Such a pathway through the parameter space of network connectivity could be utilized during development, with the integrator network beginning in a more topographically organized form and moving to a more distributed connectivity pattern in the mature state, where the functional signatures of topography seem to be weaker (as discussed in Miri et al., 2011). In addition, our approach can be extended to allow greater heterogeneity in synaptic parameters or to model

circuits with nonmonotonic tuning curves (D.F., unpublished data). We have considered a single shape of synaptic activation function for all excitatory neurons, and a separate single shape for all inhibitory neurons, regardless of threshold. Relaxing this constraint might identify circuit architectures in which there are gradients Alisertib concentration in synaptic activation parameters as a function of neuronal threshold. Our work makes several predictions about the mechanisms of integration in the oculomotor integrator

and possibly other short-term memory circuits. First, in contrast to the previous spiking model of the oculomotor integrator based upon purely saturating synapses (Seung et al., 2000; Figure S4D), which modeled a single unilateral population and was generated before the inactivation experiments had been performed, our sensitivity analysis suggests that both inhibition and excitation are likely to be mediated by approximately linear or sigmoidal synaptic activation functions. Second, our quantitative fits to the drift rates following

inactivation suggest that the GSI-IX observed long integration time constants may not be solely due to network mechanisms, and instead suggest the presence of an intrinsic cellular or synaptic process with a time constant of order 1 s. Third, we suggest that integration depends critically upon the presence of a threshold mechanism. This could either take the form of a synaptic (or dendritic) threshold, as suggested by Aksay et al. (2007), or result from the circuit’s recurrent connectivity depending critically upon neurons with high eye-position thresholds, particularly for inhibition. Potential “synaptic” mechanisms consistent with a sigmoidal dependence upon presynaptic firing rate and an ∼1 s time constant are presynaptic facilitation (Wang MYO10 et al., 2006) or, postsynaptically, localized dendritic plateau potentials (Major et al., 2008 and Wei et al., 2001). The long time constants associated with these mechanisms could provide robustness against disruptions of circuit connectivity (Camperi and Wang, 1998, Goldman et al., 2003, Koulakov et al., 2002 and Mongillo et al., 2008). The high thresholds could be useful in filtering out low firing rates (Chichilnisky and Rieke, 2005), which are noisier in the oculomotor integrator than higher firing rates (Aksay et al., 2003).