  We report on the dynamic nuclear polarization of a single charge-tunable
self-assembled InAs/GaAs quantum dot in a longitudinal magnetic field of
$\sim$0.2T. The hyperfine interaction between the optically oriented electron
and nuclei spins leads to the polarization of the quantum dot nuclei measured
by the Overhauser-shift of the singly-charged excitons ($X^{+}$ and $X^{-}$).
When going from $X^{+}$ to $X^{-}$, we observe a reversal of this shift which
reflects the average electron spin optically written down in the quantum dot
either in the $X^{+}$ state or in the final state of $X^{-}$ recombination. We
discuss a theoretical model which indicates an efficient depolarization
mechanism for the nuclei limiting their polarization to ~10%.

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