Normalization.

For any node Y, multiplying S^Y and T^Y by an arbitrary constant k₁ has no effect on the dynamic programming algorithm. (Both S^Y and T^Y have to be multiplied by the same constant so that the equation $S^Y = \left ( M^{d_Y} \right )^{'} T^Y$is preserved). This can be readily verified from the definition of the cost function for DP, C(Y,X) above. Similarly, the PAS are not altered by such multiplication, as the last step normalizes the probabilities to add to 1. It is then advantageous to normalize the T and S vectors to prevent underflows which are very likely to occur for large multiple alignments. This independence from a constant factor also comes handy for indels.