On the reality of transition state dissociation constants

Transition state dissociation constants are currently considered, utilizing stopped flow equipment. The underlying theory is briefly reviewed, relating the ideas to steady state kinetics of enzyme systems. The ideas are further analyzed under the consideration of chemical relaxation. Test conditions are described which would allow an investigation of the concepts of transition state dissociation constants by chemical relaxation techniques. A discussion concerning the way in which the concepts of transition state dissociation constants relate to other theories which assume short-lived, but real, dissociation constants is included. The theory is rigorously analyzed (in a second part), revealing the nature of the assumption of a transition state dissociation constant: While they may be written in a formal manner, they are not based on reality—on kinetic grounds direct interconversions between transition states are practically impossible. This applies also to transition state dissociation constants involving protons.     

Mechanisms of telomerase binding to telomeres

There are essentially two alternative mechanisms for the binding of telomerase to telomeres, assuming that a protective component is initially bound to the telomerase binding region on the telomeres. Either the protective (or blocking) agent first dissociates and telomerase binds thereafter, or telomerase binds first and the protective agent then dissociates from the ternary complex. In the limit, this second possibility permits the ternary complex to become a transition complex (creating another possible mechanism). Numerical simulation of both rapid mixing and chemical relaxation is used to study these alternatives. We aim to determine how the mechanisms may be distinguished experimentally and identify an appropriate experimental design. We show that rapid mixing experiments are better than chemical relaxation experiments, since the latter are more affected by the statistics of single molecule kinetics. However, hidden fast steps can only be revealed by chemical relaxation. The detection of mechanistic changes hinges on linking fluorescence reporters to the reaction components, either directly (chemically) or indirectly (via an indicator reaction). Fluorescence is excited by two-photon absorption in a small reaction volume. Various detection strategies and design issues are examined, including limitations imposed by diffusion. Constant rather than stopped flow is shown to be preferable.     

Kinetics of calcium binding to fluo-3 determined by stopped-flow fluorescence

The kinetics of Ca2+ dissociation from fluo-3 was measured using stopped flow fluorimetry. Analysis of dissociation revealed, in contrast to other commonly used fluorescent Ca2+ indicators, a biexponential behaviour with two distinct dissociation rates of 550 s-1 and 200 s-1 at physiological pH and room temperature. The dissociation rate constant of the fast phase increases to 700 s-1 at physiological temperature, whereas that of the slow phase does not change markedly. While the rate constants do not depend on pH between 6.6 and 7.8, the dissociation turns out to be monoexponential at pH 5.86. The association rate of Ca2+ to fluo-3 could not be measured within the mixing dead time and is estimated to be above 10(9) M-1 s-1. Since the rate constants of fluo-3 are larger than those of other fluorescent Ca2+ indicators, fluo-3 is well suited for investigations of Ca2+ oscillations in biological systems.     

Hemoglobin/O2 systems: using short-lived intermediates for mechanistic discrimination.

The kinetics of the reaction of hemoglobin with molecular oxygen, in which rapid mixing is followed by a very fast temperature jump, is numerically simulated. Four different mechanisms are considered. In two of them, oxygen reacts with the alpha-chains first, in the other two with the beta-chains first. Furthermore, either the third or the fourth measured (Adair) dissociation constant is composed of the product of a local dissociation constant and an allosteric interconversion constant. We explore whether these alternative mechanisms may be distinguished experimentally. We show that reaction steps not resolvable by rapid mixing can be resolved by chemical relaxation at appropriate points in time. Discrimination under experimental conditions is possible at higher oxygen concentrations (above 100 microM), but high resolution in time and concentration amplitude are required.     

Kinetic mechanism of active site assembly and chemical catalysis of DNA polymerase β

It has been inferred from structural and computational studies that the mechanism of DNA polymerases involves subtle but important discrete steps that occur between binding and recognition of the correct dNTP and chemical catalysis. These steps potentially include local conformational changes involving active site residues, reorganization of Mg(2+)-coordinating ligands, and proton transfer. Here we address this broad issue by conducting extensive transient state kinetic analyses of DNA polymerase β (Pol β). We also performed kinetic simulations to evaluate alternative kinetic models. These studies provide some support for two-step subdomain closing and define constraints under which a kinetically significant prechemistry step can occur. To experimentally identify additional microscopic steps, we developed a stopped flow absorbance assay to measure proton formation that occurs during catalysis. These studies provide direct evidence that formation of the enzyme-bound 3'-O(-) nucleophile is rate determining for chemistry. We additionally show that at low pH the chemical step is rate limiting for catalysis, but at high pH, a postchemistry conformational step is rate limiting due to a pH-dependent increase in the rate of nucleotidyl transfer. Finally, we performed exhaustive analyses of [Mg(2+)] and pH effects. In contrast to published studies, the results suggest an irregular pH dependence of k(pol), which is consistent with general base catalysis involving cooperativity between two or more protonic residues. Overall, the results represent significant advancement in the kinetic mechanism of Pol β and also reconcile some computational and experimental findings.     

Kinetics of proton uptake and dye binding by photoactive yellow protein in wild type and in the E46Q and E46A mutants

We studied the kinetics of proton uptake and release by photoactive yellow protein (PYP) from Ectothiorhodospira halophila in wild type and the E46Q and E46A mutants by transient absorption spectroscopy with the pH-indicator dyes bromocresol purple or cresol red in unbuffered solution. In parallel, we investigated the kinetics of chromophore protonation as monitored by the rise and decay of the blue-shifted state I(2) (lambda(max) = 355 nm). For wild type the proton uptake kinetics is synchronized with the fast phase of I(2) formation (tau = 500 micros at pH 6.2). The transient absorption signal from the dye also contains a slower component which is not due to dye deprotonation but is caused by dye binding to a hydrophobic patch that is transiently exposed in the structurally changed and partially unfolded I(2) intermediate. This conclusion is based on the wavelength, pH, and concentration dependence of the dye signal and on dye measurements in the presence of buffer. SVD analysis, moreover, indicates the presence of two components in the dye signal: protonation and dye binding. The dye binding has a rise time of about 4 ms and is coupled kinetically with a transition between two I(2) intermediates. In the mutant E46Q, which lacks the putative internal proton donor E46, the formation of I(2) is accelerated, but the proton uptake kinetics remains kinetically coupled to the fast phase of I(2) formation (tau = 100 micros at pH 6.3). For this mutant the protein conformational change, as monitored by the dye binding, occurs with about the same time constant as in wild type but with reduced amplitude. In the alkaline form of the mutant E46A the formation of the I(2)-like intermediate is even faster as is the proton uptake (tau = 20 micros at pH 8.3). No dye binding occurred in E46A, suggesting the absence of a conformational change. In all of the systems proton release is synchronized with the decay of I(2). Our results support mechanisms in which the chromophore of PYP is protonated directly from the external medium rather than by the internal donor E46.     

Oxygen and carbon monoxide kinetics of Glycera dibranchiata monomeric hemoglobin.

Oxygen and carbon monoxide kinetics of Glycera dibranchiata monomeric hemoglobin have been studied using laser photolysis, air flash, and stopped flow techniques. The reactions of this hemoglobin with both ligands were found to be more rapid than the corresponding reactions involving myoglobin and were also biphasic in nature, the rate constants being approximately an order of magnitude different for the fast and slow phases in each case. No pH or hemoglobin concentration dependence of the pseudo-first order rate constants was apparent between pH 6 and 9 and in the concentration range of 1.25 to 40 muM heme. Both fast and slow pseudo-first order oxygen combination rate constants varied linearly with oxygen concentration between 16 and 1300 muM. A first order slow relaxation was also noted which was linearly dependent on heme concentration and inversely dependent on oxygen concentration. This reaction has been shown to be due to a replacement of oxygen by carbon monoxide. The presence of this reaction is a result of the high affinity of Glycera monomer for carbon monoxide as shown by the partition coefficient Mr = approximately 20,000 ana an equilibrium dissociation constant of the order L = 1.1 X 10(-9) M.     

Hemoglobin/O2 systems: mechanistic discrimination based on Ackers' model

The kinetics of the reaction of hemoglobin with molecular oxygen, in which rapid mixing is followed by a fast temperature jump, is numerically simulated. We use the system of Ackers (1998) which distinguishes four forms of bi-ligated hemoglobin. The data suggest the involvement of isomerization steps for bi- and triliganded hemoglobin. Our first model assumes a linear addition of oxygen with one path to and from each bi-ligated species. Our second model allows cross-overs between paths, as described by Ackers (1998). Our third model exploits the observation (Perrella et al., 1990) that two of the four bi-ligated forms are at low concentration. We explore whether these models can be distinguished experimentally. We find a narrow oxygen concentration range where Models 1 and 2 can be distinguished by rapid flow experiments. The distinction between Models 2 and 3 is larger in stopped flow experiments within a limited oxygen concentration range but not easily detectable in chemical relaxation following rapid flow. The detection of two special states of free hemoglobin may be possible at low oxygen concentration. However, the step reaction free enthalpy (or Gibbs free energy) values make it more likely that two special states are present in fully ligated hemoglobin.     

Fluorescence stopped-flow study of the interaction of tubulin with the antimitotic drug MDL 27048.

The kinetics of the binding of MDL 27048 to tubulin have been studied by fluorescence stopped flow. The binding is accompanied by a fluorescence increase. The time course can be described by a sum of two exponentials, assumed to be due to the presence of two major tubulin isoforms. The observed rate constants depend in a nonlinear way on the concentration of MDL in pseudo-first-order conditions. This concentration dependence can be described by the presence of a fast equilibrium of low affinity, followed by an isomerization of the initial complex. The dissociation kinetics have been studied by displacement experiments, in which MTC was used as a competitive ligand. The reaction enthalpy change for the first binding equilibrium and the activation energies for the forward and reverse steps of the isomerization were determined from the temperature dependence. This was possible for the two tubulin isotype populations. The kinetics of the binding of MDL to tubulin are slowed down in the presence of 3',4',5'-trimethoxyacetophenone, a fast binding analog of the colchicine A-ring, but are not influenced by the binding of tropolone methyl ether, indicating that the binding site of MDL has the A-subsite in common with colchicine, but not the C-subsite.     

Membrane transport models with fast and slow reactions: General analytical solution for a single relaxation

Summary Membrane transport models are usually expressed on the basis of chemical kinetics. The states of a transporter are related by rate constants, and the time-dependent changes of these states are given by linear differential equations of first order. To calculate the time-dependent transport equation, it is necessary to solve a system of differential equations which does not have a general analytical solution if there are more than five states. Since transport measurements in a complex system rarely provide all the time constants because some of them are too rapid, it is more appropriate to obtain approximate analytical solutions, assuming that there are fast and slow reaction steps. The states of the fast steps are related by equilibrium constants, thus permitting the elimination of their differential equations and leaving only those for the slow steps. With a system having only two slow steps, a single differential equation is obtained and the state equations have a single relaxation. Initial conditions for the slow reactions are determined after the perturbation which redistribute the states related by fast reactions. Current and zero-trans uptake equations are calculated. Curve fitting programs can be used to implement the general procedure and obtain the model parameters.     

The kinetics of binding of o-methyl red to the outer surface of unilamellar spherical phospholipid vesicles

The kinetics of adsorption of the proton carrier o-methyl red to the surface of unilamellar spherical phospholipid vesicles have been investigated by means of the temperature-jump relaxation technique with absorbance detection. Single-exponential relaxation curves were observed with time constants in the range 30-130 microseconds. o-Methyl red binds in both its anionic form A- and protonated form AH. Adsorption-desorption of the two species is coupled by two fast protolytic reactions, occurring in the aqueous bulk phase and in the surface region of the membrane. The rate constants for adsorption and desorption of the two species were obtained from the dependences of the relaxation time on lipid concentration at different pH values. The analysis yielded apparent adsorption rate constants of kasAH = 9.8 X 10(6) M-1 s-1 and kasA = 1.3 X 10(6) M-1 s-1 (expressed in terms of monomeric lipid), and kasAH = 1.2 X 10(11) M-1 s-1 and kasA = 1.6 X 10(10) M-1 s-1 (expressed in terms of vesicle concentration). From the order of these rate constants it is concluded that adsorption of both species is actually diffusion-controlled. The peculiar pH dependence of the relaxation time is a consequence of the protolytic reaction in the surface region of the membrane. Its implication for the kinetics of adsorption-desorption processes are discussed.     

Kinetics of dissociation of alpha-lactalbumin complexes with Ca2+ and Mg2+ ions

Kinetics of dissociation of the complexes of bovine alpha-lactalbumin with Ca2+ and Mg2+ ions induced by mixing of the Ca2+- or Mg2+-loaded protein with the chelator of divalent cations EDTA has been studied by means of intrinsic fluorescence stopped flow method. Within the temperature region from 10 to approximately 37 degrees C the fluorescence kinetics curves for the Ca2+ removal are well fitted by one exponent with the rate constant ranging from 6.10(-3) to 1 s-1. Taking into account rather low rate of the fluorescence changes, one can assume that the limiting stage in this case is the dissociation of the single bound Ca2+ ion from the protein but not a conformational change which occurs after the Ca2+ dissociation. At temperatures above 37 degrees C the kinetics curves are best fitted by two exponents. The second exponent seems to be due to the denaturation of the apo-form of alpha-lactalbumin which takes place at these temperatures. The values of the dissociation rate constants of Mg2+ practically coincide with the values for Ca2+.     

Kinetics of Ca2+ release shows interactions between the two classes of sites of troponin-C

The kinetics of Ca2+-release from the two high affinity sites of troponin-C (TnC) was studied by the stopped flow technique following rapid mixing with either EDTA or excess TbCl3. The rate constants obtained by the two methods were 2.8 and 0.7 s-1, respectively. For the tryptic fragment of TnC that contains only the COOH-terminal half of the molecule, both methods generate rate constants of 2.2 s-1. These results are consistent with the interpretation that binding of Tb3+ to the Ca2+-specific sites reduces the rate of dissociation of Ca2+ from, and thereby enhances the affinity for, the Ca2+-Mg2+ sites; this, in turn, suggests interactions between the two halves of the TnC molecule.     

Kinetics of proton-linked flavin conformational changes in p-hydroxybenzoate hydroxylase

p-Hydroxybenzoate hydroxylase (PHBH) is an FAD-dependent monooxygenase that catalyzes the hydroxylation of p-hydroxybenzoate (pOHB) to 3,4-dihydroxybenzoate in an NADPH-dependent reaction. Two structural features are coupled to control the reactivity of PHBH with NADPH: a proton-transfer network that allows protons to be passed between the sequestered active site and solvent and a flavin that adopts two positions: "in", where the flavin is near pOHB, and "out", where the flavin is near NADPH. PHBH uses the proton-transfer network to test for the presence of a suitable aromatic substrate before allowing the flavin to adopt the NADPH-accessible conformation. In this work, kinetic analysis of the His72Asn mutant, with a disrupted proton-transfer network, showed that flavin movement could occur in the presence or absence of NADPH but that NADPH stimulated movement to the reactive conformation required for hydride transfer. Substrate and solvent isotope effects on the transient kinetics of reduction of the His72Asn mutant showed that proton transfer was linked to flavin movement and that the conformational change occurred in a step separate from that of hydride transfer. Proton transfers during the reductive half-reaction were observed directly in the wild-type enzyme by performing experiments in the presence of a fluorescent pH-indicator dye in unbuffered solutions. NADPH binding caused rapid proton release from the enzyme, followed by proton uptake after flavin reduction. Solvent and substrate kinetic isotope effects showed that proton-coupled flavin movement and reduction also occurred in different steps in wild-type PHBH. These results allow a detailed kinetic scheme to be proposed for the reductive half-reaction of the wild-type enzyme. Three kinetic models considered for substrate-induced isomerization are analyzed in the Appendix.     

Deprotonation of the horse liver alcohol dehydrogenase-NAD+ complex controls formation of the ternary complexes

Binding of NAD+ to wild-type horse liver alcohol dehydrogenase is strongly pH-dependent and is limited by a unimolecular step, which may be related to a conformational change of the enzyme-NAD+ complex. Deprotonation during binding of NAD+ and inhibitors that trap the enzyme-NAD+ complex was examined by transient kinetics with pH indicators, and formation of complexes was monitored by absorbance and protein fluorescence. Reactions with pyrazole and trifluoroethanol had biphasic proton release, whereas reaction with caprate showed proton release followed by proton uptake. Proton release (200-550 s(-1)) is a common step that precedes binding of all inhibitors. At all pH values studied, the rate constants for proton release or uptake matched those for formation of ternary complexes, and the most significant quenching of protein fluorescence (or perturbation of adenine absorbance at 280 nm) was observed for enzyme species involved in deprotonation steps. Kinetic simulations of the combined transient data for the multiple signals indicate that all inhibitors bind faster and tighter to the unprotonated enzyme-NAD+ complex, which has a pK of about 7.3. The results suggest that rate-limiting deprotonation of the enzyme-NAD+ complex is coupled to the conformational change and controls the formation of ternary complexes.     

Kinetics and mechanism of bilirubin binding to human serum albumin

The kinetics of bilirubin binding to human serum albumin at pH 7.40, 4 degrees C, was studied by monitoring changes in bilirubin absorbance. The time course of the absorbance change at 380 nm was complex: at least three kinetic events were detected including the bimolecular association (k1 = 3.8 +/- 2.0 X 10(7) M-1 S-1) and two relaxation steps (52 = 40.2 +/- 9.4 s-1 and k3 = 3.8 +/- 0.5 s-1). The presence of the two slow relaxations was confirmed under pseudo-first order conditions with excess albumin. Curve-fitting procedures allowed the assignment of absorption coefficients to the intermediate species. When the bilirubin-albumin binding kinetics was observed at 420 nm, only the two relaxations were seen; apparently the second order association step was isosbestic at this wavelength. The rate of albumin-bound bilirubin dissociation was measured by mixing the pre-equilibrated human albumin-bilirubin complex with bovine albumin. The rate constant for bilirubin dissociation measured at 485 nm was k-3 = 0.01 s-1 at 4 degrees C. A minimum value of the equilibrium constant for bilirubin binding to human albumin determined from the ratio k1/k-3 is therefore approximately 4 X 10(9) M-1.     

Kinetics of proton release and uptake by channelrhodopsin-2

Electrophysiological experiments showed that the light-activated cation channel channelrhodopsin-2 (ChR2) pumps protons in the absence of a membrane potential. We determined here the kinetics of transient pH change using a water-soluble pH-indicator. It is shown that ChR2 released protons prior to uptake with a stoichiometry of 0.3 protons per ChR2. Comparison to the photocycle kinetics revealed that proton release and uptake match rise and decay of the P(3)(520) intermediate. As the P(3)(520) state also represents the conductive state of cation channeling, the concurrence of proton pumping and channel gating implies an intimate mechanistic link of the two functional modes. Studies on the E123T and S245E mutants show that these residues are not critically involved in proton translocation.     

Time-resolved protonation dynamics of a black lipid membrane monitored by capacitative currents

The laser-induced proton pulse (Gutman, M. (1986) Methods Enzymol. 127, 522-538) was used for transient protonation of one side of a black lipid membrane. The charging of the membrane drives an electric (voltage or current) signal selectively representing the fast proton exchange at the membrane/electrolyte interface. The sensitivity of the electric signal to the presence of buffer indicates that proton transfer is measured, not some dyes or membrane photoelectric artifact. The same event can be visualized in an analogous system consisting of a pH indicator adsorbed to neutral detergent-phospholipid mixed micelles. The time-resolved light absorption transient is equivalent to the electrically determined transient charging of the membrane surface. The sensitivity of the current measurement exceeds the spectrophotometric method by 6-8 orders of magnitudes. As little as 10(-18) mol of H+ reacting with 0.75 mm2 of the membrane surface can be monitored in a time-resolved observation. Both types of observed transients were accurately reconstructed by the numerical solution of coupled, non-linear, differential equations describing the system. The rate constants of the various proton transfer reactions were calculated and found to be of diffusion controlled reactions. There is no evidence for any barrier at the interface which either prevents protons from reaching the membrane, or keeps proton on the interface. The electric measurements can be applied for monitoring proton transfer kinetics of complex biomembrane preparations.     

Kinetic studies of anthracycline-DNA interaction by fluorescence stopped flow confirm a complex association mechanism

The kinetics of association and dissociation between calf thymus DNA and five anthracyclines, including doxorubicin, daunorubicin, and three synthetic analogues, were investigated with stopped flow using fluorescence detection. The sensitivity of this technique allowed us to work with submicromolar drug concentrations, thus excluding formation of aggregates, and with ratios of DNA base pairs to drug in the range 10-250, where site exclusion effects could be taken into account with a simple correction of DNA concentration and pseudo-first-order conditions were nearly fulfilled. In all cases, both association and dissociation reactions required a sum of three exponential terms to be fitted. However, satisfactory interpretation of reciprocal relaxation times as functions of DNA concentration was only achieved with kinetic models comprising a total of five steps. One of the extra steps was tentatively assigned to formation of a weakly bound, probably nonintercalated species. Another step was deduced from a comparison between results of association and dissociation experiments. The five steps are arranged, for convenience, in an association mechanism with two branches, though other mechanisms cannot be definitely ruled out. Correlation of cytotoxicity data with both association and dissociation rates is not found to be significant. This suggests that other factors must be involved in modulating the different biological properties of the investigated anthracyclines.