A quantitative model of myosin phosphorylation and the photomechanical response of the isolated sphincter pupillae of the frog iris.

The time courses of isometrically recorded photomechanical responses of isolated sphincter pupillae of Rana pipiens can be accurately predicted by a set of differential equations derived from phosphorylation theory of smooth muscle contraction. We compared actual light-stimulated contractions with calculated ones over a wide range of stimulus intensities (56-fold) and durations (0.4-4.0 s). The hypothetical Ca++-calmodulin-myosin light chain kinase cascade acts as a "valve" to control the flow of ATP through a phosphorylation-dephosphorylation cycle. When the rate of flow of ATP through the phosphorylation-dephosphorylation cycle is increased, the percentage of phosphorylated myosin increases. The time courses of the concentrations of phosphorylated myosin during different responses are seen to be functions of the time courses of the opening and closing of the coupling cascade "valve." The calculations predict experimentally measurable intermediate variables, which can aid the investigation of the application of quantitative phosphorylation theory to amphibian sphincter pupillae and to smooth muscle in general.     

Thermodynamic and kinetic analysis of sensitivity amplification in biological signal transduction

Based on a thermodynamic analysis of the kinetic model for the protein phosphorylation-dephosphorylation cycle, we study the ATP (or GTP) energy utilization of this ubiquitous biological signal transduction process. It is shown that the free energy from hydrolysis inside cells, DeltaG (phosphorylation potential), controls the amplification and sensitivity of the switch-like cellular module; the response coefficient of the sensitivity amplification approaches the optimal 1 and the Hill coefficient increases with increasing DeltaG. We discover that zero-order ultrasensitivity is mathematically equivalent to allosteric cooperativity. Furthermore, we show that the high amplification in ultrasensitivity is mechanistically related to the proofreading kinetics for protein biosynthesis. Both utilize multiple kinetic cycles in time to gain temporal cooperativity, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein.     

The substrate specificity of trypsin. The interrelationship between the structure and reactivity for quasi-substrates, derivatives of O-alkylmethylphosphonic acid and carboxylic acids

The kinetics of trypsin phosphorylation by thioesters of O-n-alkylmethylphosphonic acids, and reactivation of corresponding phosphoryl enzymes as well as kinetics of trypsin-catalyzed hydrolysis of p-nitrophenylcarboxylates have been studied. The rate constants for phosphorylation and dephosphorylation of trypsin depend on hydrophobicity of non-polar fragments in both substrate series in the same degree. On the other hand, the deacylation rate constants for a series of acyl trypsins do not change significantly while the apparent Michaelis constants change consistently with variations of non-polar acyl substituent. The study of substrate specificity of trypsin in terms of the transition state theory has allowed to elucidate the basis for low reactivity of trypsin towards the quasisubstrates.     

Kinetics of the course of reactivation of aminoacylase reconstituted using Mn2+ ions

The kinetic theory of the substrate reaction during irreversible change of enzyme activity previously described by Tsou (Tsou (1988),Adv. Enzymol. Relat. Areas Mol. Biol.61, 381–436] has been applied to a study of the kinetics of the course of reactivation during reconstitution of apo-aminoacylase using Mn²⁺ or Zn²⁺. The kinetic parameters for Mn²⁺-and Zn²⁺-reconstituted enzymes and the microscopic rate constants for reactivation during reconstitution were determined. The kinetic analysis suggests the presence of a second Mn²⁺ binding site in Mn²⁺-reconstituted aminoacylase.     

Kinetics of the course of reactivation of aminoacylase reconstituted using Mn2+ ions

The kinetic theory of the substrate reaction during irreversible change of enzyme activity previously described by Tsou (Tsou (1988),Adv. Enzymol. Relat. Areas Mol. Biol.61, 381–436] has been applied to a study of the kinetics of the course of reactivation during reconstitution of apo-aminoacylase using Mn²⁺ or Zn²⁺. The kinetic parameters for Mn²⁺-and Zn²⁺-reconstituted enzymes and the microscopic rate constants for reactivation during reconstitution were determined. The kinetic analysis suggests the presence of a second Mn²⁺ binding site in Mn²⁺-reconstituted aminoacylase.     

Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements

Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero-order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.     

Kinetics of reactivation during refolding of guanidine-denatured pancreatic ribonuclease A

The method aforementioned (Liu, W. and Tsou, C.L. (1987) Biochim. Biophys. Acta 916, 455-464) for the study of the kinetics of irreversible modification of enzyme activity has been applied to the reactivation of guanidine-denatured ribonuclease A, by following the hydrolysis of cyclic CMP during refolding upon diluting a guanidine-denatured enzyme with a substrate-containing buffer. Appropriate equations have been derived to deal with the kinetics of the substrate reaction during the course of activation, while the product formed, 3'CMP, is a competitive inhibitor. When the overall process consists of multiple first-order reactions, the individual rate constants could be obtained by suitable semilogarithmic plots. Moreover, in certain cases, it can be distinguished from the shapes of the plots, whether the overall process consists of parallel or consecutive first-order reactions. The kinetics for the reactivation reaction has been compared to that for the refolding of the substrate binding site, as indicated by complex formation with the competitive inhibitor, 2'CMP, and for the refolding of the molecule as a whole. At pH 6.0 and 25 degrees C, only monophasic first-order reactions could be detected by manual mixing for both the reactivation and the refolding processes. At lower temperatures (0-10 degrees C), both processes consist of two first-order reactions. In all cases, the same rate constants have been obtained for the refolding and reactivation reactions.     

A general pre-steady-state solution to complex kinetic mechanisms

We have developed a general method for solving transient kinetic equations using Laplace transforms. Laplace transforms can be used to transform systems of differential equations that describe pre-steady-state kinetics to systems of linear algebraic equations. The general form of the pre-steady-state solution is (formula; see text) where I(t) is the time dependence of the physically observed property of the system, n is the number of intermediates, lambda i are the observed rate constants (reciprocals of the relaxation times), t is time, and Ii are the amplitude coefficients associated with each observed rate constant. We have written a program in compiled BASIC to run on a personal computer to evaluate Ii and lambda i. The program will evaluate the rate constants and coefficients of a mechanism with eight intermediates and seven relaxation times in 4 s on an 8-MHz PC-XT equipped with a math coprocessor. The most complex mechanism that we have solved, a mechanism containing 20 intermediates and 19 relaxation times, required approximately 5 min. We believe that this method will be useful to evaluate the differences in transient properties of complex biochemical mechanisms.     

Secondary structure of chondroitin sulphate in dimethyl sulphoxide

The transient phase of histone H1 phosphorylation was studied by the quenched-flow method. A 'minimal' kinetic scheme of the above process was proposed. A formal kinetic analysis was given to a four-step mechanism of the reaction. Computer simulation of the transient-phase kinetics of H1 phosphorylation and the steady-state kinetics of phosphate transfer from the enzyme phosphoform to histone permitted us to estimate all kinetic constants of the proposed mechanism.     

Effects of low concentrations of guanidine . HCl on the reconstitution of lactic dehydrogenase from pig muscle in vitro. Evidence for guanidine binding to the native enzyme

The presence of low concentrations of guanidine . HCl has a pronounced effect on the overall rate of reactivation of lactic dehydrogenase from pig muscles after preceding dissociation and deactivation in various denaturants. The obseverd attenuation is a function of the amount of guanidine . HCl present during reconstitution. At a given guanidine concentration in the reactivation buffer the yield, but not the rate of reactivation, is influenced by the extent of denaturation caused initially in the process of deactivation and dissociation. As a possible explanation for the influence of guanidine . HCl on the kinetics of reconstitution, binding of the ligand to intermediates of folding and association is considered. This hypothesis is corroborated by the observation that guanidine . HCl in the relevant concentration range does bind to native lactic dehydrogenase without inactivating the enzyme or disrupting its quaternary structure. A kinetic model comprising guanidine binding to both the native enzyme and structured intermediates is proposed to describe the observed effects of guanidine . HCl on the rate of reactivation. In addition, the dissociation constants for guanidine binding to intermediates of reconstitution and to native lactic dehydrogenase are estimated.     

Inhibition kinetics of green crab (Scylla serrata) alkaline phosphatase activity by dithiothreitol or 2-mercaptoethanol

Green crab (Scylla serrata) alkaline phosphatase (EC 3.1.3.1) is a metalloenzyme which catalyzes the nonspecific hydrolysis of phosphate monoesters. Some pollutants in seawater affect the enzyme activity causing loss of the biological function of the enzyme, which affects the exuviating crab-shell and threatens the survival of the animal. The present paper studies the effects of thiohydroxyal compounds on the activity of green crab alkaline phosphatase. The results show that thiohydroxyal compounds can lead to reversible inhibition. The equilibrium constants have been determined for dithiothreitol (DTT) and mercaptoethanol (ME) binding with the enzyme and/or the enzyme-substrate complexes. The results show that both DTT and ME are non-competitive inhibitors. The kinetics of enzyme inactivation by ME at low concentrations has been studied using the kinetic method of the substrate reaction. The results suggest that at pH 10.0, the action of ME on green crab ALP is first quick equilibrium binding and then slow inactivation. The microscopic rate constants were determined for inactivation and reactivation. The rate constant of the forward inactivation (k(+0)) is much larger than that of the reverse reactivation (k(-0)). Therefore, when the ME concentration is sufficiently large, the enzyme is completely inactivated.     

Kinetic modeling and fitting software for interconnected reaction schemes: VisKin

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.     

A kinetic model of ERK cyclic pathway on substrate control

Extracellular signal-regulated kinase (ERK) is a key factor in the widely used signaling cascade of phosphorylation-dephosphorylation cycles and plays pivotal roles in many aspects of biological processes. Experimental studies in yeast and in Drosophila embryo have suggested that the phosphorylation and spatial localization of ERK are influenced by the level of its downstream substrates. However, the mechanism, through which these substrates control properties of ERK signaling, has been unclear. I propose a mass-action kinetic model of ERK cycle with its substrate, and demonstrate that the substrate can modulate the ERK activity by directly interacting with ERK. The model shows that the addition of substrate controls the level of ERK phosphorylation positively or negatively, depending on the balance between dissociation constants of ERK-substrate interaction and properties of ERK cyclic signaling in the absence of the substrate. In addition, by considering cellular compartments, cytosol and nucleus, the substrate can lead to nuclear accumulation of ERK, suggesting that the substrate can act as a nuclear anchor of ERK. The model gives a possible mechanism that can account for substrate-mediated modulation of ERK signaling.     

The computation of hyperbolic dependences in enzyme kinetics.

A computer program aimed at analysing results following Michaelis-Menten kinetics can be used unmodified in the treatment of other kinetic results provided that the kinetic equations in these cases can be written in the form of the Michaelis-Menten equation. A list is presented of the parameters to be set instead of substrate concentration and reaction rate, and of constants replacing Km and V, if such a program is applied in analysing enzyme inhibitions, activations and pH-dependences.     

Inhibitory kinetics of bromacetic acid on beta-N-acetyl-D-glucosaminidase from prawn (Penaeus vannamei)

beta-N-Acetyl-D-glucosaminidase (NAGase, EC.3.2.1.52), a composition of chitinases, cooperates with endo-chitinase and exo-chitinase to disintegrate chitin into N-acetylglucosamine (NAG). NAGase from prawn (Penaeus vannamei) is involved in digestion and molting processes. The investigation of enzymatic properties, functional groups and catalytic mechanism is an essential mission to its commercial application. Bromacetic acid (BrAc) is a specific modifier for the histidine residue in specific condition. In this paper, the effect of BrAc on prawn NAGase activity for the hydrolysis of pNP-NAG has been investigated. The results showed that BrAc can reversibly and non-competitively inhibit the enzyme activity at appropriate concentrations and the value of IC(50) was estimated to be 17.05+/-0.65 mM. The inhibition kinetics of the enzyme by BrAc has been studied using the kinetic method of the substrate reaction. And the inhibition model was set up and the microscopic rate constants for the reaction of the inhibitor with free enzyme and the enzyme-substrate complexes were determined for inactivation and reactivation. The rate constant of the forward inactivation (k(+0)), which is 1.25 x 10(-3)s(-1), is about eight times as much as that of the reverse reactivation (k(-0)), which is 1.64 x 10(-4)s(-1). Therefore, when the BrAc concentration is sufficiently large, the enzyme is completely inactivated.     

Regulation of steady state pyruvate dehydrogenase complex activity in plant mitochondria : reactivation constraints

The requirements for reactivation (dephosphorylation) of the pea (Pisum sativum L.) leaf mitochondrial pyruvate dehydrogenase complex (PDC) were studied in terms of magnesium and ATP effects with intact and permeabilized mitochondria. The requirement for high concentrations of magnesium for reactivation previously reported with partially purified PDC is shown to affect inactivation rather than reactivation. The observed rate of inactivation catalyzed by pyruvate dehydrogenase (PDH) kinase is always greater than the reactivation rate catalyzed by PDH-P phosphatase. Thus, reactivation would only occur if ATP becomes limiting. However, pyruvate which is a potent inhibitor of inactivation in the presence of thiamine pyrophosphate, results in increased PDC activity. Analysis of the dynamics of the phosphorylation-dephosphorylation cycle indicated that the covalent modification was under steady state control. The steady state activity of PDC was increased by addition of pyruvate. PDH kinase activity increased threefold during storage of mitochondria suggesting that there may be an unknown level of regulation exerted on the enzyme complex.     

Understanding glucose transport by the bacterial phosphoenolpyruvate:glycose phosphotransferase system on the basis of kinetic measurements in vitro

The kinetic parameters in vitro of the components of the phosphoenolpyruvate:glycose phosphotransferase system (PTS) in enteric bacteria were collected. To address the issue of whether the behavior in vivo of the PTS can be understood in terms of these enzyme kinetics, a detailed kinetic model was constructed. Each overall phosphotransfer reaction was separated into two elementary reactions, the first entailing association of the phosphoryl donor and acceptor into a complex and the second entailing dissociation of the complex into dephosphorylated donor and phosphorylated acceptor. Literature data on the K(m) values and association constants of PTS proteins for their substrates, as well as equilibrium and rate constants for the overall phosphotransfer reactions, were related to the rate constants of the elementary steps in a set of equations; the rate constants could be calculated by solving these equations simultaneously. No kinetic parameters were fitted. As calculated by the model, the kinetic parameter values in vitro could describe experimental results in vivo when varying each of the PTS protein concentrations individually while keeping the other protein concentrations constant. Using the same kinetic constants, but adjusting the protein concentrations in the model to those present in cell-free extracts, the model could reproduce experiments in vitro analyzing the dependence of the flux on the total PTS protein concentration. For modeling conditions in vivo it was crucial that the PTS protein concentrations be implemented at their high in vivo values. The model suggests a new interpretation of results hitherto not understood; in vivo, the major fraction of the PTS proteins may exist as complexes with other PTS proteins or boundary metabolites, whereas in vitro, the fraction of complexed proteins is much smaller.     

The kinetics of inhibition of erythrocyte cholinesterase by monomethylcarbamates

1. The kinetics of the interaction of erythrocyte cholinesterase with 1-naphthyl N-methylcarbamate, 2-isopropoxyphenyl N-methylcarbamate and phenyl N-methylcarbamate were studied. Rate constants for inhibition and rate constants for spontaneous reactivation were determined. The calculated rate constants for spontaneous reactivation agreed well with those obtained experimentally. 2. The degree of inhibition obtained after preincubation of enzyme and inhibitor was found to be independent of both the substrate concentration and the dilution of the inhibited enzyme. 3. The reaction between the enzyme and the inhibitor was consistent with carbamates being regarded as poor substrates of cholinesterases. There was no evidence for the formation of a reversible complex between the enzyme and the carbamate.     

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.