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A dendritic spine is a very small structure (~0.1 {\mu}m$^3$) of a neuronthat processes input timing information. Why are spines so small? Here, weprovide functional reasons; the size of spines is optimal for informationcoding. Spines code input timing information by the probability of Ca$^{2+}$increases, which makes robust and sensitive information coding possible. Wecreated a stochastic simulation model of input timing-dependent Ca$^{2+}$increases in a cerebellar Purkinje cell's spine. Spines used probability codingof Ca$^{2+}$ increases rather than amplitude coding for input timing detectionvia stochastic facilitation by utilizing the small number of molecules in aspine volume, where information per volume appeared optimal. Probability codingof Ca$^{2+}$ increases in a spine volume was more robust against inputfluctuation and more sensitive to input numbers than amplitude coding ofCa$^{2+}$ increases in a cell volume. Thus, stochasticity is a strategy bywhich neurons robustly and sensitively code information.

Stochasticity in Ca$^{2+}$ increase in spines enables robust and sensitive information coding