The initial alignments are converted into the profile space and a PSSM is constructed. The PSSM is updated (using the EM algorithm) until the alignments converge to a local optimal solution. The Exit-point methodology is then employed to escape out of this local optimal solution to compute nearby first tier local optimal solutions. This process is then repeated on promising first tier solutions to obtain second tier solutions. As shown in Fig. 4, from the original local optimal solution, various exit points and their corresponding new local optimal solutions are computed along each eigenvector direction. Sometimes two directions may yield the same local optimal solution. This can be avoided by computing the saddle point corresponding to the exit point on the stability boundary [24]. There can be many exit points, but there will only be a unique saddle point corresponding to the new local minimum. However, in high dimensional problems, this is not very efficient. Hence, we have chosen to compute the exit points. For computational efficiency, the Exit-point approach is only applied to promising initial alignments (i.e. random starts with higher Information Content score). Therefore, a threshold A(Q) score is determined by the average of the three best first tier scores after 10–15 random starts; any current and future first tier solution with scores greater than the threshold is considered for further analysis. Additional random starts are carried out in order to aggregate at least ten first tier solutions. The Exit-point method is repeated on all first tier solutions above a certain threshold to obtain second tier solutions.