Computerized evaluation of mean residence times in multicompartmental linear system and pharmacokinetics.

Deriving mean residence times (MRTs) is an important task both in pharmacokinetics and in multicompartmental linear systems. Taking as starting point the analysis of MRTs in open or closed (Garcia-Meseguer et al., Bull Math Biol 2003, 65, 279) multicompartmental linear systems, we implement a versatile software, using the Visual Basic 6.0 language for MS-Windows, that is easy to use and with a user-friendly format for the input of data and the output of results. For any multicompartmental linear system of up to 512 compartments, whether closed or open, with traps or without traps and with zero input in one or more of the compartments, this software allows the user to obtain the symbolic expressions, in the most simplified form, and/or the numerical values of the MRTs in any of its compartments, in the entire system or in a part of the system. As far as we known from the literature, such a software has not been implemented before. The advantage of the present software is that it reduces on the work time needed and minimizes the human errors that are frequent in compartmental systems even those that are relatively staightforward. The software bioCelTer, along with instructions, can be downloaded from http://oretano.iele-ab.uclm.es/~fgarcia/bioCelTer/.

Competitive and uncompetitive inhibitors simultaneously acting on an autocatalytic zymogen activation reaction.

The time course of the residual enzyme activity of a general model consisting of an autocatalytic zymogen activation process inhibited by an irreversible competitive inhibitor and an irreversible uncompetitive inhibitor has been studied. Approached analytical expressions which furnish the time course of the residual enzyme activity from the onset of the reaction depending on the rate constants and initial concentration have been obtained. The goodness and limitations of the analytical equations were checked by comparing with the results obtained from the numerical integration, i.e. with the simulated progress curves. A dimensionless parameter giving the relative contributions of both the activation and the inhibitions routes is suggested, so that the value of this parameter determines whether the activation or the inhibitions routes prevail or if both processes are balanced during the time for which the analytical expressions are valid. The effects of the initial zymogen, free enzyme and inhibitors concentrations are analysed. Finally an experimental design and kinetic data analysis is proposed to evaluate simultaneously the kinetic parameters involved and to discriminate between different zymogen activation processes which can be considered particular cases of the general model.

Analysis and interpretation of the action mechanism of mushroom tyrosinase on monophenols and diphenols generating highly unstable o-quinones.

Tyrosinase can act on monophenols because of the mixture of met- (E(m)) and oxy-tyrosinase (E(ox)) which exists in the native form of the enzyme. The latter form is active on monophenols, while the former is not. However, the kinetics are complicated because monophenols can bind to both enzyme forms. This situation becomes even more complex since the products of the enzymatic reaction, the o-quinones, are unstable and continue evolving to generate o-diphenols in the medium. In the case of substrates such as L-tyrosine, tyrosinase generates very unstable o-quinones, in which a process of cyclation and subsequent oxidation-reduction generates o-diphenol through non-enzymatic reactions. However, the release of o-diphenol through the action of the enzyme on the monophenol contributes to the concentration of o-diphenol in the first pseudo-steady-state [D(0)](ss). Hence, the system reaches an initial pseudo-steady state when t-->0 and undergoes a transition phase (lag period) until a final steady state is reached when the concentration of o-diphenol in the medium reaches the concentration of the final steady state [D(f)](ss). These results can be explained by taking into account the kinetic and structural mechanism of the enzyme. In this, tyrosinase hydroxylates the monophenols to o-diphenols, generating an intermediate, E(m)D, which may oxidise the o-diphenol or release it directly to the medium. We surmise that the intermediate generated during the action of E(ox) on monophenols, E(m)D, has axial and equatorial bonds between the o-diphenol and copper atoms of the active site. Since the orbitals are not coplanar, the concerted oxidation-reduction reaction cannot occur. Instead, a bond, probably that of C-4, is broken to achieve coplanarity, producing a more labile intermediate that will then release the o-diphenol to the medium or reunite it diaxially, involving oxidation to o-quinone. The non-enzymatic evolution of the o-quinone would generate the o-diphenol ([D(f)](ss)) necessary for the final steady state to be reached after the lag period.

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.

Oxidation by mushroom tyrosinase of monophenols generating slightly unstable o-quinones.

Tyrosinase can act on monophenols because of the mixture of mettyrosinase (Em) and oxytyrosinase (Eox) that exists in the native form of the enzyme. The latter form is active on monophenols although the former is not. However, the kinetics are complicated because monophenols can bind to both enzyme forms. This situation becomes even more complex as the products of the enzymatic reaction, the o-quinones, are unstable and continue evolving to generate o-diphenols in the medium. In the case of substrates such as 4-methoxyphenol, 4-ethoxyphenol and 4-tert-butylphenol, tyrosinase generates o-quinones which become unstable with small constants of approximately < 10-3 s-1. The system evolves from an initial steady state, reached when t-->0, through a transition state towards a final steady state, which is never reached because the substrate is largely consumed. The mechanisms proposed to explain the enzyme's action can be differentiated by the kinetics of the first steady state. The results suggest that tyrosinase hydroxylates monophenols to o-diphenols, generating an intermediate Em-diphenol in the process, which may oxidize the o-diphenol or release it directly into the medium. In the case of o-quinone formation, its slow instability generates o-diphenol which activates the enzymatic system yielding parabolic time recordings.

Use of a windows program for simulation of the progress curves of reactants and intermediates involved in enzyme-catalyzed reactions.

A program that performs simulation of the kinetics of enzyme-catalyzed reactions with up to 32 species is described. The program is written in C++ for MS Windows 95/98/NT and uses a simple text file to define the kinetic model. The use of the program is illustrated with some examples. WES is available free of charge on request from the authors (e-mail: fgarcia@iele-ab.uclm.es).

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 program for the equations describing the steady state of enzyme reactions.

MOTIVATION: The derivation of steady-state equations is frequently carried out in enzyme kinetic studies. Done manually, this becomes tedious and prone to human error. The computer programs now available which are able to accept reaction mechanisms of some complexity are focused only on the strict steady-state approach. RESULTS: Here we present a computer program called REFERASS, with a short computation time and a user-friendly format for the input and output files, able to derive the strict steady-state equations and/or those corresponding to the usual assumption that one ore more of the reversible steps are in rapid equilibrium. This program handles enzyme-catalysed reactions with mechanisms involving up to 255 enzyme species connected by up to 255 reaction steps, subject to limits imposed by the memory and disk space available.

Kinetic analysis of the opened bicyclic enzyme cascades.

A kinetic analysis of the opened bicyclic enzyme cascade is presented. It includes the time-dependence of the concentrations of the modified and unmodified forms of the interconvertible enzymes, as well as their fractional modifications, from the onset of the reaction to its completion. The transient phase equations obtained allow the definition of new regulatory properties. The expressions corresponding to the concentrations and fractional modification in the steady-state are derived as particular cases of the general transient phase equations. These steady-state expressions agree with those obtained by other authors.