kinetics as a function of solvent and temperature has been determined. Exchange involving unfolding of the protein is characterized by a high activation energy, in the range of 50 to 60 Cal per mol. The activiation energy (Eapp) of the rates of exchange directly from the folded protein is approximately 20 to 25 Cal per mol. Because for the proton transfer step, Eapp approximately equal to 20 Cal per mol, the activation energy for any contributing protein conformational process(es) is approximately equal to 0 to 5 Cal per mol. Most, if not all, of the peptide amide protons in a folded protein can exchange directly with solvent without the protein unfolding. The number of "slowly" exchanging protons at a given condition of pH and temperature is not related to a discrete structural unit, but rather to the distribution of observed rates within the broader distribution of actual rates. The large attenuation of hydrogen exchange rates in folded proteins, resulting in a distribution of first order rates over 6 orders of magnitude, is primarily due to the effects of restricted solvent accessibility of labile protons in the three-dimensional structure. Any protein conformational process, such as protein fluctuations, invoked to explain the solvent accessibility must be of low activation energy and attenuated by ethanol and other co-solvents (Woodward, C. K., Ellis, L. M., and Rosenberg, A. (1974) J. Biol. Chem. 250, 440-444).