Stability of the Memory Eye Position in a Recurrent Network of Conductance-Based Model Neurons

Memory-related neural activity in the oculomotor integrator is modeled with a network of conductance-based neurons interacting by recurrent synaptic excitation. The recurrent network maintains distributed patterns of persistent activity that encode eye position in an analog manner. Analog persistence is not a generic property of the network architecture, but is achieved by a careful design process involving a reduced model derived by the method of averaging, a synaptic weight matrix with outer product structure, and precise tuning of positive feedback so that saturation and threshold nonlinearity compensate for each other. In the state space of the reduced model, tuning produces a one-dimensional manifold of points at which drift is very small. These points are the persistent activity patterns of the network, and constitute an approximation to a continuous dynamical attractor. Eye position is encoded as the coordinate along the manifold, so that there is a threshold linear relationship between eye position and firing rate, which is consistent with single unit recordings of real integrator neurons.