The nephron-arterial network and its interactions.

Tubuloglomerular feedback and the myogenic mechanism form an ensemble in renal afferent arterioles that regulate single-nephron blood flow and glomerular filtration. Each mechanism generates a self-sustained oscillation, the mechanisms interact, and the oscillations synchronize. The synchronization generates a bimodal electrical signal in the arteriolar wall that propagates retrograde to a vascular node, where it meets similar electrical signals from other nephrons. Each signal carries information about the time-dependent behavior of the regulatory ensemble. The converging signals support synchronization of the nephrons participating in the information exchange, and the synchronization can lead to formation of nephron clusters. We review the experimental evidence and the theoretical implications of these interactions and consider additional interactions that can limit the size of nephron clusters. The architecture of the arterial tree figures prominently in these interactions.

Architecture of the rat nephron-arterial network: analysis with micro-computed tomography.

Among solid organs, the kidney's vascular network stands out, because each nephron has two distinct capillary structures in series and because tubuloglomerular feedback, one of the mechanisms responsible for blood flow autoregulation, is specific to renal tubules. Tubuloglomerular feedback and the myogenic mechanism, acting jointly, autoregulate single-nephron blood flow. Each generates a self-sustained periodic oscillation and an oscillating electrical signal that propagates upstream along arterioles. Similar electrical signals from other nephrons interact, allowing nephron synchronization. Experimental measurements show synchronization over fields of a few nephrons; simulations based on a simplified network structure that could obscure complex interactions predict more widespread synchronization. To permit more realistic simulations, we made a cast of blood vessels in a rat kidney, performed micro-computed tomography at 2.5-µm resolution, and recorded three-dimensional coordinates of arteries, afferent arterioles, and glomeruli. Nonterminal branches of arcuate arteries form treelike structures requiring two to six bifurcations to reach terminal branches at the tree tops. Terminal arterial structures were either paired branches at the tops of the arterial trees, from which 52.6% of all afferent arterioles originated, or unpaired arteries not at the tree tops, yielding the other 22.9%; the other 24.5% originated directly from nonterminal arteries. Afferent arterioles near the corticomedullary boundary were longer than those farther away, suggesting that juxtamedullary nephrons have longer afferent arterioles. The distance separating origins of pairs of afferent arterioles varied randomly. The results suggest an irregular-network tree structure with vascular nodes, where arteriolar activity and local blood pressure interact.

Multinephron dynamics on the renal vascular network.

Tubuloglomerular feedback (TGF) and the myogenic mechanism combine in each nephron to regulate blood flow and glomerular filtration rate. Both mechanisms are nonlinear, generate self-sustained oscillations, and interact as their signals converge on arteriolar smooth muscle, forming a regulatory ensemble. Ensembles may synchronize. Smooth muscle cells in the ensemble depolarize periodically, generating electrical signals that propagate along the vascular network. We developed a mathematical model of a nephron-vascular network, with 16 versions of a single nephron model containing representations of both mechanisms in the regulatory ensemble, to examine the effects of network structure on nephron synchronization. Symmetry, as a property of a network, facilitates synchronization. Nephrons received blood from a symmetric electrically conductive vascular tree. Symmetry was created by using identical nephron models at each of the 16 sites and symmetry breaking by varying nephron length. The symmetric model achieved synchronization of all elements in the network. As little as 1% variation in nephron length caused extensive desynchronization, although synchronization was maintained in small nephron clusters. In-phase synchronization predominated among nephrons separated by one or three vascular nodes and antiphase synchronization for five or seven nodes of separation. Nephron dynamics were irregular and contained low-frequency fluctuations. Results are consistent with simultaneous blood flow measurements in multiple nephrons. An interaction between electrical signals propagated through the network to cause synchronization; variation in vascular pressure at vessel bifurcations was a principal cause of desynchronization. The results suggest that the vasculature supplies blood to nephrons but also engages in robust information transfer.

Nephron blood flow dynamics measured by laser speckle contrast imaging.

Tubuloglomerular feedback (TGF) has an important role in autoregulation of renal blood flow and glomerular filtration rate (GFR). Because of the characteristics of signal transmission in the feedback loop, the TGF undergoes self-sustained oscillations in single-nephron blood flow, GFR, and tubular pressure and flow. Nephrons interact by exchanging electrical signals conducted electrotonically through cells of the vascular wall, leading to synchronization of the TGF-mediated oscillations. Experimental studies of these interactions have been limited to observations on two or at most three nephrons simultaneously. The interacting nephron fields are likely to be more extensive. We have turned to laser speckle contrast imaging to measure the blood flow dynamics of 50-100 nephrons simultaneously on the renal surface of anesthetized rats. We report the application of this method and describe analytic techniques for extracting the desired data and for examining them for evidence of nephron synchronization. Synchronized TGF oscillations were detected in pairs or triplets of nephrons. The amplitude and the frequency of the oscillations changed with time, as did the patterns of synchronization. Synchronization may take place among nephrons not immediately adjacent on the surface of the kidney.

Coupling-induced complexity in nephron models of renal blood flow regulation.

Tubular pressure and nephron blood flow time series display two interacting oscillations in rats with normal blood pressure. Tubuloglomerular feedback (TGF) senses NaCl concentration in tubular fluid at the macula densa, adjusts vascular resistance of the nephron's afferent arteriole, and generates the slower, larger-amplitude oscillations (0.02-0.04 Hz). The faster smaller oscillations (0.1-0.2 Hz) result from spontaneous contractions of vascular smooth muscle triggered by cyclic variations in membrane electrical potential. The two mechanisms interact in each nephron and combine to act as a high-pass filter, adjusting diameter of the afferent arteriole to limit changes of glomerular pressure caused by fluctuations of blood pressure. The oscillations become irregular in animals with chronic high blood pressure. TGF feedback gain is increased in hypertensive rats, leading to a stronger interaction between the two mechanisms. With a mathematical model that simulates tubular and arteriolar dynamics, we tested whether an increase in the interaction between TGF and the myogenic mechanism can cause the transition from periodic to irregular dynamics. A one-dimensional bifurcation analysis, using the coefficient that couples TGF and the myogenic mechanism as a bifurcation parameter, shows some regions with chaotic dynamics. With two nephrons coupled electrotonically, the chaotic regions become larger. The results support the hypothesis that increased oscillator interactions contribute to the transition to irregular fluctuations, especially when neighboring nephrons are coupled, which is the case in vivo.

New insight into erythrocyte through in vivo surface-enhanced Raman spectroscopy.

The article presents a noninvasive approach to the study of erythrocyte properties by means of a comparative analysis of signals obtained by surface-enhanced Raman spectroscopy (SERS) and resonance Raman spectroscopy (RS). We report step-by-step the procedure for preparing experimental samples containing erythrocytes in their normal physiological environment in a mixture of colloid solution with silver nanoparticles and the procedure for the optimization of SERS conditions to achieve high signal enhancement without affecting the properties of living erythrocytes. By means of three independent techniques, we demonstrate that under the proposed conditions a colloid solution of silver nanoparticles does not affect the properties of erythrocytes. For the first time to our knowledge, we describe how to use the SERS-RS approach to study two populations of hemoglobin molecules inside an intact living erythrocyte: submembrane and cytosolic hemoglobin (Hb(sm) and Hb(c)). We show that the conformation of Hb(sm) differs from the conformation of Hb(c). This finding has an important application, as the comparative study of Hb(sm) and Hb(c) could be successfully used in biomedical research and diagnostic tests.

Novel chiroptical analysis of hemoglobin by surface enhanced resonance Raman optical activity spectroscopy.

The metalloprotein hemoglobin (Hb) was studied using surface enhanced resonance Raman spectroscopy (SERRS) and surface enhanced resonance Raman optical activity (SERROA). The SERROA results are analyzed and compared with the SERRS, and the later to the resonance Raman (RRS) performed on Hb. The SERRS measurements careful optimization, with respect to the concentration and volume ratio of the analyte to colloids, enables for the first time SERROA of this molecule. We observed that the most intense SERROA signals were attributed the nu(4), nu(20), and nu(21) vibrations, which are sensitive to the redox state of the heme's iron ion, and to the presence of its sixth site, bound to exogenous ligand; O(2), NO or CO. However, in this study, the SERROA signals corresponding to these vibrations appear more sensitive to the Hb oxygen-binding properties than they appear in the SERRS or RRS. Moreover, the SERROA signal of Hb has successfully been monitored as a function of time, and was observed to be stable for 4-5 min. To our knowledge, the SERROA results of Hb, and its comparison to SERRS and RRS, are here reported for the first time.

Phase-modulation laser interference microscopy: an advance in cell imaging and dynamics study.

We describe how phase-modulation laser interference microscopy and wavelet analysis can be applied to noninvasive nonstained visualization and study of the structural and dynamical properties of living cells. We show how phase images of erythrocytes can reveal the difference between various erythrocyte forms and stages of hemolysis and how phase images of neurons reveal their complex intracellular structure. Temporal variations of the refractive index are analyzed to detect cellular rhythmic activity on different time scales as well as to uncover interactions between the cellular processes.

Noise controlled synchronization in potassium coupled neural models.

The paper applies biologically plausible models to investigate how noise input to small ensembles of neurons, coupled via the extracellular potassium concentration, can influence their firing patterns. Using the noise intensity and the volume of the extracellular space as control parameters, we show that potassium induced depolarization underlies the formation of noise-induced patterns such as delayed firing and synchronization. These phenomena are associated with the appearance of new time scales in the distribution of interspike intervals that may be significant for the spatio-temporal oscillations in neuronal ensembles.

Neural synchronization via potassium signaling.

Using a relatively simple model we examine how variations of the extracellular potassium concentration can give rise to synchronization of two nearby pacemaker cells. With the volume of the extracellular space and the rate of potassium diffusion as control parameters, the dual nature of this resource-mediated coupling is found to be responsible for the coexistence of competing patterns of in- and anti-phase synchronization between identical cells. Cell heterogeneity produces significant modifications of the dynamical regimes in the control parameter plane. By comparison with conventional gap junctional coupling, potassium signaling gives rise to considerable changes of the cellular response to external stimuli.

Mechanism-based modeling of complex biomedical systems.

Mechanism-based modeling is an approach in which the physiological, pathological and pharmacological processes of relevance to a given problem are represented as directly as possible. This approach allows us (i) to test whether assumed hypotheses are consistent with observed behaviour, (ii) to examine the sensitivity of a system to parameter variation, (iii) to learn about processes not directly amenable to experimentation, and (iv) to predict system behavior under conditions not previously experienced. The paper illustrates different aspects of the application of mechanism-based modeling through three different examples of relevance to the treatment of diabetes and hypertension: subcutaneous absorption of insulin, pulsatile insulin secretion in normal young persons, and synchronization of the pressure and flow regulation in neighbouring nephrons. The underlying ideas are that each regulatory mechanism represents the target for intervention and that the development of new and more effective drugs must be based on a deeper understanding of the biological processes.

Synchronization phenomena in nephron-nephron interaction.

Experimental data for tubular pressure oscillations in rat kidneys are analyzed in order to examine the different types of synchronization that can arise between neighboring functional units. For rats with normal blood pressure, the individual unit (the nephron) typically exhibits regular oscillations in its tubular pressure and flow variations. For such rats, both in-phase and antiphase synchronization can be demonstrated in the experimental data. For spontaneously hypertensive rats, where the pressure variations in the individual nephrons are highly irregular, signs of chaotic phase and frequency synchronization can be observed. Accounting for a hemodynamic as well as for a vascular coupling between nephrons that share a common interlobular artery, we develop a mathematical model of the pressure and flow regulation in a pair of adjacent nephrons. We show that this model, for appropriate values of the parameters, can reproduce the different types of experimentally observed synchronization. (c) 2001 American Institute of Physics.

Mapping of redox state of mitochondrial cytochromes in live cardiomyocytes using Raman microspectroscopy.

This paper presents a nonivasive approach to study redox state of reduced cytochromes c, c1 and b of complexes II and III in mitochondria of live cardiomyocytes by means of Raman microspectroscopy. For the first time with the proposed approach we perform studies of rod- and round-shaped cardiomyocytes, representing different morphological and functional states. Raman mapping and cluster analysis reveal that these cardiomyocytes differ in the amounts of reduced cytochromes c, c1 and b. The rod-shaped cardiomyocytes possess uneven distribution of reduced cytochromes c, c1 and b in cell center and periphery. Moreover, by means of Raman spectroscopy we demonstrated the decrease in the relative amounts of reduced cytochromes c, c1 and b in the rod-shaped cardiomyocytes caused by H2O2-induced oxidative stress before any visible changes. Results of Raman mapping and time-dependent study of reduced cytochromes of complexes II and III and cytochrome c in cardiomyocytes are in a good agreement with our fluorescence indicator studies and other published data.

Electrotonic vascular signal conduction and nephron synchronization.

Tubuloglomerular feedback (TGF) and the myogenic mechanism control afferent arteriolar diameter in each nephron and regulate blood flow. Both mechanisms generate self-sustained oscillations, the oscillations interact, TGF modulates the frequency and amplitude of the myogenic oscillation, and the oscillations synchronize; a 5:1 frequency ratio is the most frequent. TGF oscillations synchronize in nephron pairs supplied from a common cortical radial artery, as do myogenic oscillations. We propose that electrotonic vascular signal propagation from one juxtaglomerular apparatus interacts with similar signals from other nephrons to produce synchronization. We tested this idea in tubular-vascular preparations from mice. Vascular smooth muscle cells were loaded with a fluorescent voltage-sensitive dye; fluorescence intensity was measured with confocal microscopy. Perfusion of the thick ascending limb activated TGF and depolarized afferent arteriolar smooth muscle cells. The depolarization spread to the cortical radial artery and other afferent arterioles and declined with distance from the perfused juxtaglomerular apparatus, consistent with electrotonic vascular signal propagation. With a mathematical model of two coupled nephrons, we estimated the conductance of nephron coupling by fitting simulated vessel diameters to experimental data. With this value, we simulated nephron pairs to test for synchronization. In single-nephron simulations, the frequency of the TGF oscillation varied with nephron length. Coupling nephrons of different lengths forced TGF frequencies of both pair members to converge to a common value. The myogenic oscillations also synchronized, and the synchronization between the TGF and the myogenic oscillations showed an increased stability against parameter perturbations. Electronic vascular signal propagation is a plausible mechanism for nephron synchronization. Coupling increased the stability of the various oscillations.

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

The paper presents a study of synchronization phenomena in a system of 22 nephrons supplied with blood from a common cortical radial artery. The nephrons are assumed to interact via hemodynamic and vascularly propagated coupling, both mediated by vascular connections. Using anatomic and physiological criteria, the nephrons are divided into groups: cortical nephrons and medullary nephrons with short, intermediate and long Henle loops. Within each of these groups the delay parameters of the internal feedback regulation are given a random component to represent the internephron variability. For parameters that generate simple limit cycle dynamics in the pressure and flow regulation of single nephrons, the ensemble of coupled nephrons showed steady state, quasiperiodic or chaotic dynamics, depending on the interaction strengths and the arterial blood pressure. When the solutions were either quasiperiodic or chaotic, cortical nephrons synchronized to a single frequency, but the longer medullary nephrons formed two clusters with different frequencies. Under no physiologically realistic combination of parameters did all nephrons assume a common frequency. Our results suggest a greater variability in the nephron dynamics than is apparent from measurements performed on cortical nephrons only. This variability may explain the development of chaotic dynamics in tubular pressure records from hypertensive rats.

Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats.

We searched for synchronization among autoregulation mechanisms using wavelet transforms applied to tubular pressure recordings in nephron pairs from the surface of rat kidneys. Nephrons have two oscillatory modes in the regulation of their pressures and flows: a faster (100-200 mHz) myogenic mode, and a slower (20-40 mHz) oscillation in tubuloglomerular feedback (TGF). These mechanisms interact; the TGF mode modulates both the amplitude and the frequency of the myogenic mode. Nephrons also communicate with each other using vascular signals triggered by membrane events in arteriolar smooth muscle cells. In addition, the TGF oscillation changes in hypertension to an irregular fluctuation with characteristics of deterministic chaos. The analysis shows that, within single nephrons of normotensive rats, the myogenic mode and TGF are synchronized at discrete frequency ratios, with 5:1 most common. There is no distinct synchronization ratio in spontaneously hypertensive rats (SHR). In normotensive rats, full synchronization of both TGF and myogenic modes is the most probable state for pairs of nephrons originating in a common cortical radial artery. For SHR, full synchronization is less probable; most common in SHR is a state of partial synchronization with entrainment between neighboring nephrons for only one of the modes. Modulation of the myogenic mode by the TGF mode is much stronger in hypertensive than in normotensive rats. Synchronization among nephrons forms the basis for an integrated reaction to blood pressure fluctuations. Reduced synchronization in SHR suggests that the effectiveness of the coordinated response is impaired in hypertension.

Application of wavelet-based tools to study the dynamics of biological processes.

The article makes use of three different examples (sensory information processing in the rat trigeminal complex, intracellular interaction in snail neurons and multimodal dynamics in nephron autoregulation) to demonstrate how modern approaches to time-series analysis based on the wavelet-transform can provide information about the underlying complex biological processes.

Oscillator clustering in a resource distribution chain.

The paper investigates the special clustering phenomena that one can observe in systems of nonlinear oscillators that are coupled via a shared flow of primary resources (or a common power supply). This type of coupling, which appears to be quite frequent in nature, implies that one can no longer separate the inherent dynamics of the individual oscillator from the properties of the coupling network. Illustrated by examples from microbiological population dynamics, renal physiology, and electronic oscillator theory, we show how competition for primary resources in a resource distribution chain leads to a number of new generic phenomena, including partial synchronization, sliding of the synchronization region with the resource supply, and coupling-induced inhomogeneity.

Nonlinear interactions in renal blood flow regulation.

We have developed a model of tubuloglomerular feedback (TGF) and the myogenic mechanism in afferent arterioles to understand how the two mechanisms are coupled. This paper presents the model. The tubular model predicts pressure, flow, and NaCl concentration as functions of time and tubular length in a compliant tubule that reabsorbs NaCl and water; boundary conditions are glomerular filtration rate (GFR), a nonlinear outflow resistance, and initial NaCl concentration. The glomerular model calculates GFR from a change in protein concentration using estimates of capillary hydrostatic pressure, tubular hydrostatic pressure, and plasma flow rate. The arteriolar model predicts fraction of open K channels, intracellular Ca concentration (Ca(i)), potential difference, rate of actin-myosin cross bridge formation, force of contraction, and length of elastic elements, and was solved for two arteriolar segments, identical except for the strength of TGF input, with a third, fixed resistance segment representing prearteriolar vessels. The two arteriolar segments are electrically coupled. The arteriolar, glomerular, and tubular models are linked; TGF modulates arteriolar circumference, which determines vascular resistance and glomerular capillary pressure. The model couples TGF input to voltage-gated Ca channels. It predicts autoregulation of GFR and renal blood flow, matches experimental measures of tubular pressure and macula densa NaCl concentration, and predicts TGF-induced oscillations and a faster smaller vasomotor oscillation. There are nonlinear interactions between TGF and the myogenic mechanism, which include the modulation of the frequency and amplitude of the myogenic oscillation by TGF. The prediction of modulation is confirmed in a companion study (28).

Frequency encoding in renal blood flow regulation.

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.