Simulated annealing algorithm for the multiple sequence alignment problem: the approach of polymers in a random medium.

We propose a probabilistic algorithm to solve the multiple sequence alignment problem. The algorithm is a simulated annealing that exploits the representation of the multiple alignment between D sequences as a directed polymer in D dimensions. Within this representation we can easily track the evolution of the alignment through local moves of low computational cost. In contrast with other probabilistic algorithms proposed to solve this problem, our approach allows the creation and deletion of gaps without extra computational cost. The algorithm was tested by aligning proteins from the kinase family. When D=3 the results are consistent with those obtained using a complete algorithm. For D>3 where the complete algorithm fails, we show that our algorithm still converges to reasonable alignments. We also study the space of solutions obtained and show that depending on the number of sequences aligned the solutions are organized in different ways, suggesting a possible source of errors for progressive algorithms. Finally, we test our algorithm in artificially generated sequences and prove that it may perform better than progressive algorithms. Moreover, in those cases in which a progressive algorithm works better, its solution may be taken as an initial condition of our algorithm and, again, we obtain alignments with lower scores and more relevant from the biological point of view.