Estimates and implications of co-operativity for enzyme kinetics in the intact liver: method of flow invariants

For substrates rapidly equilibrated between blood and liver cells, steady-state co-operative enzyme kinetics determines combinations of inlet and outlet substrate concentrations which do not change with the rate of blood flow recirculating through an isolated perfused liver. The mathematical forms of these combinations (here called flow invariants) are different for each value of the Hill co-operativity constant which can therefore be estimated, on a set of intact perfused preparations, from that flow invariant which is stochastically least dependent on experimental changes in the flow rate. This estimate, made in a narrow range of substrate concentrations, is illustrated using previously published data on the phosphorylation of galactose by galactokinase in rat liver. Changes (if any) of hepatocellular Hill constants in liver disease could be of clinical interest. A conspicuous difference between effects of negative and positive cooperativity in the intact perfused organ is found: for negative (but not for positive) co-operativity, complete extraction of the substrate in a single pass through a shunt-free liver is predicted from Hill's equation for a specified range of finite input concentrations and flow rates. Substrates with negative co-operativity in vivo would therefore facilitate the quantification of intrahepatic shunts.