Substitution matrix based kernel functions for protein secondary structure prediction

Different approaches to using substitution matrices in kernel functions for protein secondary structure prediction (PSSP) with support vector machines are investigated. This work introduces a number of kernel functions that calculate inner products between amino acid sequences based oil the entries of a substitution matrix (SM), i.e. a matrix that contains evolutionary information about the substitutability of the different amino acids that make up proteins. The starting point is always the same, i.e. a pseudo inner product (PI) between amino acid sequences making use of a SM. It is shown what conditions a SM should satisfy in order for the PI to make sense and subsequently it is shown how, a substitution distance (SD) based on the PI can be defined. Next different ways of using both the PI and the SD in kernel functions for support vector machine (SVM) learning are discussed. In a series of experiments the different kernel functions are compared with each other and with other kernel functions that do not make use of a SM. The results show that the information contained in a SM can have a positive influence on the PSSP results, provided that it is employed in the correct way.