Compartment models for the electrical stimulation of retinal bipolar cells

Abstract

Bipolar cells of the retina are among the smallest neurons of the nervous system. For this reason, compared to other neurons, their delay in signaling is minimal. Additionally, the small bipolar cell surface combined with the low membrane conductance causes very little attenuation in the signal from synaptic input to the terminal. The existence of spiking bipolar cells was proven over the last two decades, but until now no complete model including all important ion channel types was published. The present study amends this and analyzes the impact of the number of model compartments on simulation accuracy. Characteristic features like membrane voltages and spike generation were tested and compared for one-, two-, four- and 117-compartment models of a macaque bipolar cell. Although results were independent of the compartment number for low membrane conductances (passive membranes), nonlinear regimes such as spiking required at least a separate axon compartment. At least a four compartment model containing the functionally different segments dendrite, soma, axon and terminal was needed for understanding signaling in spiking bipolar cells. Whereas for intracellular current application models with small numbers of compartments showed quantitatively correct results in many cases, the cell response to extracellular stimulation is sensitive to spatial variation of the electric field and accurate modeling therefore demands for a large number of short compartments even for passive membranes.

A presynaptic source drives differing levels of surround suppression in two mouse retinal ganglion cell types

“…To investigate whether electrical compartmentalization can support functionally divergent signals from a BC, we generated a morphologically detailed NEURON cable model 28 from an EM reconstruction of a type 6 BC, including the location of all 91 ribbon output synapses and 120 presynaptic inhibitory synapses (Fig 6a). Although BCs are often modeled using only passive membrane properties [29][30][31] , multiple studies have measured voltage-gated ion conductances from BCs which could lead to greater electrical compartmentalization [32][33][34][35] . Thus we performed all experiments in both a passive model and an active model containing L-type Ca 2+ channels 36,37 , KV + channels 38 , and HCN2 channels 39,40 (see Methods for model details, Table 3 for parameter values, and Supplementary Fig.…”

A Multi-Domain Continuum Model of Electrical Stimulation of Healthy and Degenerate Retina

“…4.2. Representation of a discretised biological fibre cable model by pure resistances connecting compartments in series is widely accepted in the literature as seen, for example, in (Rattay et al, 2017(Rattay et al, , 2018 and (Freeman et al, 2011).…”

Two mathematical frameworks for vesicle release from a ribbon synapse of a retinal bipolar cell

“…The effect of extracellular stimulation generated by a single microelectrode on transient release, which is more similar to situations in retinal implants, was also tested. The test suggested no difference between active and passive cells for small pulse durations because the BC terminal membrane senses the same potential in both cases (Rattay et al 2018). However, for long pulses, spiking BCs exhibit more transient release because the generated spike would reach the terminal quickly, leading to a magnification of the membrane depolarization.…”

“…The modelV has no signal delay, while the modelCa has a maximum signal delay of 0.43 ms, similar to other works that suggest millisecond delay (Baden et al 2011, Singer andDiamond 2003; see discussion) ( Fig 10). To compare vesicle release in spiking and non-spiking BCs, two cells with the same geometry are considered in extracellular stimulation because the geometry of the cells defines the shape and amplitude of the potential exerted to the compartments (Rattay et al 2018). Thus, an imaginary spiking BC with the same shape was made by adding sodium and potassium channels to the axon.…”