Figure 5. Changing mushroom spine size... | Rockefeller University Press

Figure 5.

Changing mushroom spine size modulates calcium dynamics and synaptic weight change. (a and b) Spatial plots illustrating Ca2+ localization at 15 and 30 ms for medium mushroom spines with three different neck lengths, 0.13, 0.10, and 0.08 µm (a) and three different volumes, 0.080, 0.271, and 0.643 µm3 (b). The number above each geometry corresponds to the number of Ca2+ in the frame. Two random seeds are shown as examples for each geometry. Scale bars, 0.5 µm. (c) Mean (solid) and SD (shaded area) of Ca2+ transients across 50 simulations for each of the three mushroom spines with different neck lengths. (d) Variance of Ca2+ over time for the mushroom spines with different neck length, displayed as variance divided by 1,000 ions. (e) Mean (solid) and SD (shaded area) of Ca2+ transients across 50 simulations for each of the three mushroom spine sizes. (f) Variance of Ca2+ over time for the mushroom spines of different sizes, displayed as variance divided by 1,000 ions. (g) The mean and SEM (n = 50) of the peak number of Ca2+ in different mushroom spine sizes and with different neck lengths show an overall increasing trend. The spines of different sizes show statistically significant differences between the each size; P12 = 4.1244 × 10–13; P23 = 6.6467 × 10–15; P13 = 7.8934 × 10–32 from two-tailed t test, where 1, 2, and 3 denote the different sized spines in increasing size. We fitted the trend in peak Ca2+ as a linear function of volume-to-surface-area ratio, ζ; r2 = 0.5474 for the linear fit. (h) 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 mushroom spine sizes; P12 = 6.8175 × 10−6; P23 = 6.4075 × 10−6; P13 = 1.1118 × 10−10 from two-tailed t test, where 1, 2, and 3 denote the different sized spines in increasing size. The mean decay time constants as a function of volume-to-surface-area ratio, ζ, were fitted with an exponential a exp(bζ); r2 = 0.2380 for the exponential fit. (i) The mean and SEM (n = 50) of the calculated synaptic weight change at the last time point in the simulation for all mushroom spine sizes and neck lengths show an increasing trend against the volume-to-surface-area ratio. We fitted the trend in synaptic weight increase as a linear function of volume-to-surface-area ratio, ζ; r2 = 0.4224 for the linear fit. The spines of different sizes show statistically significant differences between all sizes; P12 = 5.1012 × 10−10; P23 = 2.0097 × 10−11; P13 = 2.1447 × 10−23 from two-tailed t-test, where 1, 2, and 3 denote the different sized spines in increasing size. Inset to right of i: legend for g–i.

Changing mushroom spine size modulates calcium dynamics and synaptic weight change. (a and b) Spatial plots illustrating Ca²⁺ localization at 15 and 30 ms for medium mushroom spines with three different neck lengths, 0.13, 0.10, and 0.08 µm (a) and three different volumes, 0.080, 0.271, and 0.643 µm³ (b). The number above each geometry corresponds to the number of Ca²⁺ in the frame. Two random seeds are shown as examples for each geometry. Scale bars, 0.5 µm. (c) Mean (solid) and SD (shaded area) of Ca²⁺ transients across 50 simulations for each of the three mushroom spines with different neck lengths. (d) Variance of Ca²⁺ over time for the mushroom spines with different neck length, displayed as variance divided by 1,000 ions. (e) Mean (solid) and SD (shaded area) of Ca²⁺ transients across 50 simulations for each of the three mushroom spine sizes. (f) Variance of Ca²⁺ over time for the mushroom spines of different sizes, displayed as variance divided by 1,000 ions. (g) The mean and SEM (n = 50) of the peak number of Ca²⁺ in different mushroom spine sizes and with different neck lengths show an overall increasing trend. The spines of different sizes show statistically significant differences between the each size; P₁₂ = 4.1244 × 10^–13; P₂₃ = 6.6467 × 10^–15; P₁₃ = 7.8934 × 10^–32 from two-tailed t test, where 1, 2, and 3 denote the different sized spines in increasing size. We fitted the trend in peak Ca²⁺ as a linear function of volume-to-surface-area ratio, ζ; r² = 0.5474 for the linear fit. (h) 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 mushroom spine sizes; P₁₂ = 6.8175 × 10⁻⁶; P₂₃ = 6.4075 × 10⁻⁶; P₁₃ = 1.1118 × 10⁻¹⁰ from two-tailed t test, where 1, 2, and 3 denote the different sized spines in increasing size. The mean decay time constants as a function of volume-to-surface-area ratio, ζ, were fitted with an exponential a exp(bζ); r² = 0.2380 for the exponential fit. (i) The mean and SEM (n = 50) of the calculated synaptic weight change at the last time point in the simulation for all mushroom spine sizes and neck lengths show an increasing trend against the volume-to-surface-area ratio. We fitted the trend in synaptic weight increase as a linear function of volume-to-surface-area ratio, ζ; r² = 0.4224 for the linear fit. The spines of different sizes show statistically significant differences between all sizes; P₁₂ = 5.1012 × 10⁻¹⁰; P₂₃ = 2.0097 × 10⁻¹¹; P₁₃ = 2.1447 × 10⁻²³ from two-tailed t-test, where 1, 2, and 3 denote the different sized spines in increasing size. Inset to right of i: legend for g–i.