Sp App size modulates synaptic weight change in thin spines. (a) Spatial plots at 15 and 30 ms for thin spines with SpApp of different volumes (spine cytosolic volumes of 0.026, 0.030, and 0.033 μm³). The numbers on top of the shape indicate the total number of calcium ions at that instant in both the SpApp and cytoplasm. (b and c) Calcium ions over time as mean and SD (b) and variance, displayed as variance divided by 1,000 ions (c), for all three thin spines with different SpApp sizes. Shaded regions in b denote SD. (d) Peak calcium ion number for each thin spine with a SpApp, with the mean and SEM (n = 50), show statistically significant differences between two of the three paired cases; *, P = 0.0461; ***, P = 0.0453 from two-tailed t test. We fitted the trend in peak values with a linear function against the cytoplasm volume; r² = 0.0145 for the linear fit. (e) We fitted the decay dynamics of each calcium transient with c · exp(−kt) and report the decay time constant, k, as a mean and SEM (n = 50). We found statistically significant differences only between the second and third spines; *, P = 0.0289 from a two-tailed t test. We fitted the trend in decay time constants as a function of cytosolic volume with an exponential a · exp(−bV), where V is the cytosolic volume; r² = 0.0177 for the fit. (f) Calculated synaptic weight change at the last time point for all three thin spines shows no statistically significant difference due to SpApp size. (g and h) We also plotted peak calcium ion number and decay time constant against the cytosolic volume-to-surface-area ratio (g and h, respectively). (g) We fitted the trend in peak values with a linear function against the volume-to-surface-area ratio; r² = 0.0214 for the linear fit. (h) We fitted the trend in decay time constants as a function of volume-to-surface-area ratio with an exponential a · exp(−bζ), where ζ is the volume-to-surface-area ratio; r² = 0.0178 for the fit.