In the random wiring model, neurons receive multiple independent inputs that are anterior DS, posterior DS, or non-DS. The random wiring model is constrained by the previous experimental observation PD0325901 in vitro that mouse dLGN neurons receive one to three strong inputs from the retina (with probabilities: one input [p1], two inputs [p2], and three inputs [p3 = 1 − p1 + p2]), from which they derive their stimulus selectivity ( Cleland et al., 1971a, 1971b; Mastronarde, 1987, 1992; Usrey et al., 1999; Chen and Regehr, 2000). Importantly, the basic results of the model are robust

against the addition of dLGN neurons that receive more than three strong retinal inputs. The model assumes that input from DSRGCs must be nearly pure to generate a DSLGN or ASLGN, since linear summation of inputs only produces direction or axis selectivity (i.e., 0.5 DSI/ASI)

if over 90% of the inputs to a cell are of the required type(s). In the model, random wiring is defined such that the probability of Epigenetics inhibitor input to a dLGN neuron from a given type of RGC is equal to the total proportion of input to superficial dLGN belonging to that RGC type (f). We assume that the fractions of input to superficial dLGN of either anterior or posterior DSRGCs are equal and that upward and downward DSRGCs do not project to the superficial region, yielding 2f for the total fraction of DS input. Together, these assumptions define a set of equations for the probability of each possible type of cell (Table S1). The sum of probabilities for observing DSLGNs with one, two, or three inputs in the model is equal to the total fraction of DSLGNs, p(DS). Similar reasoning applies to ASLGNs with two or three inputs, yielding Rutecarpine p(AS) (see Supplemental Experimental Procedures for a full derivation). In the model, not all values for p(DS) and p(AS) are possible given

random wiring; however, the range of possibilities is large (Figure 4B, light gray region). Cleland et al. (1971a) performed paired RGC-LGN recordings in cats and found that very few dLGN neurons (8.8%, 5/57) had a single RGC input that accounted for all of its recorded spikes. This provides bounds on the likely fraction of dLGN neurons receiving only one driving RGC input (p1 = 0.038–0.19, 95% confidence interval [CI] using the Wilson interval for binomial variables with 5/57 single input LGN cells). Applying these bounds to p1 limits the possible solutions for fractions of ASLGNs and DSLGNs, which are consistent with the random wiring model (dark gray region of Figure 4B). The experimentally observed fractions of ASLGNs (p(AS) = 0.043, binomial 95% CI 0.026–0.069) and DSLGNs (p(DS) = 0.051, binomial 95% CI 0.033–0.