Biomedical subjects

B H Havsteen

Publications and source records attributed to B H Havsteen.

At least 19 recordsLinked to original sources

PubMed2006

Kinetic analysis of a general model of activation of aspartic proteinase zymogens.

Starting from a simple general reaction mechanism of activation of aspartic proteinase zymogens involving an uni- and a bimolecular simultaneous route, the time course equation of the concentration of the zymogen and of the activated enzyme have been derived. From these equations, an analysis quantifying the relative contribution to the global process of the two routes has been carried out for the first time. This analysis suggests a way to predict the time course of the relative contribution as well as the effect of the initial zymogen and activating enzyme concentrations, on the relative weight. An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed. Finally, we apply some of our results to experimental data obtained by other authors in experimental studies of the activation of some aspartic proteinase zymogens.

Animals↗

PubMed2005

The influence of product instability on slow-binding inhibition.

We present a kinetic study of an enzyme reaction that takes place with slow-binding inhibition where the immediate product undergoes a spontaneous or induced process of decomposition. A kinetic study of an enzyme process, in which a slow-binding inhibition process and a decomposition of the immediate product of the reaction take place simultaneously is performed. The corresponding explicit concentration-time equations were obtained. Using the analytical solutions obtained, which were tested numerically, we suggest a procedure that allows the discrimination between the particular cases considered and the evaluation of the principal kinetic parameters of the reaction.

Enzyme Inhibitors↗

PubMed2003

Mean residence times in linear compartmental systems. Symbolic formulae for their direct evaluation.

A complete analysis has been performed of the mean residence times in linear compartmental systems, closed or open, with or without traps and with zero input. This analysis allows the derivation of explicit and simple general symbolic formulae to obtain the mean residence time in any compartment of any linear compartmental system, closed or open, with or without traps, as well as formulae to evaluate the mean residence time in the entire system like the above situations. The formulae are given as functions of the fractional transfer coefficients between the compartments and, in the case of open systems, they also include the excretion coefficients to the environment from the different compartments. The relationship between the formulae derived and the particular connection properties of the compartments is discussed. Finally, some examples have been solved.

Algorithms↗

PubMed2002

Evidence of quasi-linear gas transport through sperm whale myoglobin.

The diffusion of molecular oxygen or its isosteric analogue, carbon monoxide, from the surface of myoglobin to its deeply imbedded haem appears to represent one of the simplest protein functions. Hence, it was chosen for the study of the possible role of a global controlling effect like an attractor. However, whereas the six statistical criteria of the classical non-linear dynamic analysis for the existence of an attractor in myoglobin were fulfilled and invariant to the Fourier transformation, the properties of this attractor were not as simple as anticipated. The parameters were tested and confirmed by alternative approaches, the interpoint distance method of Judd and Fourier transformation. If the diffusion were approximately linear, the order of the attractor would be expected to be near one. However, a clearly higher value, 1.46+/-0.03, was found, indicating the existence of additional steps. Later, the latter were identified as a 90 degrees rotation of CO followed by a translocation by 0.4 A to a transient pocket. These additional steps may explain the high number of regulatory factors found, 10+/-1. The autocorrelation function was damped with a correlation length of at least 20 residues. The Poincaré plot showed a dense domain compatible with the cross-section of a quasi-spherical attractor. The first Lyapunov exponent, lambda(1), was clearly positive. The Hurst fractal coefficient was 1.90+/-0.22, indicating a clear departure from simple linear diffusion.

Animals↗

PubMed2001

Time course equations of the amount of substance in a linear compartmental system and their computerized derivation.

In this contribution, we present the symbolic time course equations corresponding to a general model of a linear compartmental system, closed or open, with or without traps and with zero input. The steady state equations are obtained easily from the transient phase equations by setting the time --> infinity. Special attention has been given to the open systems, for which an exhaustive kinetic analysis has been developed to obtain important properties. Besides, the results have been particularized to open systems without traps and an alternative expression for the distribution function of exit times has been provided. We have implemented a versatile computer program, that is easy to use and with a user-friendly format of the input of data and the output of results. This computer program allows the user to obtain all the information necessary to derive the symbolic time course equations for closed or open systems as well as for the derivation of the distribution function of exit times.

Computer Simulation↗

PubMed2001

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves.

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.

Binding Sites↗

PubMed1999

An esterolytic antibody with vibrational properties of a catalytic H-chain and a non-catalytic L-chain.

An analysis of the temperature factors of an abenzyme has been performed to gain information on the possible role of deterministic chaos in the catalytic mechanism of such artificial proteins. The H-chain displayed a regular attractor of the dimension 3.0 +/- 0.3, whereas the L-chain showed one of = 7.5 +/- 0.5. The abenzyme also displayed a stochastic attractor of the dimension ca. 0.9. The H-chain attractor has one dimension more than those of the native hydrolases chymotrypsin and lysozyme. The additional degree of freedom of the abenzyme offers a likely explanation of the low specific catalytic activities of these artificial enzymes. The dimension of the attractor in the L-chain falls in the range found for other antibodies. Hence, a clear dichotomy seems to rule in this abenzyme; the H-chain displays the vibrational properties of an enzyme and the L-chain those of an antibody. The new data supports the hypothesis of an important role of attractors in biochemical mechanisms by reduction of the number of degrees of freedom (entropy) of reaction partners. A hierarchy of attractors is associated with specific protein functions.

Animals↗

PubMed1999

Transient phase of enzyme reactions. Time course equations of the strict and the rapid equilibrium conditions and their computerized derivation.

In this contribution, we present the derivation, from the strict transient phase equations of enzyme reactions, of the transient phase equations under the usual assumptions that one or more of the reversible steps involved in the mechanism of the enzyme reaction are assumed to be in rapid equilibrium. Moreover, we present the transient phase equations of all of the species in a general enzyme system model, valid for the partial or total rapid equilibrium conditions, as well as the particular case of the strict transient phase equations. In the case of the rapid equilibrium assumptions, the equations may be given either as functions of the individual rate constants in the reversible steps assumed in rapid equilibrium or as functions of the corresponding equilibrium constants. The steady state equations are easily obtained from the transient phase equations by setting the time --> infinity. We have implemented a computer program, easy to use and with a user-friendly format for the input of data and output of results, which allows the user to derive the symbolic strict transient phase equations and/or those corresponding to the assumption that one or more of the reversible reaction steps are in rapid equilibrium.

Computer Simulation↗

PubMed1999

Attractor control of the redox reactions of bovine cytochrome c.

Although the conformational changes accompanying the oxidation of ferrocytochrome c by the transfer of an electron to cytochrome a are small, they may contribute to the regulation of the electron transfer by transient storage of the liberated energy as strain and atomic vibrations. Both the electron transfer and the conformational changes seem to be controlled by an attractor, i.e. by a manifestation of a deterministic chaos. The putative attractor is regular and is, for the reaction involving the inner monomer of ferricytochrome c (I), of the order of 3.03 +/- 0.03. The conformational changes involving the outer monomer of ferricytochrome c (O) seem also to be controlled by a regular attractor, but its order is 4.2 +/- 0.2. The low order of the coupled reactions of electron transfer and conformational change suggests that it is essential to the electron transfer process in the respiratory chain. Since the order of attractors of other proteins correlates with the vectorial description of the function (1.0 for myoglobin, 2.0 for chymotrypsin and lysozyme, 3.0 for an abenzyme), the value for cyt. c indicates that not only the electron transfer, but also an additional reaction, e.g. the conformational change, are essential for the function of this protein. Hence, the study of protein attractors may yield information on important details, which could not be obtained by other methods.

Animals↗

PubMed1998

Kinetics of enzyme systems with unstable suicide substrates.

This paper deals with kinetic studies of enzyme reaction mechanisms with enzyme inactivation induced by an unstable suicide substrate. An initial steady-state of the catalytic route is assumed and the time course equations for the total active enzyme forms and the reaction product have been derived. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters is suggested and the time course equations of an important reaction mechanisms involving a stable suicide substrate and which can be regarded as particular case of that under study has also been derived from the corresponding equations. The simplicity of our method allows its systematic application to more complex mechanisms.

Enzyme Inhibitors↗

PubMed1996

Time-dependent control of metabolic systems by external effectors.

The expression of elasticity coefficients for time-dependent enzyme inhibition/activation by an external effector was initially derived. Only a limited number of restrictive assumptions were used, for example, the enzyme was considered to obey Michaelis-Menten kinetics and effectors were taken to be competitive. Then, a simple metabolic system under the control of a time-dependent effector (inhibitor or activator) was analysed and the expressions of the control coefficients were obtained. In addition, two numerical examples were used to represent the control coefficients as functions of time and effector concentration. The results indicate that the control coefficients vary in a relatively limited range of values; however, for certain intervals of time and of effector concentration local minima or major modifications of the coefficients may be recorded. The physiological importance of non-steady state analysis of metabolic systems controlled by external effectors was also discussed. It was stressed that the non-steady state treatment may contribute to creating a more realistic image of the metabolic control processes.

Animals↗

PubMed1996

An analysis of the kinetics of enzymatic systems with unstable species.

We present a general kinetic analysis of the Michaelis-Menten mechanism for the case in which the substrate, the enzyme-substrate complex, and the product are unstable. The equations for the rapid equilibrium conditions are obtained as a particular case of the general equations of the transient-phase. The kinetic data analysis which we suggest is based on the time progress curve of the product of the enzymatic reaction, or on the progress curve of the species into which the immediate product is transformed. This analysis allows the determination of the rate and equilibrium constants if adequate experimental results are available. It assumes, in contrast to most previous treatments of enzyme kinetics, that the concentration of the enzyme is much higher than that of the substrate. Since this condition often is satisfied inside cells, it can be more relevant to physiological problems than the classical assumption, [E] << [S], which sooner pertains to the situation in the laboratory.

Computer Simulation↗

PubMed1994

Kinetics of an enzyme reaction in which both the enzyme-substrate complex and the product are unstable or only the product is unstable.

A kinetic analysis of the Michaelis-Menten mechanism has been made for the case in which both the enzyme-substrate complex and the product are unstable or only the product is unstable, either spontaneously or as the result of the addition of a reagent. This analysis allows the derivation of equations which under conditions of limiting enzyme concentration relate the concentration of all of the species to the time. A kinetic data analysis is suggested, which leads to the evaluation of the kinetic parameters involved in the reaction. The analysis is based on the equation which describes the formation of products with time and one's experimental progress curves. We demonstrate the method numerically by computer simulation of the reaction with added experimental errors and experimentally by the use of data from the kinetic study of the action of tyrosinase on dopamine.

Basidiomycota↗

PubMed1994

Kinetic analysis of reversible closed bicyclic enzyme cascades covering the whole course of the reaction.

A kinetic analysis of the closed bicyclic enzyme cascades is presented. 1. It includes the dependence on time from the onset of the reaction, of the concentration of the modified and unmodified enzyme species involved and the time course equations of the modificational fractions of the interconvertible enzymes. 2. The transient phase equations obtained allow the definition of new regulatory modification properties. 3. The expressions for concentrations of the unmodified and modified forms of the interconvertible enzymes, as well as those of the fractional modifications in the steady state are derived as particular cases of the general equations. 4. These steady state expressions coincide with those obtained by other authors. 5. The analytical results obtained are discussed in relation to the Escherichia coli glutamine synthetase cascade.

Enzymes↗

PubMed1993

Time course of the uridylylation and adenylylation states in the glutamine synthetase bicyclic cascade.

A kinetic analysis of the glutamine synthetase bicyclic cascade is presented. It includes the dependence on time from the onset of the reaction of both the uridylylation of Shapiro's regulatory protein and the adenylylation of the glutamine synthetase. The transient phase equations obtained allow an estimation of the time elapsed until the states of uridylylation and adenylylation reach their steady-states, and therefore an evaluation of the effective sensitivity of the system. The contribution of the uridylylation cycle to the adenylylation cycle has been studied, and an equation relating the state of adenylylation at any time to the state of uridylylation at the same instant has been derived.

Adenosine Triphosphate↗

PubMed1993

Kinetic analysis of a Michaelis-Menten mechanism in which the enzyme is unstable.

A kinetic analysis of the Michaelis-Menten mechanism is made for the cases in which the free enzyme, or the enzyme-substrate complex, or both, are unstable, either spontaneously or as a result of the addition of a reagent. The explicit time-course equations of all of the species involved has been derived under conditions of limiting enzyme concentration. The validity of these equations has been checked by using numerical simulations. An experimental design and a kinetic data analysis allowing the evaluation of the parameters and kinetic constants are recommended.

Catalysis↗

PubMed1993

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.

Enzyme Activation↗

PubMed1992

Kinetics of a model of autocatalysis, coupling of a reaction in which the enzyme acts on one of its substrates.

A global kinetic analysis is presented of a model of an enzyme autocatalytic process, to which a reaction is coupled, in which the enzyme acts upon one of its substrates. The kinetic equations of both the transient phase and the steady state are derived for this mechanism. In addition, we determine the corresponding kinetic equations for several particular cases which are characterized by certain relations between the rate constants. Finally, a kinetic data analysis is proposed for one of these particular cases. It can easily be extended to any of the other cases.

Catalysis↗