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

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/.

Mean lifetime and first-passage time of the enzyme species involved in an enzyme reaction. Application to unstable enzyme systems

Taking as starting point the complete analysis of mean residence times in linear compartmental systems performed by Garcia-Meseguer et al. (Bull. Math. Biol. 65:279-308, 2003) as well as the fact that enzyme systems, in which the interconversions between the different enzyme species involved are of first or pseudofirst order, act as linear compartmental systems, we hereby carry out a complete analysis of the mean lifetime that the enzyme molecules spend as part of the enzyme species, forms, or groups involved in an enzyme reaction mechanism. The formulas to evaluate these times are given as a function of the individual rate constants and the initial concentrations of the involved species at the onset of the reaction. We apply the results to unstable enzyme systems and support the results by using a concrete example of such systems. The practicality of obtaining the mean times and their possible application in a kinetic data analysis is discussed.

Interpretation of the reactivity of peroxidase compound II with phenols and anilines using the Marcus equation

The catalytic cycle of heme peroxidases involves three processes: the formation of compound I, its conversion to compound II and regeneration of the native enzyme. Each of the processes consists of a reversible binding stage followed by an irreversible transformation stage. Our group has proposed a continuous, sensitive and reliable chronometric method for measuring the steady-state rate of peroxidase activity. Furthermore, we have derived an analytical expression for the steady-state rate and simplified it, taking into consideration the experimental values of the rate constants of some stages previously determined by other authors in stopped-flow assays. We determined the value of the constant for the transformation of a series of phenols and anilines by compound II, and found that it involves a deprotonation step and an electron transfer step. Study of the solvent deuterium isotope effect on the oxidation of phenol revealed the non-rate-limiting character of the deprotonation step in a proton inventory study. Usage of the Marcus equation showed that the electronic transfer step is rate-limiting in both cases, while phenols and anilines were oxidised at different rates for the same potentials. This can be attributed to the shorter electron-tunnelling distance for electron transfer to the iron ion in the phenols than in the anilines.

Kinetic study of the effects of calcium ions on cationic artichoke (Cynara scolymus L.) peroxidase: calcium binding, steady-state kinetics and reactions with hydrogen peroxide

The apparent catalytic constant (k(cat)) of artichoke (Cynara scolymus L.) peroxidase (AKPC) with 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid) (ABTS) increased 130-fold in the presence of calcium ions (Ca2+) but the affinity (K(m)) of the enzyme for ABTS was 500 times lower than for Ca2+-free AKPC. AKPC is known to exhibit an equilibrium between 6-aquo hexa-coordinate and penta-coordinate forms of the haem iron that is modulated by Ca2+ and affects compound I formation. Measurements of the Ca2+ dissociation constant (K(D)) were complicated by the water-association/dissociation equilibrium yielding a global value more than 1000 times too high. The value for the Ca2+ binding step alone has now been determined to be K(D) approximately 10 nM. AKPC-Ca2+ was more resistant to inactivation by hydrogen peroxide (H(2)O(2)) and exhibited increased catalase activity. An analysis of the complex H(2)O(2) concentration dependent kinetics of Ca2+-free AKPC is presented.