Extended Fig. 8. Dynamic spine geometries induce modest levels of apparent spine turnover that cannot explain the turnover measured in vivo.
To study potential effects of fluctuations in spine geometry, we used values for the means and variances of dendrite radius, spine length, and spine radius that were determined by electron microscopy17,34. We then computationally examined how time-dependent fluctuations in these parameters would affect determinations of spine surviving fraction (Supplementary Methods, §VII).
(a) We examined how fluctuations in dendrite radius, spine radius, spine length and spine angle — individually (colored data points) and all together (black data) — affect the spine surviving fraction when the fluctuating geometric parameters are chosen stochastically in each of two imaging sessions, as a function of the parameter’s time-correlation between the two sessions (Supplementary Methods, §VII). As expected, when the two sessions involved image pairs that were perfectly correlated, the surviving fraction reached 100%. Fluctuations in all four parameters had greater effects than fluctuations in individual geometric parameters.
(b) To estimate the time-dependence of the surviving fraction of scorable spines from (a), we assumed all geometric parameters evolved according to the time-correlation function that we empirically determined from in vivo imaging data (Extended Fig. 9d).
(c) The apparent surviving fraction is the product of the true surviving fraction and the surviving fraction of scorable spines (Supplementary Methods, §VII). For the best-fit kinetic model, the apparent surviving fraction is very close to the true surviving fraction.
(d) The difference between the fitted timescale of the apparent surviving fraction and the true survival timescale is small across the range of model parameters consistent with the in vivo data (Supplementary Methods, §VII).
(e) The graph plots the lower bound of the surviving fraction of scorable merged spines as a function of the time-correlation function shared by all four geometric parameters, for different merged spine orders. As this lower bound increases rapidly with the merged spine order, artifactual turnover due to unscorable spines is unlikely when spine merging is common (Supplementary Methods, §VII).
(f) We combined Fig. 4c and Extended Fig. 8e to bound the turnover that could result from unscorable spines (Supplementary Methods, §VII). As the empirically measured surviving fraction falls below the lower bound obtained for the surviving fraction of scorable merged spines, ongoing changes in the geometric parameters of spines cannot account for the observed spine turnover.