Escherichia coli chaperonin, GroEL, helps proteins fold under nonpermissive conditions. During the reaction cycle, GroEL undergoes allosteric transitions in response to binding of a substrate protein (SP), ATP, and the cochaperonin GroES. Using coarse-grained representations of the GroEL and GroES structures, we explore the link between allosteric transitions and the folding of a model SP, a de novo-designed four-helix bundle protein, with low spontaneous yield. The ensemble of GroEL-bound SP is less structured than the bulk misfolded structures. Upon binding, which kinetically occurs in two stages, the SP loses not only native tertiary contacts but also experiences a decrease in helical content. During multivalent binding and the subsequent ATP-driven transition of GroEL the SP undergoes force-induced stretching. Upon encapsulation, which occurs upon GroES binding, the SP finds itself in a "hydrophilic" cavity in which it can reach the folded conformation. Surprisingly, we find that the yield of the native state in the expanded GroEL cavity is relatively small even after it remains in it for twice the spontaneous folding time. Thus, in accord with the iterative annealing mechanism, multiple rounds of binding, partial unfolding, and release of the SP are required to enhance the yield of the folded SP.