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

Potassium (K+) is an essential electrolyte that plays a key role in many physiological processes, including mineralcorticoid action, systemic blood-pressure regulation, and hormone secretion and action. Indeed, maintaining K+ balance is critical for normal cell function, as too high or too low K+ levels can have serious and potentially deadly health consequences. K+ homeostasis is achieved by an intricate balance between the intracellular and extracellular fluid as well as balance between K+ intake and excretion. This is achieved via the coordinated actions of regulatory mechanisms such as the gastrointestinal feedforward effect, insulin and aldosterone upregulation of Na+-K+-ATPase uptake, and hormone and electrolyte impacts on renal K+ handling. We recently developed a mathematical model of whole body K+ regulation to unravel the individual impacts of these regulatory mechanisms. In this study, we extend our mathematical model to incorporate recent experimental findings that showed decreased fractional proximal tubule reabsorption under a high-K+ diet. We conducted model simulations and sensitivity analyses to investigate how these renal alterations impact whole body K+ regulation. Model predictions quantify the sensitivity of K+ regulation to various levels of proximal tubule K+ reabsorption adaptation and tubuloglomerular feedback. Our results suggest that the reduced proximal tubule K+ reabsorption under a high-K+ diet could achieve K+ balance in isolation, but the resulting tubuloglomerular feedback reduces filtration rate and thus K+ excretion.NEW & NOTEWORTHY Potassium homeostasis is maintained in the body by a complex system of regulatory mechanisms. This system, when healthy, maintains a small extracellular potassium concentration, despite large fluctuations of dietary potassium. The complexities of the system make this problem well suited for investigation with mathematical modeling. In this study, we extend our mathematical model to consider recent experimental results on renal potassium handling on a high potassium diet and investigate the impacts from a whole body perspective.

Mathematical modeling of calcium homeostasis in female rats: An analysis of sex differences and maternal adaptations.

Calcium plays a vital role in various biological processes, including muscle contractions, blood clotting, skeletal mineralization, and cell signaling. While extracellular calcium makes up less than 1% of total body calcium, it is tightly regulated since too high or too low extracellular calcium concentration can have dangerous effects on the body. Mathematical modeling is a well-suited approach to investigate the complex physiological processes involved in calcium regulation. While mathematical models have been developed to study calcium homeostasis in male rats, none have been used to investigate known sex differences in hormone levels nor the unique physiological states of pregnancy and lactation. Calcitriol, the active form of vitamin D, plays a key role in intestinal calcium absorption, renal calcium reabsorption, and bone remodeling. It has been shown that, when compared to age-matched male rats, females have significantly lower calcitriol levels. In this study we first seek to investigate the impact of this difference as well as other known sex differences on calcium homeostasis using mathematical modeling. Female bodies differ from male bodies in that during their lifetime they may undergo massive adaptations during pregnancy and lactation. Indeed, maternal adaptations impact calcium regulation in all mammals. In pregnant rodents, intestinal absorption of calcium is massively increased in the mother's body to meet the needs of the developing fetus. In a lactating rodent, much of the calcium needs of milk are met by bone resorption, intestinal absorption, and renal calcium reabsorption. Given these observations, the goal of this project is to develop multi-scale whole-body models of calcium homeostasis that represents (1) how sex differences impact calcium homeostasis in female vs. male rats and (2) how a female body adapts to support the excess demands brought on by pregnancy and lactation. We used these models to quantify the impact of individual sex differences as well as maternal adaptations during pregnancy and lactation. Additionally, we conducted "what if" simulations to test whether sex differences in calcium regulation may enable females to better undergo maternal adaptations required in pregnancy and lactation than males.

Effect of pregnancy and hypertension on kidney function in female rats: Modeling and functional implications.

Throughout pregnancy, the kidneys undergo significant adaptations in morphology, hemodynamics, and transport to achieve the volume and electrolyte retention required to support a healthy pregnancy. Additionally, during pregnancies complicated by chronic hypertension, altered renal function from normal pregnancy occurs. The goal of this study is to analyze how inhibition of critical transporters affects gestational kidney function as well as how renal function is affected during chronic hypertension in pregnancy. To do this, we developed epithelial cell-based multi-nephron computational models of solute and water transport in the kidneys of a female rat in mid- and late pregnancy. We simulated the effects of key individual pregnancy-induced changes on renal Na+ and K+ transport: proximal tubule length, Na+/H+ exchanger isoform 3 (NHE3) activity, epithelial Na+ channel activity (ENaC), K+ secretory channel expression, and H+-K+-ATPase activity. Additionally, we conducted simulations to predict the effects of inhibition and knockout of the ENaC and H+-K+-ATPase transporters on virgin and pregnant rat kidneys. Our simulation results predicted that the ENaC and H+-K+-ATPase transporters are essential for sufficient Na+ and K+ reabsorption during pregnancy. Last, we developed models to capture changes made during hypertension in female rats and considered what may occur when a rat with chronic hypertension becomes pregnant. Model simulations predicted that in hypertension for a pregnant rat there is a similar shift in Na+ transport from the proximal tubules to the distal tubules as in a virgin rat.

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.

Adaptive changes in single-nephron GFR, tubular morphology, and transport in a pregnant rat nephron: modeling and analysis.

Normal pregnancy is characterized by massive increases in plasma volume and electrolyte retention. Given that the kidneys regulate homeostasis of electrolytes and volume, the organ undergoes major adaptations in morphology, hemodynamics, and transport to achieve the volume and electrolyte retention required in pregnancy. These adaptations are complex, sometimes counterintuitive, and not fully understood. In addition, the demands of the developing fetus and placenta change throughout pregnancy. For example, during late pregnancy, K+ retention and thus enhanced renal K+ reabsorption are required despite many kaliuretic factors. The goal of this study was to unravel how known adaptive changes along the nephrons contribute to the ability of the kidney to meet volume and electrolyte requirements in mid and late pregnancy. We developed computational models of solute and water transport in the superficial nephron of the kidney of a rat in mid and late pregnancy. The midpregnant and late-pregnant rat superficial nephron models predicted that morphological adaptations and increased activity of Na+/H+ exchanger 3 (NHE3) and epithelial Na+ channel are essential for the enhanced Na+ reabsorption observed during pregnancy. Model simulations showed that for sufficient K+ reabsorption, increased activity of H+-K+-ATPase and decreased K+ secretion along the distal segments is required in both mid and late pregnancy. The model results also suggested that certain known sex differences in renal transporter pattern (e.g., the higher NHE3 protein abundance but lower activity in the proximal tubules of virgin female rats compared with male rats) may serve to better prepare females for the increased transport demand in pregnancy.NEW & NOTEWORTHY Normal pregnancy in mammals is generally characterized by massive changes in plasma volume and electrolyte retention. This study provides insights into how the volume and electrolyte requirement in different pregnancy stages are met by coordinated adaptive changes in the kidney. The model results also suggested that certain known sex differences in the renal transporter pattern may serve to better prepare females for the increased transport demand in pregnancy.