Fig. 9. Simulation results for the integrate-and-fire model—I. Snapshots in all rows except B andC are taken at a constant phase of the theta rhythm.A, Self-focusing, formation, and propagation of the activity packet in a six-chart network. The network consists of P and I layers. Each pixel on the figure represents a P unit. Each plate consists of 256 × 192 pixels. Boundary conditions are periodic for all charts. The four plates A1–A4 show the four sequential theta cycles that correspond to different stages of spontaneous self-focusing of activity on the chart 1. Spikes arranged according to this chart are represented by red; the background is blue. When the same units are arranged according to chart 2 (not shown), their spikes appear almost uniformly scattered and some are grouped into small patches. B, Simulated phase precession. The self-focused activity packet propagates to the right; the simulated rat location (same on all 4 plates) is shown by the white arrow. Only one chart is represented. B1 through B4 correspond to the four phases of the same theta cycle (0, 90, 180, and 270°). The center of the distribution clearly oscillates in the direction of motion, which resembles the phenomenon shown in C.C, Real phase precession of the activity packet in CA1 reconstructed from experimental data. Color on each plate represents an average firing rate distribution on a chart, where the momentary rat location and head direction is shown by the arrow in thecenter. High activity is coded by red. The two ends of the arrow are images of the two infrared light-emitting diodes attached to the rat’s head, spaced 0.15 m from each other (for details, see Wilson and McNaughton, 1993). The average firing rate was computed from spikes that occurred within a narrow phase window with respect to the local EEG theta oscillations. Four consecutive phases were selected. Each plot was constructed as described in the caption to Figure 1 (Fig. 1 shows the average of the same data, taken over all phases). These oscillations of the distribution with phase in the direction of motion (fromleft to right) are known as thephase precession phenomenon (O’Keefe and Recce, 1993). This spatiotemporal structure of the experimentally observed activity packet was independent (within the error level) of the current trajectory configuration (e.g., left vsright turns), as well as of the velocity and the acceleration of the rat. This observation indicates that the spatiotemporal structure of the activity packet is probably a result of intrinsic dynamics of the hippocampal networks and does not reflect other brain representations, such as future plans or recent memories, goals, or intentions of the animal. (Some of these data can be viewed as movies at http://www.nsma.arizona.edu/alexei.) D, The activity packet performs path integration. Four consecutive moments of the activity packet motion are represented. The simulated rat trajectory is a circle (dashed line); the simulated rat’s position is shown by the arrow; the speed is constant. The head direction system was not simulated explicitly, as described in the text; therefore, the direction represented by the active I layer was always consistent with the direction of motion of the simulated rat. After self-focusing at a particular location on the chart, which is taken as the image of the starting point, the activity packet moves around a circle; however, a systematic error in the activity packet position accumulates with time. In this simulation, visual input to the P layer was absent. Spikes are represented byyellow. E, F, G, The role of visual input. E, The activity packet performs path integration, similarly to D, but now the simulated rat trajectory is a straight line. The actual simulated rat’s position is shown by the cross; stimulation of the P array by V is turned off. F, Addition of a gaussian-shaped stimulation to the P layer centered at the cross changes the activity packet velocity. The stimulation is relatively weak; the activity packet accelerates following the center of the stimulated area. G, The stimulation is strong enough to cause the activity packet to jump to the center of the stimulated area. The jump occurs with a certain probability, when the stimulation magnitude exceeds a certain threshold. The duration of the jump is approximately one to two theta cycles (time scales are different in Fand G).