Interacting information streams on the nephron arterial network

Abstract

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.

Keywords: arterial networks; frontiers; myogenic mechanism; nephron clusters; partial synchronization; renal autoregulation; synchronization; tubuloglomerular feedback.

FIGURE 1

Upper panel: Causal loop diagram of a single nephron. This model was used for each of the nephron-afferent arteriole ensembles shown in Figure 2. Tubular pressure, flow rates, and NaCl concentrations were solved with a set of partial differential equations, using glomerular filtration rate, end distal tubule hydrostatic pressure, and initial NaCl concentration as boundary conditions. NaCl concentration in tubular fluid at the macula densa generates a signal that modulates Ca ²⁺ conductance in afferent arteriolar smooth muscle cells. Increases in the Ca ²⁺ current and the K ⁺ current produce changes in membrane potential difference of opposite sign because the reversal potential, V _ca and V _K , respectively and the membrane potential have opposite signs. Membrane potential between the afferent arteriole and its adjacent vascular node (not shown in the diagram) is propagated along the vascular net of Figure 2, interacting with similar electrical signals from other nephrons. Myosin light chain abundance (MLC) varies with intracellular Ca ²⁺ concentration and the change in cross-bridge abundance modulates the circumference of fhe afferent arteriole. The afferent arteriole was represented with a set of initial valued ordinary differential equations. Reproduced from Laugesen et al. (2010). Lower panel: Predicted time series of tubular pressure from a 1 nephron version of the nephron-afferent arteriole model.

FIGURE 2

Diagram of the nephron-arterial network used for simulations. Not drawn to scale. The distribution of afferent arterioles corresponds to the distribution found in a renal vascular cast Marsh et al. (2017). Terminal arteries end in paired afferent arterioles. Sub-terminal arteries supply terminal arteries.

FIGURE 3

Time series of proximal tubule pressures in a run of the model shown in Figure 2.

FIGURE 4

Time series of proximal tubule pressures in a run of the same model shown in Figure 3, extended to a duration of 3,000s.

FIGURE 5

Time series of vascular hydrostatic pressures in the same run shown in Figure 3. Numbers at the right refer to the nodes in Figure 2. Pressure in node 11 was 85 mmHg throughout the simulation.

FIGURE 6

Time series of vascular hydrostatic pressures in the same run shown in Figure 4. Numbers at the right refer to the nodes in Figure 2. Pressure in node 11 was 85 mmHg throughout the simulation.