The nephron arterial network and its interactions: nonlinear and information theoretic analyses.

Nephrons receive blood from a tree-shaped network of arteries and arterioles and regulate demand by actions that affect the diameters of their afferent arterioles. The network structure is asymmetric. The flow of blood requires a gradient of hydrostatic pressure so that the blood pressure at the origins of different afferent arterioles must differ from each other. Nephron mechanisms that act on afferent arterioles include a myogenic mechanism, a common feature of smooth muscle cells throughout the body, and tubuloglomerular feedback (TGF), a negative feedback mechanism that senses concentrations of common electrolytes in tubular fluid as it passes from the thick ascending limb into the distal tubule. The myogenic mechanism generates an autonomous oscillation in the electrical potential difference of the plasma membrane. The TGF signal also oscillates, albeit at a lower frequency, and modulates the frequency and amplitude of the myogenic mechanism's potential difference oscillation. The interaction of TGF with the myogenic mechanism generates a bimodal electrical signal that enters the adjacent arterial segment. The arterial segments of the network are electrically conductive, providing a channel for nephrons to interact with each other. In addition, the oscillation of nephron blood flow caused by the myogenic-TGF interaction leads to changes in local arterial blood pressure, providing a hemodynamic interaction among nephrons. We developed a mathematical model that incorporates these features. The model demonstrates renal autoregulation and the oscillations in tubular fluid flow and pressure found in experiments. The results illustrate the effects of interactions on the network. In this paper we estimate Lyapunov exponents to establish the dynamic state of each nephron, and mutual information to provide quantitative evaluations of the importance of each of the information streams on nephron dynamics. The results indicate that all nephrons operate in a state of weak chaotic dynamics and that electrical signaling through the arteries exerts a greater influence on nephron dynamics than do hemodynamic interactions. Chaotic attractors are sensitive to initial conditions, and we suggest that the nephron cluster is therefore sensitive to the information streams in the system, enabling the cluster to adapt to changing external conditions.