Determining RuBisCO activation kinetics and other rate and equilibrium constants by simultaneous multiple non-linear regression of a kinetic model

The forward and reverse rate constants involved in carbamylation, activation, carboxylation, and inhibition of D-ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) have been estimated by a new technique of simultaneous non-linear regression of a differential equation kinetic model to multiple experimental data. Parameters predicted by the model fitted to data from purified spinach enzyme in vitro included binding affinity constants for non-substrate CO2 and Mg2+ of 200 +/- 80 mu M and 700 +/- 200 mu M, respectively, as well as a turnover number (k(cat)) of 3.3 +/- 0.5 s(-1), a Michaelis half-saturation constant for carboxylation (K-M,K-C) of 10 +/- 4 mu M and a Michaelis constant for RuBP binding (K-M,K-RuBP) of 1.5 +/- 0.5 mu M. These and other constants agree well with previously measured values where they exist. The model is then used to show that slow inactivation of RuBisCO (fallover) in oxygen-free conditions at low concentrations of CO2 and Mg2+ is due to decarbamylation and binding of RuBP to uncarbamylated enzyme. In spite of RuBP binding more tightly to uncarbamylated enzyme than to the activated form, RuBisCO is activated at high concentrations of CO2 and Mg2+. This apparent paradox is resolved by considering activation kinetics and the fact that while RuBP binds tightly but slowly to uncarbamylated enzyme, it binds fast and loosely to activated enzyme. This modelling technique is presented as a new method for determining multiple kinetic data simultaneously from a limited experimental data set. The method can be used to compare the properties of RuBisCO from different species quickly and easily.