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

Abstract

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.

A modeling analysis of whole-body potassium regulation on a high potassium diet: Proximal tubule and tubuloglomerular feedback effects

“…(We have previously found that the distal tubule target resulted in similar results to collecting duct reabsorption [39]. )…”

“…In our previous study [39], we used our mathematical model to conduct "what-if" simulations of muscle-kidney cross talk under short-term K + loading or depletion. Specifically, we found that in our baseline model (i.e., no muscle-kidney cross talk) after 4 days of K + loading (high K + intake), plasma [K + ] levels started to reach hyperkalemic levels and intracellular [K + ] levels remained high for several days after returning to normal K + intake [39]. When the muscle-kidney cross talk signal was included, model simulations predicted that intracellular [K + ] levels remained within normal range.…”

“…We direct readers to Ref. [39] or Appendix B for details on the model representation of these segments.…”

Modeling magnesium and calcium transport along male rat kidney and the effects of diuretics

“…A whole-body Mg 2+ balance model may help answer that question. By incorporating the present model into whole-body electrolyte balance models (e.g., [56][57][58][59]), one can obtain an integrative model to study wholebody Mg 2+ balance.…”

Potassium homeostasis and therapeutic intervention with sodium zirconium cyclosilicate: A model‐informed drug development case study

“…Many times, clinical trial measurements are made before the first meal in the morning, at which time sK + levels are near their lowest for the day, and therefore least likely to be above the normal range. 6,7 The model currently includes limited physiological detail (e.g., GI compartments) and limited detail on the complexity of K + regulation; this could be expanded upon in the future using information from literature based on detailed physiological experiments and data from large trials of drugs that influence K + handling (e.g., aldosterone antagonists), as explored by Stadt et al 18 and Maddah and F I G U R E 4 Model application to SZC dosing in emergency settings. Top: Flow chart of process to adjust model to simulate severe hyperkalemia to mimic desired trial population and simulate different SZC dosing regimens.…”