Linear and Nonlinear Behaviors of the Photoreceptor Coupled Network

Abstract

Photoreceptors are electrically coupled to one another, and the spatiotemporal properties of electrical synapses in a two-dimensional retinal network are still not well studied, because of the limitation of the single electrode or pair recording techniques which do not allow simultaneously measuring responses of multiple photoreceptors at various locations in the retina. A multiple electrode recording system is needed. In this study, we investigate the network properties of the two-dimensional rod coupled array of the salamander retina (both sexes were used) by using the newly available multiple patch electrode system that allows simultaneous recordings from up to eight cells and to determine the electrical connectivity among multiple rods. We found direct evidence that voltage signal spread in the rod-rod coupling network in the absence of I _h (mediated by HCN channels) is passive and follows the linear cable equation. Under physiological conditions, I _h shapes the network signal by progressively shortening the response time-to-peak of distant rods, compensating the time loss of signal traveling from distant rods to bipolar cell somas and facilitating synchronization of rod output signals. Under voltage-clamp conditions, current flow within the coupled rods follows Ohm's law, supporting the idea that nonlinear behaviors of the rod network are dependent on membrane voltage. Rod-rod coupling is largely symmetrical in the 2D array, and voltage-clamp blocking the next neighboring rod largely suppresses rod signal spread into the second neighboring rod, suggesting that indirect coupling pathways play a minor role in rod-rod coupling.

Keywords: HCN channels; Ih; ZD7288; junctional resistance; linear cable equation; photoreceptor coupling; rod–rod coupled network; space constant; time-to-peak.

Figure 1.

A, Locations of seven rods recorded in flat-mounted salamander retina with the multiple patch electrode recording system. RodXY are rod locations in the 2D array and e1–e7 are electrode numbers. B, Original locations of the seven rods before recording, as rods were slightly pushed from original positions (yellow circles) by the patch electrodes. Large circles, rods; small circles, cones. Red resistors are coupling resistance between rods (coupling resistance between rods and cones are much higher and thus not shown). C, Voltage responses of Rods1,0; 2,0; 3,0; 3,−1; 1,−2; and 0,−2 to a −1 nA current step (1 s) injected into Rod0,0. D, Repeating experiments in C in the presence of 100 µM ZD7288.

Figure 2.

A, Schematic diagram of infinite linear cable representation of the rod coupled network. We reduced the two-dimensional lattice into a one-dimensional (x direction) cable by lumping coupling resistance in the y direction with the rod’s leak resistance, resulting in a membrane resistance r_m= 250 MΩ·10 µm. The internal resistance is the cytoplasmic resistance between two adjacent rods (20 µm apart) r_i= R_j/20 µm = 2,000 MΩ/20 µm (Zhang and Wu, 2005, 2009b). These yield a space constant λ = 5 µm and time constant τ = 78.5 ms. B, Normalized responses of Rod0,0 (red), 1,0 (green), 2,0 (brown), and 3,0 (blue) in the absence (top 4 curves) and presence of ZD (bottom 4 curves). The time of response peak of Rod1,0; 2,0; and 3,0 in the absence of ZD are shown as t1, t2, and t3, respectively. C, In the presence of ZD, we replotted the onset charge curves in B (inverted display) and found that they agree with the predictions of the infinite cable equation (complementary error function solutions, black curves in the colored traces; Equation 6 in Materials and Methods, The infinite cable model; Johnston and Wu, 1994). D, Average (n = 5) steady-state response amplitudes (with standard deviations as error bars) of Rod0,0; 1,0; 2,0; and 3,0 in ZD normalized against the amplitude of Rod0,0 (colored dots) versus distance in the cable (X = x/λ), and they agree with the steady-state solution of the cable equation with a space constant 5 µm (black solid curve; Eq. 5 in Materials and Methods, The infinite cable model). Error bars are standard deviations.

Figure 3.

A, Current responses of four rods in a linear array (rod locations are shown in B) to a voltage-clamp step (−40 to −80 mV, 0.5 s) in Rod0,0. Rod1,0; Rod2,0; and Rod3,0 were voltage clamped at −40 mV sequentially and the peak values of I_j01 and I_j02 agree with the prediction of the Ohm’s law (see text for statistics). C, Normalized current responses of Rod1,0; Rod2,0; and Rod3,0 exhibited identical waveforms, suggesting that current flow within the coupled array under voltage clamp is linear. D, schematic diagram of internal resistance (r_i), coupling resistance (R_j), and junctional currents (I_j) in the four coupled rods.

Figure 4.

A, Five rods recorded in flat-mounted salamander retina with the multiple patch electrode recording system. B, Original locations of the five rods before recording. C, Voltage responses of Rod1,0; Rod0,−1; Rod−1,0; and Rod0,1 to a −1 nA current step (1 s) injected into Rod0,0. D, Same experiments as in C in the presence of 100 µM ZD7288. E, Average voltage responses of eight five-rod clusters to −1 nA current injection into the center rod. Rod−1,0/Rod1,0 and Rod0,1/Rod0,−1 are in two orthogonal directions. Error bars are standard deviations, and p values from t test indicate that there are no statistical significant differences between Rod−1,0 and Rod1,0 responses, between Rod0,1 and Rod0,−1 responses, and between the two orthogonal rod pairs.

Figure 5.

A, Four rods recorded in flat-mounted salamander retina with the multiple electrode recording system. B, Original locations of the four rods before recording. C, Voltage responses of Rod1,0; Rod0,1; Rod0,2; and Rod0,1 to a −1 nA current step (1 s) injected into Rod0,0. D, Same experiments as in C except that Rod0,1 was voltage clamped at −40 mV.