Renal countercurrent system: role of collecting duct convergence and pelvic urea predicted from a mathematical model

The Haldane malaria hypothesis: facts, artifacts, and a prophecy

Heterozygous thalassemia and sickle cell disease produce mild hematological symptoms but provide protection against malaria mortality and severe malaria symptoms. Two explanations for resistance are considered in the literature - impaired growth of the parasite or enhanced removal by the host immune cells. A critical overview of studies that connect malaria resistance with impaired intra-erythrocytic growth is presented. All studies are fraught with two kinds of bias. The first one resides in the impossibility of reproducing the in vivo situation in the simplified model in vitro. The second stems from the generalized use of RPMI 1640 culture medium. RPMI 1640 has critically low levels of several amino acids; is devoid of hypoxanthine (essential for parasite growth) and adenine; and is low in reduced glutathione. Analysis of representative studies indicates that impaired parasite growth in heterozygous red blood cells (RBCs) may derive from nutrient limitations and, therefore, possibly be of artefactual origin. This conclusion seems plausible because studies were performed with RPMI 1640 medium at relatively high hematocrit and for prolonged periods of time. Mutations considered are particularly sensitive to nutrient deprivation because they have higher metabolic demands due to permanent oxidant stress related to unpaired globin chains, sickle hemoglobin and high levels of membrane-free iron. In addition, non-parasitized AS- and thalassemic-RBCs are dehydrated and microcytic. Thus, the number of metabolically active elements per unit of blood volume is remarkably larger in mutant RBCs compared to normocytes. The latter point may represent a confirmation of Haldane's prophetic statement: 'The corpuscles of the anaemic heterozygotes are smaller than normal, and more resistant to hypotonic solutions. It is at least conceivable that they are also more resistant to attacks by the sporozoa which cause malaria.'

Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla

Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, epsilon, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting epsilon to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L-1 can be generated by forces of the order of 20 mosm L-1. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.

Effect of varying salt and urea permeabilities along descending limbs of Henle in a model of the renal medullary urine concentrating mechanism

Modelling studies have played an important role in research on the mechanism of urine concentration and dilution by the medulla of the kidney ever since Hargitay and Kuhn (1951, Z. Elektrochem. 55, 539-558) first proposed that the parallel tubular structures in the kidney medulla must function as a "countercurrent multiplication" system. Present-day models, in keeping with our considerably improved understanding of most aspects of medullary structure-function relationships, have evolved into rather sophisticated systems of parallel tubes. In spite of this increasing complexity, it has remained the case that "model medullas" do not concentrate as well as the real kidney, especially in the inner medulla where only passive, diffusional transport occurs. Inasmuch as these models take into account the majority of contemporary ideas making up our global hypothesis about the functioning of this system, their failure to behave physiologically indicates that our understanding remains incomplete. The purpose of the present modelling study was to evaluate the implications of some recent measurements showing that permeabilities of NaCl (Ps) and urea (Pu) vary along the length of the descending thin limbs of Henle (Imai et al., 1988, Am. J. Physiol. 254, F323-F328), rather than being constant throughout this segment as had been assumed earlier. It was hoped that these newly measured values might explain, by a passive, diffusional process, the net solute addition at the bend of Henle's loop observed under some circumstances and heretofore attributed (though without any supporting experimental evidence) to active transport into the descending limb. The results of the present study show that whereas incorporation of the new values for Ps and Pu in the descending limbs of short nephrons does indeed improve the concentrating power of the model, these new values are nonetheless not sufficient to allow the model to build an osmolarity gradient that increases all the way through the inner medulla. This failing, which is common to virtually all modelling studies to date using measured values from rat kidneys, probably points to a key role for preferential exchange supposed by some to exist among certain tubule segments within vascular bundles in species whose kidneys have the highest concentrating power.

Countercurrent system

Urinary concentration is achieved by countercurrent multiplication in the inner medulla. The single effect in the outer medulla is active NaCl absorption from the thick ascending limb. While the single effect in the inner medulla is not definitively established, the majority of experimental data favors passive NaCl absorption from the thin ascending limb. Continued experimental studies in inner medullary nephron segments will be needed to elucidate fully the process of urinary concentration.

Mathematical analysis of multisolute renal flow in a single nephron model of the kidney

A single nephron model, which includes the Bowman's space, Cortical interstitium, and Pelvis as well-stirred baths, is investigated. A boundary value problem, which allows for pelvic reflux, is established for the fluid-multisolute flow in the nephron. The implicit function theorem is used to establish the existence and uniqueness of a solution of the boundary value problem for the case of small permeability coefficients and transport rates.

Urea permeability of mammalian inner medullary collecting duct system and papillary surface epithelium

To compare passive urea transport across the inner medullary collecting ducts (IMCDs) and the papillary surface epithelium (PSE) of the kidney, two determinants of passive transport were measured, namely permeability coefficient and surface area. Urea permeability was measured in isolated perfused IMCDs dissected from carefully localized sites along the inner medullas of rats and rabbits. Mean permeability coefficients (X 10(-5) cm/s) in rat IMCDs were: outer third of inner medulla (IMCD1), 1.6 +/- 0.5; middle third (IMCD2), 46.6 +/- 10.5; and inner third (IMCD3), 39.1 +/- 3.6. Mean permeability coefficients in rabbit IMCDs were: IMCD1, 1.2 +/- 0.1; IMCD2, 11.6 +/- 2.8; and IMCD3, 13.1 +/- 1.8. The rabbit PSE was dissected free from the underlying renal inner medulla and was mounted in a specially designed chamber to measure its permeability to urea. The mean value was 1 X 10(-5) cm/s both in the absence and presence of vasopressin (10 nM). Morphometry of renal papillary cross sections revealed that the total surface area of IMCDs exceeds the total area of the PSE by 10-fold in the rat and threefold in the rabbit. We conclude: the IMCD displays axial heterogeneity with respect to urea permeability, with a high permeability only in its distal two-thirds; and because the urea permeability and surface area of the PSE are relatively small, passive transport across it is unlikely to be a major source of urea to the inner medullary interstitium.

On the solution of equations for renal counterflow models

The results of a comparative study of three discretization techniques and the solution of the resulting algebraic equations by three methods is given. For this study, a four-tube central core model with diffusion in the core was selected and equations were derived for a coherent and efficient implementation. The results of this study show that sparse matrix techniques that take the physiological connectivity of the kidney lead to significant savings in computer storage, running time and overall cost.

Membrane cross bonding in red cells in favic crisis: a missing link in the mechanism of extravascular haemolysis

Red cells of G6PD (D-glucose-6-phosphate:NADP+ 1-oxidoreductase; G6PD) deficient (Mediterranean variant) subjects were studied during a fava bean haemolytic crisis. Two representative cases are described. In Case 1, haemolysis was still going on. In more than 50% of the red cells the Hb was confined to one part of the cell, leaving the other part as transparent as a Hb-free ghost. In this part the membranes appeared tightly bonded because swelling did not peel apart the bonded membrane areas. This feature is defined as membrane cross bonding (MCB). In Case 2, haemolysis had terminated and MCB-cells were less than 1%. MCB was reproduced in vitro by incubating G6PD-deficient whole blood with 1 mM divicine for up to 10 h. Subsequent shrinkage of red cells in hypertonic plasma (400 mOsm) resulted in the rapid formation of MCB. Membrane modifications by divicine, contained in fava beans, followed by osmotic shrinkage in the kidney and/or squeezing in the microcirculation are proposed as the cause of MCB during the favic crisis. MCB reduces the effective surface area of red cells. This is a plausible cause for sequestration by the reticulo-endothelial system. Intravascular haemolysis observed in favic crisis cannot be explained by mechanical forces, but it is possible that the effective surface area is reduced by MCB to such an extent that red cells lyse osmotically.

Examination of transepithelial exchange of water and solute in the rat renal pelvis

Severance of the ureter beyond the renal papilla causes a fall in urinary osmolality, which suggests that exchange of water or solute between urine and renal parenchyma normally occurs in the intact renal pelvis. We examined water and solute flux in the renal pelvis with micropuncture and microcatheterization techniques. Four groups of antidiuretic rats were studied. Group I (n = 17) underwent micropuncture through the intact contracting ureter. Urine samples were obtained at the papillary tip, and in the pelvis beside the base of the extrarenal papilla. Urinary osmolality at the base, 880 +/- 97 mosmol/kg H2O (mean +/- SE), was less than that at the tip, 1,425 +/- 104 mosmol/kg H2O (P less than 0.005). In group II (n = 24), samples were analyzed for inulin and osmolality. In 15 rats (group IIA), comparison was made between base and tip samples. In the other nine animals (group IIB), comparisons were made among base, tip, and bladder samples and urea was also measured. In group II (A and B combined) urine-to-plasma (U/P) osmolality was lower at the base, 4.31 +/- 0.27, than at the tip, 6.08 +/- 0.23 (P less than 0.001), and U/P inulin was lower at the base, 192 +/- 25, than at the tip, 306 +/- 16 (P less than 0.001). In group IIB, the bladder urine had a lower U/P osmolality, 5.27 +/- 0.25, than the tip, 6.01 +/- 0.31 (P less than 0.02). The U/P urea was 59 +/- 10.6 (base), 98 +/- 9.4 (tip) (base vs. tip, P less than 0.05), and 81 +/- 6.5 (bladder, P less than 0.005, compared with tip). In group III (n = 8), samples were obtained by microcatheter from the fornices, the deepest intrarenal extensions of the pelvis, and compared with samples at the tip. Urinary osmolality was lower in the fornix, 646 +/- 106 mosmol/kg H2O, than at the tip, 1,296 +/- 99 mosmol/kg H2O (P less than 0.001). Similarly, U/P inulin was lower in the fornix, 48 +/- 14, than at the tip, 128 +/- 12 (P less than 0.001). The lower U/P inulin in the pelvic urine is the result of either the addition of fluid to the pelvis, or the backleak of inulin across the epithelium lining the pelvis. To verify that the pelvic epithelium was impermeable to inulin, in group IVA (n = 4) the left renal pelvis was superfused with a solution of chemical inulin. Cumulative absorption of inulin from the left kidney was 0.15 +/- 0.08% of that superfused. Using [14C]inulin in group IVB (n= 3), similar results were obtained (0.05 +/- 0.02%). These findings indicate that in the renal pelvis, fluid is added to urine after it emerges from the collecting ducts. We suggest that reflux of hyperosmotic urine over the renal papilla creates a transepithelial gradient for the flux of water into the pelvis. A model that incorporates diffusive and convective forces for water and solute transport is proposed to account for these findings.

Mechanism of action of divicine in a cell-free system and in glucose-6-phosphate dehydrogenase-deficient red cells

Favism is an acute hemolysis occurring in glucose-6-phosphate dehydrogenase (G6PD)-deficient (Mediterranean variant) individuals after intake of fava beans. Divicine (D), 2,6-diamino-4,5-dihydroxypyrimidine, is present in high amounts in the beans, and is suspected to play a role in hemolysis. Its mechanism of action was studied in a cell-free system and in G6PD (Mediterranean variant)-deficient red cells (RBC). Upon hydrolysis of the inactive beta-glucoside vicine, reduced divicine is formed. Oxygen acts as a one- or two-electron acceptor; superoxide anion and hydrogen peroxide are formed, respectively, together with the semiquinoid free-radical form of D. This free radical gives an electron spin resonance (ESR) signal, which is similar to that of the alloxan free radical. Added reduced glutathione (GSH) is rapidly oxidized with a stoichiometry of one to one, and the ESR signal is abolished. Additional GSH is oxidized by hydrogen peroxide and by a slow redox cycle which continuously regenerates oxidized D. The fast-direct and the slow-indirect oxidation result in nonstoichiometric oxidation of GSH. D added to G6PD-deficient RBC rapidly oxidizes GSH with an end point kinetics and a stoichiometry of one to one. Hydrogen peroxide and superoxide anion are scavenged in the RBC and no redox cycling is taking place. No GSH is regenerated even after long incubation periods. After the primary event, i.e., oxidation of GSH and--SH groups, a number of metabolic, rheologic, and membrane modifications, together with increased erythrophagocytosis take place in G6PD-deficient, D-treated RBC only.(ABSTRACT TRUNCATED AT 250 WORDS)