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We have carried out a molecular dynamics simulation for the mixture of a cubic ice nucleus, supercooled water and a molecule of alanine dipeptide. The dipeptide molecule has been allocated near the nucleus surface. The dipeptide is found to approach the surface by the effect of hydrogen bond between two hydrophilic sites of the dipeptide and water molecules nearest to the liquid region in the ice nucleus. It is also found that the other hydrophilic sites far from the surface change their location with time due to the wobbling motion of the dipeptide molecule. This causes additional fluctuation of water molecules. These two sites and the hydrophobic site attenuate the approach of water molecules to the alanine dipeptide molecule or the ice surfaces.