Figure 3. Climbing activity in the LIF model based on the positive feedback loop illustrated in Figure 2. A, Left, State space spanned by the instantaneous FR of the LIF neuron and the gADP conductance averaged across interspike intervals (〈gADP〉). The 〈gADP〉 nullcline (dashed) is the curve that gives for each firing rate the level of 〈gADP〉 generated at that rate. The FR nullcline (black, solid) gives for each firing rate the amount of 〈gADP〉 that would be required to maintain exactly that rate. Wherever these curves intersect or overlap, the neuron receives exactly what it needs to maintain the corresponding firing rate. Here the FR nullcline is just slightly below the 〈gADP〉 nullcline from ∼10 to 75 Hz, such that the neuron over this range receives slightly more ADP current than would be needed to maintain any of these rates. Inset, Magnified area of the graph within the box, to better visualize the distance between nullclines. The gray line is the trajectory that the system takes through 〈gADP〉/FR space when briefly excited by afferent inputs. The small bump in the trajectory is caused by the brief stimulus. Right, Time graph corresponding to the left side. After a brief stimulation at 5 sec (Stim), the instantaneous firing rate slowly climbs over tens of seconds. B, C, Same as A for configurations in which the FR nullcline is shifted further downward (left) such that climbing activity rises faster (right). D, Climbing activity in an LIF neuron (solid traces) coupled to a response neuron (dashed traces) from which it receives feedback inhibition. Traces for two different synaptic input weights producing very slow or faster climbing activity are shown. Note that the system was adjusted to maintain a basal firing rate at ∼10–20 Hz, as observed in thalamus (Komura et al., 2001) and some prefrontal cortex neurons (Quintana and Fuster, 1999; Rainer et al., 1999), from which climbing activity smoothly emerges at the time of cue presentation. The slight parallel dislocation of the nullclines such that the line attractor vanishes and the system starts climbing was achieved in this case by injecting a small depolarizing current (or by stimulating excitatory external synapses) with trial onset. In a working memory or prediction task, such a stimulation might originate from neurons with plateau-like delay activity that are turned on by the cue stimulus (Fuster, 1973, 2000; Funahashi et al., 1989; Durstewitz et al., 2000). E, Climbing activity is still preserved in the presence of noise from background synaptic input.