‘Steady/equilibrium approximation’ in relaxation and fluctuation: I. Procedure to simplify first-order reaction

A general procedure to simplify a complex first-order reaction by two approximations, the principle of fast equilibration and the steady-state approximation, is presented. Rate constants are classified into two groups: those of the order of unity and those of the order of ?(? 1) or less, and are represented in the schemes by thick and thin arrows, respectively. The fast and the slow components are defined: from the fast component at least one thick arrow originates and from the slow component no thick arrow originates. Fast components are divided into several groups. In a group, the fast components are connected by thick arrows in both directions in each reaction step. When at least one thick arrow originates from the components in a group G and terminates on a component not belonging to group G (group G is open), then the steady-state approximation or principle of fast equilibration holds on each component in group G after an induction period T°. When no thick arrow originating from group G is directed to components not belonging to group G (group G is closed), the principle of fast equilibration holds on the fast components in group G after T°. The induction period T° is less than the order of I/?.     

Reactions of 1-N6-ethenoadenosine nucleotides with myosin subfragment 1 and acto-subfragment 1 of skeletal and smooth muscle

The fluorescent nucleotides epsilon ADP and epsilon ATP were used to study the binding and hydrolysis mechanisms of subfragment 1 (S-1) and acto-subfragment 1 from striated and smooth muscle. The quenching of the enhanced fluorescence emission of bound nucleotide by acrylamide analyzed either by the Stern-Volmer method or by fluorescence lifetime measurements showed the presence of two bound nucleotide states for 1-N6-ethenoadenosine triphosphate (epsilon ATP), 1-N6-ethenoadenosine diphosphate (epsilon ADP), and epsilon ADP-vanadate complexes with S-1. The equilibrium constant relating the two bound nucleotide states was close to unity. Transient kinetic studies showed two first-order transitions with rate constants of approximately 500 and 100 s-1 for both epsilon ATP and epsilon ADP and striated muscle S-1 and 300 and 30 s-1, respectively, for smooth muscle S-1. The hydrolysis of [gamma-32P] epsilon ATP yielded a transient phase of small amplitude (less than 0.2 mol/site) with a rate constant of 5-10 s-1. Consequently, the hydrolysis of the substrate is a step in the mechanism which is distinct from the two conformational changes induced by the binding of epsilon ATP. An essentially symmetric reaction mechanism is proposed in which two structural changes accompany substrate binding and the reversal of these steps occurs in product release. epsilon ATP dissociates acto-S-1 as effectively as ATP. For smooth muscle acto-S-1, dissociation proceeds in two steps, each accompanied by enhancement of fluorescence emission. A symmetric reaction scheme is proposed for the acto-S-1 epsilon ATPase cycle. The very similar kinetic properties of the reactions of epsilon ATP and ATP with S-1 and acto-S-1 suggest that two ATP intermediate states also occur in the ATPase reaction mechanism.     

Effects of deuterium oxide on elementary steps in the ATPase reaction. Evidence for the similarity of key intermediates in contractile and transport ATPase.

The effects of D2O on the elementary steps in the contractile and transport ATPase [EC 3.6.1.3] reactions were studied, and the following results were obtained: 1. The rate of H-meromyosin ATPase in the steady state decreased in D2O to 60% of that in H2O. Deuterium oxide did not affect the size or rate of the initial burst of Pi liberation, i.e. the amount or rate of formation of the reactive myosin-phosphate-ADP complex, MADPP. Moreover, neither the rate of change in the fluorescence spectrum of H-meromyosin induced by ATP (the rate of formation of the second enzyme-ATP complex, M2ATP) nor the rate constant of decomposition of MADPP into M degrees + ADP + Pi was affected by D2O. However, the equilibrium constant of the step M2ATP in equilibrium MADPP decreased in D2O to about 1/2 the value in H2O. 2. In the case of the Na+-K+-dependent ATPase reactin, neither the rate constant of formation of the second enzyme-ATP complex, E2ATP, nor that of decomposition of a phosphorylated intermediate, EADP approximately P, was affected by D2O. However, the equilibrium constant of the step E2ATP in equilibrium EADP approximately P decreased in D2O to about 1/2.5-1/4 of the value in H2O. These results suggest a similarity between the modes of binding of phosphate in MADPP in the myosin ATPase reaction and in EADP approximatley P in the Na+-K+-dependent ATPase reaction.     

Gene Conversion, Linkage, and the Evolution of Multigene Families

The evolution of the probabilities of genetic identity within and between the loci of a multigene family is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, and the location dependence of the probabilities of identity is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. For interchromosomal conversion, the equilibrium probabilities of identity are within order epsilon [i.e., O(epsilon)] of those in a simple model that has no location dependence and, at equilibrium, no linkage disequilibrium. At equilibrium, the linkage disequilibria are of O(epsilon); they are evaluated explicitly with an error of O(epsilon 2); they may be negative if symmetric heteroduplexes occur. The ultimate rate and pattern of convergence to equilibrium are within O(epsilon 2) and O(epsilon), respectively, of that of the same simple model. If linkage is loose (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), the linkage disequilibria are reduced to O(epsilon) in a time of O(-ln epsilon). If intrachromosomal conversion is incorporated, the same results hold for loose linkage, except that, if the crossover rates are much less than 1/2, then the linkage disequilibria generally exceed those for pure interchromosomal conversion.     

First-order kinetics of muscle oxygen consumption, and an equivalent proportionality between QO2 and phosphorylcreatine level. Implications for the control of respiration

In frog sartorius muscle, after a tetanus at 20 degrees C, during which an impulse-like increase occurs in the rate of ATP hydrolysis, the rate of O2 consumption (QO2) reaches a peak relatively quickly and then declines monoexponentially, with a time constant not dependent on the tetanus duration (tau = 2.6 min in Rana pipiens and 2.1 min in Rana temporaria). To a good approximation, these kinetics are those of a first-order impulse response, and the scheme of reactions that couple O2 consumption to extramitochondrial ATP hydrolysis thus behaves as a first-order system. It is first deduced and then demonstrated directly that while QO2(t) is monoexponential, it changes in parallel with the levels of creatine and phosphorylcreatine, with proportionality constants +/- 1/tau p, where p is the P/O2 ratio in vivo. From this, it is further deduced that the mitochondrial creatine kinase (CK) reaction is pseudo-first order in vivo. The relationship between [creatine] and QO2 predicted by published models of the control of respiration is markedly different from that actually observed. As shown here, the first-order kinetics of QO2 are consistent with the hypothesis that respiration is rate-limited by the mitochondrial CK reaction; this has as a corollary the "creatine shuttle" hypothesis.     

Changes in the binding of "fast"-form alpha 2-macroglobulin to 3T3-L1 cells after differentiation to adipocytes

Human alpha 2-macroglobulin (alpha 2M)-CH3NH2 specifically binds to 3T3-L1 fibroblasts and adipocytes with an apparent Kd of 0.3 nM at 4 degrees C. Binding to fibroblasts follows first-order kinetics only for the first 20-30 min of reaction, k1 = 160 microM-1 h-1, and then proceeds in a non-first-order reaction that takes 28 h to reach steady state. Receptor activity is 120 fmol of alpha 2M-CH3NH2/mg of cell protein or 60 000 molecules/cell. Binding is nondissociable. In contrast, binding to adipocytes follows first-order kinetics, k1 = 720 microM-1 h-1, and reaches steady state in 6-8 h. Receptor activity is 35 fmol of alpha 2M-CH3NH2/mg of cell protein or 60 000 molecules/cell. Binding is reversible with a k2 of 0.4 h-1. Control studies with 3T3-C2 cells, which do not differentiate after hormone treatment, indicate that these differences are not due to hormone treatment alone. Binding to both fibroblasts and adipocytes is specific for "fast"-form alpha 2M but not for native alpha 2M. Inhibition studies with neoglycoproteins demonstrate that binding does not occur via any of the known carbohydrate receptors. Some cross-reactivity with antithrombin III-trypsin complexes is demonstrated. Both fibroblasts and adipocytes take up and degrade alpha 2M-CH3NH2 at 37 degrees C. For both cell types, the concentration of alpha 2M-CH3NH2 needed for half-maximal uptake is 65 nM.(ABSTRACT TRUNCATED AT 250 WORDS)     

Characterization of the ethenoadenosine diphosphate binding site of myosin subfragment 1. Energetics of the equilibrium between two states of nucleotide.S1 and vanadate-induced global conformation changes detected by energy transfer

The fluorescence decay of 1,N6-ethenoadenosine diphosphate (epsilon ADP) bound to myosin subfragment 1 (S1) was studied as a function of temperature. The decay was biexponential, and the two lifetimes were quenched relative to the single lifetime of free epsilon ADP. The temperature dependence of the fractional intensities of the decay components showed two states of the S1.epsilon ADP complex. At pH 7.5 in 30 mM TES, 60 mM KCl, and 3 mM MgCl2, the equilibrium constant for the conversion of the low-temperature state (S1L.epsilon ADP) to the high-temperature state (S1H.epsilon ADP) was 40 at physiological temperatures, and delta H degrees = 13 kcal.mol-1 and delta S degrees = 49 cal.deg-1.mol-1. At 10 degrees C the equilibrium constant of S1 for epsilon ADP was 5, indicating that S1H.epsilon ADP was the dominant state, and that for the vanadate complex epsilon ADP.Vi was 0.7, suggesting that in S1.epsilon ADP.Vi the dominant state of the S1-nucleotide complex was converted from S1H.epsilon ADP to S1L.epsilon ADP. The single rotational correlation time of bound epsilon ADP at 10 degrees C decreased from 107 ns in S1.epsilon ADP to 74 ns in S1+.epsilon ADP.Vi. Conversion of the binary complex to the ternary vanadate complex resulted in a 3-A decrease in the energy transfer distance between bound epsilon ADP and N-[4-(dimethylamino)-3,5-dinitrophenyl]maleimide attached to SH1 and a decrease of the average distance between bound epsilon ADP and bound Co2+ from 12.6 to 8.3 A.(ABSTRACT TRUNCATED AT 250 WORDS)     

Conformation and dynamics of the deoxyribose rings of a (nogalamycin)2-d (5''-GCATGC)2 complex studied in solution by 1H-n.m.r. spectroscopy.

The conformation and dynamics of the deoxyribose rings of a (nogalamycin)2-d(5'-GCATGC)2 complex have been determined from an analysis of 1H-1H vicinal coupling constants and sums of coupling constants (J1'-2',J1'-2",epsilon 1', epsilon 2' and epsilon 2") measured from one-dimensional n.m.r. spectra and from H-1'-H-2' and H-1'-H-2" cross-peaks in high-resolution phase-sensitive two-dimensional correlation spectroscopy (COSY) and double-quantum-filtered correlation spectroscopy (DQF-COSY) experiments. The value of J3'-4' has also been estimated from the magnitude of H-3'-H-4' cross-peaks in DQF-COSY spectra and H-1'-H-4' coherence transfer cross-peaks in two-dimensional homonuclear Hartman-Hahn spectroscopy (HOHAHA) spectra. The data were analysed, in terms of a dynamic equilibrium between North (C-3'-endo) and South (C-2'-endo) conformers, by using the graphical-analysis methods described by Rinkel & Altona [(1987) J. Biomol. Struct. Dyn. 4,621-649]. The data reveal that the sugars of the 2C-5G and 3A-4T base-pairs, which form the drug-intercalation site, have strikingly different properties. The deoxyribose rings of the 2C-5G base-pair are best described in terms of an equilibrium heavily weighted in favour of the C-2'-endo geometry (greater than 95% 'S'), with a phase angle, P, lying in the range 170-175 degrees and amplitude of pucker between 35 and 40 degrees, as typically found for B-DNA. For the deoxyribose rings of the 3A-4T base-pair, however, the analysis shows that, for 3A, the C-2'-endo and C3'-endo conformers are equally populated, whereas a more limited data set for the 4T nucleotide restricts the equilibrium to within 65-75% C-2'-endo. The deoxyribose rings of the 1G-6C base-pair have populations of 70-80% C-2'-endo, typical of nucleotides at the ends of a duplex. Although drug-base-pair stacking interactions are an important determinant of the enhanced duplex stability of the complex [Searle, Hall, Denny, & Wakelin (1988) Biochemistry 27, 4340-4349], the current findings make it clear that the same interactions can be associated with considerable variations in the degree of local structural dynamics at the level of the sugar puckers.     

Iron oxidation and transferrin formation by phosvitin.

The catalytic activity of phosvitin in Fe(II) oxidation and the addition of iron to transferrin were studied under various conditions. It was concluded that the Fe(II) oxidized by phosvitin would bind to apotransferrin, although an appreciable fraction of Fe(III) remained bound to phosvitin. Fe(III) also migrated from phosvitin to apotransferrin. This reaction was first-order with respect to Fe(III)-phosvitin concentration with a half-time (t1/2) of 10 min, and a first-order rate constant, k=0.069min-1, in 700 muM-phosphate buffer, pH 7.2, at 30 degrees C. The catalysis of the oxidation of Fe(III) by phosvitin was proportional to O2 concentration, and is quite different from the relative O2 independence of Fe(II) oxidation as catalysed by ferroxidase. A scheme for the mobilization and transfer of iron in the chicken, including the role of ferroxidase, phosyitin and transferrin, is presented.     

A pulse-radiolysis study of the manganese-containing superoxide dismutase from Bacillus stearothermophilus. A kinetic model for the enzyme action.

The enzymic reaction mechanism of a manganese-containing superoxide dismutase from Bacillus stearothermophilus was studied by using pulse radiolysis. During catalysis (pH 8.9; 25 degrees C), changes occurring in the kinetics of substrate disappearance and in the visible absorption of the enzyme at 480 nm established that the simple two-step mechanism found for copper- and iron-containing superoxide dismutases is not involved. At a low ratio (less than 15) of substrate concentration to enzyme concentration the decay of O2--is close to exponetial, whereas at much higher ratios (greater than 100) the observed decay is predominantly zero-order. The simplest interpretation of the results invokes a rapid one-electron oxidation-reduction cycle ('the fast cycle') and, concurrently, a slower reaction giving a form of the enzyme that is essentially unreactive towards O2-- but which undergoes a first-order decay to yield fully active native enzyme ('the slow cycle'). The fast cycle involves the native enzyme EA and a form of the enzyme EB which can be obtained also by treating the form EA with H2O2. Computer calculations made with such a simple model predict behaviour in excellent agreement with the observed results.     

Starting D-optimal designs for batch kinetics studies of enzyme-catalyzed reactions in the presence of enzyme deactivation.

This paper describes a strategy for the starting experimental design of experiments required by general research in the field of biochemical kinetics. The type of experiments that qualify for this analysis involve batch reactions catalyzed by soluble enzymes where the activity of the enzyme decays with time. Assuming that the catalytic action of the enzyme obeys a Michaelis-Menten rate expression and that the deactivation of the enzyme follows a first-order decay, the present analysis employs the dimensionless, integrated form of the overall rate expression to obtain a criterion (based on the maximization of the determinant of the derivative matrix) that relates the a priori estimates of the parameters with the times at which samples should be withdrawn from the reacting mixture. The analysis indicates that the initial concentration of substrate should be as large as possible, and that the samples should be taken at times corresponding to substrate concentrations of approximately 2/3, 1/4, and I/epsilon of the initial concentration (where epsilon should be as large as possible).     

Fluorescence polarization and intensity kinetic studies of antifluorescein antibody obtained at different stages of the immune response.

Kinetic studies of reactions between fluorescein and antifluorescein antibody produced during early, intermediate, and late stages of the immune response have been carried out utilizing both fluorescence intensity and polarization measurements in the static (time constant similar to 5 sec) and in the stopped-flow modes (time constant similar to 5 msec). During maturation of the immune response, it was found that the "on" second-order association rate constant increased its value only by a factor of three, whereas the "off" dissociation first-order rate constant decreased by a factor of over 1000. Hence, it is the rate of dissociation which largely determines the stability of the hapten-antihapten complex. Furthermore, since second-order rate behavior was found for even heterogeneous antibody, most of the heterogeneity with respect to binding affinity occurs as a result of the heterogeneity in the rate of dissociation of the hapten-antihapten complex and not from the primary combination of hapten and antibody. Antifluorescein antibody which exhibits both high binding affinity (K similar to 5 x 10(11) M-1) and homogeneity with respect to equilibrium binding has been shown to obey second-order association kinetics over wide ranges in concentration. Despite the fact that the value of the second-order rate constant for this fluorescein-antifluorescein reaction is as large as that for most other hapten-antihapten reactions (1.4 x 10(8) M-1 sec-1), the binding reaction has an appreciable activation energy (7 kcal/mol). This is true for both divalent and univalent antibody. Furthermore, the reaction rate parameters are markedly affected by specific anions. The value of the second-order rate constant (18.5 degrees) increases according to the following scheme: salicylate less than trichloroacetate less than SCN- less than ClO4- less than Cl- less than F- less than phosphate. The activation energy increases as follows: trichloroacetate less than phosphate less than F- less than Cl- less than ClO4- less than SCN- less than salicylate, whereas estimates of the entropy of activation indicate that deltaS++ increases as follows: tricholroacetate less than phosphate similar to F- less than Cl- less than ClO4- less than SCN- less than salicylate. The same mechanism which was previously proposed by us for the antigen-antibody reaction is also consistent with the kinetics of the fluorescein-antifluorescein reaction. This mechanism postulates a bimolecular process with structural rearrangements (conformational changes and/or the loss of water) in the formation of the transition state complex. The reaction between the fluorescein hapten and its antibody hence is not diffusion limited.     

Temperature dependence of the rate constants of the Escherichia coli RNA polymerase-lambda PR promoter interaction. Assignment of the kinetic steps corresponding to protein conformational change and DNA opening

The kinetics of formation and of dissociation of open complexes (RPo) between Escherichia coli RNA polymerase (R) and the lambda PR promoter (P) have been studied as a function of temperature in the physiological range using the nitrocellulose filter binding assay. The kinetic data provide further evidence for the mechanism R + P in equilibrium I1 in equilibrium I2 in equilibrium RPo, where I1 and I2 are kinetically distinguishable intermediate complexes at this promoter which do not accumulate under the reaction conditions investigated. The overall second-order association rate constant (ka) increases dramatically with increasing temperature, yielding a temperature-dependent activation energy in the range 20 kcal (near 37 degrees C) to 40 kcal (near 13 degrees C) (1 kcal = 4.184 kJ). Both isomerization steps (I1----I2 and I2----RPo) appear to be highly temperature dependent. Except at low temperatures (less than 13 degrees C) the step I1----I2, which we attribute to a conformational change in the polymerase with a large negative delta Cp degrees value, is rate-limiting at the reactant concentrations investigated and hence makes the dominant contribution to the apparent activation energy of the pseudo first-order association reaction. The subsequent step I2----RPo, which we attribute to DNA melting, has a higher activation energy (in excess of 100 kcal) but only becomes rate-limiting at low temperature (less than 13 degrees C). The initial binding step R + P in equilibrium I1 appears to be in equilibrium on the time-scale of the isomerization reactions under all conditions investigated; the equilibrium constant for this step is not a strong function of temperature and is approximately 10(7) M-1 under the standard ionic conditions of the assay (40 mM-Tris . HCl (pH 8.0), 10 mM-MgCl2, 0.12 M-KC1). The activation energy of the dissociation reaction becomes increasingly negative at low temperatures, ranging from approximately -9 kcal near 37 degrees C to -30 kcal near 13 degrees C. Thermodynamic (van't Hoff) enthalpies delta H degrees of open complex formation consequently are large and temperature-dependent, increasing from approximately 29 to 70 kcal as the temperature is reduced from 37 to 13 degrees C. The corresponding delta Cp degrees value is approximately -2.4 kcal/deg. We propose that this large negative delta Cp degrees value arises primarily from the burial of hydrophobic surface in the conformational change (I1 in equilibrium I2) in RNA polymerase in the key second step of the mechanism.(ABSTRACT TRUNCATED AT 400 WORDS)     

Oxygen-pulse curves in rat liver mitochondrial suspensions. Some observations and deductions.

1. The inference, implicit in the chemiosmotic hypothesis, that protons move into the bulk phase during ATP synthesis was investigated. 2. Incubation of rat liver mitochondria in the presence of the cation exchanger CM-Sephadex C-50 caused alkalinization in the medium, though total ATP synthesis remained unchanged. The addition of N-ethylmaleimide prevented the alkalinization, but there was still no indication of protons passing into the medium. The expected proton movement [Mitchell & Moyle (1967) Biochem. J. 105, 1147--1162] was readily detected when as an equivalent acid pulse. 3. Analysis of delta H+ decay curves after O2 pulses (3 micrograms-atoms of O/g of protein) indicated the presence of fast and slow components of decay, with first-order rate constants (k) of 0.24s-1 and 0.032s-1. The fast decay was finite and was eliminated in the presence of N-ethylmaleimide. 4. These observations are interpreted as evidence for the development of unmasking of fixed charges on the outer surface of the mitochondrial inner membrane during energization and for the existence of proton-retentive electrical fields (rho-zones) on this surface. The charge concentration is calculated as about 1 charge/10nm2. 5. A cycle of changes in a single fixed-charge molecule is proposed which mediates both Ca2+ uptake and the first step in the utilization of the rho-zone protonmotive force, delta p rho.     

Effect of temperature on the creatine kinase equilibrium.

The effect of temperature on the apparent equilibrium constant of creatine kinase (ATP:creatine N-phosphotransferase (EC 2.7.3.2)) was determined. At equilibrium the apparent K' for the biochemical reaction was defined as [formula: see text] The symbol sigma denotes the sum of all the ionic and metal complex species of the reactant components in M. The K' at pH 7.0, 1.0 mM free Mg2+, and ionic strength of 0.25 M at experimental conditions was 177 +/- 7.0, 217 +/- 11, 255 +/- 10, and 307 +/- 13 (n = 8) at 38, 25, 15, and 5 degrees C, respectively. The standard apparent enthalpy or heat of the reaction at the specified conditions (delta H' degree) was calculated from a van't Hoff plot of log10K' versus 1/T, and found to be -11.93 kJ mol-1 (-2852 cal mol-1) in the direction of ATP formation. The corresponding standard apparent entropy of the reaction (delta S' degree) was +4.70 J K-1 mol-1. The linear function (r2 = 0.99) between log10 K' and 1/K demonstrates that both delta H' degree and delta S' degree are independent of temperature for the creatine kinase reaction, and that delta Cp' degree, the standard apparent heat capacity of products minus reactants in their standard states, is negligible between 5 and 38 degrees C. We further show from our data that the sign and magnitude of the standard apparent Gibbs energy (delta G' degree) of the creatine kinase reaction was comprised mostly of the enthalpy of the reaction, with 11% coming from the entropy T delta S' degree term. The thermodynamic quantities for the following two reference reactions of creatine kinase were also determined. [formula: see text] The delta H degree for Reaction 2 was -16.73 kJ mol-1 (-3998 cal mol-1) and for Reaction 3 was -23.23 kJ mol-1 (-5552 cal mol-1) over the temperature range 5-38 degrees C. The corresponding delta S degree values for the reactions were +110.43 and +83.49 J K-1 mol-1, respectively. Using the delta H' degree of -11.93 kJ mol-1, and one K' value at one temperature, a second K' at a second temperature can be calculated, thus permitting bioenergetic investigations of organs and tissues using the creatine kinase equilibria over the entire physiological temperature range.     

Gene Conversion, Linkage, and the Evolution of Repeated Genes Dispersed among Multiple Chromosomes

The evolution of the probabilities of genetic identity within and between the loci of a multigene family dispersed among multiple chromosomes is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, but the same for every chromosome; the dependence of the probabilities of identity on the location on each chromosome is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. Under the assumption of loose linkage (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), explicit approximations are obtained for the equilibrium values of the probabilities of identity and of the linkage of disequilibria. The probabilities of identity are of order one [i.e., O(1)] and do not depend on location; the linkage disequilibria are of O(epsilon) and, within each chromosome, depend on location through the crossover rates. It is demonstrated also that the ultimate rate and pattern of convergence to equilibrium are close to that of a much simpler, location-independent model. If intrachromosomal conversion is absent, the above results hold even without the assumption of loose linkage. In all cases, the relative errors are of O(epsilon). Even if the conversion rate between genes on nonhomologous chromosomes is considerably less than between genes on the same chromosome or homologous chromosomes, the probabilities of identity between the former genes are still almost as high as those between the latter, and the rate of convergence is still not much less than with equal conversion rates. If the crossover rates are much less than 1/2, then most of the linkage disequilibrium is due to intrachromosomal conversion. If linkage is loose, the reduction of the linkage disequilibria to O(epsilon) requires only O(-ln epsilon) generations.     

Comparative thermal stabilities of recombinant adenoviruses and hexon protein

Differential scanning calorimetry was used to identify the thermal stability profile of the replication deficient and protein IX deleted recombinant adenovirus type 5 that contains the p53 transgene (rAd/p53) in phosphate buffered saline (vPBS) or 10% glycerol (TRIS/phosphate buffer). The wildtype adenovirus (Ad/WT) and purified hexon protein (major capsid protein) were also evaluated in 10% glycerol (TRIS/phosphate buffer) as controls. The thermal profile of rAd/p53 revealed three endothermic transitions (T1, T2 and T3) occurring between 25 degrees C and 90 degrees C. T1, which occurred at 46.7 degrees C in vPBS and 49.4 degrees C in TRIS/PO4 10% glycerol buffer, was irreversible following repeated scanning and attributed to the degradation of the intact vector. The latter two endothermic transitions, T2 and T3, occurring at 69 degrees C and 78 degrees C, respectively, corresponded with the two transitions of purified hexon in temperature and amount of heat absorbed. The thermal profile of Ad/WT revealed four endothermic transitions at 51.5 degrees C (T1), 70.5 degrees C (T2A), 73.6 degrees C (T2B), and 77.4 degrees C (T3). The higher temperature of degradation as well as additional transition was attributed to the presence of protein IX associated with the hexon. The positions and excess molar heat capacities of the intact rAds were found to be affected by pH, glycerol, vector concentration and the presence or absence of protein IX in the capsid. Irreversibility of T1 implied that the degradation of the intact virus may follow first-order kinetics. The thermal scan rate dependence of T1 further confirmed that degradation of the intact virus may be first-order. The apparent activation energies for the degradation of the intact vectors were determined from the scan rate dependence of T1 and shown to be affected by protein IX in the capsid and solution conditions. Analysis of rAd samples incubated at 45 degrees C by Field Emission Electron Microscopy (FESEM) confirmed that loss of single particles was first-order. Although aggregates were observed in the samples, degradation appeared to be the dominant reaction leading to disappearance of single virions from the aqueous matrix. Based on thermal and FESEM analysis, an empirical model was proposed that accounted for the disappearance of single rAd particles. At or near T1, degradation of rAd particles followed a unidirectional, pseudo-first order reaction. However, at lower temperatures, disappearance of single virions resulted from competing irreversible degradation and aggregation reactions.     

Carbon-13 NMR in conformational analysis of nucleic acid fragments. 4. The torsion angle distribution about the C3''-O3'' bond in DNA constituents.

Carbon-13 and proton NMR spectra of a series of oligodeoxynucleotides (d(CT), d(CC), d(TA), d(AT), d(CG), d(GC), d(AG), d(AAA), d(TATA) and d(GGTAAT] were measured at various temperatures. The three coupling constants that are related to the magnitude of backbone angle epsilon (J(C4'-P), J(C2'-P) and J(H3'-P] are analyzed in terms of a three-state equilibrium about this bond. Two epsilon (trans) angles occur, which differ in magnitude depending on the conformation (N or S) of the adjoining deoxyribose ring. The S-type deoxyribose ring is associated with a smaller epsilon (trans) angle: epsilon (t,S) = 192 degrees. The N-type deoxyribose ring is associated with a larger epsilon (trans) angle epsilon (t,N) = 212 degrees. The third rotamer participating in the conformational equilibrium, is a gauche(-) (epsilon (-] conformer and occurs exclusively in combination with the S-type sugar ring (epsilon (-,S) = 266 degrees). Within the limits of experimental error, the magnitude of these three angles appears to be independent of the particular base sequence, except in the case of d(CG) where a slightly larger epsilon (t,S) angle (197 degrees) is indicated. A simple equation is proposed which may be used to calculate the population of epsilon (t,S) conformer in cases where only J(H3'-P) is known.     

Reactions of the Wurster's red radical cation with hemoglobin and glutathione during the cooxidation of N,N-dimethyl-p-phenylenediamine [correction of phenlenediamine] and oxyhemoglobin in human red cells.

N,N-Dimethyl-p-phenylenediamine (DMPD) reacted directly with oxyhemoglobin under formation of ferrihemoglobin and, presumably, the N,N-dimethyl-p-phenylenediamine radical cation (DMPP.+). The apparent second-order rate constant of this reaction was 1 M-1 s-1 (pH 7.4, 37 degrees C). The reaction rate was diminished by catalase (by 1/3) and by superoxide dismutase (by 1/5). The apparent second-order rate constant of ferrihemoglobin formation by DMPD.+ was 5 x 10(3) M-1 s-1. Since DMPD.+ is disproportionated by 50% at pH 7.4, the quinonediimine could not be excluded as the ultimate ferrihemoglobin forming oxidant. To prove this hypothesis, the disproportionation equilibrium was shifted to the radical side by addition of excess DMPD. Ferrihemoglobin formation was thereby increased, indication that the radical was the responsible oxidant. In contrast to ferrihemoglobin formation, reactions with glutathione occurred predominantly with the quinonediimine. The second-order rate constant of this reaction was 4 x 10(5) M-1 s-1 which approaches the value obtained with p-benzoquinone. In contrast to the corresponding reactions of the N,N,N',N'-tetramethyl-p-phenylenediamine radical cation, the disporportionation reaction of DMPD.+ was very fast, k = 2 x 10(6) M-1 s-1. Formation of glutathione disulfide was negligible and the main reaction products were two isomeric glutathione adducts, 2- and 3-(glutathione-S-yl)-N,N-dimethyl-p-phenylenediamine. In human erythrocytes, DMPD produced many equivalents of ferrihemoglobin, diminished glutathione and produced both thioethers. In contrast to ferrihemoglobin formation, DMPD and glutathione disappearance as well as thioether appearance occured only after a marked lag phase. The calculated steady state concentration of DMPD.+ was only 4 x 10(-6) the DMPD concentration, as long as ferrihemoglobin was low. At increasing ferrihemoglobin higher steady state concentrations of the radical are attained. In fact, preformed ferrihemoglobin in red cells significantly accelerated DMPD and glutathione disappearance. This effect was completely prevented in the presence of ferrihemoglobin-complexing cyanide. The presented experiments once more appoint blood as a metabolically competent organ for the biotransformation of aromatic amines.     

Reversible unfolding and refolding behavior of a monomeric aldolase from Staphylococcus aureus.

Thermal and GdmCl-induced unfolding transitions of aldolase from Staphylococcus aureus are reversible under a variety of solvent conditions. Analysis of the transitions reveals that no partially folded intermediates can be detected under equilibrium conditions. The stability of the enzyme is very low with a delta G0 value of -9 +/- 2 kJ/mol at 20 degrees C. The kinetics of unfolding and refolding of aldolase are complex and comprise at least one fast and two slow reactions. This complexity arises from prolyl isomerization reactions in the unfolded chain, which are kinetically coupled to the actual folding reaction. Comparison with model calculations shows that at least two prolyl peptide bonds give rise to the observed slow folding reactions of aldolase and that all of the involved bonds are presumably in the trans conformation in the native state. The rate constant of the actual folding reaction is fast with a relaxation time of about 15 s at the midpoint of the folding transition at 15 degrees C. The data presented on the folding and stability of aldolase are comparable to the properties of much smaller proteins. This might be connected with the simple and highly repetitive tertiary structure pattern of the enzyme, which belongs to the group of alpha/beta barrel proteins.