The results above suggest that, in order for CRP switch values to shift adaptively with changes in the strength of the RF stimulus, the strength of inhibition must depend on the relative strengths of the competitor and RF stimuli, rather than just on the strength of the competitor alone. In other words, the term I in Equation 4 must depend on relative-stimulus strength. From a circuit perspective, the simplest modification
to achieve this goal is to have the inhibitory units inhibit each other (reciprocal inhibitory connections; Figure 4A). Indeed, structural support for such a circuit motif in the Imc has been found in an anatomical study (Wang et al., 2004). The study showed that in addition to projecting to the OTid, Imc axonal branches also terminate within the Imc itself (Figure 4B). Such reciprocal connections will cause the inhibitory units representing each location to inhibit the C646 mw inhibitory units representing all other locations. As a result, the activity of each inhibitory unit should depend on the strength of its excitatory drive relative to the excitatory drive to other inhibitory units. To model the reciprocal connectivity, we first modeled each inhibitory unit as being affected by a combination of
input and output divisive inhibition (along with an implicit subtractive MEK inhibitor component; Equation 6). This formulation was general, because it allowed for the inhibition onto inhibitory units to be any arbitrary combination of the commonly observed forms of inhibition in the literature. equation(6) I(t)=(1iout(t)+1)·(miin(t)+1+h(lklk+s50k+(iin(t))k)) Here, I(t) is the inhibitory activity at computational time-step t. iin(t) and iout(t) were the input and output divisive factors at time-step
t, modeled as being proportional to the activity of the inhibitory units at the previous time step (compare to Equation 4): equation(7) iin(t)=rin·I(t−1),iout(t)=rout·I(t−1)iin(t)=rin·I(t−1),iout(t)=rout·I(t−1)rin Tryptophan synthase and rout are proportionality constants. In this formulation, transmission and synaptic delays were assumed to be equal to one computational time step, for simplicity. These equations were applied iteratively until there was no further change in the inhibitory activity, i.e., I(t) = I(t+1). The resulting steady-state activity of the inhibitory units was referred to as Iss. Consequently, at steady state, the input and output divisive factors in Equation 7 reduce to equation(8) iin=rin·Iss,iout=rout·Issiin=rin·Iss,iout=rout·Iss The single-stimulus-response functions of the inhibitory and excitatory units were unchanged from before. Before exploring the effect of reciprocal inhibition on output unit activity, we first analyzed its effect on the steady-state inhibitory activity. We plotted Iss for inhibitory unit 2 during a CRP measurement protocol, with an RF stimulus of strength 8°/s ( Figures S3A and S3B).