The significant difference in the DNA sequence may not correspond to such a great difference in the amino acid sequence (as the third nucleotide of a codon is usually irrelevant for the encoded aminoacid and also many amino acids are encoded by different codons and different organisms use these codons with different frequency (codon usage)). Furthermore, if the important regions such as the active and regulatory centers are simillar, the human protein will be able to do the same job in mice :)