## Ca^{2+} increases in the stochastic model.

**A, B**, Ca^{2+} increase due to stimulation of PF and CF inputs with Δt = 160 msec (**A**) and Δt = −400 msec (**B**) in the stochastic model in a spine volume (gray lines, n = 2,000 for each timing, 20 examples are shown) and in a cell volume (black lines, n = 20 for each timing). **C**, Distributions of the Ca^{2+} response in a spine volume with Δt = 160 msec (solid line) and Δt = −400 msec (dashed line). Black and white arrowheads indicate the means of the Ca^{2+} response in a cell volume with Δt = 160 msec and Δt = −400 msec, respectively. Note that Ca^{2+} increases in a cell volume were almost the same between trials, leading to the overlap of the time courses (**A**, **B**). **D**, The distribution of the Ca^{2+} response (upper panel) was divided into the distribution with Ca^{2+} spikes (*s* = 1, black) and the distribution without Ca^{2+} spikes (*s* = 0, gray with dashed line). Then, each right (*s* = 1) and left (*s* = 0) distribution is decomposed into the probability components, which is probability of Ca^{2+} spiking (middle panel), and amplitude components, which is distribution of the Ca^{2+} response conditioned by Ca^{2+} spiking (lower panel). See materials and methods for the detailed descriptions.