A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls

Maintaining normal potassium (K(+)) concentrations in the extra- and intracellular fluid is critical for cell function. K(+) homeostasis is achieved by ensuring proper distribution between extra- and intracellular fluid compartments and by matching K(+) excretion with intake. The Na(+)-K(+)-ATPase pump facilitates K(+) uptake into the skeletal muscle, where most K(+) is stored. Na(+)-K(+)-ATPase activity is stimulated by insulin and aldosterone. The kidneys regulate long term K(+) homeostasis by controlling the amount of K(+) excreted through urine. Renal handling of K(+) is mediated by a number of regulatory mechanisms, including an aldosterone-mediated feedback control, in which high extracellular K(+) concentration stimulates aldosterone secretion, which enhances urine K(+) excretion, and a gastrointestinal feedforward control mechanism, in which dietary K(+) intake increases K(+) excretion. Recently, a muscle-kidney cross talk signal has been hypothesized, where the K(+) concentration in skeletal muscle cells directly affects urine K(+) excretion without changes in extracellular K(+) concentration. To understand how these mechanisms coordinate under different K(+) challenges, we have developed a compartmental model of whole-body K(+) regulation. The model represents the intra- and extracellular fluid compartments in a human (male) as well as a detailed kidney compartment. We included (i) the gastrointestinal feedforward control mechanism, (ii) the effect of insulin and (iii) aldosterone on Na(+)-K(+)-ATPase K(+) uptake, and (iv) aldosterone stimulation of renal K(+) secretion. We used this model to investigate the impact of regulatory mechanisms on K(+) homeostasis. Model predictions showed how the regulatory mechanisms synthesize to ensure that the extra- and intracelluller fluid K(+) concentrations remain in normal range in times of K(+) loading and fasting. Additionally, we predict that without the hypothesized muscle-kidney cross talk signal, the model was unable to predict a return to normal extracellular K(+) concentration after a period of high K(+) loading or depletion.