Fig 1.
Illustration of behavior-dependent sweeps reported in [15].
Within each theta cycle, the trajectory represented by the place cell population starts at the position where the animal was located at some point in the past (e.g., 1 s ago), and sweeps to the position where the animal will be located at at some point in the future (e.g., in 1 s) assuming the animal ran at its typical speed at each position (top). As a result, theta sweeps are shorter where animals typically run slower (middle left) and longer where they typically run faster (middle right). At the single cell level, this effect manifests as smaller place fields with steeper phase precession where animals run slower (bottom left) and larger place fields with shallower phase precession where animals run faster (bottom right).
Fig 2.
Network connectivity models of phase precession and proposed mode of operation.
A: In the network connectivity model of phase precession, each theta cycle starts with spikes (short vertical lines) of place cells that code for the current position of the animal, that is, cells that receive strong external inputs at that location. Activity then propagates forward through synaptic connections to cells coding for positions progressively ahead. As a result, an individual cell fires at progressively earlier positions within the theta sequences as the animal approaches the location encoded by a cell, generating phase precession. B: Two variants of network connectivity models. Either sequences of place fields are initially driven by external spatial inputs and the connections between cells are learned afterwards, or the connections between cells are present from the start and the association with spatial inputs is learned afterwards. C: Principle underlying our model of behavior-dependent sweeps. A rat runs on a linear track with a characteristic slow-fast-slow speed profile. Top: If activity in an internally driven sequence propagates at a fixed pace in neuronal space, neighbouring units become associated with positions closer to each other where the animal runs slowly and further apart where the animal runs faster. Bottom: Same as above, but displaying each neuron at the position it becomes associated with. The neuronal space could be seen as elastic, becoming stretched out in areas of high running speed, and compressed in areas of low running speed.
Fig 3.
Elastic mapping of space by internally generated sequences.
A: Model architecture. A preconfigured recurrent network of place cells (colored disks and black arrows) receives inputs from weakly spatially tuned cells through plastic weights Ws (green disks and arrows), as well as rhythmic excitation and inhibition iθ. Weakly spatially tuned cells and place cells take continuous activation values in the ranges [-1, 1] and [0, 1], respectively. B: Recurrent weights matrix. Dashed line represents identity. C: Temporal evolution of iθ, the rhythmic excitation and inhibition to all the cells in the network, and βθ, which defines the window in which the cells receive spatial inputs. D: The network activations as the simulated rat runs multiple laps on a novel linear track. The activity in the network is initialized at the first place cells at the beginning of each lap. In the first few laps, activity propagates further in the network in slow laps that take longer to complete. However, in later runs, spatial inputs (green) arriving at the beginning of each theta cycle anchor the activity of the network in space. E: Regions of high activation (> 0.5) in the network are contoured in black and overlaid onto the short-term synaptic depression, D, and facilitation, F, of the outgoing recurrent synapses of the place cells. When emerging from the rhythmic inhibition, an activity bump forms at the cells whose recurrent connections are most facilitated and least depressed, (1 − D)F (bottom panel). This ensures that the each theta sequence starts slightly ahead of where the last one started. Note that due to the threshold used for plotting the black contour, the activity bump actually forms slightly before it, within the yellow band.
Fig 4.
The model develops larger place fields with shallower phase precession in areas of higher running speed.
A: Mean activation of each unit at each position along the track for one run of the simulation. B: Place field sizes increase as a function of the mean running speed through the place field. Each dot corresponds to a place field, pooled across 10 different simulation runs. The color of the dot represents the position of the place field peak. The coloured line shows the average place field size at each spatial bin along the track with at least 8 samples. C: Examples of theta phase precession from the same simulation run as in A. D: Theta phase precession becomes shallower where the animal runs faster. E, F: Individual place field sizes and inverse phase precession slopes are largely invariant of instantaneous running speeds. Shown is a histogram of ratios of these measures calculated using the top and bottom 20% of instantaneous running speeds at every location. There is a tendency for a modest decrease as the mean of the distribution (dotted line) is below a ratio of 1. G: The density of place fields calculated in 10 cm sliding windows decreases as a function of the mean speed in the window.
Fig 5.
A: Decoding represented positions from a well trained network during one lap. B: The look-behind distance (how far behind the real position of the animal the decoded sweep starts) increases with the mean speed at the corresponding real position (color coded). Each dot corresponds to a theta sweep, pooled across laps and across 10 different simulation runs. The coloured line shows the average look-behind distance at each spatial bin along the track. C: Same for the look-ahead distance (how far ahead of the real position of the animal the decoded sweep ends), and D: for the total length of the sweep. E: An example of a measured place field that was calculated from the activation of a cell and of a true place field that was calculated based on the spatial inputs that drive the cell. The dashed lines mark the positions of their peaks, and the difference between them is what we call the place field shift. F: Shifts between each place field and its spatial input field. Same conventions as in Fig 4B. G: The look-behind distance of theta sweeps at a given location corresponds roughly to the place field shift at that location. The dashed black line represents identity.