A Quantitative Systems Pharmacology Model of Plasma Potassium Regulation by the Kidney and Aldosterone

Plasma potassium regulation within a narrow range is vital for life. The risk for hyperkalemia increases when kidney function is impaired and with therapeutic interventions such as mineralocorticoid receptor antagonists (MRAs). The kidney maintains potassium homeostasis by matching potassium intake and excretion, in part through the action of aldosterone. A mechanistic mathematical model was developed and used to investigate the effect of renal impairment and MRAs on plasma potassium levels. The model describes renal potassium filtration, reabsorption, and secretion along the nephron; potassium-aldosterone regulatory feedbacks; whole body potassium balance; and the pharmacologic effects of MRAs. The model was calibrated by fitting (1) the plasma potassium and aldosterone response to potassium infusion in humans on high/low potassium diets, and (2) the acute potassium excretion response to spironolactone. The model was validated by predicting steady-state plasma potassium with sustained spironolactone treatment in hyperaldosteronism patients. The model was then used to demonstrate that (1) declining renal function alone has a small effect on plasma potassium for GFR > 30 ml/min, but an increasing effect as GFR approaches end stage renal disease (GFR ~ 15 ml/min) (2) the effect of increasing potassium intake has minimal effect at normal GFRs but increasing effect on plasma potassium as GFR declines, and 3) MRAs have a minor effect on plasma potassium when GFR is normal, but cause larger increases as GFR falls below 60 ml/min. This model provides a quantitative framework for investigating integrated impacts of diseases and therapies in this complex system.