Cellular Automaton: A Key Approach in Modeling the Outer Plexiform Layer

To the Editor: The retina in all vertebrates is composed of three layers of nerve cell bodies and two layers of synapses. The first area of neuropil, where synaptic contacts occur, is the outer plexiform layer, in which connections between rod and cones, and vertically running bipolar cells and horizontally oriented horizontal cells, occur. 1

Experimental data suggests that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate versus stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. 2 In addition, chemical coupling by neurotransmitter release has been seen in the inner plexiform layer of the retina, where amacrine cells, bipolar cells, and ganglion cells have chemical synapses, and it has been shown that amacrine cells play a synchronization role by giving feedback on ganglion cells for generating spontaneous activity in developing vertebrate retina. 3, 4 In order to simulate this spontaneous behavior, Godfrey and Swindale 3 used deterministic cellular automaton.

Cellular automaton is a discrete model studied in complex systems such as biological systems. It consists of a regular grid of cells, each in one of a finite number of states. The grid can be in any finite number of dimensions. Time is also discrete, and the state of a cell at the present time is a function of the states of a finite number of cells (called its neighborhood) at a previous time. These neighbors are a selection of cells interacting with the specified cell and do not change (though the cell itself may be in its neighborhood, it is not usually considered a neighbor). Every cell has the same rule for updating, based on the values in this neighborhood. Each time the rules are applied to the whole grid (lattice), a new generation is created. 5

On the other hand, in the outer plexiform layer, photoreceptors, horizontal cells, and bipolar cells have synapses. Horizontal cell hyperpolarization generates a feedback signal to the photoreceptors. 6 We previously hypothesized that horizontal cells have a functional role in synchronization of photoreceptors, 7 which leads to bursting activity in bipolar cells. To model such a neuropil, we propose the cellular automaton approach. Each cell of the cellular automaton represents a photoreceptor cell. The horizontal cells, which are responsible for interactions between photoreceptors, may be modeled by neighborhood rules of cellular automaton. To determine the new state of the lattice, we consider the previous state of each cell, other cell interactions on the desired cell, and the logarithm of input light intensity. Finally, we let the model evolve.

By proposing such a modeling approach, the horizontal cell role in transferring data from the outer plexiform layer to the inner plexiform layer may be elucidated explicitly. Moreover, we will be able to investigate precisely “off-on” pathways and disease states, which result in decreasing the “a-wave” amplitude and increasing its latency. By defining such a model, we may achieve a more profitable definition of electrical behavior of the outer plexiform layer, which emerged in an a-wave pattern that is important in clinical trials.