The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain. II. Kinetic characterization of phosphointermediates

(1) The kinetics of the phosphorylated enzymic intermediates of (Na+ + K+)-ATPase from ox brain, which are formed by incubation of the enzyme with 25 microM AT32P, 150 mM Na+ and 1 mM Mg2+, have been studied in dephosphorylation experiments at 1 degree C. The dephosphorylation of the 32P-labelled enzyme was initiated by addition of either 1 mM unlabelled ATP, 2.5 mM ADP or 1 mM unlabelled ATP + ADP in concentrations from 25 to 1000 microM. (2) In the absence of ADP the dephosphorylation curve was linear in a semilogarithmic plot almost from t = 0, whereas by addition of ADP a biphasic behaviour was obtained. The slope of the slow phase of dephosphorylation was virtually independent of the ADP concentration. (3) The results were analysed by the mathematical equation corresponding to the simplest possible model for the interconversion and breakdown of the phosphointermediates: (formula: see text) where alpha, beta, H and G are functions of all the rate constants and H and G furthermore are functions of the initial values for [E1P] and [E2P]. (4) The analysis confirmed the model and enabled the determination of all the rate constants. (5) k-1 was found to be equal to k'-1 + k"-1 . [ADP] indicating an ADP-independent 'spontaneous' dephosphorylation of E1P. The rate constant for this process was close to that for dephosphorylation of E2P, i.e., k'-1 congruent to k3. Also the value of k"-1 was determined. (6) k3 was found to be at least 10 . k-2. The implication of this for the role of the E1P to E2P transition in the Na+ + K+)-stimulated ATP hydrolysis will be discussed in detail in the following paper (Plesner, I.W., Plesner, L., N?rby, J.G. and Klodos, I. (1981) Biochim. Biophys. Acta 643, 483--494). (7) A refinement of the model, accounting for the effect of Na+ on the steady-state ratio between [E1P] and [E2P] is proposed: (formula: see text). At [Na+] = 150 mM as used here, E1P(Na) and E'1P are assumed to be in rapid equilibrium. (8) Comparison of our results with those of others underlines the general validity of the conclusions of the present paper.     

Single channel gating events in tracer flux experiments I. Theory

Tracer ion flux measurements are a commonly used method for studying ion transport through membranes of cellular systems, where the rate of ion flow is determined by gating processes which control the opening and closing of transmembrane channels. Due to recent advances in the theoretical analysis of tracer flux from or into closed membrane structures (CMS), the mechanism of gating reactions can, in principle, be derived from flux data. A physically well founded analysis is presented for the dependence of the total tracer ion content of a collection of CMS on the gating processes. For functionally uncoupled gating units a mean single channel flux contribution [equation, see text] can be defined, where k is the intrinsic single channel flux coefficient, t the time over which flux is measured, and p(tau,t) is the probability that a given channel was open for a total period tau during t. This quantity reflects the mean time course of the tracer content due to flux through a single channel. Expressions for are derived that explicitly take into account a distribution in the lifetime of open channels. On the basis of the results, kinetic and thermodynamic parameters of multiphasic gating reactions can be determined from the time course of the overall tracer content in a colleciion of CMS.     

Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons.

The kinetics of ion channels have been widely modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and the kinetic rate constants connecting these states are constant. In the alternative fractal model the spontaneous fluctuations of the channel protein at many different time scales are represented by a kinetic rate constant k = At1-D, where A is the kinetic setpoint and D the fractal dimension. Single-channel currents were recorded at 146 mM external K+ from an inwardly rectifying, 120 pS, K+ selective, voltage-sensitive channel in cultured mouse hippocampal neurons. The kinetics of these channels were found to be statistically self-similar at different time scales as predicted by the fractal model. The fractal dimensions were approximately 2 for the closed times and approximately 1 for the open times and did not depend on voltage. For both the open and closed times the logarithm of the kinetic setpoint was found to be proportional to the applied voltage, which indicates that the gating of this channel involves the net inward movement of approximately one negative charge when this channel opens. Thus, the open and closed times and the voltage dependence of the gating of this channel are well described by the fractal model.     

Gating kinetics of batrachotoxin-modified Na+ channels in the squid giant axon. Voltage and temperature effects.

The gating kinetics of batrachotoxin-modified Na+ channels were studied in outside-out patches of axolemma from the squid giant axon by means of the cut-open axon technique. Single channel kinetics were characterized at different membrane voltages and temperatures. The probability of channel opening (Po) as a function of voltage was well described by a Boltzmann distribution with an equivalent number of gating particles of 3.58. The voltage at which the channel was open 50% of the time was a function of [Na+] and temperature. A decrease in the internal [Na+] induced a shift to the right of the Po vs. V curve, suggesting the presence of an integral negative fixed charge near the activation gate. An increase in temperature decreased Po, indicating a stabilization of the closed configuration of the channel and also a decrease in entropy upon channel opening. Probability density analysis of dwell times in the closed and open states of the channel at 0 degrees C revealed the presence of three closed and three open states. The slowest open kinetic component constituted only a small fraction of the total number of transitions and became negligible at voltages greater than -65 mV. Adjacent interval analysis showed that there is no correlation in the duration of successive open and closed events. Consistent with this analysis, maximum likelihood estimation of the rate constants for nine different single-channel models produced a preferred model (model 1) having a linear sequence of closed states and two open states emerging from the last closed state. The effect of temperature on the rate constants of model 1 was studied. An increase in temperature increased all rate constants; the shift in Po would be the result of an increase in the closing rates predominant over the change in the opening rates. The temperature study also provided the basis for building an energy diagram for the transitions between channel states.     

Kinetic mechanism of myofibril ATPase.

The kinetic mechanism of myofibril ATPase was investigated using psoas and mixed back muscle over a range of ionic strengths. Myofibrils were labeled with pyrene iodoacetamide to measure the rate constants for the binding of ATP and formation of the weakly attached state. The velocity of shortening was measured by stopping the contraction at various times by mixing with pH 4.5 buffer. The transient and steady-state rates of ATP hydrolysis were measured by the quench flow method. The results fitted the kinetic scheme [formula: see text] The rate constants (or equilibrium constants for steps 1 and 6) were obtained for the six steps. k5 was calculated from the KM for shortening velocity, K1, and k2. The rate constants were essentially equal for myofibrils and acto-S-1 at low ionic strength. Increasing the ionic strength up to 100 mM in NaCl increased the rate of the hydrolysis step and the size of the phosphate burst and the effective rate of product release became the rate-limiting step. The step calculated from the velocity of shortening, k5, and k2 is 15 nm, based on a model in which step 4 is the force-generating step.     

Molecular asymmetry in alkaline phosphatase of Escherichia coli

Thermal inactivation of alkaline phosphatase of Escherichia coli has been studied at different temperatures (45 to 70 degrees C) and pHs (7.5, 9.0, and 10.0) for the commercial, buffer-dialyzed (pH 9.0) and EDTA-dialyzed (pH 9.0) enzymes. In each case, the inactivation exhibits biphasic kinetics consistent with the rate equation, (formula; see text) where A0 and A are activities at time zero and t, and k1 and k2 are first-order rate constants for the fast and slow phase, respectively. Values of k1 and k2 change independently with temperature, pH, and pretreatment (dialysis) of the enzyme. Time course of inactivation of the enzyme with excess EDTA and effect of Zn2+ ion concentration on the activity of EDTA-dialyzed enzyme have been investigated. The data suggest that the dimeric enzyme protein has two types of catalytic sites which have equal catalytic efficiency (or specific activity) but differ in several other properties. Structural implications of these results have been discussed.     

Kinetic studies of mobilization of copper(II) from human serum albumin with chelating agents

The kinetics of the mobilizing reactions of five chelating agents for human serum albumin (HSA)-bound copper(II) [Cu(II)] have been studied spectrophotometrically. The decreasing sequence of reaction rate has been determined to be EDTA greater than DTPA greater than EGTA greater than NTA greater than IDA. A group of mathematical models were established to define the mechanisms of the competitive reactions between low-molecular-weight ligand and macromolecular ligand. All reactions of the five chelating agents follow a process involving the intermediate ternary complexes: (formula; see text) The reactions of DTPA and EDTA were found to be different from those of EGTA, NTA, and IDA. In the former cases, the reactions are likely following an overlapping mechanism in which the rate constant k1 was closed to k2. The reactions involving the other three chelators are different in k1 much greater than k2.     

Reaction velocities in vivo: standardization of kinetic "constants" by correction for blood flow

1. The results of kinetic studies in vitro are difficult to apply to metabolic reactions in vivo. 2. In living vertebrates reaction rates are usually first-order and for a particular reaction the rate "constant", k, varies with the several thousand-fold variations in metabolic rate. 3. Therefore, in the kinetic equation (formula: see text) since K varies with metabolic rate, Vmax and/or Km will aslo vary. 4. However, reaction rates for a series of different substrates were similar in animals varying widely in metabolic rate if corrections were made for differences in blood flow. 5. The observation that metabolic rate (reaction rate) is directly dependent on blood flow (Coulson et al., 1977) allowed derivation of new kinetic constants which were valid in vivo. 6. Introduction of a flow term into the observed first-order equations yields an "affinity constant", K, or a "flow constant", KF, somewhat analogous to Km, which allows one to predict reaction rates in animals of different metabolic rates. 7. The defining equations are (formula: see text) where V = reaction velocity in mmol/hr/kg tissue, [S] = millimolar substrate concentration in the blood, k = In 2/tau (tau the half-life) and F = blood flow in 1/hr/kg tissue. 8. Thus, K = k/F = 1/KF. The KF's for the initial step in the degradation of 17 amino acids in rats, dogs, lizards, turtles and alligators were similar, demonstrating the similarity of enzyme affinities in different species.     

General method of analysis of kinetic equations for multistep reversible mechanisms in the single-exponential regime: application to kinetics of open complex formation between Esigma70 RNA polymerase and lambdaP(R) promoter DNA

A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Esigma70 RNA polymerase (R)-lambdaPR promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I1, I2), [equation: see text], where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] > [P]) to form long-lived complexes (RPo and I2) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (ka), isomerization (ki), and dissociation (kd) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Esigma70 RNA polymerase (R)-lambdaP(R) promoter (P) open complex formation.     

Relationships between basic life history parameters and population size

We consider an ideal population with a stable age composition changing according Lotka equation. Additional assumptions are made concerning the constancy of population size, independence of specific mortality rate on age, and linear dependence of female fecundity on its weight. A relationship has been obtained [formula: see text] where N0 is initial numbers of a generation, N[alpha, omega] is total numbers of the mature part of the population, w[alpha, omega] is a mean weight of a mature individual, s is sex ratio, c is specific fecundity (per unit of weight) and l0 is the probability of larval surviving. The growth of an individual is described by the Bertalanffy function. Methods of calculation of life history parameters are discussed. A method is proposed to calculate the age of maturity (alpha) and at the end (omega) of the reproduction period as first and second inflection points of the growth rate curve. Based upon data on development of 27 populations of several species of fishes of inland waters of Russia the following relationship have been obtained: [formula: see text] for populations with [formula: see text] < or = 100 g, [formula: see text] for populations with [formula: see text] > 100 g, and [formula: see text] for all populations.     

Thermodynamic and kinetic studies of the gating behavior of a K+- selective channel from the sarcoplasmic reticulum membrane

A voltage-dependent, K+-selective ionic channel from sarcoplasmic reticulum of rabbit skeletal muscle has been studied in a planar phospholipid bilayer membrane. The purpose [corrected] of this work is to study the mechanism by which the channel undergoes transitions between its conducting and nonconducting states. Thermodynamic studies show that the "open" and "closed" states of the channel exist in a voltage-dependent equilibrium, and that the channel displays only a single open state; the channel conductance is 120 pmho in 0.1 M K+. The channel's gating process follows single exponential kinetics at all voltages tested, and the individual opening and closing rate constants are exponentially dependent on voltage. The individual rate constants may also be determined from a stochastic analysis of channel fluctuations among multiple conductance levels. Neither the thermodynamic nor the kinetic parameters of gating depend on the absolute concentration of channels in the bilayer. The results are taken as evidence that the channel gates by an unusually simple two-state conformational mechanism in which the equivalent of 1.1 net charges are moved across the membrane during the formation of the open channel.     

Kinetics and concentration dependence of reversible cAMP-induced modification of the surface cAMP receptor in Dictyostelium

We have previously reported that extracellular cAMP induced a reversible shift, from apparent Mr = 40,000 to 43,000, in the electrophoretic mobility of a polypeptide identified by photoaffinity labeling with [32P]8-N3-cAMP as the cAMP receptor of Dictyostelium (Klein, P., Theibert, A., Fontana, D., and Devreotes, P. (1985) J. Biol. Chem. 260, 1757-1764). In this report, we examine the kinetics and concentration dependence of this stimulus-induced receptor modification. Prior to stimulation, 90% of the receptors migrated as the higher mobility form (Mr = 40,000) and 10% as the lower mobility form (Mr = 43,000). Following 15 min of persistent stimulation with 1 microM cAMP, the per cent of receptors migrating as the lower mobility form rose to 80%. This transition occurred with a half-time of 2.5 min. Removal of the stimulus initiated a return to the basal state which occurred with a half-time of about 6 min at 22 degrees C. No reversal occurred at 0 degrees C. Addition and removal of a 50 nM cAMP stimulus induced transitions with similar kinetics, but the final plateau value reached was only 40% lower mobility form. The stimulus concentration which induced 50% of the maximal transition from higher to lower mobility forms at steady state was 27 nM, similar to the KD for [3H]cAMP binding. Scatchard analysis of [3H]cAMP binding indicated that, although a 20% down-regulation occurs during cAMP stimulation, there is no significant difference in the affinities of the higher and lower mobility forms of the receptor. The unoccupied higher and lower mobility forms of the receptor, designated R and D, are considered to be in rapid equilibrium with liganded forms, designated RL and DL. The rate constants for interconversion of the receptor forms R (Formula: see text) D and RL (Formula: see text) DL were calculated from the kinetic data: k1 = 0.012, k-1 = 0.104, k2 = 0.222, and k-2 = 0.055. The interconversion steps are not at equilibrium, suggesting that an energy expenditure occurs during the receptor modification. The pattern of modulation of the cAMP-induced receptor modification suggests that it may be the biochemical mechanism of adaptation.     

Modulation of 4-AP block of a mammalian A-type K channel clone by channel gating and membrane voltage.

We examined the state-, voltage-, and time dependences of interaction between 4-AP and a mammalian A-type K channel clone (rKv1.4) expressed in Xenopus oocytes using whole-cell and single-channel recordings. 4-AP blocked rKv1.4 from the cytoplasmic side of the membrane. The development of block required channel opening. Block was potentiated by removing the fast inactivation gate of the channel (deletion mutant termed "Del A"). A short-pulse train that activated rKv1.4 without inactivation induced more block by 4-AP than a long pulse that activated and then inactivated the channel. These observations suggest that both activation and inactivation gates limit the binding of 4-AP to the channel. Unblock of 4-AP also occurred during channel opening, because unblock required depolarization and was accelerated by more frequent or longer depolarization pulses (use-dependent unblock). Analysis of the concentration dependence of rate of block development indicated that 4-AP blocked rKv1.4 with slow kinetics (at -20 mV, binding and unbinding rate constants were 3.2 mM-1 s-1 and 4.3 s-1). This was consistent with single-channel recordings: 4-AP induced little or no changes in the fast kinetics of opening and closing within bursts, but shortened the mean burst duration and, more importantly, reduced the probability of channel opening by depolarization. Depolarization might decrease the affinity of 4-AP binding site in the open channel, because stronger depolarization reduced the degree of steady-state block by 4-AP. Furthermore, after 4-AP block had been established at a depolarized holding voltage, further depolarization induced a time-dependent unblock. Our data suggest that 4-AP binds to and unbinds from open rKv1.4 channels with slow kinetics, with the binding site accessibility controlled by the channel gating apparatus and binding site affinity modulated by membrane voltage.     

Gating kinetics of potassium channel in rat dorsal root ganglion neurons analyzed with fractal model

The kinetics of ion channels have been widely modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and kinetic rate constants connecting these states are constant. To study the gating kinetics of voltage-dependent K(+) channel in rat dorsal root ganglion neurons, K(+) channel current were recorded using cell-attached patch-clamp technique. The K(+) channel characteristic of kinetics were found to be statistically self-similar at different time scales as predicted by the fractal model. The fractal dimension D for the closed times and for the open times depend on the pipette potential. For the open and closed times of kinetic setpoint, it was found dependent on the applied pipette potential, which indicated that the ion channel gating kinetics had nonlinear kinetic properties. Thus, the open and closed durations, which had the voltage dependence of the gating of this ion channel, were well described by the fractal model.     

Catalytic properties of porcine pancreatic elastase: a steady-state and pre-steady-state study

Pre-steady-state and steady-state kinetics for the p.p. elastase-catalysed hydrolysis of ZAlaONp, one of the most favourable substrates for this serine protease, have been studied between pH 4.0 and 8.0. The results are consistent with the minimum three-step mechanism: (formula; see text) Under pre-steady-state conditions, where [E0] much greater than [S0], the values of the dissociation constant of the E X S complex (Ks = k-1/k+1) and of the individual rate constants for the catalytic steps (k+2 and k+3) have been determined over the whole pH range explored. Under steady-state conditions, where [S0] much greater than [E0], the values of kcat and Km have been obtained over the same pH range. The pH profiles of k+2, k+3, k+2/Ks, kcat, kcat/Km reflect the ionization of a group, probably His57, with a pKa value of 6.85 +/- 0.10. The values of Ks and Km are pH independent. The steady-state parameters for the p.p. elastase-catalysed hydrolysis of a number of p-nitrophenyl esters of N-alpha-carbobenzoxy-L-amino acids have been also determined between pH 4.0 and 8.0 and compared with those of b.beta-trypsin and b.alpha-chymotrypsin. For all the substrates examined the acylation step (k+2) is rate limiting in the p.p. elastase catalysis, between pH 4.0 and 8.0. The different catalytic behaviours of p.p. elastase, b.beta-trypsin and b.alpha-chymotrypsin are consistent with the known three-dimensional structures of these serine proteases.     

Kinetic mechanism of calcium binding to whiting parvalbumin

Calcium binding to whiting parvalbumin induces large changes in the fluorescence, absorption, and circular dichroism spectra of the protein. The fluorescence emission maximum of the single tryptophan shifts from 325 to 348 nm upon the removal of calcium and decreases in intensity by 50%. All of the spectral changes are linear between 0 and 2 mol of calcium bound/mol of protein, which suggests that the only protein species present in significant concentration are PA0 and Pa-Ca2. The kinetics of calcium binding measured by stopped-flow fluorescence are accurately single exponential from 2 X 10(-7) to 2 X 10(-4) M free calcium. The kinetics of calcium dissociation show a pronounced lag and are best fit by two rate constants of 1.2 and 3.0 s-1. The minimal kinetic mechanism that adequately describes the rate and equilibrium data is a branched pathway mechanism in which the rate and equilibrium constants are markedly different for each pathway: (formula; see text) At [Ca] less than 2 microM the upper kinetic pathway of calcium binding predominates whereas at [Ca] greater than 2 microM calcium binding occurs predominantly by the lower kinetic pathway. Calcium dissociates primarily by the upper kinetic pathway.     

New tandem-repeating peptide structures in polysialoglycoproteins from the unfertilized eggs of kokanee salmon

New polysialoglycoproteins, designated PSGP(On), were isolated from the fertilized and unfertilized eggs of the kokanee salmon, Oncorhynchus nerka adonis. The polysialylglycan chains consisting of alpha-2,8-linked O-acetylated poly(N-glycolylneuraminyl) chains have recently been characterized. We have now determined the complete amino acid sequence of the tandem-repeating units of PSGP(On) from the unfertilized eggs of kokanee salmon and found that the following two distinct forms are present in PSGP(On) in almost identical amounts: [formula: see text] and [formula: see text] where * denotes the O-glycosylation site and mean value of m, n = about 20. Upon fertilization these high-molecular-weight forms of PSGP(On) were proteolytically cleaved to the corresponding repeating units, low-molecular-weight PSGP(On), by the action of a specific protease (PSGPase) at the position two residues set C-terminally to the Pro residue and N-terminally to the Asp residue, i.e. -Pro-Ser-Xaa-Asp-: [formula: see text] and [formula: see text].     

Study of fractal properties of single ionic channel gating mechanism by the fast Fourier transform]

Sets of the channel open times (tau o), closed times (tau c) and the full set of the channel open and closed times (tau o, tau c) in the activity of single Ca(2+)-activated K+ channels in cultured kidney cells Vero were analyzed using the fast Fourier transform. It was found that in the low-frequency range (about 0.01-10 Hz), power density can be described by the equation S(f) approximately f-alpha (as a rule, 0 < alpha < 1), and this part of the Fourier spectrum usually consists of narrow peaks at almost multiple frequencies. It was shown that the upper frequency boundary of this spectrum is determined by the kinetic parameters tau o [symbol: see text] tau c. The data obtained show that ion channel gating is a fractal process (correlated in time) and can be regarded as a random signal modulated by some periodical functions (sinuses). The data obtained by the Fourier method are in agreement with the earlier results obtained using the rescaled-range analysis.     

Inhibition of Na,K-ATPase by a new ATP analog, adenosine-5-N'-(2,4-dinitro-5-fluorophenyl)phosphohydrazide.

A new ATP analog, adenosine-5-N'-(2,4-dinitro-5-fluorophenyl) phosphohydrazide (DNPH-AMP), has been synthesized, which is an irreversible inhibitor of Na,K-ATPase. Interaction of the analog with the enzyme in the presence of K+ is described by the scheme: [formula: see text] and corresponding kinetic constants k3 and Ki are found equal to 2.5 min-1 and 1.6 mM. In the presence of Na+ the time course of enzyme inactivation by DNPH-AMP is a biphasic curve in the semilogarithmic plot. The k3 and Ki values calculated for this case according to Fritzsch [Fritzsch (1985) J. Theor. Biol. 117, 397] are equal to 2.45 min-1 and 2.5 mM, respectively. ATP transforms the K(+)-type of Na,K-ATPase inactivation into the one that takes place in the presence of Na+.