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

Interacting information streams on the nephron arterial network

Blood flow and glomerular filtration in the kidney are regulated by two mechanisms acting on the afferent arteriole of each nephron. The two mechanisms operate as limit cycle oscillators, each responding to a different signal. The myogenic mechanism is sensitive to a transmural pressure difference across the wall of the arteriole, and tubuloglomerular feedback (TGF) responds to the NaCl concentration in tubular fluid flowing into the nephron's distal tubule,. The two mechanisms interact with each other, synchronize, cause oscillations in tubular flow and pressure, and form a bimodal electrical signal that propagates into the arterial network. The electrical signal enables nephrons adjacent to each other in the arterial network to synchronize, but non-adjacent nephrons do not synchronize. The arteries supplying the nephrons have the morphologic characteristics of a rooted tree network, with 3 motifs characterizing nephron distribution. We developed a model of 10 nephrons and their afferent arterioles in an arterial network that reproduced these structural characteristics, with half of its components on the renal surface, where experimental data suitable for model validation is available, and the other half below the surface, from which no experimental data has been reported. The model simulated several interactions: TGF-myogenic in each nephron with TGF modulating amplitude and frequency of the myogenic oscillation; adjacent nephron-nephron with strong coupling; non-adjacent nephron-nephron, with weak coupling because of electrical signal transmission through electrically conductive arterial walls; and coupling involving arterial nodal pressure at the ends of each arterial segment, and between arterial nodes and the afferent arterioles originating at the nodes. The model predicted full synchronization between adjacent nephrons pairs and partial synchronization among weakly coupled nephrons, reproducing experimental findings. The model also predicted aperiodic fluctuations of tubular and arterial pressures lasting longer than TGF oscillations in nephrons, again confirming experimental observations. The model did not predict complete synchronization of all nephrons.

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.

Renal autoregulation in health and disease

Intrarenal autoregulatory mechanisms maintain renal blood flow (RBF) and glomerular filtration rate (GFR) independent of renal perfusion pressure (RPP) over a defined range (80-180 mmHg). Such autoregulation is mediated largely by the myogenic and the macula densa-tubuloglomerular feedback (MD-TGF) responses that regulate preglomerular vasomotor tone primarily of the afferent arteriole. Differences in response times allow separation of these mechanisms in the time and frequency domains. Mechanotransduction initiating the myogenic response requires a sensing mechanism activated by stretch of vascular smooth muscle cells (VSMCs) and coupled to intracellular signaling pathways eliciting plasma membrane depolarization and a rise in cytosolic free calcium concentration ([Ca(2+)]i). Proposed mechanosensors include epithelial sodium channels (ENaC), integrins, and/or transient receptor potential (TRP) channels. Increased [Ca(2+)]i occurs predominantly by Ca(2+) influx through L-type voltage-operated Ca(2+) channels (VOCC). Increased [Ca(2+)]i activates inositol trisphosphate receptors (IP3R) and ryanodine receptors (RyR) to mobilize Ca(2+) from sarcoplasmic reticular stores. Myogenic vasoconstriction is sustained by increased Ca(2+) sensitivity, mediated by protein kinase C and Rho/Rho-kinase that favors a positive balance between myosin light-chain kinase and phosphatase. Increased RPP activates MD-TGF by transducing a signal of epithelial MD salt reabsorption to adjust afferent arteriolar vasoconstriction. A combination of vascular and tubular mechanisms, novel to the kidney, provides for high autoregulatory efficiency that maintains RBF and GFR, stabilizes sodium excretion, and buffers transmission of RPP to sensitive glomerular capillaries, thereby protecting against hypertensive barotrauma. A unique aspect of the myogenic response in the renal vasculature is modulation of its strength and speed by the MD-TGF and by a connecting tubule glomerular feedback (CT-GF) mechanism. Reactive oxygen species and nitric oxide are modulators of myogenic and MD-TGF mechanisms. Attenuated renal autoregulation contributes to renal damage in many, but not all, models of renal, diabetic, and hypertensive diseases. This review provides a summary of our current knowledge regarding underlying mechanisms enabling renal autoregulation in health and disease and methods used for its study.

Mathematical modeling of renal hemodynamics in physiology and pathophysiology

In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease.

Light microscopic visualization of podocyte ultrastructure demonstrates oscillating glomerular contractions

Podocytes, the visceral epithelial cells of the kidney glomerulus, elaborate primary and interdigitating secondary extensions to enwrap the glomerular capillaries. A hallmark of podocyte injury is the loss of unique ultrastructure and simplification of the cell shape, called foot process effacement, which is a classic feature of proteinuric kidney disease. Although several key pathways have been identified that control cytoskeletal regulation, actin dynamics, and polarity signaling, studies into the dynamic regulation of the podocyte structure have been hampered by the fact that ultrastructural analyses require electron microscopic imaging of fixed tissue. We developed a new technique that allows for visualization of podocyte foot processes using confocal laser scanning microscopy. The combination of inducible and mosaic expression of membrane-tagged fluorescent proteins in a small subset of podocytes enabled us to acquire light microscopic images of podocyte foot processes in unprecedented detail, even in living podocytes of freshly isolated glomeruli. Moreover, this technique visualized oscillatory glomerular contractions and confirmed the morphometric evaluations obtained in static electron microscopic images of podocyte processes. These data suggest that the new technique will provide an extremely powerful tool for studying the dynamics of podocyte ultrastructure.

Dynamics of nephron-vascular network

The paper presents a modeling study of the spatial dynamics of a nephro-vascular network consisting of individual nephrons connected via a tree-like vascular branching structure. We focus on the effects of nonlinear mechanisms that are responsible for the formation of synchronous patterns in order to learn about processes not directly amenable to experimentation. We demonstrate that: (i) the nearest nephrons are synchronized in-phase due to a vascular propagated electrical coupling, (ii) the next few branching levels display a formation of phase-shifted patterns due to hemodynamic coupling and mode elimination, and (iii) distantly located areas show asynchronous behavior or, if all nephrons and branches are perfectly identical, an infinitely long transient behavior. These results contribute to the understanding of mechanisms responsible for the highly dynamic and limited synchronization observed among groups of nephrons despite of the fairly strong interaction between the individual units.

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.

C-type period-doubling transition in nephron autoregulation

The functional units of the kidney, called nephrons, utilize mechanisms that allow the individual nephron to regulate the incoming blood flow in response to fluctuations in the arterial pressure. This regulation tends to be unstable and to generate self-sustained oscillations, period-doubling bifurcations, mode-locking and other nonlinear dynamic phenomena in the tubular pressures and flows. Using a simplified nephron model, the paper examines how the regulatory mechanisms react to an external periodic variation in arterial pressure near a region of resonance with one of the internally generated mode-locked cycles. We show how the stable and unstable resonance cycles generated in this response undergo interconnected cascades of period-doubling bifurcations and how each period doubling leads to the formation of a new pair of saddle-node bifurcation curves along the edges of the resonance zone. We also show how period doubling of the resonance cycles is accompanied by a torus-doubling process in the quasiperiodic regime that exists outside of the resonance zone.

Informational dynamics of vasomotion in microvascular networks: a review

Vasomotion refers to spontaneous oscillation of small vessels observed in many microvascular beds. It is an intrinsic phenomenon unrelated to cardiac rhythm or neural and hormonal regulation. Vasomotion is found to be particularly prominent under conditions of metabolic stress. In spite of a significant existent literature on vasomotion, its physiological and pathophysiological roles are not clear. It is thought that modulation of vasomotion by vasoactive substances released by metabolizing tissue plays a role in ensuring optimal delivery of nutrients to the tissue. Vasomotion rhythms exhibit a great variety of temporal patterns from regular oscillations to chaos. The nature of vasomotion rhythm is believed to be significant to its function, with chaotic vasomotion offering several physiological advantages over regular, periodic vasomotion. In this article, we emphasize that vasomotion is best understood as a network phenomenon. When there is a local metabolic demand in tissue, an ideal vascular response should extend beyond local microvasculature, with coordinated changes over multiple vascular segments. Mechanisms of information transfer over a vessel network have been discussed in the literature. The microvascular system may be regarded as a network of dynamic elements, interacting, either over the vascular anatomical network via gap junctions, or physiologically by exchange of vasoactive substances. Drawing analogies with spatiotemporal patterns in neuronal networks of central nervous system, we ask if properties like synchronization/desynchronization of vasomotors have special significance to microcirculation. Thus the contemporary literature throws up a novel view of microcirculation as a network that exhibits complex, spatiotemporal and informational dynamics.

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.