Real Valued Sequence Alignment using Adapted Smith Waterman Algorithms

Abstract

Smith-Waterman is a dynamic programming algorithm that locally aligns sequences of discrete values by rewarding matched elements and penalizing mismatched elements. We present an adapted algorithm that aligns sequences of real-valued vectors, applied in our case to the output of nanopore DNA sequencing experiments using MspA. We choose each step of the algorithm to correspond to a driving behavior, such as a polymerase's synthesis and proofreading, and each penalty to be the logarithm of the probability that the step occurs. This allows us to interpret the total score of an alignment as its probability of being the true alignment. Given a known sequence but unknown kinetics, optimizing the score with respect to the penalties will set the penalties to the probabilistic values. This is a useful source of information about molecular motor kinetics. The algorithm's modularity and direct relation to physical behavior make it potentially useful for any physical probes of discrete time series. This work was supported by NIH/NHGRI grant R01HG005115 and R01HG006321.