A Computational Study on the Role of Gap Junctions and Rod Ih Conductance in the Enhancement of the Dynamic Range of the Retina

Recent works suggest that one of the roles of gap junctions in sensory systems is to enhance their dynamic range by avoiding early saturation in the first processing stages. In this work, we use a minimal conductance-based model of the ON rod pathways in the vertebrate retina to study the effects of electrical synaptic coupling via gap junctions among rods and among AII amacrine cells on the dynamic range of the retina. The model is also used to study the effects of the maximum conductance of rod hyperpolarization activated current Ih on the dynamic range of the retina, allowing a study of the interrelations between this intrinsic membrane parameter with those two retina connectivity characteristics. Our results show that for realistic values of Ih conductance the dynamic range is enhanced by rod-rod coupling, and that AII-AII coupling is less relevant to dynamic range amplification in comparison with receptor coupling. Furthermore, a plot of the retina output response versus input intensity for the optimal parameter configuration is well fitted by a power law with exponent . The results are consistent with predictions of more theoretical works and suggest that the earliest expression of gap junctions along the rod pathways, together with appropriate values of rod Ih conductance, has the highest impact on vertebrate retina dynamic range enhancement.


Supporting Information
The retina conductance based model was created using the NEURON software [37] and it is composed of single compartment neuron models with passive parameters described in Table 1 of the main text. The conductances and reversal potentials for the neuron models are described in Table 1. For all conductances in the model we used the Hodgkin-Huxley formulation [46] where the activation, inactivation and noninactivating variables (m,n,h) were numerically calculated as : where x represents any of the m,n,h variables, and α and β are the voltage-dependent activation and inactivation rates. For all compartments in the neuron models that express calcium dependent channels the same calcium removal mechanism was used. The calcium influx is controlled by the voltage gated calcium and calcium dependent channels while the efflux is given by the second term in the following expression : where k = 0.1, d = 1µm, K T = 10 −4 mM/ms, K d = 10 −4 mM and F is the Faraday constant.
Rod photoreceptor The rod model is based on the single compartment model described in our previous work [16]. The modified model has a potassium current with fast dynamics responsible to accelerate the response to light stimulus (I Kx ), a potassium current with rectifier characteristics (I Kv ), a calcium dependent potassium current (I KCa ), a hyperpolarization activated current (I h ), a L-type calcium current (I Ca ) and a calcium dependent chloride current (I Cl(Ca) ) with parameters and dynamics taken from the references indicated in Table 2 and Table 4.
Cone photoreceptor The cone model is a modified version of the single compartment model described by Kourennyi and others [17]. The modified model has a potassium current with rectifier characteristics (I Kv ), a calcium dependent potassium current (I KCa ), a hyperpolarization activated current (I h ), a calcium current (I Ca ) and a calcium dependent chloride current (I Cl(Ca) ) with parameters and dynamics taken from the references indicated in Table 2 and Table 4.
Rod and cone bipolar cell The bipolar cells participate in both the rod and cone circuits connecting AII amacrine cells and ganglion cells [2,3]. In this work we used the same model to simulate both the rod bipolar cell and the cone bipolar cell. The only difference between the single compartment models is that the rod bipolar cell model expresses the TEA sensitive I A current [19]. The model is based on the single compartment model described by Usui and others [19] and has a potassium current with rectifier characteristics (I Kv ), a calcium dependent potassium current (I KCa ), a hyperpolarization activated current (I h ), a calcium current (I Ca ) and a TEA-sensitive potassium current (I A ) with parameters and dynamics taken from the references indicated in Table 2 and Table 6.
AII amacrine cell The AII amacrine cell model is a modified version of the single-compartment model described by Smith and Vardi [24]. The modified model has only the Hodgkin-Huxley sodium and potassium channels [46] with parameters and dynamics taken from the references indicated in Table 2 of the main text and Table  7. The potassium current is activated when the cell is depolarized to -20mV while the sodium current is activated at -30 mV [24].

Ganglion cell
The ganglion cell model is a modified version of the single-compartment model described by Fohlmeister and Miller [25]. The modified model has a potassium current with rectifier characteristics (I Kv ), a calcium dependent potassium current (I KCa ), a calcium current (I Ca ), a TEA-sensitive potassium current (I A ) and the Hodgkin-Huxley sodium channels with parameters and dynamics taken from the references indicated in Table 2 and Table 8.