Slow deactivation of ribulose 1,5-bisphosphate carboxylase/oxygenase elucidated by mathematical models

Ribulose 1,5-bisphosphate carboxylase/oxygenase (RuBisCO) is the key enzyme of the Calvin cycle, catalyzing the fixation of inorganic carbon dioxide to organic sugars. Unlike most enzymes, RuBisCO is extremely slow, substrate unspecific, and catalyzes undesired side-reactions, which are considered to be responsible for the slow deactivation observed in vitro, a phenomenon known as fallover. Despite the fact that amino acid sequences and the 3D structures of RuBisCO from a variety of species are known, the precise molecular mechanisms for the various side reactions are still unclear. In the present study, we investigate the kinetic properties of RuBisCO using mathematical models. Initially, we formulate a minimal model that quantitatively reflects the kinetic behavior of RuBisCOs from different organisms. By relating rate parameters for single molecular steps to experimentally determined K(m) and V(max) values, we can examine mechanistic differences among species. The minimal model further demonstrates that two inhibitor producing side reactions are sufficient to describe experimentally determined fallover kinetics. To explain the observed kinetics of the limited capacity of RuBisCO to accept xylulose 1,5-bisphosphate as substrate, the inclusion of other side reactions is necessary. Our model results suggest a yet undescribed alternative enolization mechanism that is supported by the molecular structure. Taken together, the presented models serve as a theoretical framework to explain a wide range of observed kinetic properties of RuBisCOs derived from a variety of species. Thus, we can support hypotheses about molecular mechanisms and can systematically compare enzymes from different origins.