Measurement of rate constants for actin filament elongation in solution

This paper describes a simple method to measure the rate constants for actin filament elongation using pyrene-actin fluorescence as a measure of the polymer concentration and unlabeled actin filaments as nuclei. With careful selection of conditions, the initial rate of polymerization is directly proportional to the actin monomer concentration above the critical concentration. Plots of initial rate versus actin concentration give the critical concentration (x intercept), the association rate constant, k+ (slope), and the dissociation rate constant, k-(y intercept). By calibrating the system under conditions where the absolute values of these rate constants are known from previous electron microscopic experiments [T. D. Pollard and M. S. Mooseker (1981) J. Cell Biol. 88, 654-659; J. A. Cooper, S. B. Walker, and T. D. Pollard (1983) J. Muscle Res. Cell Motil. 4, 253-262], one can calculate the absolute values of the rate constants under other conditions as well as the length of the filaments used as a nuclei. This approach has proven useful for evaluating the effect of actin-binding proteins on the polymerization process.     

Determination of rate constants for the irreversible inhibition of acetylcholine esterase by continuously monitoring the substrate reaction in the presence of the inhibitor

The kinetics of the irreversible inhibition of acetylcholinesterase (acetylcholine acetylhydrolase, EC 3.1.1.7) by diisopropyl fluorophosphate and paraoxon have been studied by the approach of following the substrate reaction continuously in the presence of both the substrate and the inhibitor based on kinetic equations previously derived (Tsou, C.-L. (1965) Acta Biochim. Biophys. Sinica 5, 387-417). From determinations of the effects of different concentrations of substrate and the inhibitors on the apparent rate constants for the irreversible inhibition reactions it can be shown that these inhibitors are of the competitive complexing type. Both the reversible dissociation constant for the enzyme inhibitor complex and the rate constant for the subsequent phosphorylation step can be obtained from suitable plots of the experimental data.     

Refining the measurement of rate constants in the BIAcore

When estimating rate constants using the BIAcore surface plasmon resonance (SPR) biosensor, one must have an accurate mathematical model to interpret sensogram data. Several models of differing complexity are discussed, including the effective rate constant (ERC) approach. This model can be shown formally to be good within O(Da) in the limit of small Damköhler number Da, which is the ratio of the reaction rate to the rate of transport to the surface. Numerical results are presented that show that except for very slow reactions, parameter estimates from the ERC model are very close to those estimated using a more complicated model. The BIAcore measures the behavior of an evanescent wave whose signal strength decays as it penetrates into the device. It is shown that this decay does not appreciably affect the sensogram readout at low Da, but at moderate Da can lead to situations where two vastly different rate constants can produce the same short-time sensogram data.Mathematics Subject Classification (2000): 35B20, 35C15, 35K60, 45J05, 92C45This work was supported in part by NIGMS Grant 1R01GM067244-01.Revised version: 1 August 2003     

Direct measurement of actin polymerization rate constants by electron microscopy of actin filaments nucleated by isolated microvillus cores

We used actin filament bundles isolated from intestinal brush-border microvilli to nucleate the polymerization of pure muscle actin monomers into filaments. Growth rates were determined by electron microscopy by measuring the change in the length of the filaments as a function of time. The linear dependence of the growth rates on the actin monomer concentration provided the rate constants for monomer association and dissociation at the two ends of the growing filament. The rapidly growing ("barbed") end has higher association and dissociation rate constants than the slowly growing ("pointed") end. The values of these rate constants differ in 20 mM KCl compared with 75 mM KCl, 5 mM MgSO4. 2 microM cytochalasin B blocks growth entirely at the barbed end, apparently by reducing both association and dissociation rate constants to near zero, but inhibits growth at the pointed end to only a small extent.     

Inversion of Markov processes to determine rate constants from single-channel data.

The determination of rate constants from single-channel data can be very difficult, in part because the single-channel lifetime distributions commonly analyzed by experimenters often have a complicated mathematical relation to the channel gating mechanism. The standard treatment of channel gating as a Markov process leads to the prediction that lifetime distributions are exponential functions. As the number of states of a channel gating scheme increases, the number of exponential terms in the lifetime distribution increases, and the weights and decay constants of the lifetime distributions become progressively more complicated functions of the underlying rate constants. In the present study a mathematical strategy for inverting these functions is introduced in order to determine rate constants from single-channel lifetime distributions. This inversion is easy for channel gating schemes with two or fewer states of a given conductance, so the present study focuses on schemes with more states. The procedure is to derive explicit equations relating the parameters of the lifetime distribution to the rate constants of the scheme. Such equations can be derived using the equality between symmetric functions of eigenvalues of a matrix and sums over principle minors, as well as expressions for the moments, derivatives, and weights of a lifetime distribution. The rate constants are then obtained as roots to this system of equations. For a gating scheme with three sequential closed states and a single gateway state, exact analytical expressions were found for each rate constant in terms of the parameters of the three-exponential closed-time distribution. For several other gating schemes, systems of equations were found that could be solved numerically to obtain the rate constants. Lifetime distributions were shown to specify a unique set of real rate constants in sequential gating schemes with up to five closed or five open states. For kinetic schemes with multiple gating pathways, the analysis of simulated data revealed multiple solutions. These multiple solutions could be distinguished by examining two-dimensional probability density functions. The utility of the methods introduced here are demonstrated by analyzing published data on nicotinic acetylcholine receptors, GABA(A) receptors, and NMDA receptors.     

Rate constants of primary reversible reactions of electron transfer do not depend on temperature. Numerical experiment

The process of irreversible photochemical charge separation in photosynthetic bacterial reaction centers is proposed to be characterized by the effective rate constant. A formula to compute this effective rate constant is derived. Similar rate constant was previously considered by R.A. Marcus (Marcus R.A. 1956. J. Chem. Phys. 24, 966–978) in order to describe nonphotochemical intermolecular electron transfer. The effective rate constant of the irreversible charge separation in photosynthetic bacterial reaction centers is shown to depend on the temperature. In contrast, rate constants of the forward electron transfer from the excited singlet primary donor to the bacteriochlorophyll and from its ion-radical to the bacteriopheophytin acceptor do not depend on temperature.     

Cooperative polymerization reactions. Analytical approximations, numerical examples, and experimental strategy

How does one obtain kinetic rate constants from the time course of a reversible and cooperative polymerization reaction? We examine a simple version of the homogeneous nucleation-elongation model with both analytical and numerical techniques to test some common assumptions and develop an experimental strategy. The assumption of irreversible polymer formation is found to be a useful and adequate approximation for the numerical determination of monomer disappearance. The assumption of early "pre-equilibrium" between monomer and seed, however, is shown numerically and analytically to produce significant errors over a wide range of parameters, particularly for small seed lengths. We exhibit numerical solutions for many different parameters, and also discuss analytical techniques that allow approximate solutions for several conditions: the high-concentration limit; the long-time limit; and the long-seed-length, lows concentration limit. The overall reaction simplifies when the monomer concentration is large. An experimental strategy for elucidating the seed size and the rate constants for polymerization and depolymerization is presented.     

Probing Neuroserpin Polymerization and Interaction with Amyloid-β Peptides Using Single Molecule Fluorescence

Neuroserpin is a member of the serine proteinase inhibitor superfamily. It can undergo a conformational transition to form polymers that are associated with the dementia familial encephalopathy with neuroserpin inclusion bodies and the wild-type protein can inhibit the toxicity of amyloid-β peptides in Alzheimer's disease. We have used a single molecule fluorescence method, two color coincidence detection, to determine the rate-limiting steps of the early stages of the polymerization of fluorophore-labeled neuroserpin and have assessed how this process is altered in the presence of Aβ_1-40. Our data show that neuroserpin polymerization proceeds first by the unimolecular formation of an active monomer, followed by competing processes of both polymerization and formation of a latent monomer from the activated species. These data are not in keeping with the recently proposed domain swap model of polymer formation in which the latent species and activated monomer are likely to be formed by competing pathways directly from the unactivated monomeric serpin. Moreover, the Aβ_1-40 peptide forms a weak complex with neuroserpin (dissociation constant of 10 ± 5 nM) that increases the amount of active monomer thereby increasing the rate of polymerization. The Aβ_1-40 is displaced from the complex so that it acts as a catalyst and is not incorporated into neuroserpin polymers.     

Determination of netropsin-DNA binding constants from footprinting data

A theory for deriving drug-DNA site binding constants from footprinting data is presented. Plots of oligonucleotide concentration, as a function of drug concentration, for various cutting positions on DNA are required. It is assumed that the rate of cleavage at each nucleotide position is proportional to the concentration of enzyme at that nucleotide and to the probability that the nucleotide is not blocked by drug. The probability of a nucleotide position not being blocked is calculated by assuming a conventional binding equilibrium for each binding site with exclusions for overlapping sites. The theory has been used to evaluate individual site binding constants for the antiviral agent netropsin toward a 139 base pair restriction fragment of pBR-322 DNA. Drug binding constants, evaluated from footprinting data in the presence of calf thymus DNA and poly(dGdC) as carrier and in the absence of carrier DNA, were determined by obtaining the best fit between calculated and experimental footprinting data. Although the strong sites on the fragment were all of the type (T.A)4, the value of the binding constant was strongly sequence dependent. Sites containing the dinucleotide sequence 5'-TA-3' were found to have significantly lower binding constants than those without this sequence, suggesting that an adenine-adenine clash produces a DNA structural alteration in the minor groove which discourages netropsin binding to DNA. The errors, scope, and limitations associated with the method are presented and discussed.     

关于基本物理常数之间的定量关系

本研究揭示出了基本物理常数之间的定量关系。基本物理常数是通过两个普适的数学常数”和em（e＆在本文中代表数学常数e）相联系的。由此一个基本物理常数可以由其它的基本物理常数和这两个数学常数计算得到。例如,普朗克常数h可以通过电子的电荷m。和质量,光速c以及数学常数”和e＆来计算,即h=2×10-12咖。c3π3-3e数。     

Determination of reaction rate constants in the mammillary system

It is shown that the individual rate constants can be determined for the composite chemical system: $$A + B_i \rightleftarrows C_i ; i = 1...N$$ with only measurements of the unbound species,A(t), required. The dissociation rate constants can be determined by direct analysis of a single steady state tracer study. The association constants then follow from the analysis of stable equilibrium determinations reported earlier (Hart, 1965). An approximate solution when tracer methods are in-applicable is also given.     

Determination of rate constants for nucleotide dissociation from Na,K-ATPase.

A method for determining individual rate constants for nucleotide binding to and dissociation from membrane bound pig kidney Na,K-ATPase is presented. The method involves determination of the rate of relaxation when Na,K-ATPase in the presence of eosin is mixed with ADP or ATP in a stopped-flow fluorescence apparatus. It is shown that the nucleotide dependence of this rate of relaxation--taken together with measured equilibrium binding values for eosin and ADP--makes possible a reasonably reliable determination of the rate constant for dissociation of nucleotide, i.e., determination of the rate constant k-1 in the following model (where E denotes Na,K-ATPase): [formula: see text] All experiments are carried out at about 4 degrees C in a buffer containing 200 mM sucrose, 10 mM EDTA, 25 mM Tris and 73 mM NaCl (pH 7.4). Values obtained for the rate constants for dissociation are about 6 s-1 for ADP and 2-3 s-1 for ATP.     

Concerning the kinetics of polypeptide synthesis on polyribosomes

The kinetics of biosynthesis of polypeptides on polyribosomes is analyzed in accordance with a simple mathematical model. Each ribosome is assumed to block L adjacent. (m-RNA) template sites but to move a distance of one, and only one, template site (nucleotide triplet) upon the addition of each monomer unit to the growing polypeptide chain bound to it. Solutions are sought, for the probability, n_j(t), that a template possesses, at time t, a polypeptide chain that has reached degree of polymerization j. Several classes of steady-state solutions are obtained via machine computation. These correspond to various choices of relative rates of initiation, polymerization along templates, and termination (release of completed chains from templates). Experimental data available from radioactive pulse labeling experiments are discussed. The data obtained by Dintzis, and by Winslow and Ingram, in studies of the synthesis of the α chain of rabbit hemoglobin and human hemoglobin, respectively, are consistent with steady-state solutions obtained from the current theoretical calculations when the rates of initiation and termination are of comparable magnitude and rate-determining. In this case, a (relatively) small number of chains are polymerized at a (relatively) fast rate each near the beginning of the template, and there exists a transition to a situation near the end of the template in which a (relatively) large number of chains are polymerized at a (relatively) slow rate each. For this solution the situation near the end of the template is entirely analogous to a traffic jam in automobile traffic.     

The influence of poly(ethylene glycol) 6000 on the properties of skeletal-muscle actin.

Poly(ethylene glycol) 6000 affected many of the properties of skeletal-muscle actin. It accelerated the rate and increased the extent of actin polymerization as measured by light-scattering and sedimentation studies respectively. Moreover, intrinsic-fluorescence measurements showed that addition of poly(ethylene glycol) 6000 decreased the rate of EDTA-induced denaturation of actin monomer and increased the temperature at which irreversible conformational changes occur in actin monomer. These effects occurred without any apparent direct binding interaction and are postulated to be a consequence of the effect of excluded volume on the thermodynamic activity of actin. A relationship based on spherical geometry was formulated which described the co-volume increment that occurs upon addition of a monomer to a long linear polymer in the presence of a space-filling macromolecule. The application of this relationship to the poly(ethylene glycol) 6000-actin system was not without assumption, but it permitted quantitative estimation of the co-volume increment which proved to be of the sign and magnitude required to explain the increased extent of actin polymerization found experimentally in the presence of various concentrations of poly(ethylene glycol) 6000. It is suggested that, in vivo, excluded volume may play a role in actin-filament formation and in the maintenance of the native G-actin structure.     

Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

Anion-induced increases in the rate of colchicine binding to tubulin.

The rate of binding of colchicine to tubulin to tubulin is enhanced by certain anions. Among the inorganic anions tested, only sulfate was effective. The organic anions include mostly dicarboxylic acids, among which tartrate was the most effective. This effect occurs onlt at low concentrations of colchicine (less than 0.6 X 10(-5) M). The rate increase dor sulfate and L-(+)-tartrate is ca. 2.5-fold at 1.0 mM and plateaus at a limiting value of ca. 4-fold at 100mM. The overall dissociation rate of the colchicine from the complex, which includes both the true rate of dissociation and the rate of irreversible denaturation of tubulin, is not influenced by 1.0 mM tartrate. The affinity constants for colchicine determined from the rate constants are 8.7 X 10(6) and 2.1 X 10(7) M-1 in the absence and the presence of 1.0 mM L-(+)-tartrate. The limiting value is 3.2 X 10(7) M-1. The affinity constant calculated from steady-state measurements is 3.2 X 10(6) M-1 with or without anions. The binding of other ligands like podophyllotoxin, vinblastine, and 1 -anilino-8-naphthalenesulfonate to tubulin is not affected by tartrate. No major conformational changes resulting from anion treatment could be detected by circular dichroism or intrinsic fluorescence. However, the ability of tubulin to polymerize is inhibited by L-(+)-tartrate at concentrations that increase the rate of colchicine binding. We conclude that anions must have a local effect at or near the binding site which enhances the binding rate of colchicine and which may be related to inhibition of polymerization.     

Use of acivicin in the determination of rate constants for turnover of rat renal gamma-glutamyltranspeptidase

The specific enzymatic activity of renal gamma-glutamyltranspeptidase is decreased from control levels (0.86 unit-1 mg-1) to minimal values within 2 h postinjection of 100-g rats with acivicin, an irreversible inhibitor of the enzyme. The recovery of transpeptidase specific activity was followed from 2 to 24 h postinjection and the data were used to calculate the absolute rate constants for degradation (kd = 0.47 +/- 0.03 day-1) and synthesis (ks = 0.41 +/- 0.04 unit-1 mg-1 day-1). This corresponds to a half-life for the renal transpeptidase of 1.46 +/- 0.09 days and 99% recovery of the specific activity by 10 days postinjection. Recovery was followed for 14 days and closely approximates this theoretical curve. The data from control experiments designed to test for secondary effects of the drug, acivicin, show that neither the relative rate of synthesis nor apparent rate of degradation for either total protein or gamma-glutamyltranspeptidase is significantly altered by acivicin treatment of rats. The results also show that the acivicin-inhibited transpeptidase is not degraded differently than enzymatically active enzyme. The individual heterodimer subunits also exhibit similar apparent half-lives in both control and treated animals. Thus, recovery of renal gamma-glutamyltranspeptidase specific activity after acivicin treatment can be used in vivo to determine absolute values of ks and kd for this enzyme. These values have not been reported for any other constituent of the renal brush-border membrane.     

Bounds on rate constants and relative potentials in electron transport chains

Minimization of free-energy losses requires that the rate constants for reaction in both forward and reverse directions be several times the net rate of a reaction. In an electron transfer between bound molecules, the forward and reverse rate constants contribute separate factors to the free-energy drop across the reaction. If such a reaction has a reverse rate constant which is much greater than the net rate of reaction, then the midpoint potential of the acceptor may economically be more negative than the midpoint potential of the donor.     

Theory and experimental method for determining individual kinetic constants of fast-acting, irreversible proteinase inhibitors

A theory and experimental method are presented to characterize the kinetics of fast-acting, irreversible proteinase inhibitors. The theory is based upon formal analysis of the case of an irreversible inhibitor competing with a substrate for the active-site of a proteinase. From this theory, an experimental method is described by which the individual microscopic kinetic constants for the interaction of the inhibitor with the proteinase can be determined. These are, for a two-step inhibition reaction sequence, the equilibrium dissociation constant and the first-order rate constant for inhibition, and, for a one-step inhibition reaction sequence, the second-order rate constant for inhibition. The theory and experimental method were validated by an analysis of the inhibition of trypsin by the two-step synthetic inhibitor p-nitrophenyl p-guanidinobenzoate and the one-step protein inhibitor bovine pancreatic trypsin inhibitor. The substrate used in these experiments is a new, fluorogenic substrate for trypsin-like serine proteinases (Cbz-Ile-Pro-Arg-NH)2-Rhodamine, the synthesis and properties of which are described.     

Mechanism of free radical-induced hemolysis of human erythrocytes: comparison of calculated rate constants for hemolysis with experimental rate constants.

We previously developed a simple competitive reaction model between lipid peroxidation and protein oxidation in erythrocyte membranes that accounts for radical-induced hemolysis of human erythrocytes. In this study, we compared the rate constants calculated from the hemolysis curves of erythrocytes in the presence of radical initiators with those obtained from experiments using erythrocyte ghosts treated with radicals. 2,2'-Azobis(amidinopropane) dihydrochloride and 2,2'-azobis(2,4-dimethylvaleronitrile) were used as radical initiators. Plots of the logarithm of concentration of the radical initiator against the logarithm of the rate constant gave straight lines. The slope of the lines for the calculated lipid peroxidation was nearly equal with the experimental value. Similar results were obtained for oxidation of membrane proteins, except for band 3 oxidation. The values for the rate constants calculated from hemolysis curves seem to be accurate. The slope of the lines for the calculated rate constants for proteins was larger than the experimental value for band 3 oxidation, because band 3 oxidation is accompanied by aggregation or redistribution of band 3 proteins to form hemolytic holes. These results indicate that the competitive reaction model may be useful for analyzing radical-induced hemolysis.