Descriptors calculated from a specific representation scheme encode only one part of the chemical information. For this reason, there is a need to construct novel graphical representations of proteins and novel protein descriptors that can provide new information about the structure of proteins. Here, a new set of protein descriptors based on computation of bilinear maps is presented. This novel approach to biomacromolecular design is relevant for QSPR studies on proteins. Protein bilinear indices are calculated from the kth power of nonstochastic and stochastic graph-theoretic electronic-contact matrices, M(m)(k) and (s)M(m)(k), respectively. That is to say, the kth nonstochastic and stochastic protein bilinear indices are calculated using M(m)(k) and (s)M(m)(k) as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of amino acid properties as weightings. Classification models based on a protein bilinear descriptor that discriminate between Arc mutants of stability similar or inferior to the wild-type form were developed. These equations permitted the correct classification of more than 90% of the mutants in training and test sets, respectively. To predict t(m) and Delta DeltaG(f)(o) values for Arc mutants, multiple linear regression and piecewise linear regression models were developed. The multiple linear regression models obtained accounted for 83% of the variance of the experimental t(m). Statistics calculated from internal and external validation procedures demonstrated robustness, stability and suitable power ability for all models. The results achieved demonstrate the ability of protein bilinear indices to encode biochemical information related to those structural changes significantly influencing the Arc repressor stability when punctual mutations are induced.