Simplification of complex kinetic models used for the quantitative analysis of nuclear magnetic resonance or radioactive tracer studies

Abstract

A method for simplifying the mathematical models describing the dynamics of tracers (e.g.¹³C, ³¹P, ¹⁴C, as used in NMR studies or radioactive tracer experiments) in (bio-)chemical reaction systems is presented. This method is appropriate in the cases where the system includes reactions, the rates of which differ by several orders of magnitude. The basic idea is to adapt the rapid-equilibrium approximation to tracer systems. It is shown with the aid of the Perron–Frobenius theorem that for tracer systems, the conditions for applicability of this approximation are satisfied whenever some reactions are near equilibrium. It turns out that the specific enrichments of all of the labelled atoms that are connected by fast reversible reactions can be grouped together as ‘pool variables’. The reduced system contains fewer parameters and can, thus, be fitted more easily to experimental data. Moreover, the method can be employed for identifying non-equilibrium and near-equilibrium reactions from experimentally measured specific enrichments of tracer. The reduction algorithm is illustrated by studying a model of the distribution of ¹³C-tracers in the pentose phosphate pathway.