Mathematical model of biliary lipid secretion: a quantitative analysis of physiological and biochemical data from man and other species.

We propose a simple mathematical model to account for the coupling of secretion rates of bile salts, lecithin, and cholesterol into bile. The model assumes that: 1) molecules of "biliary" lecithin and cholesterol enter a functional compartment located in the endoplasmic reticulum of the hepatocyte from which they are secreted into bile, and in the case of cholesterol, also catabolized to bile salts; 2) the rates at which lecithin and cholesterol enter the "secretory" compartment are regulated independently by feedback loops that control their synthesis and/or uptake; 3) lecithin secretion is coupled by an unknown transport mechanism, possibly micellar or vesicular, to the flux of bile salts passing through the compartment; 4) cholesterol secretion is coupled by a similar mechanism to lecithin secretion and not to bile salt secretion directly; and 5) bile salt synthesis is proportional to the cholesterol content of the compartment. The model predicts that in the steady state the dependences, lecithin secretion vs bile salt secretion; cholesterol secretion vs lecithin secretion; and cholesterol secretion vs bile salt secretion, will all have the form of rectangular hyperbolae. Four independent parameters related to the postulated mechanisms of biliary lipid synthesis, uptake, and transport determine the quantitative features of these hyperbolae. These four "secretion parameters" also determine how the biliary lipid composition of hepatic and "fasting" gallbladder bile varies with bile salt secretion rate. A quantitative analysis of biochemical and physiological data on biliary lipid secretion in rat, dog, and man confirms the general predictions of the model. Deductions of the secretion parameters are made for each species and are compared with other relevant data on biliary lipid metabolism. From this analysis, we offer new insights into: i) the species differences in biliary lipid secretion and bile composition; ii) the influence of obesity on biliary lipid secretion in man; and iii) the causes of cholesterol super-saturation in fasting gallbladder bile.