A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls
Authors: Stadt Melissa M. , Leete Jessica , Devinyak Sophia , Layton Anita T. 
Published: September 2022

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.