Integrating with Action Potentials

The sustained activity seen in the oculomotor inteIntegrating with Action Potentials grator, like that shown in the figure, provides a representation of the running integral of the burst neuron inputs. Similar types of sustained activity have been seen in a When we add a long list of numbers in our heads, we number of brain areas in monkeys doing tasks that remust keep track of the running total while performing quire short-term memory of transient stimuli (Fuster, the individual summations. Neural circuits integrating 1995). They have been interpreted in this context as a information must similarly retain a representation of neural correlate of working memory (Goldman-Rakic, what has been gathered up to a given point in time, so 1994; Fuster, 1995). Therefore, the question of what susthat this can be augmented by further information as it tains this activity is important for understanding not only becomes available. Integration, the task of summing and neural integrators, but potential mechanisms of shortaccumulating a series of inputs, involves both computaterm memory as well. tion (addition) and memory (retention of the sum). ModAn idea going back to Hebb (1949) is that a persistent els of neural circuits performing integration suggest that response to a transient input can be generated when the memory part of the task is the more challenging to feedback input from other neurons within an integrator accomplish and difficult to understand. or memory circuit substitutes for the transient external There is considerable experimental evidence supportdrive (Amit, 1989). For this mechanism to work, the reing the ability of neural circuits to act as integrators in current connections within the circuit must provide each tasks such as target selection (Schall and Thompson, neuron with exactly what it needs to maintain an appro1999), sensory discrimination (Gold and Shadlen, 2000), priate level of activity. This requirement is particularly and oculomotor control (Robinson, 1989). The oculomostringent in an integrator circuit, as opposed to an assotor system is the subject of a theoretical study by Seung, ciative memory network (Amit, 1989), because the inteLee, Reis, and Tank appearing in this issue of Neuron grator must be capable of sustaining activity at virtually (Seung et al., 2000). Neurons in the prepositus hypoany level to represent all values of the quantity being glossi and medial vestibular nucleus of the mammalian integrated. Not surprisingly, this requires some fine tunoculomotor system, and in an analogous oculomotor ing. If neurons in the circuit receive slightly too much circuit of the goldfish modeled by Seung et al., maintain, input from each other during the sustained period, netin their persistent activity, a memory trace of the horiwork activity will rise, creating even more input. This can zontal position of the eyes. This information is obtained lead to uncontrolled growth of activity. If the recurrent by integrating the transient outputs of burst neurons excitation is too weak, the network will fail to sustain that signal changes in eye position. Brief pulses from the itself, and activity will decline to zero. The presence of burst neurons shift the activity of the integrator neurons inhibitory input shifts the point at which sustained firing either upward or downward, and that activity is mainoccurs, but it does not alleviate the fine-tuning problem. tained between burst discharges as in the upper trace The goldfish oculomotor circuit being modeled by of the figure. Following a path set by earlier work (RobSeung et al. is not a perfect integrator, but it is remarkinson, 1989; Seung, 1996), Seung et al. show that inteably good. The level of activity during sustained periods gration can be achieved in a network of relatively realisdrifts with a time constant greater than 10 s. The time tic spiking model neurons. scale for the retention of activity in the absence of finely tuned recurrent excitation in the model of Seung et al. is roughly equal to the decay time of its excitatory synaptic conductances. This is set to 100 ms, similar to the decay time of NMDA conductances, which is obviously much shorter than the required 10 s. Increasing the decay time for self-sustained activity from 100 ms to greater than 10 s requires adjusting the network interactions to an accuracy better than 1%. Seung et al. achieved this fine tuning by performing a least-squares fit of the recurrent input generated by the circuit to the required input. Such a calculation is difficult in the type of spiking, conductance-based model they use. They therefore constructed an approximate description of their model in terms of firing rates and average synaptic inputs, and performed the matching calculation within the firing rate model. The firing rate model provides an accurate enough description of the spiking model that this proceCartoon of the Activity of a Neuron in an Integrator Circuit dure worked. This is a reassuring result for neural modelThe arrows at the bottom represent transient input to a neural circuit. ers who flip between spiking and firing rate descriptions The two traces show different types of responses. The lower trace