Nitric oxide and superoxide transport in a cross section of the rat outer medulla. II. Reciprocal interactions and tubulovascular cross talk

Renal oxygenation: From data to insight

Computational models have made a major contribution to the field of physiology. As the complexity of our understanding of biological systems expands, the need for computational methods only increases. But collaboration between experimental physiologists and computational modellers (ie theoretical physiologists) is not easy. One of the major challenges is to break down the barriers created by differences in vocabulary and approach between the two disciplines. In this review, we have two major aims. Firstly, we wish to contribute to the effort to break down these barriers and so encourage more interdisciplinary collaboration. So, we begin with a "primer" on the ways in which computational models can help us understand physiology and pathophysiology. Second, we aim to provide an update of recent efforts in one specific area of physiology, renal oxygenation. This work is shedding new light on the causes and consequences of renal hypoxia. But as importantly, computational modelling is providing direction for experimental physiologists working in the field of renal oxygenation by: (a) generating new hypotheses that can be tested in experimental studies, (b) allowing experiments that are technically unfeasible to be simulated in silico, or variables that cannot be measured experimentally to be estimated, and (c) providing a means by which the quality of experimental data can be assessed. Critically, based on our experience, we strongly believe that experimental and theoretical physiology should not be seen as separate exercises. Rather, they should be integrated to permit an iterative process between modelling and experimentation.

Diffusive shunting of gases and other molecules in the renal vasculature: physiological and evolutionary significance

Countercurrent systems have evolved in a variety of biological systems that allow transfer of heat, gases, and solutes. For example, in the renal medulla, the countercurrent arrangement of vascular and tubular elements facilitates the trapping of urea and other solutes in the inner medulla, which in turn enables the formation of concentrated urine. Arteries and veins in the cortex are also arranged in a countercurrent fashion, as are descending and ascending vasa recta in the medulla. For countercurrent diffusion to occur, barriers to diffusion must be small. This appears to be characteristic of larger vessels in the renal cortex. There must also be gradients in the concentration of molecules between afferent and efferent vessels, with the transport of molecules possible in either direction. Such gradients exist for oxygen in both the cortex and medulla, but there is little evidence that large gradients exist for other molecules such as carbon dioxide, nitric oxide, superoxide, hydrogen sulfide, and ammonia. There is some experimental evidence for arterial-to-venous (AV) oxygen shunting. Mathematical models also provide evidence for oxygen shunting in both the cortex and medulla. However, the quantitative significance of AV oxygen shunting remains a matter of controversy. Thus, whereas the countercurrent arrangement of vasa recta in the medulla appears to have evolved as a consequence of the evolution of Henle’s loop, the evolutionary significance of the intimate countercurrent arrangement of blood vessels in the renal cortex remains an enigma.

Mathematical modeling of urea transport in the kidney

Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

Mathematical modeling of kidney transport

In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.

Modeling Transport and Flow Regulatory Mechanisms of the Kidney

The kidney plays an indispensable role in the regulation of whole-organism water balance, electrolyte balance, and acid-base balance, and in the excretion of metabolic wastes and toxins. In this paper, we review representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, and regulation of renal oxygen transport. We discuss how such modeling efforts have significantly expanded our understanding of renal function in both health and disease.

How NaCl raises blood pressure: a new paradigm for the pathogenesis of salt-dependent hypertension

Excess dietary salt is a major cause of hypertension. Nevertheless, the specific mechanisms by which salt increases arterial constriction and peripheral vascular resistance, and thereby raises blood pressure (BP), are poorly understood. Here we summarize recent evidence that defines specific molecular links between Na(+) and the elevated vascular resistance that directly produces high BP. In this new paradigm, high dietary salt raises cerebrospinal fluid [Na(+)]. This leads, via the Na(+)-sensing circumventricular organs of the brain, to increased sympathetic nerve activity (SNA), a major trigger of vasoconstriction. Plasma levels of endogenous ouabain (EO), the Na(+) pump ligand, also become elevated. Remarkably, high cerebrospinal fluid [Na(+)]-evoked, locally secreted (hypothalamic) EO participates in a pathway that mediates the sustained increase in SNA. This hypothalamic signaling chain includes aldosterone, epithelial Na(+) channels, EO, ouabain-sensitive α(2) Na(+) pumps, and angiotensin II (ANG II). The EO increases (e.g.) hypothalamic ANG-II type-1 receptor and NADPH oxidase and decreases neuronal nitric oxide synthase protein expression. The aldosterone-epithelial Na(+) channel-EO-α(2) Na(+) pump-ANG-II pathway modulates the activity of brain cardiovascular control centers that regulate the BP set point and induce sustained changes in SNA. In the periphery, the EO secreted by the adrenal cortex directly enhances vasoconstriction via an EO-α(2) Na(+) pump-Na(+)/Ca(2+) exchanger-Ca(2+) signaling pathway. Circulating EO also activates an EO-α(2) Na(+) pump-Src kinase signaling cascade. This increases the expression of the Na(+)/Ca(2+) exchanger-transient receptor potential cation channel Ca(2+) signaling pathway in arterial smooth muscle but decreases the expression of endothelial vasodilator mechanisms. Additionally, EO is a growth factor and may directly participate in the arterial structural remodeling and lumen narrowing that is frequently observed in established hypertension. These several central and peripheral mechanisms are coordinated, in part by EO, to effect and maintain the salt-induced elevation of BP.

Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide

We expanded our region-based model of water and solute exchanges in the rat outer medulla to incorporate the transport of nitric oxide (NO) and superoxide (O(2)(-)) and to examine the impact of NO-O(2)(-) interactions on medullary thick ascending limb (mTAL) NaCl reabsorption and oxygen (O(2)) consumption, under both physiological and pathological conditions. Our results suggest that NaCl transport and the concentrating capacity of the outer medulla are substantially modulated by basal levels of NO and O(2)(-). Moreover, the effect of each solute on NaCl reabsorption cannot be considered in isolation, given the feedback loops resulting from three-way interactions between O(2), NO, and O(2)(-). Notwithstanding vasoactive effects, our model predicts that in the absence of O(2)(-)-mediated stimulation of NaCl active transport, the outer medullary concentrating capacity (evaluated as the collecting duct fluid osmolality at the outer-inner medullary junction) would be ∼40% lower. Conversely, without NO-induced inhibition of NaCl active transport, the outer medullary concentrating capacity would increase by ∼70%, but only if that anaerobic metabolism can provide up to half the maximal energy requirements of the outer medulla. The model suggests that in addition to scavenging NO, O(2)(-) modulates NO levels indirectly via its stimulation of mTAL metabolism, leading to reduction of O(2) as a substrate for NO. When O(2)(-) levels are raised 10-fold, as in hypertensive animals, mTAL NaCl reabsorption is significantly enhanced, even as the inefficient use of O(2) exacerbates hypoxia in the outer medulla. Conversely, an increase in tubular and vascular flows is predicted to substantially reduce mTAL NaCl reabsorption. In conclusion, our model suggests that the complex interactions between NO, O(2)(-), and O(2) significantly impact the O(2) balance and NaCl reabsorption in the outer medulla.

Cellular mechanisms underlying nitric oxide-induced vasodilation of descending vasa recta

It has been observed that vasoactivity of explanted descending vasa recta (DVR) is modulated by intrinsic nitric oxide (NO) and superoxide (O(2)(-)) production (Cao C, Edwards A, Sendeski M, Lee-Kwon W, Cui L, Cai CY, Patzak A, Pallone TL. Am J Physiol Renal Physiol 299: F1056-F1064, 2010). To elucidate the cellular mechanisms by which NO, O(2)(-) and hydrogen peroxide (H(2)O(2)) modulate DVR pericyte cytosolic Ca(2+) concentration ([Ca](cyt)) and vasoactivity, we expanded our mathematical model of Ca(2+) signaling in pericytes. We incorporated simulations of the pathways that translate an increase in [Ca](cyt) to the activation of myosin light chain (MLC) kinase and cell contraction, as well as the kinetics of NO and reactive oxygen species formation and their effects on [Ca](cyt) and MLC phosphorylation. The model reproduced experimentally observed trends of DVR vasoactivity that accompany exposure to N(ω)-nitro-L-arginine methyl ester, 8-Br-cGMP, Tempol, and H(2)O(2). Our results suggest that under resting conditions, NO-induced activation of cGMP maintains low levels of [Ca](cyt) and MLC phosphorylation to minimize basal tone. This results from stimulation of Ca(2+) uptake from the cytosol into the SR via SERCA pumps, Ca(2+) efflux into the extracellular space via plasma membrane Ca(2+) pumps, and MLC phosphatase (MLCP) activity. We predict that basal concentrations of O(2)(-) and H(2)O(2) have negligible effects on Ca(2+) signaling and MLC phosphorylation. At concentrations above 1 nM, O(2)(-) is predicted to modulate [Ca(cyt)] and MCLP activity mostly by reducing NO bioavailability. The DVR vasoconstriction that is induced by high concentrations of H(2)O(2) can be explained by H(2)O(2)-mediated downregulation of MLCP and SERCA activity. We conclude that intrinsic generation of NO by the DVR wall may be sufficient to inhibit vasoconstriction by maintaining suppression of MLC phosphorylation.

Nitric oxide and superoxide transport in a cross section of the rat outer medulla. I. Effects of low medullary oxygen tension

To examine the impact of the complex radial organization of the rat outer medulla (OM) on the distribution of nitric oxide (NO), superoxide (O(2)(-)) and total peroxynitrite (ONOO), we developed a mathematical model that simulates the transport of those species in a cross section of the rat OM. To simulate the preferential interactions among tubules and vessels that arise from their relative radial positions in the OM, we adopted the region-based approach developed by Layton and Layton (Am J Physiol Renal Physiol 289: F1346-F1366, 2005). In that approach, the structural organization of the OM is represented by means of four concentric regions centered on a vascular bundle. The model predicts the concentrations of NO, O(2)(-), and ONOO in the tubular and vascular lumen, epithelial and endothelial cells, red blood cells (RBCs), and interstitial fluid. Model results suggest that the large gradients in Po(2) from the core of the vascular bundle toward its periphery, which stem from the segregation of O(2)-supplying descending vasa recta (DVR) within the vascular bundles, in turn generate steep radial NO and O(2)(-) concentration gradients, since the synthesis of both solutes is O(2) dependent. Without the rate-limiting effects of O(2), NO concentration would be lowest in the vascular bundle core, that is, the region with the highest density of RBCs, which act as a sink for NO. Our results also suggest that, under basal conditions, the difference in NO concentrations between DVR that reach into the inner medulla and those that turn within the OM should lead to differences in vasodilation and preferentially increase blood flow to the inner medulla.