Calcium dynamics and synaptic weight change in filopodia-shaped spines depend on spine volume-to-surface ratio. (a) Spatial plots illustrating Ca²⁺ localization at 15 and 30 ms for filopodia-shaped spines with different volumes (0.017, 0.058, and 0.138 µm³). The number above each geometry corresponds to the number of Ca²⁺ in that frame. Two random seeds are shown as examples for each geometry. Scale bars, 2 μm. (b) Mean (solid) and SD (shaded area) of Ca²⁺ transients across 50 simulations for each of the three filopodia-shaped spine sizes. (c) Variance of Ca²⁺ over time, displayed as variance divided by 1,000 ions. (d) The mean and SEM (n = 50) of the peak number of Ca²⁺ in different filopodia-shaped spine sizes shows statistically significant differences; *, P = 2.0262 × 10⁻¹¹; **, P = 9.898 × 10⁻⁸; ***, P = 4.362 10⁻²⁶ using two-tailed t-test. We fitted the trend in peak Ca²⁺ as a linear function of volume-to-surface-area ratio, ζ; r² = 0.5521 for the linear fit. (e) The decay time scales of each Ca²⁺ transient were estimated by fitting with an exponential decay function c exp(kt). The mean and SEM (n = 50) of the decay time constant, k, shows statistically significant differences across filopodia-shaped spine sizes; *, P = 1.6331 × 10⁻⁴; **, P = 0.0209; ***, P = 1.3381 × 10⁻⁶ from two-tailed t test. The mean decay time constants as a function of volume-to-surface-area ratio, ζ, were fitted with an exponential a exp(bζ); r² = 0.203 for the exponential fit. (f) The mean and SEM (n = 50) of the calculated synaptic weight change at the last time point in the simulation for all filopodia-shaped spine sizes, plotted against the volume-to-surface-area ratio, shows statistically significant differences between all cases; P₁₂ = 2.7290 × 10⁻⁵; P₂₃ = 2.8626 × 10⁻⁶; P₁₃ = 1.6321 × 10⁻¹⁴ from two-tailed t test, where 1, 2, and 3 refer to the spines in increasing size. We fitted the trend in synaptic weight as a linear function of volume-to-surface-area ratio, ζ; r² = 0.3594 for the linear fit.