Theta sequences are essential for internally generated hippocampal firing fields. Yingxue Wang, Sandro Romani, Brian Lustig, Anthony Leonardo, Eva Pastalkova Supplementary Materials Supplementary Modeling (Supplementary Table 1 Model parameters) Supplementary Figure 1 The effects of muscimol injection on theta rhythm, task performance and behavior. Supplementary Figure 2 The relationship between cell firing, LFP, time and running speed during wheel running. Supplementary Figure 3 The effect of muscimol injection on firing fields of cells in the wheel. Supplementary Figure 4 The effect of muscimol and saline injection on the firing properties of cells in the wheel. Supplementary Figure 5 Theta sequences of cells in the wheel. Supplementary Figure 6 The effect of muscimol injection on the firing properties of cells in the maze. Supplementary Figure 7 The effect of muscimol and saline injection on the firing properties of cells in the maze. Supplementary Figure 8 Theta sequences of cells in the maze. Supplementary Figure 9 Short-term plasticity model. Supplementary Figure 10 Short-term plasticity model. Supplementary Figure 11 Firing of neurons during two subsequent visits of a novel large linear track. Supplementary Figure 12 The effects of muscimol and saline injection on theta modulation and spatial firing pattern of cells on a large unfamiliar and a large familiar platform. Supplementary Figure 13 Spatial activity of cells recorded on a large unfamiliar platform after muscimol and saline injection. 1
Supplementary Figure 14 Spatial activity of cells recorded on a large unfamiliar environment after muscimol injection. Supplementary Figure 15 Firing rate and behavioral patterns during novel environment exploration. Supplementary Figure 16 Spatial activity of cells recorded on a small round unfamiliar platform during muscimol and post-muscimol session. Supplementary Figure 17 Methods. Supplementary Methods Checklist 2
Supplementary Modeling Short-term plasticity model The 1D environment. For simplicity, and in order to avoid boundary effects we consider a network encoding a circular environment. A basic unit of the network represents a population of neurons with highly overlapping place/episode fields. A unit with field at angle θ [0,2π) on a circular manifold is described by the firing rate at time t, m(θ, t), which follows the dynamics τm (θ, t) = m(θ, t) + f I R (θ, t) + I E (θ, t). (1) f(i) = g[i] + is a threshold-linear f-i curve. The input current to a unit is a sum of a recurrent I R (θ, t) and an external contribution I E (θ, t). The recurrent contribution to the current is I R (θ, t) = 1 N W(θ, θ )m(θ, t)x(θ, t)u(θ, t) θ where the sum extends over the N units equally spaced on the circle. The synaptic strength depends on the distance between the locations assigned to the units (see Fig. 3b): W(θ, θ e ) = J k cos θ θ δ 1 J 0, where J 1 measures the strength of the map-specific interaction, δ measures the strength of asymmetry in the connections, and J 0 corresponds to a uniform feedback inhibition. The parameter k sets the coupling width; I 0 (k) is the modified Bessel function of order 0. This form of interaction promotes the formation of spatially coherent activity (a bump ) on the map (Ben- Yishai et al., PNAS, 1995; Tsodyks and Sejnowski, Int. J. Neur. Sys., 1995). The asymmetry induces a movement of the bump along the ring, with direction and speed determined by the asymmetry. The dynamic variable x(θ, t) represents the depression strength of the connections from the pre-synaptic unit θ to all its post-synaptic neighbors. This variable follows the dynamics (Tsodyks and Markram, PNAS, 1997; Tsodyks et al., Neur. Comp., 1998) I 0 (k) x (θ, t) = 1 x(θ,t) τ R u(θ, t)x(θ, t)m(θ, t), (2) 3
where τ R is the time constant of recovery from synaptic depression, and u(θ, t) is the fraction of utilized synaptic resources released by each spike (release probability). The utilization of synaptic resources u(θ, t) is a dynamical variable, described by the dynamics u (θ, t) = U u(θ,t) τ F + U 1 u(θ, t) m(θ, t), (3) where τ F is the facilitation recovery time constant and U denotes the baseline utilization fraction. Equations 2,3 are just the extension of the dynamics used for a single homogeneous population (Tsodyks et al., Neur. Comp., 1998) to the spatially continuous case. The external current contains three terms I E (θ, t) = I + I Θ cos(2πf Θ t) + I L cos θ θ ext (t) + η(t). I is a spatially uniform and stationary current. The second term is a theta-modulated input with frequency f Θ and the amplitude I Θ. The third term is a place specific input, with amplitude I L, peaked at the location of the simulated animal θ ext (t) (Fig. 3a). The last term represent an Ornstein-Uhlenbeck process with a time constant of 10ms driven by white noise with a standard deviation σ = 5. The network parameters used are: τ = 10 ms, J 1 = 15, J 0 = 30, τ R = 0.1s, τ F = 0.3s, U = 0.05, g = 1.5, k = 2.5, δ = 0.2rad, N = 100. The parameters we used for the external current are listed in Supplementary Table 1. The 2D environment. For the case of a network storing a map of a toroidal environment, each unit is characterized by two angles, (θ 1, θ 2 ). The dynamics is identical to the one used for the 1d environment, but the synaptic interaction has the form 4
W(θ, θ e ) = J k [cos θ 1 θ 1 +cos θ 2 θ 2 ] 1 J I 0 (k) 0, and the spatially tuned component of the external input is e k ext [cos θ 1 θ ext 1 (t) +cos θ 2 θ ext 2 (t) ] I L I 0 (k ext ) The location of the simulated animal (θ 1 ext (t), θ 2 ext (t)) was either a straight line at constant speed ( 2π 5 rad/s) (Supplementary Figure 10d), or a correlated random walk with constant speed ( 2π 5 rad/s) and angular standard deviation of 0.05 rad (Supplementary Figure 10d). The network parameters used are: τ = 10 ms, J 1 = 4, J 0 = 50, τ R = 0.5s, τ F = 0.5s, U = 0.15, g = 1.5, k = 2.5, k ext = 1, σ = 0, N = 400. Parameters for the external currents can be found in Supplementary Table 1. Supplementary table 1. Model parameters (Fig. 3) no theta/ no cues theta/ no cues no theta/ cues theta / cues 2D Environment I (Hz) 2 2 2 2-1 I Θ (Hz) 0 30 0 30 20 I L (Hz) 0 0 5 5 10 f Θ (Hz) 0 7 0 8 8 5
6
Supplementary figure 1. The effects of muscimol injection on theta rhythm, task performance and behavior. (a) Average LFP theta power (top) and theta peak frequency (bottom) in muscimol (blue / gray) and saline (green / gray) experiments. (b) Example power spectrum of LFP recorded during wheel running in a muscimol experiment. (c) Task performance in saline experiments. (d) Running speed on the wheel (left) and in the maze (right) in muscimol (blue / gray) and saline (green / gray) experiments. (e) The relationship between running speed and error rate in the wheel (left) and in the maze (right). (f) Amount of time animals spent in the delay area before they initiated wheel runs in muscimol (left) and saline (right) experiments. (g) Example trajectories of three animals (rows) in the maze before (left), during (middle) and after (right) the effect of muscimol injection. (h) Example wheel running speed profiles of three animals (rows) before (left), during (middle) and after (right) the effect of muscimol injection. Gray values indicate performance in the task. Muscimol: 13 recordings from 3 animals. Saline: 7 recordings from 2 animals. Error bars: SEM. 7
8
Supplementary figure 2. The relationship between cell firing, LFP, time and running speed during wheel running. (a) Relationship between mean running speed of animals in the wheel and the frequency (left) and power (right) of LFP theta oscillation. Note that the running speed tends to be faster in the wheel. 332 trials from 4 animals. (b) Firing rate maps of 8 example neurons (neuron 1 8) during wheel running plot with respect to time (left), number of theta cycles (middle) and distance (right) animals traversed from the beginning of each trial. Trials are sorted according to mean running speed, slow trials on the top. Title: correlation between average firing rate profile of the same neuron during slow and fast trials. (c) Relationship between the correlation values obtained for individual neurons (dots) when activity of neurons was plotted with respect to specified variables. (d) Distribution of the peak firing rate in the wheel (left) and in the maze (right). 158 neurons from 3 animals. 9
10
Supplementary figure 3. The effect of muscimol injection on firing fields of cells in the wheel. (a) Firing fields of 30 simultaneously recorded cells in the wheel before (left), during (middle) and after (right) the effect of muscimol injection. Firing rate is color-coded. White letters: mean firing rate (Hz). (b) Firing pattern of 4 pyramidal cells (left), theta modulation of interneurons (right top) and performance of the animal (right bottom) before (trial 1-10), during (blue, trial 11-77) and after (trial 78-85) the effect of muscimol injection. This recording had exceptionally late onset of the injection effect. Data from the trials 11-30 were excluded from all data analysis. 11
12
Supplementary figure 4. The effect of muscimol and saline injection on the firing properties of cells in the wheel. (a) Activity of 6 cells recorded during wheel running before (left), during (middle) and after (right) muscimol injection. Firing rate is color-coded. Note that these neurons formed firing fields at the beginning of the wheel runs after muscimol injection. These neurons were not recorded during the same recording. (b) Activity of 6 simultaneously recorded cells during wheel running before (left) and after (right) saline injection. Firing rate is color-coded. White letters: mean firing rate (Hz). (c) Theta modulation (left), mean firing rate (middle) and firing field information (right) of cells in the wheel before (dark gray), during (color) and after (light gray) the effect of muscimol (top) and saline (bottom) injection. Insets: p- values from the Kolmogorov-Smirnov test. Muscimol: 158 neurons from 3 animals. Saline: 50 neurons from 2 animals. 13
14
Supplementary figure 5. Theta sequences of cells in the wheel. (a) Percentage of time windows with significant theta sequences that consisted of a specific number of neurons (x-axis) out of all time windows with qualified sequences (left) and out of all time windows with significant sequences (right). Insets: p-values from the Kolmogorov-Smirnov test. (b) Percentage of trials varying with the proportion of significant sequences per trial. (c) Examples of firing fields (traces) and of two theta sequences (empty and filled circles) formed by 4 neurons (black to gray color). Scale bars: 0.2 s. (d) Raw (thin line) and smoothed (thick line) histograms of inter-spike intervals (i.e. cross-correlograms, CCG) between a pair of episode cells before (top), during (middle) and after (bottom) the effect of muscimol injection. Triangles: the peak of the smoothed short (pink) and long (green) timescale CCGs. (e) Long versus short time scale CCG peak location for individual episode cell pairs before (top), during (middle) and after (bottom) the effect of muscimol injection. (f) Left: Sequence of four firing fields. Red dots: peaks of the firing fields. Right: Short-time scale CCG for each pair of the four cells. Red dots: the peak of each CCG. Black values: a score describing the offset of the CCG-peak from zero. The total score was used to evaluate the quality of the sequence (see Methods). (g) Number of high-score (see Methods) sequences consisting of at least 3 cells. (h) Distribution of sequence scores in muscimol experiments. 158 neurons from 3 animals. 15
16
Supplementary figure 6. The effect of muscimol injection on the firing properties of cells in the maze. (a) Activity of 27 simultaneously recorded cells in the maze before (left), during (middle) and after (right) the effect of muscimol injection. Firing rate is color-coded. Gray lines: trajectory of an animal. White letters: mean firing rate (Hz). (b) Firing patterns of 6 simultaneously recorded neurons during maze (left) and wheel (right) runs before (upper panels) and during (lower panels) the effect of muscimol injection. Firing rate is color-coded. Left: gray line: trajectory of an animal. Black dashed square: an approximate position of the wheel in the maze. 17
18
Supplementary figure 7. The effect of muscimol and saline injection on the firing properties of cells in the maze. Theta modulation (top), mean firing rate (middle) and firing field information (bottom) of cells in the maze before (dark gray), during (color) and after (light gray) the effect of muscimol (left) and saline (right) injections. Insets: p-values from Kolmogorov-Smirnov test. 19
20
Supplementary figure 8. Theta sequences of cells in the maze. (a) Percentage of time windows with significant theta sequences that consisted of a specific number of neurons (x-axis) out of all time windows with qualified sequences (left) and out of all time windows with significant sequences (right). Insets: p-values from the Kolmogorov-Smirnov test. (b) Percentage of trials varying with the proportion of significant sequences per trial. (c) Long versus short timescale CCG peak location for individual place cell pairs before (top), during (middle) and after (bottom) the effect of muscimol injection. (d) Number of high-score (see Methods) sequences consisting of at least 3 cells. (e) Distribution of sequence scores in muscimol experiments. 21
22
Supplementary figure 9. Short-term plasticity model. (a) Square pulse (top) induced change in depression, facilitation (middle) and overall synaptic efficacy (bottom-red). (b) Left: the speed of theta sequences and of firing field sequences as a function of connection asymmetry. Right: ratio of the theta sequence speed to the firing field sequence speed as a function of connection asymmetry. The green lines mark the parameter used in the final model. (c) Synaptic efficacy (color map) changes in the entire population of episode cells across three theta cycles (top trace). Firing rate of the cells is shown as contour lines. (d) Firing rate profile of the model at the low (top) and high (bottom) temporal resolution after removal of short-term plasticity. (e) Theta phase (top), firing rate profile (bottom, black) and synaptic efficacy (bottom, red) inside of a firing field. (f) Top: membrane potential outside and inside of a firing field. Gray line: low-pass filtered version of the membrane potential. Bottom: power spectrum of the membrane potential outside and inside of a firing field. (g) Firing field duration (top) and ratio of theta sequence speed to episode field sequence speed (bottom) as a function of theta frequency and theta power. 23
24
Supplementary figure 10. Short-term plasticity model. (a) Top: 2-D firing field of an example neuron. Blue: random walk of the model at constant speed (~ 17 min of exploration). Bottom: Firing rate of the same neuron as a function of time and theta phase. Note that this neuron phase precesses with respect to the ongoing theta oscillation. (b) Firing rate profile after theta input removal with control (top) and high (bottom) amplitude of DC input. (c) Coherence (top) and speed (bottom) of the firing field sequence as a function of the DC and noise input amplitude in the presence (left) and absence (right) of theta input. (d) Square pulse (top) induced change in depression, facilitation (middle) and overall synaptic efficacy (bottom-red) in the depression model 44. (e) Firing rate profile of the depression model 44. Note the high speed of the bump in comparison to Fig. 3c. (f) Firing field size as a function of synaptic release probability. Green arrow: values used in the facilitating model presented in this paper. Blue arrow: values used in the depression model 44. (g) Speed of the firing field sequence as a function of synaptic release probability. Green arrow: values used in12 the facilitating model presented in this paper. Blue arrow: values used in the depression model 44. Note that the slow speed of the firing field sequence in the facilitating model compared to the depression model 44. 25
26
Supplementary figure 11. Firing of neurons during two subsequent visits of a novel large linear track. (a) Spiking maps (left) and firing rate maps (right) of 13 example neurons during two subsequent visits of the same linear track (Control 1, Control 2). Inset: firing field information and mean firing rate. (b) Firing field information (left) and theta modulation (right). 136 neurons from 2 animals. Statistics: Wilcoxon rank-sum test. Error bars: SEM. 27
28
Supplementary figure 12. The effects of muscimol and saline injection on theta modulation and spatial firing pattern of cells on a large novel and a large familiar platform. (a) Firing rate maps of example neurons in different experimental conditions. White numbers: mean firing rate (Hz). (b) Firing field information, (c) sparsity, (d) theta modulation of cell firing, (e) and mean firing rate for each experimental group. Gray: control groups. Blue: muscimol injection. Statistics: Wilcoxon rank-sum test. Error bars: SEM. (f) Location of firing field peaks on a novel (left) and familiar (right) platform after muscimol (top) and saline (bottom) injection. Neurons with good firing fields (spatial information above 1.1 bit, the first and the third plot) were plot separately from neurons without firing fields (spatial information bellow 1.1 bit, the second and the fourth plot). Dashed line: the border between the periphery and the middle of the platform. Bottom values: counts of firing fields located at the periphery and in the middle of the platform. (g) Spatial distribution of spikes generated on a large novel platform by neurons with above (left) and bellow (right) average firing field information during control (top) and muscimol (bottom) recordings. Note that spikes on a novel platform during muscimol condition are generated mostly on the edge of the platform. Control-novel: 247 neurons from 4 animals. Muscimol-novel: 145 neurons from 5 recordings. Control-familiar: 337 neurons from 4 animals. Muscimol-familiar: 161 neurons from 4 animals. 29
30
Supplementary figure 13. Spatial activity of cells recorded on a large novel platform after muscimol (top) and saline (bottom) injection. Spike maps (left) and firing rate maps (right). 30 neurons with the highest firing field information in each recording are shown. Neurons are ordered based on their firing field information. Gray line: trajectory of an animal. Red dots: position of the animal at the moment of a spike. Black numbers: mean firing rate (Hz). White numbers: firing field information (bits). 31
32
Supplementary figure 14. Spatial activity of cells recorded on a large novel platform after muscimol injection. Spiking maps (left columns) and firing rate maps (right columns) of 17 cells during the four 15 min segments of an hour long recording (1-60 min). Gray line: trajectory of an animal. Red dots: position of the animal at the moment of a spike. White numbers: firing field information (bits). 33
34
Supplementary figure 15. Firing rate and behavioral patterns during novel environment exploration. (a) Firing rate of neurons during repeated visits of the same environment before (Day 1-3) and after familiarization (Familiar). M: recordings after muscimol injection. Post: recordings after animals recovered from the effect of the injection. Hash mark: three-day familiarization procedure. Range of 39 75 neurons from 3 animals. Error bars: SEM. Statistics: Wilcoxon rank-sum test. (b) Running speed under different conditions. (c) Trajectory of animals on the platform under different conditions. 35
36
Supplementary figure 16. Spatial activity of cells recorded on a small round novel platform during muscimol and post-muscimol session. (a) Spike maps (even columns) and firing rate maps (odd columns) shown for two different animals (left/right half of the figure, respectively). 10 example neurons shown for each animal. Gray line: trajectory of an animal. Red dots: position of the animal at the moment of a spike. Black numbers: mean firing rate (Hz). White numbers: firing field information (bits). (b) Firing field information (left) and theta modulation (right) for each animal during muscimol (blue) and post-muscimol (gray) session. 223 neurons from 2 animals. 37
38
Supplementary figure 17. Methods. (a) Illustration of the parameters used to identify firing fields of episode cells (see method section Firing fields of episode cells ). Black curve: the firing rate profile of a neuron. FRm: mean firing rate, Thp2m: threshold of the peak to mean firing rate ratio, Thh and Thl: high and low thresholds to determine the field boundary. (b) Illustration of the shuffling method used in theta sequence detection (see method section Theta sequence detection ). Red square: a time window in the original data. Black square: one shuffle of the original data. Light blue column: 10,000 shuffles of Win1. Bottom left: the distribution of the sequence scores of the shuffled data, red vertical line: the score of the original data. Pink row: percent of significant sequences (PSS) was calculated based on each row. Right: the distribution of PSS in the shuffled data, red vertical line: PSS of the original data. 39