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.

Kinetic analysis of the general modifier mechanism of Botts and Morales involving a suicide substrate.

Suicide substrates are widely used in enzymology for studying enzyme mechanisms and designing potential drugs. The presence of a reversible modifier decreases or increases the rate of substrate-induced inactivation, with evident physiological and experimental consequences. To date, only the action of a competitive or uncompetitive inhibitor of an enzyme system involving suicide substrate has been reported. In this paper, we analyse the kinetics of enzyme-catalysed reactions which evolve in accordance with the general modifier mechanisms of Botts and Morales in which enzyme inactivation is induced by suicide substrate. Rapid equilibrium of all of the reversible reaction steps involved is assumed and the time course equations for the residual enzyme activity, the inactive enzyme forms and the reaction product are derived. Partition ratios giving the relative weight of the product and inactive enzyme concentrations, and the relative contribution to the product formation of each of the unmodified and modified catalytic routes, are studied. New indices pointing to the conditions under which the modifier acts as inhibitor or as activator are suggested. The goodness of the analytical solutions is tested by comparison with the simulated curves obtained by numerical integration. An experimental design and kinetic data analysis to evaluate the kinetic parameters from the time progress curves of the product are proposed. From these results, those corresponding to several reaction mechanisms involving both a suicide substrate and a modifier, and which can be regarded as particular cases of the general case analysed here, can be directly and easily derived.

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.