The rank of data matrices in a spectrophotometric study of a ligand-biopolymer complex formation

The dependences of concentrations of ligand-linear polymer complex species vs. the concentration of free ligand were calculated. The analysis of the data suggests that the variance of the property studied considerably depends on the parameters of ligand-polymer complex formation (cooperativity and the average number of monomers occupied by the ligand). The rank of the matrix of concentration fractions of species was estimated using the singular value decomposition by the method of principal component analysis. As the cooperativity increases, the rank matrix decreases from 4 to 2. An increase in the average number of monomers occupied by the ligand at high cooperativity leads to an increase in the matrix rank from 2 to 3.