The combined effects of temperature and assay time on the catalytic ability and stability of 1,4-β-d-glucan cellobiohydrolase I

A new method is proposed to describe the combined effects of temperature and assay time on the reaction rates of 1,4-β-d-glucan cellobiohydrolase I (CBHI). The method involves determination of the product (PNP) released from substrate (PNPC) that was monitored spectroscopically and calculated by area under curve (AUC). The combined effects of temperature and assay time on the catalytic reaction rates were expressed as the composite function of the instantaneous reaction rate (vinst)(vinst) termed c−vinstc−vinst, denoted as dy/dT = dy/dt × dt/dT  . And the total instantaneous increment of product expressed as the complete differential of c−vinstc−vinst equals to the sum of the partial derivative of temperature and time denoted as: c−vinst=(∂p/∂T)tdT+(∂p/∂t)Tdtc−vinst=(∂p/∂T)tdT+(∂p/∂t)Tdt. The kinetic curves of c−vinstc−vinst and c−vinstc−vinst can be directly derived from the UV spectra by numerical differentiation and do not require any assumption of complex rate equations. The optimum temperature (Topt) and the heat-inactivated temperature (Tinac-50) were estimated based on the relationship between the first derivative of composite function (c−vinst)(c−vinst) and the second derivative (c−vsec)(c−vsec). This approach is particularly suited for biotechnological applications, given its precision and simplicity. The unsuitability of the Michaelis–Menten equation as used for determining the effect of temperature on reaction rates was discussed.