Alignment Networks and Electrical Networks

In the analysis of biological sequences there arises the question of attributing weights to each element of a set of objects in such a way that similar objects do not overly influence deductions based on the entire set of objects. Since there is no known precise statement of this problem, we introduce two axioms that these weights should fulfill. It is then easy to see that this formulation includes one commonly used method. Further we apply the axiomatic framework to the new problem of attributing weights to alignments between two sequences. Viewing a sequence alignment as a directed network, an analogy to electrical networks is developed. This connection is used to prove the existence of the weights and develop other characteristics of an alignment network. Keyworh: Sequence alignment; Weighting methods; Electrical networks; Least squares estimation