Figure 1.

Theoretical limitations of GrC input combinations based on MFR-to-GrC ratios. A, Schematic diagram illustrating the MFR-GrC-Purkinje circuit and terminology. MFRs with IDs w-z converge onto a specific GrC. This combination of MFRs to this GrC represents the quartet for the illustrated GrC. Throughout the study, we examined how the diversity of MFR combinations onto GrCs relates to patterns of MFR inputs. B, The number of theoretical permutations of MFRs is given by the binomial coefficient, defined by n choose k with replacement, where n is the number of MFRs and k is the number of inputs combined per GrC. The binomial coefficient, for n choose 4 with replacement (black), is overlaid with the linear function (red) showing the ratio of GrCs to MFRs. The intersections of the curves indicate that, based on the linear relationship of MFRs to GrCs, GrCs could fully permute a maximum of 5 unique MFRs. C, Similar to B, but with the linear function relating GrCs to MFs, taking into account multiple MFRs per MF axon. D, The binomial coefficient (black trace; n choose 4 with replacement) is plotted against the number of unique MF IDs that could theoretically be permuted (equivalent to n). The cat cerebellum contains an estimated 2–4 billion GrCs (red lines), indicating that the cat GCL could fully permute 470–560 different MFRs. To distribute those MFR identities over the 77 million MFRs estimated to occupy the cat cerebellum, these unique sources would have to be duplicated between 2735 and 4595 times. PKJ, Purkinje.