Angiotensin II production and distribution in the kidney: I. A kinetic model
2006; Elsevier BV; Volume: 69; Issue: 9 Linguagem: Inglês
10.1038/sj.ki.5000303
ISSN1523-1755
AutoresMaarten A.D.H. Schalekamp, A.H. Jan Danser,
Tópico(s)Hormonal Regulation and Hypertension
ResumoInformation on the levels of angiotensin II (Ang II) and its receptors in the various renal tissue compartments is still incomplete. A model is presented describing the kinetics of Ang II production, distribution, and disposal in the renal cortex. Basic features are: (1) the model is designed to derive, from Ang II measurements in blood and in whole tissue, estimates of the local densities of the Ang II type 1 (AT1) and type 2 (AT2) receptors, and to calculate the concentrations of endocrine and paracrine Ang II they actually 'see'; (2) glomerular and peritubular tissue are conceived as separate regions (glomerular region (Glom), peritubular region (Pt)); (3) in Glom and in Pt, Ang II is homogeneously distributed in capillary blood and in interstitial fluid; (4) the model allows for local Ang II concentration gradients between interstitium and blood; (5) Ang II from the circulation diffuses into the interstitium of Glom after convective transcapillary transport; (6) Ang II produced in tubules or Pt enters the microcirculation through diffusive overflow from interstitium; (7) the presence of cell-surface-bound Ang II depends on the reaction with AT1 and AT2 receptors, and the presence of intracellular Ang II depends on the internalization of Ang II – AT1 receptor complex; and (8) the model provides for glomerular filtration, vasopeptidase-mediated degradation, and intracellular degradation as mechanisms of elimination. This model can serve as a framework for detailed quantitative studies of the renin–angiotensin system in the kidney. Information on the levels of angiotensin II (Ang II) and its receptors in the various renal tissue compartments is still incomplete. A model is presented describing the kinetics of Ang II production, distribution, and disposal in the renal cortex. Basic features are: (1) the model is designed to derive, from Ang II measurements in blood and in whole tissue, estimates of the local densities of the Ang II type 1 (AT1) and type 2 (AT2) receptors, and to calculate the concentrations of endocrine and paracrine Ang II they actually 'see'; (2) glomerular and peritubular tissue are conceived as separate regions (glomerular region (Glom), peritubular region (Pt)); (3) in Glom and in Pt, Ang II is homogeneously distributed in capillary blood and in interstitial fluid; (4) the model allows for local Ang II concentration gradients between interstitium and blood; (5) Ang II from the circulation diffuses into the interstitium of Glom after convective transcapillary transport; (6) Ang II produced in tubules or Pt enters the microcirculation through diffusive overflow from interstitium; (7) the presence of cell-surface-bound Ang II depends on the reaction with AT1 and AT2 receptors, and the presence of intracellular Ang II depends on the internalization of Ang II – AT1 receptor complex; and (8) the model provides for glomerular filtration, vasopeptidase-mediated degradation, and intracellular degradation as mechanisms of elimination. This model can serve as a framework for detailed quantitative studies of the renin–angiotensin system in the kidney. The renin–angiotensin system is part of the complex regulation of blood pressure, renal function, and body sodium and water homeostasis. The most important biologically active end product of this system, angiotensin (Ang) II, is thought to act both as a circulating hormone and as a paracrine factor. The physiological significance of paracrine Ang II, as opposed to circulating Ang II, is still not well understood. In humans, under normal conditions, the concentration of Ang II in blood plasma is approximately 10 pM at a daily sodium intake typical of Western industrialized countries,1Nussberger J. Brunner D.B. Waeber B. Brunner H.R. True versus immunoreactive angiotensin II in human plasma.Hypertension. 1985; 7: I1-I7Google Scholar, 2Admiraal P.J.J. Danser A.H.J. Jong M.S. et al.Regional angiotensin II production in essential hypertension and renal artery stenosis.Hypertension. 1993; 21: 173-184Google Scholar which is close to the threshold level required to elicit a physiological response. After dietary sodium restriction, either alone or in combination with the use of a diuretic, Ang II can increase 10-fold. Under pathological conditions, it can increase 100-fold or even more. In anesthetized animals, the concentration of circulating Ang II is often higher than the levels normally encountered in humans. In humans as well as in anesthetized animals, the Ang II concentration in some tissues (per gram of tissue), including the kidney, is higher than in plasma (per ml).3Campbell D.J. Kladis A. Duncan A.M. Nephrectomy, converting enzyme inhibition, and angiotensin peptides.Hypertension. 1993; 22: 513-522Google Scholar, 4Danser A.H.J. van Kats J.P. Admiraal P.J.J. et al.Cardiac renin and angiotensins. Uptake from plasma versus in situ synthesis.Hypertension. 1994; 24: 37-48Google Scholar, 5Campbell D.J. Duncan A.M. Kladis A. Angiotensin-converting enzyme inhibition modifies angiotensin but not kinin peptide levels in human atrial tissue.Hypertension. 1999; 34: 171-175Google Scholar, 6Nussberger J. Circulating versus tissue angiotensin II.in: Epstein M. Brunner H.R. Angiotensin II Receptor Antagonists. Hanley & Belfus Inc., Philadelphia2000: 69-78Google Scholar, 7van Kats J.P. Schalekamp M.A.D.H. Verdouw P.D. et al.Intrarenal angiotensin II: interstitial and cellular levels and site of production.Kidney Int. 2001; 60: 2311-2317Google Scholar Some authors measured Ang II levels in the nanomolar range in cardiac and renal tissue fluid,8Seikaly M.G. Arant Jr, B.S. Seney Jr, F.D. Endogenous angiotensin concentrations in specific intrarenal fluid compartments of the rat.J Clin Invest. 1990; 86: 1352-1357Google Scholar, 9Dell'Italia L.J. Meng Q.C. Balcells E. et al.Compartmentalization of angiotensin II generation in the dog heart. Evidence for independent mechanisms in intravascular and interstitial spaces.J Clin Invest. 1997; 100: 253-258Google Scholar, 10Siragy H.M. Howell N.L. Ragsdale N.V. Carey R.M. Renal interstitial fluid angiotensin. Modulation by anesthesia, epinephrine, sodium depletion, and renin inhibition.Hypertension. 1995; 25: 1021-1024Google Scholar, 11Nishiyama A. Seth D.M. Navar L.G. Renal interstitial fluid angiotensin I and angiotensin II concentrations during local angiotensin-converting enzyme inhibition.J Am Soc Nephrol. 2002; 13: 2207-2212Google Scholar which would fit with the value of the equilibrium dissociation constant of the Ang II–Ang II type 1 (AT1) receptor and Ang II–Ang II type 2 (AT2) receptor reactions (Kd=1–2 nM). According to others, however, the interstitial fluid levels are much lower.7van Kats J.P. Schalekamp M.A.D.H. Verdouw P.D. et al.Intrarenal angiotensin II: interstitial and cellular levels and site of production.Kidney Int. 2001; 60: 2311-2317Google Scholar, 12Wilcox C.S. Dzau V.J. Effect of captopril on the release of the components of the renin–angiotensin system into plasma and lymph.J Am Soc Nephrol. 1992; 2: 1241-1250Google Scholar, 13Campbell D.J. Alexiou T. Xiao H.D. et al.Effect of reduced angiotensin-converting enzyme gene expression and angiotensin-converting enzyme inhibition on angiotensin and bradykinin peptide levels in mice.Hypertension. 2004; 43: 854-859Google Scholar Rather, it now appears that Ang II in the tissue is cell-associated owing to its binding to cell surface AT1 and possibly also AT2 receptors. Studies in rats demonstrated AT1-receptor-dependent intrarenal accumulation of systemically infused Ang II14Zou L.X. Imig J.D. von Thun A.M. et al.Receptor-mediated intrarenal angiotensin II augmentation in angiotensin II-infused rats.Hypertension. 1996; 28: 669-677Google Scholar and provided evidence of AT1 receptor-mediated renal uptake of endogenous Ang II after dietary salt restriction.15Ingert C. Grima M. Coquard C. et al.Effects of dietary salt changes on renal renin–angiotensin system in rats.Am J Physiol Renal Physiol. 2002; 283: F995-1002Google Scholar The binding to cell surface AT1 receptors is known to be followed by rapid internalization of Ang II–AT1 receptor complex.16Thomas W.G. Thekkumkara T.J. Baker K.M. Molecular mechanisms of angiotensin II (AT1A) receptor endocytosis.Clin Exp Pharmacol Physiol. 1996; 32: S74-S80Google Scholar Experiments in pigs showed that intact 125I-Ang II from the circulation was accumulated in cardiac, renal, and adrenal tissue, and that the uptake of 125I-Ang II was greatly reduced after the animals had been treated with an AT1 receptor antagonist.17van Kats J.P. de Lannoy L.M. Danser A.H.J. et al.Angiotensin II type 1 (AT1) receptor-mediated accumulation of angiotensin II in tissues and its intracellular half-life in vivo.Hypertension. 1997; 30: 42-49Google Scholar The steady-state tissue/blood 125I-Ang II concentration ratio was adrenal>kidney>heart, which is in accordance with the order of AT1 receptor density in these tissues as well as with the order of endogenous Ang II concentration.3Campbell D.J. Kladis A. Duncan A.M. Nephrectomy, converting enzyme inhibition, and angiotensin peptides.Hypertension. 1993; 22: 513-522Google Scholar, 4Danser A.H.J. van Kats J.P. Admiraal P.J.J. et al.Cardiac renin and angiotensins. Uptake from plasma versus in situ synthesis.Hypertension. 1994; 24: 37-48Google Scholar, 7van Kats J.P. Schalekamp M.A.D.H. Verdouw P.D. et al.Intrarenal angiotensin II: interstitial and cellular levels and site of production.Kidney Int. 2001; 60: 2311-2317Google Scholar, 17van Kats J.P. de Lannoy L.M. Danser A.H.J. et al.Angiotensin II type 1 (AT1) receptor-mediated accumulation of angiotensin II in tissues and its intracellular half-life in vivo.Hypertension. 1997; 30: 42-49Google Scholar Published results of Ang II measurements in blood plasma, in tissue extracellular fluid, and in whole tissue raise a number of important questions. How can circulating, endocrine, Ang II act at such a low concentration? What are the local AT1 and AT2 receptor concentrations in tissue? What are the Ang II concentrations the AT1 and AT2 receptors in tissue actually 'see'? How much of it is of local, paracrine, origin? This paper focuses on the kidney and, to address the above questions, a quantitative model is presented describing the kinetics of the intrarenal production, distribution, and elimination of Ang II. The model is designed as a tool to calculate the intrarenal levels of extracellular and cell-bound Ang II as well as to estimate the local concentrations of cell surface AT1 and AT2 receptors, from Ang II measurements in blood plasma and in whole tissue. The aim of the model also is to provide for separate estimates of endocrine and paracrine Ang II levels. Tables 1 , 2 and 3 provide a list of abbreviations, symbols, and definitions, as well as the values of the various physical parameters and kinetic constants. An important feature is the distinction between endocrine Ang II (IIa) delivered to the tissue via the renal artery and paracrine Ang II (IIi) that is produced intrarenally. Ang IIa and Ang IIi in renal venous plasma and in tissue can be measured separately in samples obtained from animals receiving systemic infusions of radiolabeled Ang I or II.7van Kats J.P. Schalekamp M.A.D.H. Verdouw P.D. et al.Intrarenal angiotensin II: interstitial and cellular levels and site of production.Kidney Int. 2001; 60: 2311-2317Google Scholar, 17van Kats J.P. de Lannoy L.M. Danser A.H.J. et al.Angiotensin II type 1 (AT1) receptor-mediated accumulation of angiotensin II in tissues and its intracellular half-life in vivo.Hypertension. 1997; 30: 42-49Google Scholar Similarly, separate measurements of Ang Ia and Ang Ii can be obtained during a systemic infusion of radiolabeled Ang I.Table 1Abbreviations, symbols, and definitionsSymbol or abbreviationDefinitionRenal compartments PaRenal arterial plasma PvRenal venous plasma PcCapillary plasma IsfInterstitial fluid TbTubular region of renal cortex TRenal cortex GlomGlomerular region PtPeritubular region of renal cortex CsCell surface CeCell interiorAngiotensins from different sources IAng I IIAng II IIaArterially delivered Ang II IIiIntrarenally produced Ang IIAngiotensin in different compartments IIPa, IIPvPlasma Ang II in renal artery, vein IIPcGlom, IIPcPtPlasma Ang II in glomerular, peritubular capillaries IIIsfGlom, IIIsfPtAng II in glomerular, peritubular interstitial fluid IIC1AT1 receptor-dependent cell-associated (surface-bound and intracellular) Ang II IIC1Glom, IIC1PtAT1 receptor-dependent cell-associated Ang II in glomerular, peritubular region IICs1Glom, IICs1PtAng II bound to cell surface AT1 receptors in glomerular, peritubular region IICs2PtAng II bound to cell surface AT2 receptors in peritubular region IITAng II in renal cortex IITbAng II in tubular fluidReceptors AT1RCsGlom, AT1RCsPtCell surface AT1 receptors in glomerular, peritubular region AT2RCsPtCell surface AT2 receptors in peritubular regionConcentrations CI, CIIConcentration of Ang I, Ang II CAT1R, CAT2RConcentration of AT1-, AT2 receptors (CI)1,2, (CII)1,2Concentration of Ang I, Ang II in the absence of AT1- and AT2 receptor blockade (CI)1, (CII)1Concentration of Ang I, Ang II in the presence of AT2 receptor blockade (CI)2, (CII)2Concentration of Ang I, Ang II in the presence of AT1 receptor blockadeElimination mechanisms VMDVasopeptidase-mediated degradation RMEAT1 receptor-mediated endocytosis ClRMEClearance by RMEPhysical parameters VPcGlom, VPcPtVolume of glomerular, peritubular capillary blood plasma VIsfGlom, VIsfPtVolume of glomerular, peritubular interstitial fluid QRenal cortical plasma flow FFFiltration fraction ClDiffPtDiffusive clearance across peritubular capillariesKinetic constants KdEquilibrium dissociation constant of the Ang II–AT1 and Ang II–AT2 receptor reactions kassRate constant for Ang II–AT1 receptor complex formation kdissRate constant for Ang II–AT1 receptor complex dissociation kintRate constant for AT1 receptor-mediated Ang II endocytosis klysRate constant for (lysosomal) intracellular Ang II degradation ktelRate constant for the elimination of cell-associated (surface-bound and intracellular) Ang II Open table in a new tab Table 2Units of parametersConcentrations CIIPa CIIPv, CIIPcmol/ml of blood plasma CIIIsf, CIICsmol/ml of interstitial fluid CIITb, CIIT, CIIC1mol/g of renal cortex CAT1RCs, CAT2RCsmol/ml of interstitial fluidPhysical parameters and kinetic constants VPc, VIsfml/g of renal cortex Q, ClDiffPt, ClRMEml/min per g of renal cortex Kdmol/ml kass/(mol/ml) per min kdiss, kint, klys, ktelmin−1 RMEIImol/min per g of renal cortex VMDI, VMDIImol/min per g of renal cortex Open table in a new tab Table 3Values of physical parameters and kinetic constantsParameterValueReferenceVIsfGlom(5) × 10−3/ml per g33Tisher C.C. Madsen K.M.M. Anatomy of the kidney.in: Brenner J.M. Rector F.C. The Kidney. WB Saunders Company, Philadelphia1991: 3-75Google ScholarVIsfPt0.1 ml/g33Tisher C.C. Madsen K.M.M. Anatomy of the kidney.in: Brenner J.M. Rector F.C. The Kidney. WB Saunders Company, Philadelphia1991: 3-75Google ScholarQ2 ml/min per g34Sassen L.M. Duncker D.J. Gho B.C. et al.Haemodynamic profile of the potassium channel activator EMD 52692 in anaesthetized pigs.Br J Pharmacol. 1990; 101: 605-614Google ScholarFF0.2035Hvistendahl J.J. Pedersen T.S. Jorgensen H.H. et al.Renal hemodynamic response to gradated ureter obstruction in the pig.Nephron. 1996; 74: 168-174Google ScholarClDiffPt0.3 ml/min per gSee textKd (for AT1 – and AT2 receptors)(1.5) × 10−12 mol/ml36Boissier J.R. Lechat P. Fichelle J. Advances in pharmacology and therapeutics.in: Proceedings of the Seventh International Congress of Pharmacology. Pergamon Press, Paris1978: 279-289Google Scholar, 37Verheijen I. Fierens F.L. Debacker J.P. et al.Interaction between the partially insurmountable antagonist valsartan and human recombinant angiotensin II type 1 receptors.Fund Clin Pharmacol. 2000; 14: 577-585Google Scholarkass (for AT1 receptors)(2.4) × 1010/(mol/ml) per min36Boissier J.R. Lechat P. Fichelle J. Advances in pharmacology and therapeutics.in: Proceedings of the Seventh International Congress of Pharmacology. Pergamon Press, Paris1978: 279-289Google Scholarkdiss (for AT1 receptors)(3.6) × 10−2 min−1Derived from Kd and kassktel(2.7) × 10−2 min−117van Kats J.P. de Lannoy L.M. Danser A.H.J. et al.Angiotensin II type 1 (AT1) receptor-mediated accumulation of angiotensin II in tissues and its intracellular half-life in vivo.Hypertension. 1997; 30: 42-49Google Scholarkint(35) × 10−2 min−1See textklys(2.9) × 10−2 min−1Derived from ktel and kint (see Eq. (13)) Open table in a new tab The model considers three cortical tissue regions, the glomerular region (Glom), the tubular region (Tb), and the peritubular region (Pt). The glomerular capillary plasma and interstitial fluid compartments (PcGlom, IsfGlom) are connected in series with the corresponding peritubular compartments (PcPt, IsfPt). The two plasma compartments are connected via the glomerular efferent arterioles, and the two interstitial fluid compartments are connected via the interstitium at the level of the glomerular vascular pole (Figure 1 ). Ang I and II from blood reach the glomerular ultrafiltrate via the glomerular capillaries by convection, and it is assumed that some Ang II, after its passage through the capillary endothelium, reaches glomerular (mesangial) cell surface receptors by diffusion into the interstitium (Figure 2 ). Binding of Ang II to cell surface AT1 receptors, but not AT2 receptors, is followed by internalization of the Ang II–AT1 receptor complex and degradation of Ang II by intracellular (lysosomal) enzymes.16Thomas W.G. Thekkumkara T.J. Baker K.M. Molecular mechanisms of angiotensin II (AT1A) receptor endocytosis.Clin Exp Pharmacol Physiol. 1996; 32: S74-S80Google Scholar, 18Matsubara H. Pathophysiological role of angiotensin II type 2 receptor in cardiovascular and renal diseases.Circ Res. 1998; 83: 1182-1191Google Scholar Free Ang I and II in glomerular interstitial fluid are thought to be homogeneously distributed, under steady-state conditions. It is further assumed that the release of intrarenally produced Ang I and II into the renal interstitial fluid is confined to the peritubular tissue region. The exact sites of Ang I and II production in the kidney are not known, but an extensive series of micropuncture experiments in rats by Navar and co-workers have shown that the levels of Ang I and II in proximal tubular fluid are 10 to 100 times higher than in blood plasma, and that angiotensinogen is also present in high concentrations in proximal tubular fluid.19Navar L.G. Harrison-Bernard L.M. Nishiyama A. Kobori H. Regulation of intrarenal angiotensin II in hypertension.Hypertension. 2002; 39: 316-322Google Scholar, 20Navar L.G. Harrison-Bernard L.M. Intrarenal angiotensin II augmentation in angiotensin II dependent hypertension.Hypertens Res. 2000; 23: 291-301Google Scholar These experiments also provided evidence to support that Ang I and II as well as angiotensinogen are secreted by the proximal tubular cells into the tubular fluid.20Navar L.G. Harrison-Bernard L.M. Intrarenal angiotensin II augmentation in angiotensin II dependent hypertension.Hypertens Res. 2000; 23: 291-301Google Scholar, 21Braam B. Mitchell K.D. Fox J. Navar L.G. Proximal tubular secretion of angiotensin II in rats.Am J Physiol. 1993; 264: F891-F898Google Scholar The intrarenal localization of angiotensin-converting enzyme (ACE) at the brush border of proximal tubular cells is in accordance with this hypothesis.22Metzger R. Bohle R.M. Pauls K. et al.Angiotensin-converting enzyme in non-neoplastic kidney diseases.Kidney Int. 1999; 56: 1442-1454Google Scholar In our model, a net transport of Ang I and II is therefore assumed to exist from tubular fluid into the peritubular interstitial fluid compartment and from there into the peritubular capillaries (Figure 3 ). The capillary–interstitial exchange of Ang I and II in the Pt is thought to depend on diffusion, and here our analysis, while allowing for the existence of an endothelial diffusion barrier, follows the so-called tissue homogeneity model.23Wilkinson G.R. Clearance approaches in pharmacology.Pharmacol Rev. 1987; 39: 1-47Google Scholar According to this model, capillary entrances and exits are randomly distributed throughout the tissue, and the interstitial fluid compartment as well as the plasma compartment in capillaries and veins are conceived as being well-mixed. The model implies that the presence of cell-associated Ang II in the renal cortex depends on the binding of extracellular Ang II to cell surface AT1 and AT2 receptors. Experiments using systemic infusions of 125I-Ang I or II in pigs showed more than 90% reduction of the tissue/blood 125I-Ang II concentration ratio in the renal cortex after AT1 receptor antagonist treatment.7van Kats J.P. Schalekamp M.A.D.H. Verdouw P.D. et al.Intrarenal angiotensin II: interstitial and cellular levels and site of production.Kidney Int. 2001; 60: 2311-2317Google Scholar This indicates that indeed the bulk of arterially delivered Ang II is cell-associated as a consequence of its reaction with AT1 receptors. Cell fractionation studies of porcine renal cortical tissue, with the use of differential centrifugation, indicated that not only most of systemically infused 125I-Ang II but also most endogenous Ang II is bound to cell organelles, whereas exogenous and endogenous Ang II were similarly distributed over the various subcellular fractions.24van Kats J.P. van Meegen J.R. Verdouw P.D. et al.Subcellular localization of angiotensin II in kidney and adrenal.J Hypertens. 2001; 19: 583-589Google Scholar Similar data were obtained by others.25Imig J.D. Navar G.L. Zou L.X. et al.Renal endosomes contain angiotensin peptides, converting enzyme, and AT(1A) receptors.Am J Physiol. 1999; 277: F303-F311Google Scholar, 26Zou L.X. Imig J.D. Hymel A. Navar L.G. Renal uptake of circulating angiotensin II in Val5-angiotensin II infused rats is mediated by AT1 receptor.Am J Hypertens. 1998; 11: 570-578Google Scholar The concept set out above leads to the following steady-state equations:CIaIsfGlom=CIPa(1) CIaIsfGlom=CIIPa-RMEIIaGlom/(QFF)(2) CIaISfPt=CIaPv(3) CIIaIsfpt=CIIaPv-RMEIIapt/CIDiffPt(4) Concerning the elimination of extracellular Ang IIa, the model provides for the following mechanisms: glomerular filtration, vasopeptidase-mediated degradation, and AT1 receptor-mediated endocytosis. It is known that only a small fraction of systemically infused Ang I is converted into Ang II in the kidney,27Danser A.H.J. Admiraal P.J.J. Derkx F.H.M. Schalekamp M.A.D.H. Angiotensin I-to-II conversion in the human renal vascular bed.J Hypertens. 1998; 16: 2051-2056Google Scholar and studies in pigs, with the use of infusions of either 125I-Ang I or 125I-Ang II, justify the conclusion that, for the purpose of the present analysis, Ang I–II conversion by renal vasopeptidase can be ignored and that the degradation rate constants are similar for Ang I and II.17van Kats J.P. de Lannoy L.M. Danser A.H.J. et al.Angiotensin II type 1 (AT1) receptor-mediated accumulation of angiotensin II in tissues and its intracellular half-life in vivo.Hypertension. 1997; 30: 42-49Google Scholar, 28Danser A.H.J. Koning M.M.G. Admiraal P.J.J. et al.Metabolism of angiotensin I by different tissues in the intact animal.Am J Physiol. 1992; 263: H418-H428Google Scholar, 29Danser A.H.J. Koning M.M.G. Admiraal P.J.J. et al.Production of angiotensins I and II at tissue sites in intact pigs.Am J Physiol. 1992; 263: H429-H437Google Scholar The rate of vasopeptidase-mediated degradation of Ang Ia into peptides other than Ang II, at steady state, is therefore given byVMDIa=CIPaQ(1-FF-CIaPv/CIPa)(5) Similarly,VMDIIa=CIIPaQ(1-FF-CIaPv/CIPa)(6) As mentioned above, experiments using systemic infusions of 125I-Ang I or II in pigs indicate that the bulk of Ang IIa present in tissue is cell-associated as a consequence of its reaction with AT1 receptors. Ang IIa, after its binding to cell surface AT1 receptors, reaches the cell interior through AT1 receptor-mediated endocytosis. For the purpose of the present analysis, it can be stated thatCIIaT=CIIaC1(7) CIIaC1=CIIaCs1VIsf+CIIaCe1(8) Steady-state equations describing the binding of Ang IIa to cell surface AT1 receptors, its internalization and its intracellular degradation areCIIaIsfCAT1RCskass=CIIaCs1(kdiss+kint)(9) RMEIIa=CIIaCs1V1sfkint(10) CIIaCs1V1sfkint=CIIaCe1k1ys(11) The experiments in pigs mentioned above showed a quasi-mono-exponential decrease of 125I-Ang II from the renal cortex after the infusion of tracer had been stopped. It can therefore be stated thatRMEIIa=CIIaTktel(12) From Eqs. (7), (8), and (10), (11) and (12), it follows thatktel=kintklys(kint+klys)(13) In accordance with Eqs. (7) and (12), it follows from Eqs. (2) and (4) thatCIIaIsfGlom=CIIpa−CIIaC1Glomktel/(QFF)(14) CIIaIsfpt=CIIaPv−CIIaC1ptktel/CIDiffpt(15) The implicit assumption underlying Eqs. (14) and (15) is that ktel has the same value in the glomerular and peritubular tissue regions. In Eqs. (5), (6), and (12), the rates of vasopeptidase-mediated Ang Ia and IIa degradation and the rate of AT1 receptor-mediated Ang IIa endocytosis are expressed as a function of the plasma concentration of Ang I in the renal artery, the concentrations of Ang Ia and Ang IIa in the renal vein, and the total tissue concentration of Ang IIa in the renal cortex. These independent variables can be measured. The contribution of Ang I that is produced in the renal microcirculation by the action of circulating renin to the total concentration of Ang Ii in the renal vein is very small.29Danser A.H.J. Koning M.M.G. Admiraal P.J.J. et al.Production of angiotensins I and II at tissue sites in intact pigs.Am J Physiol. 1992; 263: H429-H437Google Scholar It can be ignored for the purpose of the present analysis and, as set out above, the same can be said for the Ang I–II conversion by renal vasopeptidase. It can therefore be stated that the spillover of Ang Ii and IIi into the microcirculation is given by the sum of the vasopeptidase-mediated degradation rate and the outflow via the renal vein. In Eqs. (5) and (6) the rates of vasopeptidase-mediated Ang Ia and IIa degradation are expressed as a fraction of the rate of delivery via the renal artery, the fraction being equal to (1-FF-CIaPv/CIPa). The rates of vasopeptidase-mediated Ang Ii and IIi degradation can be expressed in a similar way, as a fraction of the spillover rate, so thatSpillover Ii=CIiPvQ/(FF+CIapv/CIPa)(16) Spillover IIi=CIIiPvQ/(FF+CIapv/CIPa)(17) VMDIi=CIipvQ[1/(FF+CIapv/CIPa)−1](18) VMDIIi=CIIipvQ[1/(FF+CIapv/CIPa)−1](19) Spillover of Ang Ii and IIi into the microcirculation is related to the concentration gradient across the peritubular capillaries, as follows:Spillover Ii=(CIiIsfPt-CIiPv)ClDiffPt(20) Spillover IIi=(CIIiIsfPt-CIIiPv)ClDiffPt(21) From Eqs. (16), (17), (20), and (21), it follows thatCIiIsfPt=αCIiPv(22) CIIiIsfPt=αCIIiPv(23) whereα=1+Q/[(FF+CIaPv/CIPa)C1DiffPt](24) In Eqs. (16), (17), (18) and (19) and (22), (23) and (24), the spillover of Ang Ii and IIi into the microcirculation, the degradation of Ang Ii and IIi by vasopeptidases, and the concentrations of Ang Ii and IIi in interstitial fluid are expressed as a function of the plasma concentration of Ang I in the renal artery and the concentrations of Ang Ia, Ii, and IIi in the renal vein. These independent variables can be measured. In our model, it is assumed that Ang I in tissue is confined to the extracellular fluid compartments so that, in the absence of Ang I production in the glomerular tissue region, under steady-state conditionsCIiT=CIiPcPtVPcPt+CIiIsfPtVIsfPt+CIiTb(25) We further define the distribution of Ang Ii byβ=CIiTb/(CIiIsfPtVIsfPt)(26) With respect to the distribution of Ang IIi in the presence of AT1 receptor blockade and in the absence of AT1 and AT2 receptor blockade, the notations β2 and β1,2, respectively, are used. This distinction is necessary, because the clearance of Ang IIi from peritubular interstitial fluid, in contrast with the clearance of Ang Ii, does not only depend on diffusion into blood but also on AT1 receptor-mediated endocytosis. Anatomically, the tubular tissue region comprises the tubular fluid compartment as well as its cell lining. It seems, however, reasonable to assume that the basolateral tubular cell receptors are exposed to a concentration of Ang II not too different from the concentration in peritubular interstitial fluid, whereas apical receptors are indeed exposed to an Ang II concentration equal to that in the tubular fluid compartment. The apical receptors are bathed in a relatively large volume of tubular fluid and it is therefore assumed that only a small fraction of the total amount of Ang IIi in tubular fluid is bound to these receptors and that this fraction can be ignored. The term CIiPcPtVPcPt in Eq. (25) is very small as compared with CIiT 7van Kats J.P. Schalekamp M.A.D.H. Verdouw P.D. et al.Intrarenal angiotensin II: interstitial and cellular levels and site of production.Kidney Int. 2001; 60: 2311-2317Google Scholar and, for the practical purpose of our analysis, it is also ignored. Thus, in accordance with Eq. (22), it follows thatβ2=β=[(CIiT/CIiPv)/(αVIsfPt)]−1(27) β1,2=β=[(ClIIiPtRME)1,2+ClDiffPt]/ClDiffPt(28) In Eq. (27), the factor β is expressed as a function of the plasma concentration of Ang Ii in the renal vein, the total tissue concentration of Ang Ii in the renal cortex, the plasma concentration of Ang I in the renal artery, and the concentration of arterially delivered Ang I in the renal vein. These independent var
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