Frequency encoding in renal blood flow regulation

Abstract

With a model of renal blood flow regulation, we examined consequences of tubuloglomerular feedback (TGF) coupling to the myogenic mechanism via voltage-gated Ca channels. The model reproduces the characteristic oscillations of the two mechanisms and predicts frequency and amplitude modulation of the myogenic oscillation by TGF. Analysis by wavelet transforms of single-nephron blood flow confirms that both amplitude and frequency of the myogenic oscillation are modulated by TGF. We developed a double-wavelet transform technique to estimate modulation frequency. Median value of the ratio of modulation frequency to TGF frequency in measurements from 10 rats was 0.95 for amplitude modulation and 0.97 for frequency modulation, a result consistent with TGF as the modulating signal. The simulation predicted that the modulation was regular, while the experimental data showed much greater variability from one TGF cycle to the next. We used a blood pressure signal recorded by telemetry from a conscious rat as the input to the model. Blood pressure fluctuations induced variability in the modulation records similar to those found in the nephron blood flow results. Frequency and amplitude modulation can provide robust communication between TGF and the myogenic mechanism. tubuloglomerular feedback; myogenic mechanism; nonlinear interactions; amplitude modulation TUBULOGLOMERULAR FEEDBACK (TGF) and the myogenic mechanism regulate renal blood flow and glomerular filtration rate (GFR) of individual nephrons. Each generates an oscillation (7, 9, 14 -17, 25) that originates in nonlinearities of the particular system, and each acts on afferent arterioles. Because an afferent arteriolar smooth muscle cell has only one contractile mechanism, the two controllers must interact within single muscle cells. We have developed a computer simulation that models the interaction and predicts renal plasma flow, GFR, tubular hydrostatic pressure, NaCl concentration in tubular fluid at the macula densa, as well as a number of intracellular variables in arteriolar smooth muscle. The model permits comparison with experimental measurements of the plasma flow (25), the tubular variables, and GFR (7, 9, 14 -17) Simulation results with the model predicted that TGF modulates both the amplitude and the frequency of the myogenic oscillation, a result that has not been reported in the experimental literature. Frequency modulation is a variation in time of the frequency of an oscillation, and the two forms of modulation can arise because of nonlinear interactions with another oscillator. Standard spectral techniques assume that the signal being measured is stationary, a condition violated when there is frequency or amplitude modulation. We turned to wavelet transforms to measure the two forms of modulation (3). Wavelets are mathematical functions that represent a class of single waves that are soliton-like. The process of convolving them with time series, known as wavelet transforms, can provide separate measures of amplitude and frequency as continuous fu...

Vascular coupling induces synchronization, quasiperiodicity, and chaos in a nephron tree

“…A more detailed nephron model, which has a spatially distributed renal tubule, and a contractile mechanism in afferent arteriolar cells shows oscillations in both TGF and the myogenic mechanism, and the amplitudes of the oscillations increase monotonically with arterial pressure over the range 95-130 mm Hg. 11 At higher arterial pressures and higher values of coupling strength each of the nephrons in the ensemble is capable of a bifurcation to chaos. The longer medullary nephrons appear from the simulation results to operate with chaotic dynamics under most combinations of parameters and arterial pressure that are found in normal animals.…”

“…There are no measurements of proximal tubule pressure in juxtamedullary nephrons. We have used a more detailed model 11 to estimate the effect of increasing tubular length on the oscillation period. The inner medulla in the rat is 0.5 cm long.…”

“…Nephrons also communicate with each other by means of vascular signaling initiated by the TGF mechanism and propagated electrotonically and decrementally over the vascular wall. [3][4][5][6] Both TGF regulation and the myogenic mechanism are oscillating nonlinear systems that interact with each other within single nephrons 3,[7][8][9][10][11][12][13] and, by virtue of the vascularly propagated signals, between neighboring nephrons. 14,15 These interactions produce modulation of the myogenic mechanism by TGF as well as different forms of synchronization.…”

“…14,15 These interactions produce modulation of the myogenic mechanism by TGF as well as different forms of synchronization. 11,12,14 So far, these phenomena have been studied experimentally only in cortical nephrons with tubular and vascular components on the surface of the kidney, but because the deeper nephrons have similar structures and regulatory mechanisms, we assume that they, too, generate oscillations and are capable of interactions. If all or most nephrons oscillate, and if they interact, synchronization and other forms of nonlinear interactions are to be expected among nephrons along the same cortical radial artery.…”

Electrotonic vascular signal conduction and nephron synchronization

“…The oscillations are the result of nonlinearities in each system, and these two mechanisms interact because they act on a single contractile mechanism in arteriolar smooth cells (21). The interactions lead to synchronization of the oscillations and modulation of the frequency and amplitude of the myogenic mechanism by TGF (23). Because of the synchronization between the myogenic and the TGF oscillations, the frequencies of the two oscillations operate with a fixed ratio in the individual nephron, a 5:1 ratio being the most frequent.…”