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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