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 + regulation 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. Author summary Potassium (K + ) homeostasis is crucial for normal cell function. Dysregulation of K + can have dangerous consequences and is a common side effect of pathologies, medications, or changes in hormone levels. Due to its complexities, how the body maintains extra- and intracellular K + concentrations each day is not fully understood. Of particular interest is capturing how regulatory mechanisms synthesize to be able to keep extracellullar K + concentration within a tight range of 3.5-5.0 mEq/L. There are a multitude of physiological processes involved in K + balance, making its study well suited for investigation using mathematical modeling. In this study, we developed a compartment model of extra- and intracellular K + regulation including the various regulatory mechanisms and a detailed kidney model. The significance of our research is to quantify the effect of individual regulatory mechanisms on K + regulation as well as predict the potential impact of a hypothesized signal: muscle-kidney cross talk.