Kinetics of the trypsinogen activation by enterokinase and trypsin

A global kinetic analysis of the mechanisms of the trypsinogen activation by enterokinase and trypsin is presented. The kinetic equations of both the transient-phase and the steady-state of these mechanisms are presented. In addition, we here derive the corresponding kinetic equations for the case in which the condition of rapid equilibrium prevails and we propose a kinetic data analysis. The significance of this approach to the treatment of other zymogen activation processes is discussed.     

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.     

Transient-phase kinetics of enzyme inactivation induced by suicide substrates

This paper deals with the kinetic study of reaction mechanisms with enzyme inactivation induced by a suicide substrate in the presence or absence of an auxiliary substrate and in conditions of excess of substrates in relation to the enzyme concentration and vice versa. A transient-phase approach has been developed that enables explicit equations with one or two significant exponentials to be obtained, thereby showing the dependence of product concentration on time. The validity of these equations has been checked, and a comparison made with those previously obtained by other authors. We propose an experimental design to determine the corresponding parameters and kinetic constants. The simplicity of our method allows a systematic application to more complex mechanisms.     

Deriving the rate equations for product inhibition patterns in bisubstrate enzyme reactions

In this work, the full rate equations for 17 completely reversible bisubstrate enzyme kinetic mechanisms, with two substrates in the forward and two in the reverse direction, have been presented; among these are rapid equilibrium, steady-state, and mixed steady-state and rapid equilibrium mechanisms. From each rate equation eight product inhibition equations were derived, four for the forward and four for the reverse direction. All the corresponding product inhibition equations were derived in full; thus a total of 17 × 8 = 136 equations, were presented. From these equations a list of product inhibition patterns were constructed and presented in a tabular form, both for the primary plots (intercept effects) and the secondary plots (slope effects).

The purpose of this work is to help investigators in practical work, especially biologists working with enzymes, to choose quickly an appropriate product inhibition pattern for the identification of the kinetic mechanism. The practical application of above product inhibition analysis was illustrated with three examples of yeast alcohol dehydrogenase-catalyzed reactions.     

Deriving the rate equations for product inhibition patterns in bisubstrate enzyme reactions

In this work, the full rate equations for 17 completely reversible bisubstrate enzyme kinetic mechanisms, with two substrates in the forward and two in the reverse direction, have been presented; among these are rapid equilibrium, steady-state, and mixed steady-state and rapid equilibrium mechanisms. From each rate equation eight product inhibition equations were derived, four for the forward and four for the reverse direction. All the corresponding product inhibition equations were derived in full; thus a total of 17 x 8 = 136 equations, were presented. From these equations a list of product inhibition patterns were constructed and presented in a tabular form, both for the primary plots (intercept effects) and the secondary plots (slope effects). The purpose of this work is to help investigators in practical work, especially biologists working with enzymes, to choose quickly an appropriate product inhibition pattern for the identification of the kinetic mechanism. The practical application of above product inhibition analysis was illustrated with three examples of yeast alcohol dehydrogenase-catalyzed reactions.     

Kinetics of the classical complement activation cascade

Transient-phase and steady-state equations have been derived for the classical complement activation mechanism. From these equations the corresponding ones for the rapid equilibrium conditions have been derived. We propose an experimental design to determine the kinetic parameters.     

Kinetic analysis of the transient phase and steady state of open multicyclic enzyme cascades

This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.     

Improved pseudoanalytical solution for steady-state biofilm kinetics

Simple algebraic expressions for the flux of substrate into a steady-state biofilm are developed. This pseudoanalytical solution, which eliminates the need for repetitiously solving numerically a set of nonlinear differential equations, is based on an analysis of the numerical results from the numerical solution of the differential equations. The critical advantage of this new pseudoanalytical solution is that it is highly accurate for the entire range of substrate concentrations and kinetic parameters. The article also illustrates that previous pseudoanalytical solutions for steady-state biofilm kinetics are seriously inaccurate for certain ranges of substrate concentration and kinetic parameters.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.     

Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system.

A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that this is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting liner flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior.     

Application of surface plasmon resonance toward studies of low-molecular-weight antigen-antibody binding interactions

Methods for studying low-molecular-weight antigen-antibody binding interactions using surface plasmon resonance detection are presented. The experimental parameters most relevant to studies of low-molecular-weight antigen-antibody binding interactions are discussed. Direct kinetic analysis of the binding interactions is most informative, providing both apparent association and dissociation rate constants from which equilibrium constants can be calculated. Equilibrium analysis, including steady-state and solution affinity studies, offers an alternative approach to direct kinetic analysis when knowledge of the individual kinetic rate constants is not required or difficult to determine. The various methods are illustrated by studies of an anti-T(4) Fab fragment binding interaction with several thyroxine analogs. The methods utilized were dependent on the affinity of the interaction. The high-affinity anti-T(4) Fab fragment/l-T(4) binding interaction was evaluated using direct kinetic analysis. An intermediate affinity anti-T(4) Fab fragment/l-T(3) binding interaction was evaluated using a combination of direct kinetic analysis, steady-state analysis, and solution affinity analysis. The relatively weak anti-T(4) Fab fragment/l-T(2) binding interaction was evaluated using steady-state and solution affinity analysis protocols. Several thyroxine tracers that could not be immobilized to a biosensor surface were also evaluated via the solution affinity format. In cases where a given binding interaction was examined using multiple methods the results were comparable.     

The "independence principle" in the processes of water transport.

The processes of membrane transport exhibiting permeability coefficients depending on the species activities do not obey the "independence principle" and are assumed to take place by a mechanism of discrete nature, analyzable by a kinetic formalism. In this article, we study the dependence of the osmotic permeability coefficient on the water activities, from the steady-state analysis of a kinetic model of single-file water transport that simultaneously incorporates the vacancy-mediated and "knock-on" mechanisms into the state diagram. In particular, we study the relation between the near-equilibrium osmotic permeability (Pe) and the equilibrium water activity of the compartments (w). The analysis and numerical calculations performed for a simple case of the model show that, for values of the parameters consistent with experimental data, Pe exhibits only a small variation with w within the physiological range in the majority of the situations considered here. It is not possible to predict, from the study of these simple models, whether more complicated kinetic diagrams of water transport may be characterized by permeability coefficients with a more evident dependence on the water activities. Nevertheless, the results obtained here suggest that, for the case of physiological water pores, the analysis of the kinetic dependence of the permeability coefficients on the water activities may not yield evidence pointing to a discrete nature for the transport process.     

Kinetic and chemical mechanism of the dihydrofolate reductase from Mycobacterium tuberculosis

Dihydrofolate reductase from Mycobacterium tuberculosis (MtDHFR) catalyzes the NAD(P)-dependent reduction of dihydrofolate, yielding NAD(P)(+) and tetrahydrofolate, the primary one-carbon unit carrier in biology. Tetrahydrofolate needs to be recycled so that reactions involved in dTMP synthesis and purine metabolism are maintained. In this work, we report the kinetic characterization of the MtDHFR. This enzyme has a sequential steady-state random kinetic mechanism, probably with a preferred pathway with NADPH binding first. A pK(a) value for an enzymic acid of approximately 7.0 was identified from the pH dependence of V, and the analysis of the primary kinetic isotope effects revealed that the hydride transfer step is at least partly rate-limiting throughout the pH range analyzed. Additionally, solvent and multiple kinetic isotope effects were determined and analyzed, and equilibrium isotope effects were measured on the equilibrium constant. (D(2)O)V and (D(2)O)V/K([4R-4-(2)H]NADH) were slightly inverse at pH 6.0, and inverse values for (D(2)O)V([4R-4-(2)H]NADH) and (D(2)O)V/K([4R-4-(2)H]NADH) suggested that a pre-equilibrium protonation is occurring before the hydride transfer step, indicating a stepwise mechanism for proton and hydride transfer. The same value was obtained for (D)k(H) at pH 5.5 and 7.5, reaffirming the rate-limiting nature of the hydride transfer step. A chemical mechanism is proposed on the basis of the results obtained here.     

A steady-state kinetic method for the verification of the rapid-equilibrium assumption in allosteric enzymes.

A method for testing the validity of the rapid-equilibrium assumption as it might apply to allosteric enzymes using exclusively steady-state kinetic data is presented. The method is based upon a recognition that the ratio of apparent dissociation constants for the allosteric ligand, obtained under conditions of limiting and saturating substrate concentration, must yield the thermodynamic value for the coupling parameter between the substrate and allosteric ligand even in the general steady-state case. If this value is found to be equal to the apparent coupling parameter determined from the ratio of limiting values of the Michaelis constant for substrate obtained in the absence and saturating presence of the allosteric ligand, then the substrate can be correctly viewed as effectively achieving a binding equilibrium with the enzyme in the steady-state. The utility and limitations of this method are demonstrated by examining the ADP activation of beef heart mitochondrial NAD-dependent isocitrate dehydrogenase.     

A kinetic study of the suicide inactivation of an enzyme measured through coupling reactions. Application to the suicide inactivation of tyrosinase.

A systematic procedure for the kinetic study of reaction mechanisms with enzyme inactivation induced by a suicide substrate in the presence or in the absence of an auxiliary substrate, when the enzyme activity is measured through coupling reactions, enzymically catalysed or not, was developed and analysed by using the transient-phase approach. The methodology is established to determine the parameters and kinetic constants corresponding to the enzyme suicide inactivation and the coupling reactions. This approach is illustrated by a study of the suicide inactivation of tyrosinase by catechol in the presence of L-proline. Treatment of the experimental data was carried out by non-linear regression.     

Biosensor-surface plasmon resonance: quantitative analysis of small molecule-nucleic acid interactions

Surface plasmon resonance (SPR)-biosensor techniques directly provide essential information for the study and characterization of small molecule-nucleic acid interactions, and the use of these methods is steadily increasing. The method is label-free and monitors the interactions in real time. Both dynamic and steady-state information can be obtained for a wide range of reaction rates and binding affinities. This article presents the basics of the SPR technique, provides suggestions for experimental design, and illustrates data processing and analysis of results. A specific example of the interaction of a well-known minor groove binding agent, netropsin, with DNA is evaluated by both kinetic and steady-state SPR methods. Three different experiments are used to illustrate different approaches and analysis methods. The three sets of results show the reproducibility of the binding constants and agreement from both steady-state and kinetic analyses. These experiments also show that reliable kinetic information can be obtained, even with difficult systems, if the experimental conditions are optimized to minimize mass transport effects. Limitations of the biosensor-SPR technique are also discussed to provide an awareness of the care needed to conduct a successful experiment.     

On the stability of the kinetics of a certain class of biomolecular reactions

Summary By means of a formal kinetic model, an analysis of the behavior of a certain type of unbranched sequences of biomolecular reactions is made. The main results are in (i) the characterization of the steady-state, (ii) the specification of a condition under which the largest physically admissible invariant set, containing the steady-state as invariant subset, can be obtained, and (iii) the deduction of parameter restrictions sufficient to assure asymptotic stability in the large in the given invariant set with respect to the steady-state.     

Exact and user-friendly kinetic analysis of the two-step rapid equilibrium Michaelis-Menten mechanism

Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.     

The complete pathway for ERK2-catalyzed reaction. Evidence for an iso random Bi Bi mechanism

In the present study, the enzymatic mechanism of ERK2 is re-examined by a combination of steady-state kinetic studies in the absence and presence of viscosogenic agents. Kinetic studies carried out in various concentrations of sucrose revealed that both k(cat) and k(cat)/K(m) for either ATP or EtsDelta138 were highly sensitive to solvent viscosity, suggesting that the rapid equilibrium assumption is not valid for the phosphorylation of protein substrate by ERK2. Furthermore, the kinetic analysis with the minimal random Bi Bi reaction mechanism is shown to be inconsistent with the principle of the detailed balance. This inconsistent calculation strongly suggests that there is isomerization of the enzyme-substrate ternary complex. The viscosity-dependent steady-state kinetic data are combined to establish a kinetic mechanism for the ERK2-catalyzed reaction that predicts initial reaction velocities under varying concentrations of ATP and substrate. These results complement previous structure-function studies of mitogen-activated protein kinases and provide important insight for mechanistic interpretation of the kinase functions.