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Fragile-X fits from logistic model. A: Example Ca 2+ imaging dF/F raster plots from a single animal from each of two genotypes, WT and Frm1 KO, and three age groups, P9-11, P14-16 and P30-40. In each case 3 minutes of data are shown from 40 neurons. B: Example samples from the fitted logistic models, corresponding to the six groups shown in panel A. Inset shows group mean fitted logistic function, dashed vertical line represents zero. C-E: Mean firing probability (C), standard deviation of firing probabilities (D) and mean pairwise correlation across all neurons (E). Each circle represents data from a single animal, bars represent group means. F: Fitted logistic mean slope and mean threshold values for data from each WT (black circles) and Fmr1 KO (red circles) animal. Values overlaid on same firing rate (top) and correlation (bottom) maps from Figure 3C. G: Shift in mean logistic slope and threshold values from WT to KO for P9-11 (orange), P14-16 (red) and P30-40 (brown). Grey ellipses represent 95% confidence intervals (Methods). 230
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A leading theory holds that neurodevelopmental brain disorders arise from imbalances in excitatory and inhibitory (E/I) brain circuitry. However, it is unclear whether this onedimensional model is rich enough to capture the multiple neural circuit alterations underlying brain disorders. Here we combined computational simulations with analysis of in...
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... compared the 195 data from wild-type (WT) mice with Frm1 KO mice, the best studied animal model for Fragile-X 196 syndrome, across three different developmental time points: just before (P9-11) and after 197 (P14-16) the critical period, and a more mature timepoint (P30-40). Example ΔF/F raster 198 plots from each group are shown in Figure 4A. We binned the data into 1 s timebins (originally 199 . ...
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... the three summary statistics from each animal, we used a gradient descent algorithm to 216 find the five parameters of a population-level version of the logistic model that best matched 217 the activity statistics (see Methods). For each animal, we plot the mean slope and mean 218 threshold fits ( Figure 4F) on top of the previously calculated ( Figure 3C) 2D slope-threshold 219 maps of firing rate and correlation. We find that in young animals, P9-11, most points are 220 . ...
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... is important since inspection of the 2-dimensional 234 maps in Figure 2C shows that these sensitivities will differ depending on starting location within 235 the slope-threshold space. To quantify this effect, we calculated the sensitivity of both the firing 236 rate and correlations to small changes in the slope and threshold ( Figure 5, see Methods), 237 local to the fitted logistic parameter values for each animal (black and red circles in Figure 4F). 238 ...
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... bioRxiv preprint Figure 5. Sensitivity of firing rate and correlations with respect to logistic model parameters, local to the parameter fit for each animal. Sensitivity of firing probability (A) and pairwise correlations (B) to change in threshold (solid bars) and slope (striped bars) parameters of logistic model, about the fitted parameter values for each animal (circles) displayed in Figure 4F. Bars represent group means. ...
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... the relationship between these changes in firing statistics and the underlying neural 349 circuit components were unclear. Our logistic model helps bridge this gap, leading to two 350 findings: first, the direction of circuit parameter change from young (P9-11 and P14-16) to 351 mature (P30-40) animals is opposite in WT to KO mice ( Figure 4G). Similar opposing 352 switches in sensory cortex properties with age were also recently reported in Frm1 KO rats 353 (Berzhanskaya et al., 2016). ...
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... we saw no reliable 368 differences across genotypes in early postnatal animals (P9-11), Fmr1 KO animals showed 369 lower entropy than WT after the second postnatal week (P14-16), while surprisingly switching 370 to show higher entropy than WT in adult (P30-40). Notably, this switch in the direction of 371 entropy change from WT to KO during development mirrors the reversing we saw in logistic 372 model parameter changes in Figure 4G. Together, these findings suggest a perturbed 373 trajectory of cortical development during the critical period in Fmr1 KO mice (Meredith et al., 374 2012). ...
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... computed firing rates and pairwise correlations from the logistic model (Figures 3-4) in 515 the following way. First, we assumed that the fraction of active L4 neurons is described by a 516 normally distributed random variable with zero mean and unit variance: 517 ...
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... fitting the logistic model to the recorded neural firing rates and correlations (Figure 4), we 529 considered a population model where the joint probability distribution across threshold and 530 slope was specified by a 2D Gaussian, which has five parameters: threshold mean and s.d., 531 slope mean and s.d., and slope-threshold correlation. The three constraint statistics we 532 considered from the neural population data were the mean neural ON probability, the s.d. of 533 neural ON probabilities, and the mean pairwise correlations. ...
