Fig 1.
Transport of K+ in key nephron segments during normal, low, and high K+ intake.
Fig 2.
Flow chart depicting our mathematical model of K+ regulation. Green nodes represent internal K+ balance; orange, kidney function; blue, hormones (i.e., ALD and insulin); and white, constant model parameters. Pointed arrows indicate stimulation; blunted arrows indicate inhibition. ALD: aldosterone, GFR: glomerular filtration rate, GI: gastrointestinal, Interstitial: interstitial fluid, ICF: intracellular fluid, ECF: extracellular fluid
Table 1.
Model parameter values used in the baseline K+ homeostasis mathematical models.
Table 2.
Baseline model steady-state solution.
These values are used as the initial conditions in the model simulations.
Table 3.
Normal ranges for K+ concentration and amount.
Fig 3.
Percent changes in baseline model steady state solution for plasma K+ concentration (Kplasma) and intracellular K+ concentration (KIC) in response to a perturbation of 10% increase of the given parameter value.
Fig 4.
Extracellular and intracellular K+ response to a single meal.
(A) Prescribed K+ intake, (B)-(E) predicted K+ amount in various compartments, and (F)-(H) predicted K+ concentrations for a single meal load. The meal experiment occurs at time = 0 hours. Initial conditions are the baseline steady state values (see Table 2) followed by a fasting state set before the meal experiment. The yellow lines denote the K+ deficient meal (i.e., “Meal only” experiment); purple, only K+ ingestion (i.e., “KCl only” experiment); blue, meal with K+ (i.e., “Meal + KCl” experiment). Points and error bars for plasma K+ concentration (f) show experimental data from Preston et al. [17].
Fig 5.
Renal K+ response to a single meal.
Model simulation predictions for kidney K+ handling during a single meal load. The meal experiment occurs at time = 0 hours. Initial conditions are the baseline steady state values (see Table 2) with a fasting state before the meal experiment. The yellow lines denote the K+ deficient meal (i.e., “Meal only” experiment); purple, only K+ ingestion (i.e., “KCl only” experiment); blue, meal with K+ (i.e., “Meal + KCl” experiment). Points and error bars for urine K+ excretion show experimental data from Preston et al. [17].
Fig 6.
Feedforward and feedback response to a single meal.
Model simulation predictions for (A) effect of insulin concentration ([insulin]) on Na+-K+-ATPase K+ uptake, (B) aldosterone concentration effect on Na+-K+-ATPase K+ uptake, (C) gastrointestinal (GI) feedforward effect on distal tubule K+ secretion, and (D) aldosterone effect on distal tubule K+ secretion. The meal experiment occurs at 0 hours. Initial conditions are steady state with a fasting state set before the meal experiment. The yellow lines denote the K+ deficient meal (i.e., “Meal only” experiment); purple, only K+ ingestion (i.e., “KCl only” experiment); blue, meal with K+ (i.e., “Meal + KCl” experiment).
Fig 7.
Effect of feedforward and feedback controls.
Simulation results for plasma K+ concentration (B) and intracellular K+ concentration (C) for 10 days of normal K+ intake ((A);100 mEq/day, 3 typical meals) for the baseline model, baseline without gastrointestinal feedforward (GI FF) effect (γKin = 1), baseline without the ALD effect on Na+-K+-ATPase uptake (ρal = 1), baseline model without insulin effect on Na+-K+-ATPase update (ρinsulin = 1), and baseline model with all feedback effects off. Grey lines indicate normal range for Kplasma and KIC.
Fig 8.
Impact of muscle-kidney cross talk on K+ loading.
Simulation results for K+ loading experiments for the baseline model and muscle-kidney cross talk simulations (Case MKX-DT-sec and Case MKX-CD-reab). Potassium intake (A) is the same for all three simulation types. Note that Case MKX-CD-sec is not plotted since it had little impact from the baseline model results. Horizontal grey line shows normal range for plasma K+ concentration (C) and intracellular K+ concentration (E). CD: collecting duct, DT: distal tubule
Fig 9.
Impact of muscle-kidney cross talk on K+ depletion.
Simulation results for K+ depletion experiments for the baseline model and muscle-kidney cross talk simulations (Case MKX-DT-sec and Case MKX-CD-reab). Potassium intake (ΦKin) is the same for all three simulation types (A). Note that Case MKX-CD-sec is not plotted since it had little impact from the baseline model results. Horizontal grey line shows normal range for plasma K+ concentration (C) and intracellular K+ concentration (E). CD: collecting duct, DT: distal tubule