Conformational fluctuations and protein reactivity. Determination of the rate-constant spectrum and consequences in elementary biochemical processes

When a protein's active site happens to be strongly coupled with the protein structure, the rate constant of the reaction may eventually be modulated by the conformational fluctuations. Evidence for this effect has long been provided by extensive flash photolysis investigations of liganded hemoproteins and more recently of the non-heme respiratory protein hemerythrin in hydro-organic solvents. Within a given protein conformational substate, an elementary reaction step is characterized by one single free energy barrier and by a first-order rate constant, k, which changes with temperature according to an Arrhenius law. At physiological temperature and low viscosity, ultrafast conformational relaxation causes efficient averaging of the reaction rates and the protein displays exponential kinetics with an average rate constant (k). Under sufficiently general conditions, it can be shown that (k) also follows a simple Arrhenius law with 'effective' values of the pre-exponential factor Aeff and activation enthalpy Heff. It is found that Aeff strongly depends on the overall shape of the rate constant distribution and that Heff actually corresponds to the lower limit of the enthalpy of activation, i.e. the value associated with the highest possible reaction rate. The underlying distribution of rate constants can be reconstructed from a set of experiments in which the kinetics depart from an exponential, i.e. at low temperature and high viscosity. The most probable distribution of exponentials consistent with the observed kinetics of the geminate recombinations of oxygen with photodissociated hemerythrin has been determined by using a new approach, known as the maximum entropy method. The results are consistent with a single pre-exponential value and a distributed enthalpy spectrum. As expected, Heff does not coincide either with the most probable nor with the average value of the enthalpy. The most salient findings are that the probability for any protein molecule to have an enthalpy of activation equal to the effective value Heff vanishes and that Aeff differs by nearly three orders of magnitude from the true value A0. Biochemical reaction rates are actually average values, since protein reactions are measured under physiological conditions, where conformational relaxation is always fast. Our understanding of the significance of Aeff and Heff is therefore entirely dependent on the knowledge of the distribution function of the rate constants. In particular, enthalpy and entropy terms of similar reactions performed by different proteins cannot be compared as long as the distribution of the rate constants remains unknown.     

Binding of colchicine to purified microtubule protein.

The binding of colchicine to tubulin, purified by two cycles of assembly-disassembly, has been studied. Equilibrium studies indicated a dissociation constant which declined during incubation approaching a minimum value of approximately 0.30 times 10- minus 6 M after 13 hours of incubation. Because tubulin is unstable during prolonged incubation (t1/2 of 5.2 hours for free tubulin, t1/2 of 12.5 hours for tubulin bound to colchicine), the equilibrium Kd was felt to be an overestimation of the true Kd. The rate constant of dissociation (k-1 equal to 0.009 hour- minus 1 hour- minus 1) and the rate constant of association (k1 equal to 0.37 times 10-6 M-minus 1) were measured under conditions designed to circumvent or correct for tubulin instability. The dissociation constant determined by the ratio k-1/k1 was 0.024 times -minus 6 M. To determine whether the discrepancy between the "equilibrium" and "kinetic" determined dissociation constants could be accounted for on the basis of tubulin instability, the binding reaction was computer-simulated using the measured association and dissociation rate constants and the rate constants for decay of bound and free tubulin. Computer simulation was in close agreement with the experimentally determined behavior of the reaction during a 13-hour incubation. It is concluded that the Kd determined by equilibrium methodology results in a considerable overestimation due to the instability of tubulin, and that the best estimate for the Kd of the colchicine-tubulin equilibrium is the value determined by the ratio of the rate constants.     

Maximum-entropy determination of self-association distribution functions; daunorubicin and ATP.

In the present paper we show how one can use the perturbation of some molecular optical property (for example circular dichroism or chemical shift) as a function of concentration to construct cluster distribution functions describing the self-association of molecules in solution. The optical data are first converted into data giving the variation of the average extent of clustering as a function of the total concentration and then, using straightforward thermodynamics, a set of moments of the cluster distribution function can be obtained. Utilizing the maximum-entropy method, the moments are then used to calculate approximate distribution functions, where the more moments that are used the better the approximation obtained. Given the probability distribution for clusters of different sizes one can then calculate the equilibrium constant for each stage of association. Thus one converts average degree of association into equilibrium constants without having to use any specific model. By this method one can clearly tell whether the equilibrium constants remain constant, increase, or decrease with the number of molecules in a cluster. We apply the method to literature data for two systems, namely daunorubicin, which has a strong tendency to cluster in solution, and Mg(ATP)(2-) which forms weaker clusters. We find that the successive equilibrium constants for adding a monomer to a cluster are approximately constant for daunorubicin but clearly decrease as a function of increasing cluster size for Mg(ATP)(2-).     

Iron-sulfur cluster biosynthesis. A comparative kinetic analysis of native and Cys-substituted ISA-mediated [2Fe-2S]2+ cluster transfer to an apoferredoxin target

ISA type proteins mediate cluster transfer to apoprotein targets. Rate constants have been determined for cluster transfer from Schizosaccharomyces pombe ISA to apo Fd. Substitution of the cysteine residues of ISA produced derivative proteins (C72A, C136A, and C138A) that were found to be at least as active in cluster transfer reactions as the native form at 25 degrees C (k(2) approximately 170 M(-1) min(-1) for native, k(2) approximately 169 M(-1) min(-1) for C72A, k(2) approximately 206 M(-1) min(-1) for C136A, and k(2) approximately 242 M(-1) min(-1) for C138A), although the yield of cluster transfer was found to be lower as a consequence of the enhanced lability of clusters in the derivative proteins. Minor variations in rate constant for the ISA Cys derivatives do not reflect any change in the affinity of binding to the apo Fd since k(2) was found to be independent of the concentration of apo Fd over the range of 1-25 microM. The pH dependence of cluster transfer rates was found to be similar for native and C136A ISA, with an observed pK(a) of 7.8 determined from the pH profiles for cluster transfer activity of each protein. The temperature dependence of the rate constant defining the cluster transfer reaction for the wild type versus this C136A ISA derivative is distinct (DeltaH* approximately 6.3 kcal mol(-1) and DeltaS* approximately -27.3 cal K(-1) mol(-1) for native and DeltaH* approximately 2.7 kcal mol(-1) and DeltaS* approximately -38.9 cal K(-1) mol(-1) for C136A ISA). Instability of the protein-bound cluster precluded a comparison with data from pH and temperature dependencies for the two other Cys derivatives. Experiments to determine the dependence of reaction rate constants on viscosity indicate cluster transfer is rate-limiting. A comparison of cross-species rate constants for cluster transfer to apo Fd targets from Homo sapiens and S. pombe demonstrated that the identity of the Fd is less critical for promoting cluster transfer from Sp ISA (at 25 degrees C, k(2) approximately 170 M(-1) min(-1) for Sp Fd and k(2) approximately 169 M(-1) min(-1) for Hs Fd). This contrasts with an earlier observation for ISU-mediated cluster assembly [Wu, S., et al. (2002) Biochemistry 41, 8876-8885], where the rates differed for Hs and Sp target Fd's, suggesting distinct binding sites for binding of holo ISA and ISU to apo Fd.     

On true and apparent Michaelis constants in enzymology. I. Differences

Differences between both true and apparent rate constants and Michaelis constants have been examined. Rate constants of elementary stages of real mechanisms are true ones. True Michaelis constant Km is expressed by equation Km = (k(-1) + k2)/k. True constants may be determined for reliable mechanism only for which the equation of initial rate was obtained which displays physical sense of these constants and permits to find the method of their calculation. The true constant values are independent of concentration of reactants, activators, inhibitors, extraneous agents and pH. The apparent rate constants are such constants of the composite reaction which are observed when this reaction is described by the equation of simple reaction. Michaelis constant calculated by a half of the ultimate constant is an apparent constant. The apparent constants may be functions of several true rate constants and/or concentrations of reacting substances. The evident physical sense of apparent constants being absent, only formal relation between the reaction rate and reactant concentration independent of the investigated mechanism is provided.     

Iron-sulfur cluster biosynthesis. Kinetic analysis of [2Fe-2S] cluster transfer from holo ISU to apo Fd: role of redox chemistry and a conserved aspartate

ISU-type proteins mediate cluster transfer to apo protein targets. Rate constants have been determined for cluster transfer from ISU to apo Fd for both Homo sapiens and Schizosaccharomyces pombe proteins, and cross reactions have also been examined. Substitution of a key aspartate residue of ISU is found to decrease the rate of cluster transfer by at least an order of magnitude (for wild-type Hs ISU cluster transfer to Hs apo Fd, k(2) approximately 540 M(-1) min(-1), relative 56 M(-1) min(-1) for D37A ISU). This change in rate constant does not reflect any change in binding affinity of the ISU and Fd proteins. The pH dependencies of cluster transfer rates are similar for WT and D37A ISU, arguing against a role for Asp37 as a catalytic base, although evidence for general base catalysis mediating deprotonation of Cys from the apo target is supported by an observed pK(a) of 6.9 determined from the pH profiles for both WT and D37A ISU. Such a pK(a) value is at the lower limit for Cys and is common for solvent-accessible Cys thiols. The temperature dependence of the rate constant defining the cluster transfer reaction for wild type versus the aspartate derivative is distinct. Thermal activation parameters (DeltaH and DeltaS) are consistent with a solvent-accessible ISU-bound cluster, with desolvation as a principle barrier to cluster transfer. Experiments to determine the dependence of reaction rate constants on viscosity indicate cluster transfer to be rate-limiting. Fully oxidized cluster appears to be the natural state for transfer to target proteins. Reduced Fd does not readily reduce ISU-bound [2Fe-2S](2+) and does not promote cluster transfer to an apo Fd target.     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Steady-state kinetics of solitary batrachotoxin-treated sodium channels. Kinetics on a bounded continuum of polymer conformations.

The underlying principles of the kinetics and equilibrium of a solitary sodium channel in the steady state are examined. Both the open and closed kinetics are postulated to result from round-trip excursions from a transition region that separates the openable and closed forms. Exponential behavior of the kinetics can have origins different from small-molecule systems. These differences suggest that the probability density functions (PDFs) that describe the time dependences of the open and closed forms arise from a distribution of rate constants. The distribution is likely to arise from a thermal modulation of the channel structure, and this provides a physical basis for the following three-variable equation: [formula; see text] Here, A0 is a scaling term, k is the mean rate constant, and sigma quantifies the Gaussian spread for the contributions of a range of effective rate constants. The maximum contribution is made by k, with rates faster and slower contributing less. (When sigma, the standard deviation of the spread, goes to zero, then p(f) = A0 e-kt.) The equation is applied to the single-channel steady-state probability density functions for batrachotoxin-treated sodium channels (1986. Keller et al. J. Gen. Physiol. 88: 1-23). The following characteristics are found: (a) The data for both open and closed forms of the channel are fit well with the above equation, which represents a Gaussian distribution of first-order rate processes. (b) The simple relationship [formula; see text] holds for the mean effective rat constants. Or, equivalently stated, the values of P open calculated from the k values closely agree with the P open values found directly from the PDF data. (c) In agreement with the known behavior of voltage-dependent rate constants, the voltage dependences of the mean effective rate constants for the opening and closing of the channel are equal and opposite over the voltage range studied. That is, [formula; see text] "Bursts" are related to the well-known cage effect of solution chemistry.     

Reduction of methemoglobin by cobaltocytochrome c catalyzed by mediators.

The reduction of methemoglobin by cobaltocytochrome c (Cocyt c) has been measured using nine mediators of different half-reduction potentials, Em, 7. The rate increases with the increase of Em, 7 for the mediator but dropped precipitously when it becomes more positive than the Em, 7 for the methemoglobin/hemoglobin couple. The reaction is most efficient with phenzaine methosulfate, therefore it was studied in detail. The reaction is first order in the concentrations of Cocyt c and phenazine methosulfate. The average second-order rate constant for Cocyt c + phenazine methosulfate (M) k1 leads to Cocyt c+ M-. is 2.9 x 10(4) M-1 s-1 at 25 degrees C, 0.1 M phosphate pH 7.0. There is a slight negative temperature dependence of k1 at low temperature; at higher temperatures the process has deltaH not equal to approximately 27 kJ mol-1 and deltaS not equal to approxmately - 75 J mol-1 K-1. The effect of anions reflects the dependence of Em, 7 for the methemoglobin/hemoglobin couple with various anions. There is no significant effect on k1 by the addition of inositol hexakisphosphate. The variation of k1 with pH is complicated. The experimental rate constants are compared with values calculated with the theory of nonadiabatic multiphonon process of electron tunneling.     

Characteristics of thermal inactivation of lysozyme in solution

In the buffer solution (pH 6,2) at 20-80 degrees, the lysozyme thermoinactivation was studied by monitoring of its activity decrease in the lysis of M. lysodeicticus cells. Protein inactivation was characterized by effective pseudofirst order rate constants which depend on enzyme concentration and are described by equation k = k0 . exp [-alpha 0 (1-gamma/T) [E]0], where k0 is inactivation rate constant at "infinite" enzyme dilution, [E0] is an initial lysozyme concentration, alpha 0 and gamma are the coefficients independent on [E0]. By extrapolation of the "k" dependencies on [E]0 the constants k0 were determined. In the range 40-70 degrees C, the rate constant k0 is equal 4,0 X 10(11) . exp (-24 200/RT) sec-1.     

The effect of the lattice spacing change on cross-bridge kinetics in chemically skinned rabbit psoas muscle fibers. II. Elementary steps affected by the spacing change.

The actin-myosin lattice spacing of rabbit psoas fibers was osmotically compressed with a dextran T-500, and its effect on the elementary steps of the cross-bridge cycle was investigated. Experiments were performed at the saturating Ca (pCa 4.5-4.9), 200 mM ionic strength, pH 7.0, and at 20 degrees C, and the results were analyzed by the following cross-bridge scheme: [formula: see text] where A = actin, M = myosin head, S = MgATP, D = MgADP, and P = Pi = phosphate. From MgATP and MgADP studies on exponential process (C) and (D), the association constants of cross-bridges to MgADP (K0), MgATP (K1a), the rate constants of the isomerization of the AM S state (k1b and k-1b), and the rate constants of the cross-bridge detachment step (k2 and k-2) were deduced. From Pi study on process (B), the rate constants of the cross-bridge attachment (power stroke) step (k4- and k-4) and the association constant of Pi ions to cross-bridges (K5) were deduced. From ATP hydrolysis measurement, the rate constant of ADP-isomerization (rate-limiting) step (k6) was deduced. These kinetic constants were studied as functions of dextran concentrations. Our results show that nucleotide binding, the ATP-isomerization, and the cross-bridge detachment steps are minimally affected by the compression. The rate constant of the reverse power stroke step (k-4) decreases with mild compression (0-6.3% dextran), presumably because of the stabilization of the attached cross-bridges in the AM*DP state. The rate constant of the power stroke step (k4) does not change with mild compression, but it decreases with higher compression (> 6.3% dextran), presumably because of an increased difficulty in performing the power stroke. These results are consistent with the observation that isometric tension increases with a low level of compression and decreases with a high level of compression. Our results also show that the association constant K5 of Pi with cross-bridge state AM*D is not changed with compression. Our result further show that the ATP hydrolysis rate decreased with compression, and that the rate constants of the ADP-isomerization step (k6) becomes progressively less with compression. The effect of compression on the power stroke step and rate-limiting step implies that a large-scale molecular rearrangement in the myosin head takes place in these two slow reaction steps.     

Depolarization increases the single-channel conductance and the open probability of crayfish glutamate channels.

We have studied the voltage sensitivity of glutamate receptors in outside-out patches taken from crayfish muscles. We found that single-channel conductance, measured directly at the single-channel level, increases as depolarization rises. At holding potentials from -90 mV to approximately 20 mV, the conductance is 109 pS. At holding potentials positive to 20 mV, the conductance is 213 pS. This increase in single-channel conductance was also observed in cell-attached patches. In addition, desensitization, rise time, and the dose-response curve were all affected by depolarization. To further clarify these multifaceted effects, we evaluated the kinetic properties of single-channel activity recorded from cell-attached patches in hyperpolarization (membrane potential around -75 mV) and depolarization (membrane potential approximately 105 mV). We found that the glutamate dissociation rate constant (k_) was affected most significantly by membrane potential; it declined 6.5-fold under depolarization. The rate constant of channel closing (k(c)) was also significantly affected; it declined 1.8-fold. The rate constant of channel opening (k(o)) declined only 1.2-fold. The possible physiological significance of the depolarization-mediated changes in the above rate constants is discussed.     

Kinetics of disulfide exchange reactions of monomer and dimer loops of cysteine-valine-cysteine peptides

Rate constants have been determined in 3 M guanidine hydrochloride for disulfide exchange reactions between glutathione and two synthetic peptides containing a cysteine-valine-cysteine region. Equilibrium experiments demonstrate the absence of noncovalent peptide aggregation in this solvent. Procedures are given for separating seven different components in quenched reactions, including the fully reduced cysteine cluster, the monomeric disulfide loop, parallel and antiparallel dimer loops, and the three monomers containing one or two mixed disulfides with glutathione. Intramolecular rate constants for (1) formation of a sterically strained monomer loop, (2) transfer of glutathione between the two cysteines on the same peptide chain, and (3) formation of unstrained dimer loops correspond to a series of processes forming rings of increasing size. In one sequence, these rate constants are 3, 6, and about 21 s-1, respectively. The larger loops are formed more easily. In the other sequence, rate constants for formation and opening of monomer loops are accelerated 180- and 1300-fold, respectively, relative to analogous reactions in a peptide containing eight residues between the two cysteines. This gives a 7-fold smaller equilibrium constant for ring closure in the cysteine cluster. Dimer formation occurs by a mechanism utilizing the accelerated opening of monomer loops. Results provide information assisting efforts to develop strategies for directing disulfide pairing in novel protein structures. Results also help define factors contributing to formation of undesired oligomers during efforts to refold cysteine-containing proteins obtained by bacterial expression of mammalian genes.     

Fitting yeast and mammalian prion aggregation kinetic data with the Finke-Watzky two-step model of nucleation and autocatalytic growth

Recently, we reported 14 amyloid protein aggregation kinetic data sets that were fit using the "Ockham's razor"/minimalistic Finke-Watzky (F-W) two-step model of slow nucleation (A --> B, rate constant k 1) and fast autocatalytic growth (A + B --> 2B, rate constant k 2), yielding quantitative (average) rate constants for nucleation ( k 1) and growth ( k 2), where A is the monomeric protein and B is the polymeric protein [Morris, A. M., et al. (2008) Biochemistry 47, 2413-2427]. Herein, we apply the F-W model to 27 representative prion aggregation kinetic data sets obtained from the literature. Each prion data set was successfully fit with the F-W model, including three different yeast prion proteins (Sup35p, Ure2p, and Rnq1p) as well as mouse and human prions. These fits yield the first quantitative rate constants for the steps of nucleation and growth in prion aggregation. Examination of a Sup35p system shows that the same rate constants are obtained for nucleation and for growth within experimental error, regardless of which of six physical methods was used, a unique set of important control experiments in the protein aggregation literature. Also provided herein are analyses of several factors influencing the aggregation of prions such as glutamine/asparagine rich regions and the number of oligopeptide repeats in the prion domain. Where possible, verification or refutation of previous correlations to glutamine/asparagine regions, or the number of repeat sequences, in literature aggregation kinetics is given in light of the quantitative rate constants obtained herein for nucleation and growth during prion aggregation. The F-W model is then contrasted to four literature mechanisms that address the molecular picture of prion transmission and propagation. Key limitations of the F-W model are listed to prevent overinterpretation of the data being analyzed, limitations that derive ultimately from the model's simplicity. Finally, possible avenues of future research are suggested.     

The effect of pH on the kinetics of iron release from diferric ovotransferrin induced by pyrophosphate

Pyrophosphate-induced iron release from diferric ovotransferrin follows biphasic kinetics in the pH range from 6.6 to 8.6 except at pH 8.0 where the kinetics become monophasic. The rates of formation of the four molecular species, Fe2OT, FeOTN, FeOTC, and ApoOT, were studied by urea gel electrophoresis and the four microscopic rate constants were calculated at various pH values. Below pH 8.0, these intrinsic rate constants for iron release from Fe2OT follow the order k2N greater than k1N greater than k2C greater than k1C. Each constant diminishes almost proportionally with an increase in pH with the faster rate constants being affected more by the fall in hydrogen ions than the slower ones. Around pH 8.0 the four rates are approximately equal, resulting in monophasic kinetics. However, the rate constants from the C-site become faster than that from the N-site at pH above 8.2. At low pH, there is a marked preference for iron to be released from the N-site rather than from the C-site and such preference becomes less distinct as pH increases. A rather weak positive cooperativity between the two sites is demonstrated in pH between 6.8 and 7.8. The ligand responsible for the transition from biphasic to monophasic kinetics at pH 8.0 is not known. It is possible that there are different anions such as [CO3(2-)] and [HCO3-] at the two iron-binding sites, which might explain the preferential rates of iron release from these sites during protonation.     

Equilibrium muscle cross-bridge behavior. Theoretical considerations.

We have developed a model for the equilibrium attachment and detachment of myosin cross-bridges to actin that takes into account the possibility that a given cross-bridge can bind to one of a number of actin monomers, as seems likely, rather than to a site on only a single actin monomer, as is often assumed. The behavior of this multiple site model in response to constant velocity, as well as instantaneous stretches, was studied and the influence of system parameters on the force response explored. It was found that in the multiple site model the detachment rate constant has considerably greater influence on the mechanical response than the attachment rate constant. It is shown that one can obtain information about the detachment rate constants either by examining the relationship between the apparent stiffness and duration of stretch for constant velocity stretches or by examining the force-decay rate constants following an instantaneous stretch. The main effect of the attachment rate constant is to scale the mechanical response by influencing the number of attached cross-bridges. The significance of the modeling for the interpretation of experimental results is discussed.     

Kinetics and mechanism of cell membrane electrofusion.

A new quantitative approach to study cell membrane electrofusion has been developed. Erythrocyte ghosts were brought into close contact using dielectrophoresis and then treated with one square or even exponentially decaying fusogenic pulse. Individual fusion events were followed by lateral diffusion of the fluorescent lipid analogue 1,1'-dihexadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (Dil) from originally labeled to unlabeled adjacent ghosts. It was found that ghost fusion can be described as a first-order rate process with corresponding rate constants; a true fusion rate constant, k(f), for the square waveform pulse and an effective fusion rate constant, k(ef), for the exponential pulse. Compared with the fusion yield, the fusion rate constants are more fundamental characteristics of the fusion process and have implications for its mechanisms. Values of k(f) for rabbit and human erythrocyte ghosts were obtained at different electric field strength and temperatures. Arrhenius k(f) plots revealed that the activation energy of ghost electrofusion is in the range of 6-10 kT. Measurements were also made with the rabbit erythrocyte ghosts exposed to 42 degrees C for 10 min (to disrupt the spectrin network) or 0.1-1.0 mM uranyl acetate (to stabilize the bilayer lipid matrix of membranes). A correlation between the dependence of the fusion and previously published pore-formation rate constants for all experimental conditions suggests that the cell membrane electrofusion process involve pores formed during reversible electrical breakdown. A statistical analysis of fusion products (a) further supports the idea that electrofusion is a stochastic process and (b) shows that the probability of ghost electrofusion is independent of the presence of Dil as a label as well as the number of fused ghosts.     

Autoxidation studies of extracellular hemoglobin of Glossoscolex paulistus at pH 9: cyanide and hydroxyl effect

The complex oligomeric assembly of the hemoglobin subunits may influence the autoxidation rate. To understand this relation, the rate of autoxidation was studied at pH 9.0, where the Glossoscolex paulistus Hemoglobin (GpHb) dissociates. At alkaline pH, this hemoglobin is dissociated into monomers, trimers and tetramers, allowing the study of the integral protein and monomer subunit autoxidation on independent experiments. The autoxidation rate was evaluated in the presence and absence of cyanide (CN(-)), a strong field ligand to the ferric ion. The oxidation kinetic was monitored using the UV-vis absorption at 415 nm, and resulted in: i) bi-exponential kinetics for the whole hemoglobin (indicating a fast and a slow oxidative process) and ii) mono-exponential for the monomer (indicating a single process). To understand the specific characteristics of each autoxidation process, Arrhenius plots allowed the determination of the activation energy. The experimental results indicate for the whole hemoglobin in the absence of CN(-) an activation energy of 150 +/- 10 kJ mol(-1) for the fast and the slow processes. Under the same conditions the monomer displayed an activation energy of 160 +/- 10 kJ mol(-1), very close to the value obtained for the integral protein. The pseudo-second order rate constant for the whole protein autoxidation by CN(-) showed two different behaviors characterized by a rate constant k(CN1)' = 0.11 +/- 0.02 s(-1) mol(-1) L for CN(-) concentrations lower than 0.012 mol L(-1); and k(CN1)" = 0.76 +/- 0.04 s(-1) mol(-1) L at higher concentrations for the fast process, while the slow process remain constant with k(CN2) = 0.033 +/- 0.002 s(-1) mol(-1) L. The monomer has a characteristic rate constant of 0.041 +/- 0.002 s(-1) mol(-1) L for all cyanide concentrations. Comparing the results for the slow process of the whole hemoglobin and the oxidation of the monomer, it is possible to infer that the slow process has a strong contribution of the monomer in the whole hemoglobin kinetic. Moreover, as disulfide linkers sustain the trimer assembly, cooperativity may explain the higher kinetic constant for this subunit.     

Levels and rates of synthesis of ribosomal ribonucleic acid, transfer ribonucleic acid, and protein in Neurospora crassa in different steady states of growth.

The levels of ribosomes, tRNA molecules, and total protein per genome in Neurospora mycelia have been determined in eight different conditions of exponential growth. By increasing the rate of growth the number of ribosomes per genome increases dramatically while the level of total protein remains almost unchanged and the level of tRNA increases only slightly. The rates of synthesis of each of the macromolecules have been estimated. Increasing the rate of growth (mu) up to 0.5, the ratio between the rates of synthesis of tRNA and rRNA decreases reaching a constant value. The equations that best describe the dependence of the rate of synthesis of the macromolecules on the rate of growth (mu) have been determined. The rate of rRNA synthesis (rr), expressed as nucleotides polymerized, min- minus 1 per genome, is given by the equation: rr equals 6.51 times 10-7 mu-2-19. The rate of protein synthesis (rp), expressed as amino acids polymerized, min- minus 1 per genome is given by the following relationship: rp equals -1.43 times 10-7 + 3.43 times 10-8 mu. The equation describing the tRNA synthesis (rt) expressed as nucleotides, min- minus 1 per genome is rt equals 6.45 times 10-5 times exp 2.30 mu; however, more accurate determinations appear to be required for a firmer assignment of this latter equation. The significance of these equations for the studies on the regulation of rRNA and protein synthesis is discussed. For instance the rate of rRNA synthesis may set the limit for the maximal growth rate attainable by a cell, as the maximal rate of rRNA synthesis that may take place in a given cell is limited by the degree of redundancy of the rRNA genes.