Two closely related models, the mnemonic model  and the slow transition model , were developed to explain the observed positive cooperativity of GK with respect to glucose. These models invoke two kinetically distinct conformational forms of the GK enzyme, a highly reactive form that is induced under high glucose conditions, and a less active form that is also a lower energy conformation, which forms under low glucose concentrations. The reactive form is associated with a fast catalytic cycle, and the less reactive form is associated with a slower catalytic cycle. Which form of the enzyme is operational at any particular time is entirely dependant on glucose concentration. Both models are consistent with the observed kinetic profile of GK.
Crystal structures of the apo form of GK and the liganded forms helped confirm the proposals regarding how cooperativity with respect to glucose is achieved . The apo structure was found to exist in a low-energy "super-open" conformation, which was determined to be an inactive conformation because certain critical residues were absent from the active site. Upon binding glucose, a slow conformational change takes place to a higher-energy structure, the "open form''. A subsequent fast conformational change to the "closed form'' gives a complex that is able to bind the Mg • ATP2- cofactor, leading to the occurrence of the catalytic reaction and generation and release of products, G-6-P and ADP. The catalytic cycle continues in the fast cycle as long as glucose concentrations remain high, bypassing the low-energy super-open conformation, and involves a reduced degree of protein dynamics relative to the slow cycle. When the glucose concentration drops, the conformation slowly relaxes back to the low-energy super-open form. If glucose concentration remains low, then the catalytic cycle operates in the slow cycle, where GK exhibits a larger, jaw-like range of motion with an angular movement of approximately 120° of the protein occurring after product dissociation (Fig. 1) .
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