Modeling cat retinal beta-cell arrays

There were three objectives to the work undertaken for this paper: (1) to provide a comprehensive characterization of the statistical properties of arrays of beta-cell somata; (2) to develop a model that simulates cellular arrays with the same properties; and (3) to use this model to examine whether the array of beta-cells should be viewed as one array or as two arrays, one each for its OFF- and ON-center cells. Beta-cells are morphological correlates of the electrophysiological X-cells and those beta-cells whose dendrites stratify within the outer and inner sublamina of the retina's inner plexiform layer correspond, respectively, to OFF- and ON-center X-cells. Arrays of peripheral beta-cell somata from two retinas were studied. A Delaunay triangulation and a Voronoi tessellation were generated for each array and measures derived from these constructs used to analyze the arrays' spatial organization. As others have shown previously with a less complete statistical characterization, we found that the arrays of OFF- and ON-center beta-cells have similar spatial properties and are more regular than the array of all beta-cells. We developed a model to simulate cellular arrays with spatial properties like those of arrays of beta-cells. A good fit between model and real arrays was found when the model assumed an explicit spatial dependence between the placement of OFF- and ON-center cells. We propose therefore that a single array of beta-cells formed of both OFF- and ON-center cells is consistent with the data currently available for beta-cell somatic arrays.