II.6 Data analysis
II.6.4 Single unit classification
II.6.4.1 Clustering of complex spike cells and interneurons
The single unit classification consisted of a two-step process. First, to classify a unit as complex spike cell or interneuron a k-means based clustering algorithm (using the in-built Matlab function ‘kmeans’) using the squared Euclidean point-to-cluster-centroid distance and assuming two clusters was performed with action potential duration (measured from peak to trough, in ms), the first moment (i.e. mean) of the 20ms-autocorrelation (in ms) and mean firing rate (number of spikes/trial duration, in Hz) as parameters. Autocorrelations were obtained by constructing a frequency distribution of spike trains with a bin size of 0.4 ms across the whole trial. This distribution was used with the in-built Matlab function ‘xcorr’
(using the ‘unbiased’ option) to calculate the autocorrelation function across a maximum lag of 20 ms. The first moment corresponds to the mean of this function.
123 For each unit all parameters were obtained from the first trial where at least 100 spikes were fired. In case a unit never fired 100 action potentials in any trial, the trial with the most spikes was chosen.
All units classified as interneurons were discarded from subsequent data analysis.
II.6.4.2 Place cell definition
Place cells were defined as complex spike cells whose firing exhibited a statistically significant spatial tuning. Place cells were identified by comparing the spatial information content of complex spike cell rate maps to that of a null-population of rate maps based on spike-shuffled data. Spatially shuffled maps were obtained by shifting the spike train of a unit during a given trial by a random amount between a minimum shift of 30 s and a maximum shift of ‘trial duration – 30 s’. New spike times that were larger than the trial duration were wrapped around to the beginning of the trial. Shuffled rate maps (adaptively smoothed) were constructed using the shuffled spike train and spatial information content for these shuffled maps was calculated. To obtain a distribution of shuffled spatial information scores, 20,000 spatially shuffled maps for each age bin were constructed. The 95th percentiles of these distributions were used as an age-matched threshold for defining a complex spike cell as place cell (see Figure III-4).
Spatial information was only calculated for shuffled rate maps, where i) number of spikes > 75, ii) path length > 40 m and iii) number of visited bins > 520 (ca. 80% of recording environment).
Thus, trials with a bad spatial sampling of the environment and/or cells with low numbers of spikes are excluded.
124
II.6.4.3 Criteria for inclusion of place cells in analyses
The preceding section described how complex spike cells were defined as place cells (or not) on a single trial. However, all cells in this study were recorded for several trials, possibly including more than one probe trial. A further set of criteria is therefore necessary in order to decide which cells are included into an analysis, depending on the activity of the cell across a given series of trials. The way in which these series of trials were defined, and the criteria used to include place cells in analyses, is described below.
For this thesis, three slightly different inclusion criteria were employed depending on which parts of the experiments (familiar only, probe trial series), and which measures (across-trial vs.
within-trial), were to be analysed. Briefly, the different criteria were those applied to i) analysis of place cell properties in the familiar environment (see section II.6.4.3, p. 125); ii) analysis of probe trials for within-trial measures of spatial tuning (see section II.6.4.3, p. 128); iii) analysis of probe trials for across-trial measures of place field stability (see section II.6.4.3, p. 130).
For the analysis of basic place cell properties in the familiar environment only recording trials in this environment before any probe trial was run were considered.
For the analysis of probe trials the series of trials used for defining place cells was extended to include the probe itself and any familiar trials preceding or following it. This is because here the properties of place cells are to be compared between ‘familiar’ and ‘probe’ trials and place cells that are spatially tuned during the probe but not in the familiar environment (or vice versa) cannot be ignored in the data analysis.
Furthermore, different criteria are applied depending on whether within-trial spatial tuning (see section II.6.4.3, p. 128) or across-trial place field stability (see section II.6.4.3, p. 130) measures are analysed. For the latter case, only cells that are significantly spatially tuned in the
125 familiar environment (before any probe was run) and also exhibit an above threshold average stability in the familiar environment are included. This is because place cells which do not show a spatial tuning or a minimum stability across the familiar trials cannot be meaningfully compared to their respective response in the probe trials (an unstable place cell across familiar trials is not tightly bound to a certain location inside this environment, and thus a possible change of the firing field during the probe cannot be interpreted).
Further detail on each of these three inclusion criteria follows. One general comment has to be made about the potential inflation of type I errors for the method of place cell inclusion.
Regardless of the analysis type there are always multiple trials on which a potential place cell could surpass the inclusion criterion, which could result in a multiple comparisons problem.
However, since finding the exact absolute percentage of place cells from the whole population at a given age was not an aim of this work, this will not bias the results presented in this thesis.
Furthermore, the same method for place cell inclusion was applied to all age bins which would result in a similar number of multiple comparisons for each age bin. This method is much less strict than the criterion used in Wills et al. (2010) where a given unit had to surpass the criterion on every recording trial in an experiment to be deemed a place cell. The number of trials forming an experiment were however much lower in the above mentioned study. Place cell properties in young rat pups can vary quite substantially between recording trials and using a similar criterion for this thesis would generally result in only selecting the best and most reliable place cells in these young animals.
Place cell inclusion for analysis of place cell properties in familiar environment
To define a complex spike cell as place cell for the analysis of basic properties of place cells recorded inside the familiar environment the following criterion was applied. A unit’s spatial
126 information content had to exceed the 95th percentile of the corresponding age-matched distribution of spatial information based on spike-shuffled data in at least one recording trial of a trial series (see Figure II-3). For this type of analysis only recording trials inside the familiar environment before any probe trial was conducted were considered. Recording trials where i) number of spikes < 75, ii) path length < 40 m and iii) number of visited bins < 520 were excluded from this comparison.
Figure II-3: Schematic overview of place cell inclusion process for the analysis of place cell properties recorded inside the familiar environment before any probe trial was conducted. Top row shows experimental design (A). Red box indicates trials of interest for this type of analysis (‘series’). Spatial information content for a given cell was calculated for all trials of a series (B) and these were compared to the 95th percentile of the age-matched distribution of spatial information scores based on spike shuffled data (C). Only cells whose spatial information content exceeded this threshold in at least one trial of the series were deemed place cells.
127 Calculation of means for place cell properties in familiar environment
Place cell properties in familiar environment
For all included cells, the cell means for this type of data analysis were obtained by averaging the within-trial measures across the recording trials inside the familiar environment before any probe trial was conducted. For the across-trial measures means were obtained by averaging the values of the comparisons ‘familiar1’ vs. ‘familiar2’ and ‘familiar2’ vs. ‘familiar3’.
Calculation of 0.05-significance level for basic place cell properties
For calculation of the 0.05-significance level for the age means for spatial information, spatial coherence, intra-trial correlation and inter-trial correlation the following procedure was applied. For each age bin the total number of cells that passed the criterion for the definition as place cells was counted (M). Now M rate maps were selected at random from the population of maps based on spike-shuffled data and the respective place cell properties were averaged across this sample. This procedure was repeated 100,000 times for each age bin producing a distribution of means expected from populations of size M based on spike-shuffled data. The 95th percentile of these distributions was chosen as the 0.05-significance level for the respective place cell property. This means that an average observed value for a given place cell property at a given age exceeding the corresponding age-matched percentile is significantly higher than expected from a size-matched population of units firing without a spatial correlate.
128 Statistical analysis for place cell properties in familiar environment
For the analysis of the change of place cell properties inside the familiar environment across development, all within- and all across-trial measures were tested separately in MANOVAs with ‘age’ as the only factor. When a main effect of age was present, Tukey’s HSD tests were conducted for the post-hoc analysis.
Place cell inclusion for probe trials: Within-trial measures of spatial tuning
To define a complex spike as place cell for the analysis of the probe trial experiments slightly different criteria were applied depending on which properties of place cells were assessed.
For analysing within-trial properties that characterise the spatial tuning (‘spatiality’) of place cells (spatial information, spatial coherence, intra-trial correlation, field properties) a similar criterion to that from the analysis of place cell properties in the familiar environment (see Figure II-3) was used, with the exception that the series of trials used for defining place cells was extended to include the probe itself and any familiar environment trials preceding or following it. As previously, any cell whose spatial information content exceeded the 95th percentile of the corresponding age-matched distribution of spatial information based on spike-shuffled data, in at least one recording trial of a trial series, was included in the analysis (see Figure II-3).
For all included cells, the mean values of spatiality in the familiar environment was the mean spatiality across all familiar trials before any probe was run, and the spatiality in the probe was simply the spatiality in that particular probe trial (see Figure II-5C).
129 Figure II-4: Overview of method of how place cells were included according to their overall spatiality in a series (within-trial measures). A: general experimental design.
B: method of how place cells were defined according to their overall spatiality. Process is shown for two different probe series depending on whether probe of interest was the first (red box) in an experiment or a later one (green box). Note that trials forming the series for a given probe will not include any other probe trials which were part of the experiment. The trials belonging to the series included in the blue box are not shown in B.
130 Place cell inclusion for probe trials: Across-trial measures of place field stability
For analysing across-trial measures (inter-trial correlation, centre of mass shift) that characterise the stability of the spatial signal of place cells (‘stability’) a slightly different set of criteria was applied (see Figure II-5A, B). First, a unit’s spatial information content for those recording trials inside the familiar environment before any probe trial was conducted had to exceed the 95th percentile of the corresponding age-matched distribution of spatial information based on spike-shuffled data in at least one of those trials. Second, the mean inter-trial correlation across these trials (‘familiar1’ vs. ‘familiar2’ and ‘familiar2’ vs. ‘familiar3’) had to also exceed the 95th percentile of the corresponding age-matched distribution of inter-trial correlations based on spike-shuffled data (see Figure III-22). These distributions were generated from the same data as for spatial information and constructed using the same methods.
A trial series was defined in the same way as described in the previous section (see section II.6.4.3, p. 128).
Figure II-5C shows how the across-trial comparisons were defined. ‘familiar vs. probe’
correlation/centre of mass shift corresponds to the inter-trial correlation/centre of mass shift of/between the probe trial and the immediately preceding familiar trial.
Return-to-baseline correlation/centre of mass shift corresponds to the correlation/centre of mass shift between the two familiar trials encompassing a probe trial.
131 Figure II-5: Overview of method of how place cells were included according to their spatiality and stability in familiar environment. A: general experimental design. B: method of how place cells were defined according to their spatiality and stability across the recording trials inside the familiar environment before any probe was conducted (‘familiar1-3’). Process is shown for two different probe series depending on whether probe of interest was the first (red box) in an experiment or a later one (green box). C: Example of how cell means of comparisons were calculated for an individual place cell in a series of trials.
132 Statistical analysis for probe trial data
The statistical analysis of place cell properties in familiar and probe trials across development consisted of repeated measures ANOVAs for each place cell property in an age-by-environment design. In case a significant interaction between age and age-by-environment was present, a simple main effects analysis consisting of the pairwise comparisons at individual age bins was performed to analyse which of the data points actually show a significant difference between familiar and probe trials. When asterisks are indicated in a figure, p-values correspond to the results of these pairwise comparisons.