Kinetic model for the coupling between allosteric transitions in GroEL and substrate protein folding and aggregation

The bacterial chaperonin GroEL and the co-chaperonin GroES assist in the folding of a number of structurally unrelated substrate proteins (SPs). In the absence of chaperonins, SP folds by the kinetic partitioning mechanism (KPM), according to which a fraction of unfolded molecules reaches the native state directly, while the remaining fraction gets trapped in a potentially aggregation-prone misfolded state. During the catalytic reaction cycle, GroEL undergoes a series of allosteric transitions (T<-->R-->R"-->T) triggered by SP capture, ATP binding and hydrolysis, and GroES binding. We developed a general kinetic model that takes into account the coupling between the rates of the allosteric transitions and the folding and aggregation of the SP. Our model, in which the GroEL allosteric rates and SP-dependent folding and aggregation rates are independently varied without prior assumption, quantitatively fits the GroEL concentration-dependent data on the yield of native ribulose bisphosphate carboxylase/oxygenase (Rubisco) as a function of time. The extracted kinetic parameters for the GroEL reaction cycle are consistent with the available values from independent experiments. In addition, we also obtained physically reasonable parameters for the kinetic steps in the reaction cycle that are difficult to measure. If experimental values for GroEL allosteric rates are used, the time-dependent changes in native-state yield at eight GroEL concentrations can be quantitatively fit using only three SP-dependent parameters. The model predicts that the differences in the efficiencies (as measured by yields of the native state) of GroEL, single-ring mutant (SR1), and variants of SR1, in the rescue of mitochondrial malate dehydrogenase, citrate synthase, and Rubisco, are related to the large variations in the allosteric transition rates. We also show that GroEL/S mutants that efficiently fold one SP at the expense of all others are due to a decrease in the rate of a key step in the reaction cycle, which implies that wild-type GroEL has evolved as a compromise between generality and specificity. We predict that, under maximum loading conditions and saturating ATP concentration, the efficiency of GroEL (using parameters for Rubisco) depends predominantly on the rate of R-->R" transition, while the equilibrium constant of the T<-->R has a small effect only. Both under sub- and superstoichiometric GroEL concentrations, enhanced efficiency is achieved by rapid turnover of the reaction cycle, which is in accord with the predictions of the iterative annealing mechanism. The effects are most dramatic at substoichiometric conditions (most relevant for in vivo situations) when SP aggregation can outcompete capture of SP by chaperonins.