  Why is the spine of a neuron so small that only small numbers of molecules
can exist and reactions inevitably become stochastic? Despite such noisy
conditions, we previously showed that the spine exhibits robust, sensitive and
efficient features of information transfer using probability of Ca$^{2+}$
increase; however, their mechanisms remains unknown. Here we show that the
small-volume effect enables robust, sensitive and efficient information
transfer in the spine volume, but not in the cell volume. In the spine volume,
intrinsic noise in reactions becomes larger than extrinsic noise of input,
making robust information transfer against input fluctuation. Stochastic
facilitation of Ca$^{2+}$ increase occurs in the spine volume, making higher
sensitivity to lower intensity of input. Volume-dependency of information
transfer enables efficient information transfer per input in the spine volume.
Thus, we propose that the small-volume effect is the functional reasons why the
spine has to be so small.
