A purified nucleic acid molecule capable of expressing a lysosomal enzyme, e.g., iduronidase or arylsulphatase, is provided. The molecule includes a promoter of the phosphoglycerate kinase gene to facilitate expression of the lysosomal enzyme in the brain. Expressing the lysosomal enzyme in the brain of patients with lysosomal storage diseases, such as mucopolysaccharidosis, provides treatment for the neurological aspects of these diseases. The invention also provides a method of gene therapy for lysosomal storage diseases by administering the nucleic acid molecule in the form of a vector.