Fig 1.
Trajectory and place cell simulations.
A) The simulated environment with a scale rat for comparison. B) The spike probability map for a simulated place cell with a single firing field. The field parameters are given below: the centroid is the center point of the field, the coordinates are relative to the center of the map, σx and σy give the field’s standard deviation in x or y respectively, σxy gives the field’s variance in x and y and is used here to give fields an orientation oblique to the x- and y-axes. C) Place cell spikes, simulated using the probability map in b and a random walk trajectory. D) We simulated place cells with three different firing field sizes, examples exhibiting a single firing field are shown from each group, text above gives the average field radius of the group and the field parameters are given below as in b. E) We simulated 8 different random walk trajectories, these were clipped to a 4-, 16- or 64-minute duration. Shown here is one trajectory clipped to these three durations (for the kernel smoothed density estimate a 24-minute duration was used in place of the 64-minute one).
Fig 2.
Schematic showing the histogram method.
See Methods: Histogram for more detail. Schematics showing the steps involved with creating a histogram firing rate map. Position and spike data are binned separately into unsmoothed maps. Position counts are multiplied by the sampling interval of the position data to obtain the dwell map. For this example, 50 mm2 bins are used. These maps are then, optionally, smoothed with a Gaussian kernel, in this case a 5×5 bin kernel with the standard deviation set to 50 mm, to produce a smoothed dwell and spike map respectively. The spike map is then divided by the dwell map to obtain a map of average firing rate.
Fig 3.
Adaptive smoothing, pixelwise method.
See Methods: Adaptive smoothing for more detail. Schematic showing the steps involved with creating a firing rate map using the adaptive smoothing approach described by Skaggs and McNaughton [42]. A set of query points are specified, these typically form a square grid spanning the data. A circle is expanded around each point until the contents satisfy the adaptive equation (bottom of figure). The radius needed to satisfy the adaptive equation is shown for two query points. The value of the firing rate map at each query point is then equal to the number of spikes divided by the number of position samples within that circle multiplied by the sampling interval of the position data.
Fig 4.
Adaptive smoothing, convolution method.
See Methods: Adaptive smoothing for more detail. Schematic showing the steps involved with creating a firing rate map using the adaptive smoothing approach accelerated through convolution. Position and spike data are binned separately into unsmoothed dwell and spike maps respectively. For this example, 50 mm bins are used. Convolution with circular unity-gain kernels of varying sizes is used to sum the total spikes and position samples at a set of discretized radii. For each bin, the smallest radius of kernel at which the adaptive equation can be satisfied is then found. The value of the firing rate map in that bin is equal to the number of spikes divided by the number of position samples within the kernel multiplied by the sampling interval of the position data. The result is a map which is functionally identical to one generated using the pixelwise approach (Fig 3) but in a fraction of the time (S2 Fig).
Fig 5.
See Methods: Kernel smoothed density estimate for more detail. Schematics showing the steps involved with creating a kernel smoothed density estimate (KSDE) firing rate map. A set of query points are specified forming a square grid spanning the data. For each query point the distance to every position data sample and spike is calculated, these are then kernel weighted and summed. The value of the firing rate map at that query point is then equal to the spike-distance-sum divided by the position-distance-sum multiplied by the sampling interval of the position data.
Fig 6.
Qualitative assessment of firing rate maps.
A) The spike probability map of one example simulated place cell. B) Spikes simulated in a 16-minute recording session using this probability map. C-H) For each mapping method, firing rate maps generated for the spike and position data in b using a range of parameter combinations. For each method, 256 place cells were simulated and mapped in this way.
Fig 7.
Quantitative investigation of firing rate map accuracy.
A-F) For each mapping method, the error associated with a range of parameter combinations when used on 16 min duration sessions (main panel), 4- or 64-min-duration sessions (inset right). Each plot is an average of 256 simulated place cells. Also denoted are the parameter combinations associated with the minimum error and the combinations found to optimize error, computation time and place field detection accuracy in a balanced way. Note that plots are shown using a consistent color axis which may not span the full range of data values for every method.
Fig 8.
Additional firing rate map parameters.
All plots are based on the 16-minute session data and are the average of 256 simulated place cells (except temporal KSDE computation time which was estimated using 8 place cells). A-F) For each mapping method, the error in detecting place fields (main), the computation time (inset top) and the proportion of the map left empty (inset bottom) associated with each parameter combination are shown. The color axes used here do not show the full range of data values but were chosen to visually isolate low error region(s).
Fig 9.
The relationships between error, computation time and mapping parameters.
A-F) For each mapping method, the Pareto-front of optimal parameter combinations for all tested recording durations. Circled is the parameter combination selected as the most balanced. In addition to computation time and overall map error (MISE), which are plotted here, Pareto-optimization also sought to minimize the proportion of empty bins and place field detection errors. Insets show the relationship between average field radius, recording duration and balanced bin size (top) or smoothing (bottom) parameters, determined using multivariate regression. The exact regression fits can be seen in Table 1 in addition to the fits for the parameters associated with the minimum error.
Fig 10.
Error and computation time across methods.
All plots are based on the 16-minute session data. Horizontal lines denote a significant (p < .05) post-hoc comparison, for simplicity only the balanced solution groups are compared. A) The mean integrated squared error (MISE) associated with each mapping method when using the balanced or minimum error parameters. Markers denote simulated place cells and the same 256 cells were tested using each method. B) The same as a but for computation time. Some methods have a bimodal distribution, the longer computation times represent the first time a map was generated for a recording session (8 unique sessions were simulated) and a dwell time map was created. Only these 8 values are shown for the tKSDE computation times. C) The accuracy with which place fields were detected for each mapping method. D) The proportion of empty bins remaining for each mapping method. E) The spike probability map and simulated spikes for an example simulated place cell. Below this, firing rate maps for this place cell generated using each method (columns) and the balanced solution parameters (top row) or minimum error solution parameters (bottom row). Text gives the bin size and smoothing parameters used.
Table 1.
The relationship between field size, recording duration, bin size and smoothing strength.
Fig 11.
Mapping parameters in the published literature.
A) Top: bin sizes used to generate histogram firing rate maps in the literature, surveyed across 100 published papers and plotted as a function of publication year. Gaussian jitter (mean = 0, σ = 2) was added to the literature values to make visualization of overlapping data clearer. Bottom: the spike and position data for an example, simulated place cell. Firing rate maps for this cell are depicted to the right, generated using the average parameters used in the specified time period. B) Error maps overlaid with the minimum error, balanced and literature reported parameter combinations for the histogram, adaptive smoothing and KSDE methods as in Fig 7. In the published literature, researchers tend to use parameter combinations which are very close to the balanced solution. Gaussian jitter (mean = 0, σ = 2) was added to the literature values to make visualization of overlapping data clearer. See S10 Fig for example ratemaps generated using different literature values.