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The nonlinear mechanism was initially attributed to amacrine circuits because bipolar circuits were thought to be linear. But we now know that the bipolar cell synapse expresses an important nonlinear property, "rectification." The bipolar synapse releases vesicles at a low basal rate; consequently, depolarization can increase release, but hyperpo-larization cannot decrease it. Therefore, dimming an OFF bipolar cell increases release but brightening does not decrease it (and vice versa for an ON bipolar cell). This nonlinearity hardly affects a narrow-field ganglion cell because the bipolar receptive fields overlap due to cone coupling (Cohen and Sterling, 1992; Smith and Sterling, 1990). However, it strongly affects a wide-field cell because bipolar receptive fields are smaller than the extent of the convergent array (Demb et al., 2001a; Freed and Sterling, 1988). This important property of wide-field cells, which arises simply from their extent of spatial convergence, may be the clearest example at the circuit level of an "emergent property."

Sluggish Ganglion Cells: Smaller, Slower, Cheaper Nearly half of the ganglion cells fire "sluggishly." Their spike autocorrelograms show a gradual rise and plateau, and their peak rates are ~ 10-fold lower than for brisk cells (Cleland and Levick, 1974a; DeVries and Baylor, 1997). The axons of sluggish cells are thin and slowly conducting (Stone and Fukuda, 1974). Consequently, their wire volume is minimal, occupying less than 5% of the optic nerve's cross-section (Sterling, unpublished). Sluggish cells (also termed "W") comprise many types with complex response properties, such as directional selectivity and local-edge detection (e.g., Caldwell and Daw, 1978; Cleland and Levick, 1974b; Rowe and Stone, 1976a, 1976b).

Sluggish types have been relatively little studied, partly because, compared to types that fire briskly, these cells seem somehow disadvantaged. Yet, this might actually imply a different coding strategy (Meister and Berry, 1999; Victor, 1999). A cell that responds only to motion of a local edge at low velocity carries fewer possible messages than a cell that responds to a wider range of stimuli. The simpler message might be encoded efficiently by fewer spikes that cost less in energy and in wire volume (Ames and Li, 1992; Ames et al., 1992; Attwell and Laughlin, 2001; Balasubramanian and Berry, 2002). For these benefits, slower conduction velocity seems to be an acceptable cost.

Is Information Content the Sole Determinant of Wire Volume? The hypothesis that wire volume matches information content arouses a healthy skepticism and thus needs some elaboration. The hypothesis tries to unify three facts: (1) axon thickness rises with number of output synapses; (2) the neurons with thicker axons and more outputs are the ones that transmit higher temporal frequen cies; (3) higher temporal frequencies transmit more information. Points 1 and 2 are illustrated in Figure 17.8, 17.13, and 17.14; point 3 comes from Shannon's equation. The hypothesis claims that more synapses are required at the output because the information capacity of the synapse is limited (de Ruyter van Steveninck and Laughlin, 1996; Laughlin, 1994;.

Of course, there may be other reasons why a neuron might need additional synapses and thus a larger axon. For example, the brisk-transient ganglion cell (but not the brisk-sustained cell) typically sends one branch to innervate the lateral geniculate nucleus and another branch to the superior colliculus. Thus, its greater axon thickness may be partly attributable to its greater number of boutons in the genicu-late and partly to its need to support an additional arbor. In short, the hypothesis does not exclude additional determinants of wire volume.

Conclusion

Many features of retinal design seem interpretable as evolutionary adaptations to a surprisingly small number of lifestyle decisions and physical constraints:

1. Because mammals move fast, their photoreceptors must be small. Because mammals forage night and day, they need both rods and cones. So rods must be numerous and information poor, whereas cones can be sparse and information rich.

2. The two receptor arrays require different circuits. Rods must converge in large numbers—yet not accumulate noise that would swamp their information-poor signals. This requires several stages, each equipped to remove noise by nonlinear amplification. Cones must converge in smaller numbers—yet not allow their information-rich signals to saturate postsynaptic neurons. This requires bandpass filtering to reduce redundancy and noise.

3. The retina must remain thin and cannot increase its metabolic rate. Therefore, rod and cone circuits must jointly minimize total cellular volume and metabolic cost. Indeed, each circuit seems constrained to expend these quantities in proportion to its information content.

Some additional circuits (mainly amacrine) are known but not described here, and many additional amacrine circuits remain to be discovered. But quite likely their purposes will prove generally similar: to optimize signal transfer using various forms of neural adaptation or gain control. Many of the matches suggested here under the rubric of symmor-phosis lack quantitative rigor. This suggests the next large task: to quantify for each retinal circuit, its information rate, metabolic cost, and wire volume, and to test quantitatively the relationships between these three variables. When this is accomplished, the retina will finally be "understood."

Acknowledgments

I thank Drs. Robert Smith, Martin Wilson, and David Vaney for comments on the manuscript, and Sharron Fina for preparing it. My research has been supported by NEI grants EY00828 and EY08124. I thank Drs. Steven DeVries and Amy Harkins for providing unpublished data for Figures 17.9 and 17.13.

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