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A new algorithm to estimate linear in parameters models is presented.

Abstract Background B. subtilis is an important organism in the biotechnological application. The efficient expression system is desirable in production of recombinant gene products in B. subtilis. Recently, we developed a new inducible expression system in B. subtilis, which directed by B. subtilis maltose utilization operon promoter Pglv. The system demonstrated high-level expression for target proteins in B. subtilis when induced by maltose. However, the system was markedly repressed by glucose. This limited the application of the system as a high-expression tool in biotechnology field. The aim of this study was to further improve the Pglv promoter system and enhance its expression strength. Results Here, site-directed mutagenesis was facilitated to enhance the expression strength of Pglv. The transcription level from four mutants was increased. Production of β-Gal from the mutants reached the maximum 1.8 times as high as that of wildtype promoter. When induced by 5% maltose, the production of β-Gal from two mutants reached 14.3 U/ml and 13.8 U/ml, 63.5% and 57.5% higher than wildtype promoter (8.8 U/ml) respectively. Thus, site-directed mutagenesis alleviated the repression of glucose and improved the expression activity. To further improve the promoter system, the B. subtilis expression host was reconstructed, in which B. subtilis well-characterized constitutive promoter P43 replaced the promoter of the glv operon in B. subtilis chromosome through a double crossover event. The β-galactosidase production from the improved system (21.1 U/mL) increased compared to that from origin system. Meanwhile, the repression caused by glucose was further alleviated. Conclusions In this study, we obtained a mutated promoter Pglv-M1 through site-directed mutagenesis, which demonstrated high expression strength and alleviated the repression caused by glucose. Moreover, we alleviated the repression and enhanced the expression activity of the Pglv-M1 promoter system via reconstruction of the B. subtilis host. Thus, we provided a valuable expression system in B. subtilis.