Distribution of Cortisol in Human Plasma in vitro: Equilibrium Solutions for Free Cortisol Using Equations of Mass Conservation and Mass Action

Abstract

Cortisol is secreted by the human adrenal cortex and circulates in plasma as free or protein-bound cortisol. Corticosteroid binding globulin (CBG) and albumin are the principal binding proteins (BPs) for cortisol in human plasma. Plasma concentrations of total cortisol (sum of protein-bound and free cortisol) are typically measured in vitro. Determination of free cortisol adds clinical and diagnostic value to total cortisol concentration. However, direct measurement of free cortisol concentrations involves laborious separation methods, limiting clinical utility. The development and application of physiologic protein-ligand binding models and equations provide an alternative approach to assessment of free cortisol concentrations in vitro. In this chapter, we introduce a matrix notation to represent relevant mass action and mass conservation equations. The matrix notation is also used to summarize and compare several contemporary models of interest, including cubic, quadratic, and quartic polynomial equations. Second, we introduce Feldman’s equations for competitive ligand-protein binding interactions, which are represented by matrices for multiple ligands and multiple BPs, including illustrative 2 × 2 matrix; we also discuss iterative solution strategies for coupled polynomial equations. Third, we develop a theorem for albumin-cortisol binding and review related assumptions that have been used to simplify polynomial equations and their equilibrium solutions.