Figure 2. Spatial exploration gives rise to plasticity-dependent emergence of spatio-temporal structure in spontaneous activity.

(a) Snapshots of the connectivity during the exploration of a novel environment. During early exploration, the connectivity is not correlated with the place-field ordering, while during late exploration cells with neighboring place-fields are more strongly connected. (b) i. The mean cross-correlation of the activity of place cells with adjacent place fields on a novel track during exploration (sequential correlation SC). Black: SC during active exploration (theta-activity), Orange: SC during spontaneous bursts. Note the sharp transition in the SC of burst activity. ii. The SC of the total activity binned into 3 min intervals shows a steady increase preceding the transition. (c) Burst activity exhibits replay after a critical period. i. Early exploration. Top: average input to place cells before (blue star), during (black star) and after period of ‘quiet wakefulness’. Bottom: space-time plots of the place cell input and firing rate. Note the disordered spatio-temporal structure of the burst activity. ii. Later exploration. After a critical transition time bursts exhibit sequential replay of activity from the novel track. Note the sequential structure of the burst activity.

Figure 2—figure supplement 1. The evolution of the recurrent connectivity during exploration of 10 distinct tracks.

(a) The mean synaptic weight of recurrent excitatory connections as a function of time for 10 consecutive simulations of 1 hr each. The initial condition was all the weights identical and set to a value of 40. (b) the distribution of synaptic weights at the end of the 10 hr of simulation. About 10% of synaptic weights are maximally depressed to zero, 40% are maximally potentiated (threshold set to 80) and 50% take on intermediate values. As new environments are explored the distribution remains largely fixed but individual synapses change in time.

Figure 2—figure supplement 2. The emergence of replay for unidirectional motion.

(a) The evolution of the mean synaptic weight over the course of exploration of 10 distinct tracks and the resulting distribution of synaptic weights (right). (b) Snapshots of the profile of the recurrent connectivity and firing rate during exploration of a novel track, up to 15 hr. The place cell activity is calculated with respect to the maximum of the subthreshold input. Note that at later times the maximum of the place cell activity is shifted to the right (clockwise, in the direction of motion) compared to the input. In experiment this would be seen as a backward shift in the place field of cells. Note also the negative skewness in the activity. (c) Transition in the SC of burst activity (black circles) reflecting the change in the spatio-temporal structure of the bursts. The SC of the sensory-driven theta-activity shows an increase leading up to the transition. Inset: The same over 16 hr of simulation time. (d) ‘LFP’ and space-time plots of the network firing rate and external input before and after the transition. (e) The amplitudes of the even and odd Fourier modes of the recurrent connectivity after 1 hr of exploration. (f) A transition in the SC occurs only for a range of frequencies. (g) An anti-symmetric plasticity rule (left) or a rule with dominant depression at short latencies (right) does not lead to an emergence of spontaneous bursts. All parameters are the same as in Figures 2 and 3 with the exception of the following. The modulation frequency during training on the 10 tracks for one hour each is f = 5 Hz, ${\displaystyle I_1}$ = 22 Hz, and the velocity of the animal is constant with a value ${\displaystyle v}$ = 1 rad/sec. Finally, during the training period of 1 hr on each of ten distinct tracks, theta activity was always present, that is there were no bursts. Allowing for bursts during training did not alter the results qualitatively.

Figure 2—figure supplement 3. The growth of the odd mode of the recurrent connectivity is determined by the bias in the motion of the virtual animal.

(a) A sample trajectory of the virtual animal. The velocity is modeled as an Ornstein-Uhlenbeck process. Left: Position of virtual animal, i.e. the position of the maximum in the place-field input. Right: Place-cell activity. (b) The bias in the motion of the virtual animal during the first 15 min of a simulation, averaged in one-minute bins. Specifically the bias is the difference in the time spent moving clockwise versus moving counter-clockwise. The velocity of the virtual rat is an Ornstein-Uhlenbeck process with a non-zero mean as described in Materials and methods; the non-zero mean results in an overall clockwise bias. (c) The growth of the odd Fourier mode (sine mode) over time (solid line) compared to the cumulative motion bias. The cumulative motion bias is the time integral of the motion bias, scaled to match amplitudes with the normalized odd mode of the connectivity.

Figure 2—figure supplement 4. Heterogeneity in place-cell activity does not qualitatively alter the transition to replay.

(A) The SC for three identical simulations with the only difference being the degree of heterogeneity in the place-field input to place-cells. The curve with the black circles is identical to the simulation in Figure 2 of the main text, for which ${\displaystyle I_{PF}}$ = 25 Hz. The red squares are a simulation for which $I_{PF}$ is uniformly distributed between 20 and 30 Hz (and hence the mean is the same as before). The orange diamonds show an extreme case where $I_{PF}$ is uniformly distributed between 0 and 50 Hz. B. Examples of place-cell activity for the strongly heterogeneous case. Note that in this case some cells are only very weakly selective to place, for example cell 3, while others have no place field whatsoever, for example cell 4.

Figure 2—figure supplement 5. Theta sequences and phase precession emerge over time.

(a) A space-time plot of the firing rate (Hz) during early exploration. (b) The position of the most active place cell over time (solid line). The position of the animal is given by the dashed line. (c) The firing rate of a single place cell. Peaks in the theta rhythm are given by dotted vertical lines, and most likely spike times by solid lines. (d)-(f) The same as (a)-(c) for late exploration. Parameters are the same as those used for Figure 2—figure supplement 2, with the exception of ${\displaystyle f}$ = 8 Hz.

Figure 2—figure supplement 6. Forward replay occurs spontaneously, but backward replay requires location-specific input.

(a) The firing rate r (top), short-term synaptic depression variable x (middle) and external input to place cells (bottom) during a period of ßleep’ or ‘quiet wakefulness’, that is in the absence of theta-modulated place field input. Spontaneously occurring bursts always travel forward when the input is globally homogeneous, reflecting the asymmetry in the underlying recurrent connectivity. However, a strong location-specific input (just after 1 s and 8 s) can transiently depress the synapses in downstream neurons, facilitating the propagation of activity backwards. Right: blow-up of activity showing forward and backward replay. (b) Raster plot generated from the same simulation as in (a). The external input is $I_i=-0.8$ Hz except for the two spatially-modulated inputs which are presented for 50 ms each and have the form $I_i=40(1+cos{\theta }_i)$ Hz.

Figure 2—figure supplement 7. The degree of ‘burstiness’ of spontaneous activity can be modulated by a global external input.

(a) The temporal maximum of the mean firing rate (averaged over the network) as a function of the external input. The input is a constant, that is there is no place-specific input. Simulations are run for 100 s and the first 10 s are discarded to avoid transients. (b) 'LFP's of the spontaneous activity, actually the total input to the network for I = −0.8 (left), −0.35 and 1 respectively. (c) Space-time plots of the spontaneous activity shown with neurons ordered according to their place fields in the last, next-to-last and first environments explored. Parameter values are identical to those in Figure 2.

Figure 2—figure supplement 8. Changes in the recurrent connectivity stabilize in an extended, 10 hr simulation.

(a) The amplitude of the even mode of the recurrent connectivity over time. (b) Top: The SC of the SWR activity. Bottom: The mean firing rate in the network over time. The initial condition for the recurrent connectivity is the same as for the simulation shown in Figure 2, in other words that resulting from the exploration of 10 distinct tracks.