The kinetics of enzyme systems involving activation of zymogens

A general model of zymogen activation is proposed and explicit kinetic equations for the time courses of the various species and products involved are given. These equations are valid for the whole course of the reaction and therefore for both the transient phase and the steady state. This model is sufficiently general to include mechanisms possessing one or more steps of zymogen activation besides possible steps of inhibition (reversible or irreversible) or inactivation.     

Mathematical modelling of glycolysis and adenine nucleotide metabolism of human erythrocytes. I. Reaction-kinetic statements, analysis of in vivo state and determination of starting conditions for in vitro experiments

A mathematical model of energy metabolism of human red cells is presented, which includes besides the glycolytic reactions the adenine nucleotide metabolism. The model is based on the network of chemical reactions, the thermodynamic equilibrium constants of fast reversible reactions and on the kinetic equations for irreversible enzyme reactions. The model consists of a system of 16 differential equations and allows the mathematical evaluation of metabolic levels in the steady state of energy metabolism corresponding to the in vivo state erythrocytes with the kinetic data for the enzymes derived from in vitro experiments. The dependence of the levels of metabolites in the steady state on the activity of some enzymes is analysed to characterize the regulatory properties of the system. The comparison of the steady state levels of the model with experimental data makes it possible to estimate values of some controversial enzyme parameters. Estimates of the kinetic parameters of the following intracellular processes are presented: 1) rate constant of AMP-phosphatase, 2) maximum rate of adenylate deaminase, 3) activity of adenine phosphoribosylpyrophosphate transferase and 4) adenosine transport through the cell membrane. The simulation of the preparatory phase before incubation of erythrocytes indicates, that the model also permits to compute the time course of changes of levels of metabolites. To solve the initial problem the stiff differential equation system is integrated numerically by an efficient program without the application of the quasi-steady-state approximation.     

Dissipative Irreversibility from Nosé's Reversible Mechanics

Abstract

Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nosé-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox associated with steady-state statistical mechanics: the Gibbs entropy of a nonequilibrium steady state decreases continuously to minus infinity.     

Mathematical modelling of dynamics and control in metabolic networks. II. Simple dimeric enzymes

The dynamics of enzyme cooperativity are examined by studying a homotropic dimeric enzyme with identical reaction sites, both of which follow irreversible Michaelis-Menten kinetics. The problem is approached via scaling and linearization of the governing mass action kinetic equations. Homotropic interaction between the two sites are found to depend on three dimensionless groups, two for the substrate binding step and one for the chemical transformation. The interaction between the two reaction sites is shown capable of producing dynamic behavior qualitatively different from that of a simple Michaelis-Menten system; when the two sites interact to increase enzymatic activity over that of two independent monomeric enzymes (positive cooperativity) damped oscillatory behavior is possible, and for negative cooperativity in the chemical transformation step a multiplicity of steady states can occur, with one state unstable and leading to runaway behavior. Linear analysis gives significant insight into system dynamics, and their parametric sensitivity, and a way to identify regions of the parameter space where the approximate quasi-stationary and quasi-equilibrium analyses are appropriate.     

Thermal denaturation of whey proteins and its effect in dairy technology

The irreversible denaturation of the most important whey protein fractions, namely beta-lactoglobulin A and B and alpha-lactalbumin were studied. The orders of the reactions, the rate constants and the activation energies were determined. The experiments were extended to include whey protein solutions of different concentrations and mixtures of whey proteins and caseins in different proportions. The kinetic data found by experiment make it possible to calculate in advance the precise degree of irreversible denaturation. It was found that the denaturation of beta-lactoglobulin was a good test parameter in technological studies and that there was a close correlation between the degree of denaturation and the results of important dairy processes.     

Stability properties of a primitive translation mechanism

A model for a primitive polypeptide synthesis mechanism with a certain degree of fidelity is presented. From the stability analysis of its kinetic equations, it is demonstrated that a multiple steady state is possible, in some region of parameter values. It is suggested that this capibility could play a basic role with respect to the survival of biopolymers.     

Sliding of STOP proteins on microtubules

Microtubules are stabilized against cold temperature disassembly by 145-kilodalton proteins [stable tubule only polypeptides (STOPs)] that block the end-wise dissociation of subunits from the polymers. We describe here several kinetic parameters of the interaction of STOPs with microtubules. STOPs will bind to microtubules either during assembly of the polymer or at steady state. The addition appears random on the polymers and does not require the mediation of tubulin subunits. Tubulin subunits compete with microtubules for STOP binding, but binding to the polymers is apparently irreversible. We demonstrate that STOPs do not exchange measurably between polymers at steady state. Nonetheless, a displacement of STOPs within a single polymer is readily demonstrable. We have determined that the displacement is apparently due to a surface translocation, or "sliding", of STOPs on microtubules.     

Clinical Use of Aromatase Inhibitors: Current Data and Future Perspectives

Abstract

A systematic procedure for the kinetic study of irreversible inhibition when the enzyme is consumed in the reaction which it catalyses, has been developed and analysed. Whereas in most reactions the enzymes are regenerated after each catalytic event and serve as reusable transacting effectors, in the consumed enzymes each catalytic center participates only once and there is no enzyme turnover. A systematic kinetic analysis of irreversible inhibition of these enzyme reactions is presented. Based on the algebraic criteria proposed in this work, it should be possible to evaluate either the mechanism of inhibition (complexing or non-complexing), or the type of inhibition (competitive, non-competitive, uncompetitive, mixed non-competitive). In addition, all kinetic constants involved in each case could be calculated. An experimental application of this analysis is also presented, concerning peptide bond formation in vitro. Using the puromycin reaction, which is a model reaction for the study of peptide bond formation in vitro and which follows the same kinetic law as the enzymes under study, we have found that: (i) the antibiotic spiramycin inhibits the puromycin reaction as a competitive irreversible inhibitor in a one step mechanism with an association rate constant equal to 1.3 × 10⁴M^-1s^-1 and, (ii) hydroxylamine inhibits the same reaction as an irreversible non-competitive inhibitor also in a one step mechanism with a rate constant equal to 1.6 × 10^-3 M^-1s^-1.     

Competitive inhibition of lipolytic enzymes. I. A kinetic model applicable to water-insoluble competitive inhibitors

It is now becoming clear from the abundant lipolytic enzyme literature that any meaningful interpretation of inhibition data has to take into account the kinetics of enzyme action at the lipid/water interface. We attempt in the present paper to provide a kinetic model applicable to water-insoluble competitive inhibitors, in order to quantitatively compare the results obtained at several laboratories. We derived kinetic equations applicable to the pre-steady state as well as steady state. By measuring the inhibitory power, as described in the present paper, it is possible to obtain a normalized estimation of the relative efficiency of various potential inhibitors. Furthermore, with the kinetic treatment developed here, it is possible to make quantitative comparisons with the same inhibitor placed under various physico-chemical situations, i.e., micellar or monolayer states.     

Control of kinetics by cooperative interactions

Cooperative effects in ligand binding and dissociation kinetics are much less investigated than steady state kinetics or equilibrium binding. Nevertheless, cooperativity in ligand binding leads necessarily to characteristic properties with respect to kinetic properties of the system. In case of positive cooperativity as found in oxygen binding proteins, a typical property is an autocatalytic ligand dissociation behavior leading to a time dependent, apparent ligand dissociation rate. To follow systematically the influence of the various potentially involved parameters on this characteristic property, simulations based on the simple MWC model were performed which should be relevant for all types of models based on the concept of an allosteric unit. In cases where the initial conformational distribution is very much dominated by the R-state, the intrinsic kinetic properties of the T-state are of minor influence for the observed ligand dissociation rate. Even for fast conformational transition rates, the R-state properties together with the size of the allosteric unit and the allosteric equilibrium constant define the shape of the curve. In such a case, a simplified model of the MWC-scheme (the irreversible n-chain model) is a good approximation of the full scheme. However, if in the starting conformational distribution some liganded T-molecules are present (a few percent is enough), the average off-rates can be significantly altered. Thus, the assignment of the initial rates to R-state properties has to be done with great care. However, if the R-state strongly dominates initially it is even possible to get an estimation of the lower limit for the number of interacting subunits from kinetic data: similar to the Hill-coefficient for equilibrium conditions, a measure for "kinetic cooperativity" can be derived by comparing initial and final ligand dissociation rates.     

Kinetic characterization of an enzymatic irreversible inhibition measured in the presence of coupling enzymes. The inhibition of adenosine triphosphatase from sarcoplasmic reticulum by fluorescein isothiocyanate

A kinetic study of the irreversible inhibition of an enzyme measured in the presence of a coupling enzyme system has been carried out to assess the type of mechanism of the irreversible inhibition. By using the algebraic criteria proposed here it should be possible to discriminate between these mechanisms and to calculate their corresponding kinetic constants. An experimental design has been developed and applied to fluorescein isothiocyanate as inhibitor of the ATPase activity from sarcoplasmic reticulum.     

Steady state kinetics of an enzyme reaction with one substrate and one modifier

This study examines the steady state kinetics of a reaction involving an enzyme, a substrate and a modifier when the reaction follows Michaelis-Menten kinetics. Conditions for Michaelis-Menten kinetics are deduced, and it is shown that an analogue of detailed balance determines the complexity of the rate equations in these cases. A scheme to distinguish many cases of Michaelis-Menten kinetics is presented. It is shown that steady state kinetics are, in general, insufficient to specify the mechanism of a reaction, since different effects of a modifier can give identical steady state kinetic data.     

Phenomenon of Life: Between Equilibrium and Non-Linearity

A model of ordering applicable to biological evolution is presented. It is shown that a steady state (more precisely approaching to a steady state) system of irreversible processes, under conditions of disproportionation of entropy, produces a lower-entropy product, that is, ordering. The ordering is defined as restricting of degrees of freedom: freedom of motion, interactions etc. The model differs from previous ones in that it relates the ordering to processes running not far from equilibrium, described in the linear field of non-equilibrium thermodynamics. It is shown that a system, which includes adenosine triphosphate (ATP) to adenosine diphosphate (ADP) conversion meets the demands of the physical model: it provides energy maintaining steady state conditions, and hydrolysis of ATP proceeding with consumption of water can be tightly conjugated with the most important reactions of synthesis of organic polymers (peptides, nucleotide chains etc.), which proceed with release of water. For these and other reasons ATP seems to be a key molecule of prebiotic evolution. It is argued that the elementary chemical reaction proceeding under control of an enzyme is not necessarily far from equilibrium. The experimental evidence supporting this idea, is presented. It is based on isotope data. Carbon isotope distribution in biochemical systems reveals regularity, which is inherent to steady state systems of chemical reactions, proceeding not far from equilibrium. In living organisms this feature appears at the statistical level, as many completely irreversible and non-linear processes occur in organisms. However not-far-from-equilibrium reactions are inherent to biochemical systems as a matter of principle. They are reconcilable with biochemical behavior. Extant organisms are highly evolved entities which, however, show in their basis the same features, as the simplest chemical systems must have had been involved in the origin of life. Some consequences following from the model, which may be significant for understanding the origin of life and the mechanism of biological evolution, are pointed out.     

Reversible and Irreversible Inhibition of High-Affinity Choline Transport Caused by Ethylcholine Aziridinium Ion

The effect of ethylcholine aziridinium ion (AF64A) on choline transport in hippocampal, striatal, and cerebrocortical synaptosomes was studied. Synaptosomes prepared from these three brain regions were equally sensitive to AF64A. Low concentrations of AF64A produced a reversible inhibition (IC50 values = 1.35-2.25 microM), whereas higher concentrations produced an irreversible inhibition (IC50 values = 25-30 microM), which started as competitive. The irreversible component of the inhibition was independent of extracellular Na+ concentration, a finding suggesting that the choline transporter is alkylated at its outward position. The kinetics of the inhibition were rapid and similar in the three brain regions examined. The high-affinity choline transport was more sensitive to the toxin than the low-affinity choline transport. Based on these results, we propose a kinetic model that explains the reversible and the irreversible inhibitions induced by AF64A. The possible relationships between the concentrations that in vitro produce reversible and irreversible inhibition and those that in vivo produce selective and nonselective cholinergic hypofunction are discussed.     

Cyclooxygenase and peroxidase inactivation of prostaglandin-H-synthase during catalysis

Prostaglandin-H-synthase (PGHS) is a bifunctional enzyme catalyzing cyclooxygenase and peroxidase reactions and undergoing irreversible inactivation during catalysis. A new method for kinetic studies of both PGHS activities in the course of cyclooxygenase as well as peroxidase reactions and also preincubation with hydroperoxides is suggested. It is shown that peroxidase activity is retained after complete cyclooxygenase inactivation and cyclooxygenase activity is retained after complete peroxidase inactivation. Two-stage cyclooxygenase inactivation occurs on preincubation of PGHS with hydrogen peroxide. Studies on inactivation under various conditions indicate that chemical mechanisms of cyclooxygenase and peroxidase inactivation are different. The data allow development of kinetic models.     

Monotonic and non-monotonic single channel open time distributions with two sequential open states

Some conditions under which kinetic schemes including two sequential open states of identical conductance will display a non-monotonic (i.e. with a deficit of short open times and a maximum at t>0) distribution of single channel open times are described theoretically. Neither a closed cyclic scheme nor exclusively irreversible transitions between states are required for non-monotonic distributions. A required condition for the schemes considered here is that all openings are to a state from which closing is not possible. It is the presence of a precursor process to channel closing that produces the non-monotonic distribution. Following each channel opening some time is required for a transition into the second open state from which all closings proceed. Simple schemes of this sort cannot provide the basis of any experimental reports of non-monotonic distributions.     

Folding under inequilibrium conditions as a possible reason for partial irreversibility of heat-denatured proteins: computer simulation study

Using computer simulations we have studied possible effects of heating and cooling at different scan rates on unfolding and refolding of macromolecules. We have shown that even the simplest two-state reversible transition can behave irreversibly when an unfavorable combination of cooling rate, relaxation time and activation energy of refolding occurs. On the basis of this finding we suppose that apparent irreversibility of some proteins denatured by heat may result from slow relaxation on cooling rather than thermodynamic instability and/or irreversible alterations of the polypeptide chain. Using this kinetic reversible two-state model, we estimated the effects of the scan rate and kinetic parameters of the macromolecule on its unfolding-refolding process. A few recommendations are suggested on how to reach maximal possible recovery after denaturation if refolding appears to be under kinetic control.     

Role of solvation barriers in protein kinetic stability

The stability of several protein systems of interest has been shown to have a kinetic basis. Besides the obvious biotechnological implications, the general interest of understanding protein kinetic stability is emphasized by the fact that some emerging molecular approaches to the inhibition of amyloidogenesis focus on the increase of the kinetic stability of protein native states. Lipases are among the most important industrial enzymes. Here, we have studied the thermal denaturation of the wild-type form, four single-mutant variants and two highly stable, multiple-mutant variants of lipase from Thermomyces lanuginosa. In all cases, thermal denaturation was irreversible, kinetically controlled and conformed to the two-state irreversible model. This result supports that the novel molecular-dynamics-focused, directed-evolution approach involved in the preparation of the highly stable variants is successful likely because it addresses kinetic stability and, in particular, because heated molecular dynamics simulations possibly identify regions of disrupted native interactions in the transition state for irreversible denaturation. Furthermore, we find very large mutation effects on activation enthalpy and entropy, which were not accompanied by similarly large changes in kinetic urea m-value. From this we are led to conclude that these mutation effects are associated to some structural feature of the transition state for the irreversible denaturation process that is not linked to large changes in solvent accessibility. Recent computational studies have suggested the existence of solvation/desolvation barriers in at least some protein folding/unfolding processes. We thus propose that a solvation barrier (arising from the asynchrony between breaking of internal contacts and water penetration) may contribute to the kinetic stability of lipase from T. lanuginosa (and, possibly, to the kinetic stability of other proteins as well).     

DNA supercoiling by DNA gyrase

Using purified DNA gyrase to supercoil circular plasmid pBR322 DNA, we examined how the linking number attained at the steady state (‘static head’) varies with the concentrations of ATP and ADP, both in the absence and presence of spermidine. In the absence of spermidine at total adenine nucleotide concentrations between 0.35 and 1.4 mM, the static-head linking number was independent of the sum concentration of ATP and ADP, but depended strongly on the ratio of their concentrations. We established that the same linking number was attained independent of the direction from which the steady state was approached. The decrease in linking number at static head is more extensive when spermidine is present in the incubation, but remains a function of the [ATP]-to-[ADP] ratio. These results are discussed in terms of various kinetic schemes for DNA gyrase. We present one kinetic scheme that accounts for the experimental observations. According to this scheme our experimental results imply that there is significant slip in DNA gyrase when spermidine is absent. It is possible that spermidine acts through adjustment of the degree of coupling of DNA gyrase.     

Multistability: a major means of differentiation and evolution in biological systems.

Very simple biochemical systems regulated at the level of gene expression or protein function are capable of complex dynamic behaviour. Among the various patterns of regulation associated with non-linear kinetics, multistability, which corresponds to a true switch between alternate steady states, allows a graded signal to be turned into a discontinuous evolution of the system along several possible distinct pathways, which can be either reversible or irreversible. Multistability plays a significant role in some of the basic processes of life. It might account for maintenance of phenotypic differences in the absence of genetic or environmental differences, as has been demonstrated experimentally for the regulation of the lactose operon in Escherichia coli. Cell differentiation might also be explained as multistability.