Glucokinase is the enzyme primarily responsible for the phosphorylation of glucose in the livers of mammals and other vertebrates. It differs from the other hexokinases in being insensitive to inhibition by glucose 6-phosphate and in responding co-operatively to changes in the glucose concentration in the physiological range. These properties accord well with the presumed function of glucose phosphorylation in the liver as a means of controlling the blood-glucose concentration. Glucokinase has the unusual property for a co-operative enzyme of being a monomeric enzyme with a single active site. The co-operativity consequently requires a purely kinetic explanation and cannot be explained by analogy with subunit interactions in proteins that display co-operativity in equilibrium binding. The behaviour is consistent with a 'mnemonical' type of mechanism, i.e. one in which the co-operativity derives from the occurrence of two interconvertible forms of free enzyme that are not at equilibrium in the steady state. As co-operativity is observed only with glucose and not with the other substrate, MgATP2-, a corollary of this interpretation is that glucose must bind predominantly or exclusively before MgATP2-. This order of binding is supported by isotope-exchange measurements, though the alternative order also appears to be possible as a minor route of reaction. Stereochemical investigations reveal that glucokinase resembles other hexokinases in that the form of MgATP2- that reacts with the enzyme is the beta gamma-bidentate complex with the lambda-screw sense, and that the reaction proceeds with inversion of configuration at phosphorus.