Table 1.
Comparison of place field sizes and numbers in selected studies.
Fig 1.
A: Rate maps of four grid cell examples, one out of each module. B-C: Distribution of grid spacings (B) and orientations (C) in the grid cell population. Colours indicate grid module. D: Examples of weakly spatially modulated cells created with different kernel sizes (shown on the left). The numbers above each panel indicate the spatial information of the rate map. E: Distribution of spatial information for different kernel sizes. Black line shows the observed distribution in the rat LEC [44]. F: Overview of the modelled subregions. Black lines indicate connections that are fixed and used only during the learning of the grid to place transformation. Learning occurs in the plastic connections indicated by the red line. Only these connections drive CA3 activity once learning is complete. Rate maps illustrate the mixture of the input: 1/6 consists of grid cells and 5/6 of weakly spatially modulated cells.
Fig 2.
Solution of the grid-to-place transformation by a linear support vector classifier.
A: Upper panel shows the activation map of the output cell h(r) after solving Eq 3 for a place field with a radius 10cm. Middle panel shows the map when place cells below background firing threshold have been inhibited. Lower panel shows the same as the middle panel after 7% of the grid cells have been lesioned. B: The error rate in the output rate map (maximal error is 0.5, see Methods) as a function of the fraction of grid cells that are lesioned is an indicator of the robustness of the solution. Blue line represents simulations when all four grid cell modules are present in the input. Green line represents simulations when only the two modules with the largest grid spacings are included. Dashed line is the reference when the error rate would increase linearly. Red diamond indicates noise level for the lower two rate maps in (A). C: Absolute value of the weights that are assigned to grid cells in different modules in the solution. Module one contains cells with smallest spacings and module four cells with the largest spacings. D-I: Same as (A-C) for a place field with radius 25cm (D-F) and 35cm (G-I), respectively.
Fig 3.
Solution of the classifier when grid cells have large spacings or when weakly spatially modulated cells are added to the input.
A: Activation maps as in Fig 2 when the classifier is applied to a mixture of inputs from grid cells and weakly spatially modulated cells. B: Error rate as in Fig 2 when the classifier is applied to grid cell populations with a single large spacing (indicated by colored lines) or when weakly spatially modulated (wsm) cells are added to the grid cells with mixed spacings.
Fig 4.
Generating place cells in a feedforward neural network model.
A: Three examples of CA3 cell firing rate maps, one in each row, during learning (left column) and after learning (right column). B: Distributions of place field sizes in the CA3 population for different proportions of grid cells in the EC input. Thick green line shows the simulation with the default parameter. Dashed black line shows distribution for the rat CA3 [34]. C: Mean correlation of two input PVs as a function of the distance between their locations in space for different proportions of grid cells in the EC input. D: Mean place field size and mean number of fields per CA3 cell. E: Number of active cells and number of place cells. F-H: Similar to C-E, but varying the width σN of the smoothing kernel instead of the proportion of grid cells in the EC input.
Fig 5.
Effect of lesioning different EC inputs.
A: Examples of the firing rate map of three CA3 cells, one per row. Columns show firing maps when no lesion is applied, the entire LEC is lesioned, the entire MEC is lesioned and when all grid cells are lesioned. B: Error rate as a function of the number of lesioned cells. Note that the network consists of of 550 LEC cells and 550 MEC cells (including 183 grid cells). C-E: Mean number of fields (C), place field size (D) and number of active cells when different EC inputs are lesioned. Standard error over ten simulations is indicated by error bars.
Fig 6.
A: Stability of CA3 firing maps between two visits of the same environment as a function of the stability in the LEC firing map. Lines of different colour show the result of lesioning different entorhinal inputs before the animal encounters the environment the second time. Errorbars show standard errors across three simulations. B: Mean field size in CA3 as a function of LEC stability.
Fig 7.
Recurrent connectivity enlarges the firing field of a place cell.
A: A one dimensional representation of the CA3 network. Each cell receives a spatially selective input current (Eq 7) which is shown by green vertical bars. The extent of this input is indicated for two example cells by green bell-shaped curves (dashed and solid line). Because of the recurrent connectivity between the cells (red curve), the cell with a place field in the center can be activated even when the animal is located outside the space from where it receives spatial inputs, e.g., at the location of the solid green bell-shaped curves. B: Spatially modulated spiking of a representative CA3 cell (black dots) as the virtual animal randomly explored the environment. The external input current which determines the location of the place field center (Eq 7) has a Gaussian profile, indicated by the colourmap. Because of the recurrent excitatory connections, the place field of the cell is larger than the extent of the external input. C: Firing rate map of six place cells. The sizes of the detected place fields are indicated in the top right corner of each panel (in cm2).
Fig 8.
Properties of place cells generated by recurrent CA3 dynamics.
A: The distribution of field sizes in the network for different connectivity kernel widths. Place fields are larger for wider connectivity kernels. B: Cumulative distributions of field sizes for different kernel widths. The distributions are similar to experimental results for a range of kernel widths. C: The median place field size (blue line) increases as a function of the kernel width. The average number of place fields of the cell in the network (green line) decreases with the kernel width. D: Fraction of bins with erroneous activity as a function of the number of cells without spatial input.