Three dimensional principal component analysis used for the study of enzyme kinetics: An empirical approximation for the determination of the dimensions of component matrices

The effect of cation type and concentration and fermentation time on the xylanase production of four strains of Lentinus edodes was determined. Three dimensional principal component analysis (3D-PCA) followed by nonlinear mapping technique (NLMAP) was employed for the assessment of similarities and dissimilarities between the enzymatic activities. An empirical method was developed for the reduction of the dimensionality of component matrices. No linear relationship was found between the effect of cations on the enzyme production and their ion radii, concentration and charge. Enzyme production was similar up till 20 days of fermentation then changed considerably. The enzyme activities of strains also showed marked differences. The results proved that the reduction of the dimensionality of component matrices exerts a negligible effect on the variance explained but it modifies the similarities and dissimilarities among the elements of the original matrix. It was established that 3D-PCA followed by NLMAP is a valuable tool for the evaluation of three dimensional data matrices in enzyme kinetic studies.