Theory of chaperonin action: inertial model for enhancement of prokaryotic Rubisco assembly.

We have performed a computational simulation of the aggregation and chaperonin-dependent reconstitution of dimeric prokaryotic ribulose bisphosphate carboxylase/oxygenase (Rubisco), based on the data of P. Goloubinoff et al. (1989, Nature 342, 884-889) and P. V. Viitanen et al. (1990, Biochemistry 29, 5665-5671). The aggregation is simulated by a set of 12 differential equations representing the aggregation of the Rubisco folding intermediate, Rubisco-I, with itself and with aggregates of Rubisco-I, leading up to dodecamers. Four rate constants, applying to forward or reverse steps in the aggregation process, were included. Optimal values for these constants were determined using the ellipsoid algorithm as implemented by one of us (Ecker, J.G. & Kupferschmid, M., 1988, Introduction to Operations Research, Wiley, New York, pp. 315-322). Intensive exploration of simpler aggregation models did not identify an alternative that could simulate the data as well as this one. The activity of the chaperonin in this system was simulated by using this aggregation model, combined with a model similar to that proposed by Goloubinoff et al. (1989). The model assumes that the chaperonin can bind the folding intermediate rapidly, and that the chaperonin complex releases the Rubisco molecule slowly, permitting time for its spontaneous folding while interacting with the chaperonin. This is followed by self-association of the folded Rubisco monomer to yield the active dimeric Rubisco. A modification of the model that simulates temperature effects was also constructed. The most important results we obtained indicate that the chaperonin-dependent reconstitution of Rubisco can be simulated adequately without invoking any catalysis of folding by the chaperonin. In addition, the simulations predict values for the association rate constant of Rubisco-I with the chaperonin, and other variables, that are subject to experimental verification.