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An optimization problem, formulated using a nonlinear least-squares approach, was used to estimate parameters for kinetic models of the three isoforms of the kidney-specific Na-K-2Cl (NKCC2) cotransporter. Specifically, the optimization problem estimates the magnitude of model parameters (i.e., off-binding and translocation rate constants) by minimizing the distance between model unidirectional fluxes and published unidirectional [sup.86][Rb.sup.+] uptake curves for the A, B, and F isoforms of the NKCC2 cotransporter obtained in transfected Xenopus oocytes. By using different symmetry assumptions, NKCC2 models with five, six, seven, or eight parameters were evaluated. The optimization method identified parameter sets that yielded computed unidirectional fluxes consistent with the uptake data. However, the parameter values were not unique, in that systematic exploration of the parameter space revealed alternative parameter sets that fit the data with similar accuracy. Finally, we demonstrate that the optimization method can identify parameter sets for the three transporter isoforms that differ only in ion binding affinities, a result that is consistent with a published mutagenesis analysis of the molecular and structural bases for the differences in [sup.86][Rb.sup.+] uptake among the A, B, and F isoforms. These NKCC2 cotransporter models will facilitate the development of larger scale models of ion transport by thick ascending limb cells. epithelial transport; thick ascending limb; kidney

The extent to which renal blood flow dynamics vary in time and whether such variation contributes substantively to dynamic complexity have emerged as important questions. Data from Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR) were analyzed by time-varying transfer functions (TVTF) and time-varying coherence functions (TVCF). Both TVTF and TVCF allow quantification of nonstationarity in the frequency ranges associated with the autoregulatory mechanisms. TVTF analysis shows that autoregulatory gain in SDR and SHR varies in time and that SHR exhibit significantly more nonstationarity than SDR. TVTF gain in the frequency range associated with the myogenic mechanism was significantly higher in SDR than in SHR, but no statistical difference was found with tubuloglomerular (TGF) gain. Furthermore, TVCF analysis revealed that the coherence in both strains is significantly nonstationary and that low-frequency coherence was negatively correlated with autoregulatory gain. TVCF in the frequency range from 0.1 to 0.3 Hz was significantly higher in SDR (7 out of 7, >0.5) than in SHR (5 out of 6, hemodynamics; myogenic; tubuloglomerular feedback; hypertension

Single-nephron proximal tubule pressure in spontaneously hypertensive rats (SHR) can exhibit highly irregular oscillations similar to deterministic chaos. We used a mathematical model of tubuloglomerular feedback (TGF) to investigate potential sources of the irregular oscillations and the corresponding complex power spectra in SHR. A bifurcation analysis of the TGF model equations, for nonzero thick ascending limb (TAL) NaCl permeability, was performed by finding roots of the characteristic equation, and numerical simulations of model solutions were conducted to assist in the interpretation of the analysis. These techniques revealed four parameter regions, consistent with TGF gain and delays in SHR, where multiple stable model solutions are possible: 1) a region having one stable, time-independent steady-state solution; 2) a region having one stable oscillatory solution only, of frequency [f.sub.1]; 3) a region having one stable oscillatory solution only, of frequency [f.sub.2], which is approximately equal to 2 [f.sub.1]; and 4) a region having two possible stable oscillatory solutions, of frequencies [f.sub.1] and [f.sub.2]. In addition, we conducted simulations in which TAL volume was assumed to vary as a function of time and simulations in which two or three nephrons were assumed to have coupled TGF systems. Four potential sources of spectral complexity in SHR were identified: l) bifurcations that permit switching between different stable oscillatory modes, leading to multiple spectral peaks and their respective harmonic peaks; 2) sustained lability in delay parameters, leading to broadening of peaks and of their harmonics; 3) episodic, but abrupt, lability in delay parameters, leading to multiple peaks and their harmonics; and 4) coupling of small numbers of nephrons, leading to multiple peaks and their harmonics. We conclude that the TGF system in SHR may exhibit multistability and that the complex power spectra of the irregular TGF fluctuations in this strain may be explained by switching between multiple dynamic modes, temporal variation in TGF parameters, and nephron coupling. renal hemodynamics; hypertension; mathematical model; nonlinear dynamical system

We have previously suggested that fluid flow in the mouse exorbital lacrimal gland is driven by the opening of apical [Cl.sup.-] and [K.sup.+] channels. These ions move into the lumen of the gland and water follows by osmosis. In many tissues, the [Na.sup.+]-[K.sup.+]-2[Cl.sup.-] cotransporter (NKCCl) replaces the [Cl.sup.-] and [K.sup.+] ions that move into the lumen. We hypothesize that mouse exorbital lacrimal glands would have NKCCl cotransporters and that they would be important in fluid transport by this gland. We used immunocytochemistry to localize NKCCl-like immunoreactivity to the membranes of the acinar cells as well as to the basolateral membranes of the duct cells. We developed a method to measure tear flow and its composition from mouse glands in situ. Stimulation with the acetylcholine agonist carbachol produced a peak flow followed by a plateau. Ion concentration measurements of this stimulated fluid showed it was high in [K.sup.+] and [Cl.sup.-]. Treatment of the gland with furosemide, a blocker of the NKCCl cotransporter, reduced the plateau phase of fluid flow by ~30%. Isolated cells exposed to a hypertonic shock shrank by ~20% and then showed a regulatory volume increase (RVI). Both the RVI and swelling were blocked by treatment with furosemide. Cells isolated from these glands shrink by ~10% in the presence of carbachol. Blocking NKCCl with furosemide reduced the amount of shrinkage by ~50%. These data suggest that NKCCl plays an important role in fluid secretion by the exorbital gland of mice.

Identification of the two principal mediators of renal autoregulation from time-series data is difficult, as both the tubuloglomerular feedback (TGF) and myogenic (MYO) mechanisms interact and share a common effector, the afferent arteriole. Moreover, although both mechanisms can exhibit oscillations in well-characterized frequency bands, these systems often operate in nonoscillatory states not detectable by frequency-domain analysis. To overcome these difficulties, we have developed a new approach to the characterization of the TGF and MYO systems. A laser Doppler probe is used to measure fluctuations in local cortical blood flow (CBF) in response to spontaneous changes in blood pressure (BP) and to large imposed perturbations in BP, which elicit strong, simultaneous, transient, oscillatory blood flow responses. These transient responses are identified by high-resolution time-frequency spectral analysis of the time-series data. In this report, we compare four different time-frequency spectral techniques (the short-time Fourier transform (STFT), smoothed pseudo Wigner-Ville, and two recently developed methods: the Hilbert-Huang transform and time varying optimal parameter search (TVOPS)) to determine which of these four methods is best suited for the identification of transient oscillations in renal autoregulatory mechanisms. We found that TVOPS consistently provided the best performance in both simulation examples and identification of the two autoregulatory mechanisms in actual data. While the STFT suffers in time and frequency resolution as compared to the other three methods, it was able to identify the two autoregulatory mechanisms. Taken together, our experience suggests a two level approach to the analysis of renal blood flow (RBF) data: STFT to obtain a low-resolution time-frequency spectrogram, followed by the use of a higher resolution technique, such as the TVOPS, if even higher time-frequency resolution of the transient responses is required. Index Terms--Hilbert-Huang transform, myogenic, renal blood flow, short-time Fourier transform, smoothed pseudo Wigner-Ville, time-varying optimal parameter search algorithm, tubuloglomerular feedback.

Oldson, Darren R., Leon C. Moore, and Harold E. Layton. Effect of sustained flow perturbations on stability and compensation of tubuloglomerular feedback. Am J Physiol Renal Physiol 285: F972-F989, 2003. First published July 1, 2003; 10.1152/ajprenal.00377.2002.--A mathematical model previously formulated by us predicts that limit-cycle oscillations (LCO) in nephron flow are mediated by tubuloglomerular feedback (TGF) and that the LCO arise from a bifurcation that depends heavily on the feedback gain magnitude, [gamma], and on its relationship to a theoretically determined critical value of gain, [[gamma].sub.c]. In this study, we used that model to show how sustained perturbations in proximal tubule flow, a common experimental maneuver, can initiate or terminate LCO by changing the values of [gamma] and [[gamma].sub.c], thus changing the sign of [gamma] - [[gamma].sub.c]. This result may help explain experiments in which intratubular pressure oscillations were initiated by the sustained introduction or removal of fluid from the proximal tubule (Leyssac PP and Baumbach L. Acta Physiol Scand 117: 415-419, 1983). In addition, our model predicts that, for a range of TGF sensitivities, sustained perturbations that initiate or terminate LCO can yield substantial and abrupt changes in both distal NaCl delivery and NaCl delivery compensation, changes that may play an important role in the response to physiological challenge. kidney; renal hemodynamics; autoregulation; mathematical model; nonlinear dynamics

Endothelium-derived nitric oxide (NO) is thought to be short-lived in blood because of rapid removal from plasma, mainly by binding to Hb. The extent to which removal limits NO advection is unclear, especially for blood flow in the renal afferent arteriole (AA), which has a transit time of 3-30 ms. A mathematical model of AA fluid dynamics and myogenic response that includes NO diffusion, advection, degradation, and vasorelaxant action was used to estimate NO advective transport. Model simulations indicate that advective transport of locally produced NO is sufficient to yield physiologically significant NO concentrations along much of the AA. Advective transport is insensitive to NO scavenging by Hb because the NO-Hb binding rate is slow relative to AA transit time. Hence, plasma NO concentration near the vessel wall is influenced by both diffusion from endothelial cells and advection from upstream sites. Simulations also suggest that NO advection may constitute a mechanism to stabilize arteriolar flow in response to a localized vasoconstriction accompanied by enhanced NO release. kidney; renal hemodynamics; myogenic mechanism; immersed boundary method

In glands such as the liver and pancreas, gap junctions containing connexin 26 and 32 (Cx26 and Cx32, respectively) couple the secretory cells. Uncoupling these junctions compromises the secretory function of these glands. Lacrimal glands also contain extensive arrays of gap junctions consisting of Cx26 and Cx32. We wanted to determine the role of these junctions in fluid secretion. In Cx32-deficient mice, immunocytochemistry showed that, in the male lacrimal gland, the remaining Cx26 was found evenly distributed in the membrane whereas there was little in the membranes of female glands. Western blot analysis of Cx26 showed that female Cx32-deficient mice expressed Cx26. Patch-clamp analyses of acinar cell coupling showed that the cell pairs from male glands were coupled whereas those from female glands were not. Stimulated fluid production by the glands from Cx32-deficient mice was abnormally low in female glands compared with controls at low topical doses of carbachol. The protein secretory response to different doses of carbachol was the same in all animals. These data suggest that gap junctions are essential for optimal fluid secretion in lacrimal glands. connexin 26; connexin 32; mouse; tears

The influence of insulin-like growth factor I (IGF-I) on the rat renal preglomerular microvasculature was studied through the application of in vitro blood-perfused juxtamedullary nephron preparation. Findings showed that the renal vascular effects of IGF-I involve activation of two endogenous vasodilators, which are nitric oxide and vasodilatory prostaglandins. Moreover, IGF-I may also release an unknown vasoconstrictor.

A mathematical model was employed to examine how thick ascending limb luminal NaCl levels respond to tubular fluid flow oscillation. Results show that intratubular fluid NaCl levels are dependent on fluid transfer time in spatially homogeneous transport parameters and in the absence of transtubular NaCl backleak. Results demonstrate the detectability of nodal structure and nonsinusoidal oscillations.

A simple mathematical model was employed in examining tubuloglomerular feedback system (TGF) spectral properties. Results show that TGF spectral response curve has a tendency to give waveform a square waveshape when feedback gain is large. The resulting predictions were found in agreement with previous studies of in vivo TGF oscillation power spectra and waveforms.

The effects of branching topologies on the autoregulatory responses of individual afferent arterioles (AAs) were analyzed in blood-perfused juxtamedullary nephron (JMN) preparations. Analysis of JMN preparations indicated the similar heterogeneity of autoregulatory responses in paired AAs compared to proximal AAs. Furthermore, the spatial organization of pressure-induced autoregulatory responses along the AA indicated the association between autonomic pairing and functional nephron coupling.

Analysis of the distribution of L-type calcium channels in renal vascular smooth muscle cells near bifurcation points of resistance arteries shows that the L-type calcium channels are concentrated at branching points of the arteries. These branching points exhibit significant contractile responses to depolarization triggered by KCl and regulate renal hemodynamics, especially vasoconstriction.

Analysis of the relationship between instantaneous and steady-state open feedback-loop gains for tubuloglomerular feedback (TGF) in the ascending limb reveals that both gain formulations are equivalent when there is no backleak of solute into the ascending limb, while the magnitude of instantaneous gain is larger than that of steady-state gain in the presence of backleak. Calculations based on an analytical model reveal the difference between the two gains to be 5-10%. Steady-state gain may provide a lower limit for the instantaneous gain.

Studies to quantitatively assess the degree of afferent arteriolar (AA) connectivity using an HCl maceration-microdissection method in rat, rabbit, mouse and human renal vasculatures reveals the arrangement of 51 to 60% of the total AA populations into vascular units, with the origin and joining arterial unit being shared by two AAs in all the species studies. The non-random pattern of recin distribution and correlation between arteriolar lengths within anatomic pairs indicates an association between the endocrine functions of paired arterioles.

Analysis of the influence of isosmotic reductions in Na+ and Cl- concentrations on cytosolic calcium concentration Ca2+(i) in cultured rat mesangial cells (MC) shows that Na+ or Cl- induces a concentration-dependent rise in Ca2+(i). Changes in the concentration of Cl- exhibit greater influence on MC than that of Na+. Amperometric NO sensor shows that small decrease in Cl- concentrations lead to NO release from MC which explains the signal transmission of tubuloglomerular feedback response within the interstitium of juxtaglomerular apparatus.

Three new methods enable the distribution of granulated renin-positive cells in preglomerular vessel in settings where the vascular architecture is significantly preserved to be directly visualized. The variations in the optical characteristics of granulated and smooth muscle cells enable the convenient location of granulated cells in standard transillumination. Quinacrine, a fluroescent intravital strain, can be utilized to strain intracellular granules. A polyclonal anti rat renin antibody in vascular trees after cell permeabilization can be asked to achieve specific * of renin.

In vitro measurements of the intravascular pressure in the different arterial segments from the arcuate to the afferent arterioles and the glomerular capillaries were undertaken to investigate the intravascular pressure autoregulation existing inthe pre-glomerular vascular bed. Results indicate that a large proportion, 65%,of the autoregulatory function is mediated by the distal afferent arterioles. The interlobular arteries also contribute significantly to pressure autoregulation.

Layton, H. E., E. Bruce Pitman, and L. C. MoorE,. Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery. Am. J. Physiol. Renal Physiol. 278: F287-F301, 2000.--A mathematical model was used to evaluate the potential effects of limit-cycle oscillations (LCO) on tubuloglomerular feedback (TGF) regulation of fluid anti sodium delivery to the distal tubule. In accordance with linear systems theory, simulations of steady-state responses to infinitesimal perturbations in single-nephron glomerular filtration rate (SNGFR) show that TGF regulatory ability (assessed as TGF compensation) increases with TGF gain magnitude [Gamma] when [Gamma] is less than the critical value [[Gamma].sub.c], the value at which LCO emerge in tubular fluid flow and NaCl concentration at the macula densa. When [Gamma] [is greater than] [[Gamma].sub.c] and LCO are, present, TGF compensation is reduced for both infinitesimal and finite perturbations in SNGFR, relative to the compensation that could be achieved in the absence of LCO. Maxima] TGF compensation occurs when [Gamma] [approximately equals] [[Gamma].sub.c]. Even in the absence of perturbations, LCO increase time-averaged sodium delivery to the distal tubule, while fluid delivery is little changed. These effects of LCO are consequences of nonlinear elements in the TGF system. Because increased distal sodium delivery may increase the rate of sodium excretion, these simulations suggest that LCO enhance sodium excretion. kidney, renal hemodynamics, mathematical model, nonlinear dynamics

Thorup, Christian, Caroline L. Jones, Steven S. Gross, Leon C. Moore, and Michael S. Goligorsky. Carbon monoxide induces vasodilation and nitric oxide release but suppresses endothelial NOS. Am. J. Physiol. 277 (Renal Physiol. 46): F882-F889, 1999.--The vascular effects of carbon monoxide (CO) resemble those of nitric oxide (NO), but it is unknown whether the two messengers converge or exhibit reciprocal feedback regulation. These questions were examined in microdissected perfused renal resistance arteries (RRA) studied using NO-sensitive microelectrodes. Perfusion of RRA with buffers containing increasing concentrations of CO resulted in a biphasic release of NO. The NO response peaked at 100 [micro]M CO and then declined to virtually zero at 10 [micro]M. When a series of 50-s pulses of 100 nM CO were applied repeatedly (150-s interval), the amplitude of consecutive NO responses was diminished. NO release from RRA showed dependence on L-arginine but not D-arginine, and the responses to CO were inhibited by pretreatment with [N.sup.G]-nitro-L-arginine methyl ester (L-NAME), an inhibitor of NO synthases (NOS). CO (100 nM) also suppressed NO release induced by 100 [micro]M carbachol, a potent agonist for endothelial NOS (eNOS). RRA from rats in which endogenous CO production from inducible HO was elevated (cobalt chloride 12 h prior to study) also showed suppressed responses to carbachol. Furthermore, responses consistent with these findings were obtained in juxtamedullary afferent arterioles perfused in vitro, where the vasodilatory response to CO was biphasic and the response to acetylcholine was blunted. Collectively, these data suggest that the CO-induced NO release could be attributed to either stimulation of eNOS or to NO displacement from a cellular storage pool. To address this, direct in vitro measurements with an NO-selective electrode of NO production by recombinant eNOS revealed that CO dose-dependently inhibits NO synthesis. Together, the above data demonstrate that, whereas high levels of CO inhibit NOS activity and NO generation, lower concentrations of CO induce release of NO from a large intracellular pool and, therefore, may mimic the vascular effects of NO. kidney; blood vessels; endothelium; heme oxygenase; hemodynamics

The role of nongastric H+-K+-ATPase (HKA) in ion homeostasis of macula densa (MD) cells is an open question. To begin to explore this issue, we developed two mathematical models that describe ion fluxes through a nongastric HKA. One model assumes a 1H+:1K+-per-ATP stoichiometry; the other assumes a 2H+:2K+-per-ATP stoichiometry. Both models include Na+ and NH4 + competitive binding with H+ and K+, respectively, a characteristic observed in vitro and in situ. Model rate constants were obtained by minimizing the distance between model and experimental outcomes. Both 1H+(1Na+):1K+(1NH4 +)- per-ATP and 2H+(2Na+):2K+(2NH4 +)-per-ATP models fit the experimental data well. Using both models, we simulated ion net fluxes as a function of cytosolic or luminal ion concentrations typical for the cortical thick ascending limb and MD region. We observed that 1) K+ and NH4 + flowed in the lumen-to-cytosol direction, 2) there was competitive behavior between luminal K+ and NH4 + and between cytosolic Na+ and H+, 3) ion fluxes were highly sensitive to changes in cytosolic Na+ or H+ concentrations, and 4) the transporter does mostly Na+/K+ exchange under physiological conditions. These results support the concept that nongastric HKA may contribute to Na+ and pH homeostasis in MD cells. Furthermore, in both models, H+ flux reversed at a luminal pH that was <5.6. Such reversal led to Na+/H+ exchange for a luminal pH of <2 and 4 in the 1:1-per-ATP and 2:2-per-ATP models, respectively. This suggests a novel role of nongastric HKA in cell Na+ homeostasis in the more acidic regions of the renal tubules. [ABSTRACT FROM AUTHOR]

The thick ascending limb (TAL) is a major NaCl reabsorbing site in the nephron. Efficient reabsorption along that segment is thought to be a consequence of the establishment of a strong transepithelial potential that drives paracellular Na+ uptake. We used a multicell mathematical model of the TAL to estimate the efficiency of Na+ transport along the TAL and to examine factors that determine transport efficiency, given the condition that TAL outflow must be adequately dilute. The TAL model consists of a series of epithelial cell models that represent all major solutes and transport pathways. Model equations describe luminal flows, based on mass conservation and electroneutrality constraints. Empirical descriptions of cell volume regulation (CVR) and pH control were implemented, together with the tubuloglomerular feedback (TGF) system. Transport efficiency was calculated as the ratio of total net Na+ transport (i.e., paracellular and transcellular transport) to transcellular Na+ transport. Model predictions suggest that 1) the transepithelial Na+ concentration gradient is a major determinant of transport efficiency; 2) CVR in individual cells influences the distribution of net Na+ transport along the TAL; 3) CVR responses in conjunction with TGF maintain luminal Na+ concentration well above static head levels in the cortical TAL, thereby preventing large decreases in transport efficiency; and 4) under the condition that the distribution of Na+ transport along the TAL is quasi-uniform, the tubular fluid axial Cl- concentration gradient near the macula densa is sufficiently steep to yield a TGF gain consistent with experimental data. [ABSTRACT FROM AUTHOR]

Thick ascending limb (TAL) cells are capable of reducing tubular fluid Na+ concentration to as low as ~25 mM, and yet they are thought to transport Na+ efficiently owing to passive paracellular Na+ absorption. Transport efficiency in the TAL is of particular importance in the outer medulla where O2 availability is limited by low blood flow. We used a mathematical model of a TAL cell to estimate the efficiency of Na+ transport and to examine how tubular dilution and cell volume regulation influence transport efficiency. The TAL cell model represents 13 major solutes and the associated transporters and channels; model equations are based on mass conservation and electroneutrality constraints. We analyzed TAL transport in cells with conditions relevant to the inner stripe of the outer medulla, the cortico-medullary junction, and the distal cortical TAL. At each location Na+ transport efficiency was computed as functions of changes in luminal NaCl concentration ([NaCl]), [K+], [NH4+], junctional Na+ permeability, and apical K+ permeability. Na+ transport efficiency was calculated as the ratio of total net Na+ transport to transcellular Na+ transport. Transport efficiency is predicted to be highest at the cortico-medullary boundary where the transepithelial Na+ gradient is the smallest. Transport efficiency is lowest in the cortex where luminal [NaCl] approaches static head. [ABSTRACT FROM AUTHOR]

In several previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model, which represents the TAL as a rigid tube, predicts that TGF signal transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to constant intratubular fluid flow, the time interval required for an element of tubular fluid to traverse the TAL, as a function of time, is oscillatory and periodic but not sinusoidal. As a consequence, NaCl concentration in tubular fluid alongside the macula densa will be nonsinusoidal and thus contain harmonics of the original sinusoidal frequency. We hypothesized that the complexity found in power spectra based on in vivo time series of key TGF variables arises in part from those harmonics and that nonlinearities in TGF-mediated oscillations may result in increased NaCl delivery to the distal nephron. To investigate the possibility that a more realistic model of the TAL would damp the harmonics, we have conducted new studies in a model TAL that has compliant walls and thus a tubular radius that depends on transmural pressure. These studies predict that compliant TAL walls do not damp, but instead intensify, the harmonics. In addition, our results predict that mean TAL flow strongly influences the shape of the NaCl concentration waveform at the macula densa. This is a consequence of the inverse relationship between flow speed and transit time, which produces asymmetry between up- and downslopes of the oscillation, and the nonlinearity of TAL NaCl absorption at low flow rates, which broadens the trough of the oscillation relative to the peak. The dependence of waveform shape on mean TAL flow may be the source of the variable degree of distortion, relative to a sine wave, seen in experimental recordings of TGF-mediated oscillations. [ABSTRACT FROM AUTHOR]

Elevations in systolic blood pressure are believed to be closely linked to the pathogenesis and progression of renal diseases. It has been hypothesized that the afferent arteriole (AA) protects the glomerulus from the damaging effects of hypertension by sensing increases in systolic blood pressure and responding with a compensatory vasoconstriction (Loutzenhiser R, Bidani A, Chilton L. Circ Res 90: 1316-1324, 2002). To investigate this hypothesis, we developed a mathematical model of the myogenic response of an AA wall, based on an arteriole model (Gonzalez-Fernandez JM, Ermentrout B. Math Biosci 119: 127-167, 1994). The model incorporates ionic transport, cell membrane potential, contraction of the AA smooth muscle cell, and the mechanics of a thick-walled cylinder. The model represents a myogenic response based on a pressure-induced shift in the voltage dependence of calcium channel openings: with increasing transmural pressure, model vessel diameter decreases; and with decreasing pressure, vessel diameter increases. Furthermore, the model myogenic mechanism includes a rate-sensitive component that yields constriction and dilation kinetics similar to behaviors observed in vitro. A parameter set is identified based on physical dimensions of an AA in a rat kidney. Model results suggest that the interaction of Ca2+ and K+ fluxes mediated by voltage-gated and voltage-calcium-gated channels, respectively, gives rise to periodicity in the transport of the two ions. This results in a time-periodic cytoplasmic calcium concentration, myosin light chain phosphorylation, and cross-bridge formation with the attending muscle stress. Furthermore, the model predicts myogenic responses that agree with experimental observations, most notably those which demonstrate that the renal AA constricts in response to increases in both steady and systolic blood pressures. The myogenic model captures these essential functions of the renal AA, and it may prove useful as a fundamental component in a multiscale model of the renal microvasculature suitable for investigations of the pathogenesis of hypertensive renal diseases. [ABSTRACT FROM AUTHOR]

To help elucidate the causes of irregular tubular flow oscillations found in the nephrons of spontaneously hypertensive rats (SHR), we have conducted a bifurcation analysis of a mathematical model of two nephrons that are coupled through their tubuloglomerular feedback (TGF) systems. This analysis was motivated by a previous modeling study which predicts that NaCl backleak from a nephron's thick ascending limb permits multiple stable oscillatory states that are mediated by TGF (Layton et al. in Am. J. Physiol. Renal Physiol. 291:F79-F97, 2006); that prediction served as the basis for a comprehensive, multifaceted hypothesis for the emergence of irregular flow oscillations in SHR. However, in that study, we used a characteristic equation obtained via linearization from a single-nephron model, in conjunction with numerical solutions of the full, nonlinear model equations for two and three coupled nephrons. In the present study, we have derived a characteristic equation for a model of any finite number of mutually coupled nephrons having NaCl backleak. Analysis of that characteristic equation for the case of two coupled nephrons has revealed a number of parameter regions having the potential for differing stable dynamic states. Numerical solutions of the full equations for two model nephrons exhibit a variety of behaviors in these regions. Some behaviors exhibit a degree of complexity that is consistent with our hypothesis for the emergence of irregular oscillations in SHR. [ABSTRACT FROM AUTHOR]

Mathematical models have played an essential role in elucidating various functions of the kidney, including the mechanism by which the avian and mammalian kidney can produce a urine that is more concentrated than blood plasma, quasi-isosmotic reabsorption along the proximal tubule, and the control and regulation of glomerular filtration by the myogenic and tubuloglomerular feedback mechanisms. This review includes a brief description of relevant renal physiology, a summary of the contributions of mathematical models at various levels and describes our recent work toward the Renal Physiome. [ABSTRACT FROM AUTHOR]

We have previously suggested that fluid flow in the mouse exorbital lacrimal gland is driven by the opening of apical Cl- and K+ channels. These ions move into the lumen of the gland and water follows by osmosis. In many tissues, the Na+-K+-2Cl- cotransporter (NKCC1) replaces the Cl- and K+ ions that move into the lumen. We hypothesize that mouse exorbital lacrimal glands would have NKCC1 cotransporters and that they would be important in fluid transport by this gland. We used immunocytochemistry to localize NKCC1-like immunoreactivity to the membranes of the acinar cells as well as to the basolateral membranes of the duct cells. We developed a method to measure tear flow and its composition from mouse glands in situ. Stimulation with the acetylcholine agonist carbachol produced a peak flow followed by a plateau. Ion concentration measurements of this stimulated fluid showed it was high in K+ and Cl-. Treatment of the gland with furosemide, a blocker of the NKCC1 cotransporter, reduced the plateau phase of fluid flow by ∼30%. Isolated cells exposed to a hypertonic shock shrank by ∼20% and then showed a regulatory volume increase (RVI). Both the RVI and swelling were blocked by treatment with furosemide. Cells isolated from these glands shrink by ∼10% in the presence of carbachol. Blocking NKCC1 with furosemide reduced the amount of shrinkage by ∼50%. These data suggest that NKCC1 plays an important role in fluid secretion by the exorbital gland of mice. [ABSTRACT FROM AUTHOR]

Previously, we developed a dynamic model for the tubuloglomerular feedback (TGF) system in a single, short-looped nephron of the mammalian kidney. In that model, a semi-linear hyperbolic partial differential equation was used to represent two fundamental processes of solute transport in the nephron’s thick ascending limb (TAL): chloride advection by fluid flow along the TAL lumen and transepithelial chloride transport from the lumen to the interstitium. An empirical function and a time delay were used to relate glomerular filtration rate to the chloride concentration at the macula densa of the TAL. Analysis of the model equations indicated that stable limit-cycle oscillations (LCO) in nephron fluid flow and chloride concentration can emerge for sufficiently large feedback gain magnitude and time delay. In this study, the single-nephron model was extended to two nephrons, which were coupled through their filtration rates. Explicit analytical conditions were obtained for bifurcation loci corresponding to two special cases: (1) identical time delays but differing feedback gains, and (2) identical gains but differing delays. Similar to the case of a single nephron, our analysis indicates that stable LCO can emerge in coupled nephrons for sufficiently large gains and delays. However, these LCO may emerge at lower values of the feedback gain, relative to a single (i.e., uncoupled) nephron, or at shorter delays, provided the delays are sufficiently close. These results suggest that, in vivo, if two nephrons are sufficiently similar, then coupling will tend to increase the likelihood of LCO. [Copyright &y& Elsevier]

Purpose. The fluid secretory impairment of lacrimal and salivaryglands in Sjögren's syndrome (SS) is thought to be related to theextent of lymphocytic infiltration (LI) and subsequent loss of glandular tissue.In this study, we examine the correlation between the extent of tear flowreduction and the extent of LI of lacrimal glands in the NZB/W mouse, a modelof SS. Methods. We stimulated tear production by topical applicationof carbachol onto the gland while fluid was collected from the lacrimal duct.The lacrimal glands were removed after fluid collection for histology. Results. Fluid secretion in response to carbachol was less inthe majority of young NZB/W females compared to C57 control animals and noneof the glands showed LI. Fluid secretion was also impaired in the majorityof old NZB/W females, and the extent of LI was highly variable. Some of theold SW females also showed blunted fluid secretory responses and some degreeof focal LI. Young SW females showed no LI and most animals exhibited normalflow responses. Analysis of paired flow and LI measurements showed no correlationbetween LI and flow impairment in any of the groups or in the pooled data.Carbachol-stimulated protein secretion from lacrimal gland slices in vitro were similar in young and old SW and NZB/W mice. Conclusions. These results suggest that LI alone is not sufficientto explain the secretory dysfunction in the NZB/W mouse model of Sjögren'ssyndrome. [ABSTRACT FROM AUTHOR]

Objective: To develop a new method for viewing adrenergic innervation along renal preglomerular vessels; to assess nerve densities and vascular lesions along arcuate arteries (ArcA), arcuate arterial branches (ArcB), and interlobular arteries (ILA) in spontaneously hypertensive rats (SHR) and in angiotensin II (AngII) and in N[SUPG]-nitro-L-arginine methyl ester (L-NAME) hypertensive rats. Methods: Preglomerular vasculatures were isolated after HCl maceration and were immunostained against synaptophysin, a membrane protein of synaptic vesicles. Lesions were stained with Sudan black. Longitudinal nerve densities and relative frequencies of ArcA, ArcB, and ILA endowed with sudanophilic lesions were assessed separately. Results: Synaptophysin immunostaining revealed the vascular neural plexus. Nerves were adrenergic, as the plexus was destroyed by treatment with 6-hydroxy dopamine. Vascular lesions were not seen in SHR, and increased nerve density was observed along ArcA and ILA. In L-NAME- and AngII-hypertensive rats, vascular lesions affected predominantly ArcB and ILA, and nerve density was reduced by 12% and 28% (ArcA), 37% and 31% (ArcB), and by 55% and 34% (ILA), respectively, versus normotensive controls. Endo-thelin-1 receptor blockade did not affect AngII-induced hypertension but prevented both lesion development and reduction of density of the vascular neural plexus. Conclusions: The method we have devised provides a direct en face view of the vascular adrenergic innervation of isolated preglomerular vasculature. Measurements in hypertensive rat models suggest a link between vascular lesions and reduction in nerve density in hypertension. Endothelin-1 likely plays a key role in mediating both vascular injury and altered vascular nerve density in hypertension. [ABSTRACT FROM AUTHOR]