The present invention describes a method for producing a useful metabolite using a bacterium of the family Enterobacteriaceae, particularly a bacterium belonging to the genus Escherichia, which has been modified to contain a gene(s) expression system including elements of the LysR-type protein-regulated transcriptional machinery modified in such a way that auto-inducible positive feedback regulation of the system is mediated by a coinducer. The method is suitable for producing branched-chain L-amino acids, particularly L-valine, L-isoleucine and L-leucine; and D-pantothenic acid.