An online tool for calculation of free-energy balance for the renal inner medulla

Abstract

Concentrating models of the renal inner medulla can be classified according to external free-energy balance into passive models (positive values) and models that require an external energy source (negative values). Here we introduce an online computational tool that implements the equations of Stephenson and colleagues (Stephenson JL, Tewarson RP, Mejia R. Proc Natl Acad Sci USA 71: 1618-1622, 1974) to calculate external free-energy balance at steady state for the inner medulla (http://helixweb.nih.gov/ESBL/FreeEnergy). Here "external free-energy balance" means the sum of free-energy flows in all streams entering and leaving the inner medulla. The program first assures steady-state mass balance for all components and then tallies net external free-energy balance for the selected flow conditions. Its use is illustrated by calculating external free-energy balance for an example of the passive concentrating model taken from the original paper by Kokko and Rector (Kokko JP, Rector FC Jr. Kidney Int 2: 214-223, 1972).

Fig. 1.

Screen shot of user interface showing default values. A: main parameters. B: water flow and TF/P inulin. C: Na concentration, Na mass flow, and %Na delivery. D: urea concentration, urea mass flow, and %urea delivery. E: final urine osmolality output. F: net free-energy flow output.

Fig. 2.

Modified redrawing of Fig. 2 of the original Kokko-Rector paper in simplified form. A: descending limb (DL) values. B: ascending limb (AL) values. C: interstitial values. D: collecting duct values at the outer-inner medullary junction (OIJ). Xs, nonreabsorbable solute, i.e., solutes in the collecting duct other than urea and NaCl viz. all salts, including potassium, ammonium, and organic molecules. E: urine values. Brackets denote concentration. OM, outer medulla; IM, inner medulla; TF/P, tubular fluid-to-plasma concentration ratio.

Fig. 3.

Free-Energy Calculator results for nominal Kokko-Rector values. A: descending limb values. B: ascending limb values. C: ascending (AVR) and descending vasa recta (DVR) values. In the original paper, the mass balance for the vasa recta was not fully specified. To represent the Kokko-Rector model, we assigned the interstitial concentrations assigned in the original paper to both AVR and DVR. D: collecting duct (CD) values. E: urine values. To achieve steady-state mass balance, the urea concentration was calculated to be −2,194 mM, a physically impossible value. Therefore, the nominal Kokko-Rector values were incompatible with mass balance in the inner medulla.

Fig. 4.

Free-Energy Calculator results for modified Kokko-Rector values with adjusted vasa recta concentrations. A: descending limb values. B: ascending limb values. C: ascending and DVR values. The Kokko-Rector value of 938 mM urea in the final urine could be obtained by lowering the AVR and DVR concentration of urea from 625 to 241 mM with a concomitant increase in the Na concentration from 323 to 521 mM. The inner medullary free-energy balance for this steady state was calculated to be 31.8 mJ/min, consistent with a passive mechanism. D: collecting duct values at OIJ. The Kokko-Rector values for urea converted to percent delivery for urea are 174% of the filtered load of urea at the beginning of the inner medullary collecting duct. This requires extensive net urea secretion before the inner medullary collecting duct at sites outside of the inner medulla. E: urine values.

Fig. 5.

Free-Energy Calculator results for modified Kokko-Rector values with no net urea secretion. A: descending limb values. B: ascending limb values. C: AVR and DVR values. D: collecting duct values at OIJ. Urea delivery in the inner medullary collecting duct (IMCD) was lowered to a level that requires no net secretion, that is, a percent delivery of 70%. E: urine values. Here, the urine osmolality was calculated to be 3,006 mosmol/kgH₂O. However, the inner medullary free-energy balance for this condition is negative and is thus inconsistent with a passive concentration of the inner medulla, i.e., it would require an energy input.