David Sankoff

SIMULTANEOUS SOLUTION OF THE RNA FOLDING, ALIGNMENT AND PROTOSEQUENCE PROBLEMS*

The alignment of finite sequences, the inference of ribonucleic acid secondary structures (folding), and the reconstruction of ancestral sequences on a phylogenetic tree, are three problems which have dynamic programming solutions, which we formulate in a common mathematical framework. Combining the objective functions for alignment (parsimony, or minimal mutations) and folding (free energy), we present an algorithm which solves all three problems simultaneously for a set of N sequences of length n in time proportional to

RNA secondary structures and their prediction

n^{3N}

Minimal Mutation Trees of Sequences

and storage

The social correlates and linguistic processes of lexical borrowing and assimilation

n^{2N}

Comparison of Musical Sequences

. Incorporating a “cutting corners” constraint against biologically unlikely alignments reduces these requirements so that they are proportional to

A formal grammar for code‐switching 1

n^{3}

Exact and Approximation Algorithms for Sorting by Reversals, with Application to Genome Rearrangement

and

The coffee genome provides insight into the convergent evolution of caffeine biosynthesis

n^{2}

Genome rearrangement with gene families

, respectively, for fixed N.

Gene Order Breakpoint Evidence in Animal Mitochondrial Phylogeny

This is a review of past and present attempts to predict the secondary structure of ribonucleic acids (RNAs) through mathematical and computer methods. Related areas covering classification, enumeration and graphical representations of structures are also covered. Various general prediction techniques are discussed, especially the use of thermodynamic criteria to construct an optimal structure. The emphasis in this approach is on the use of dynamic programming algorithms to minimize free energy. One such algorithm is introduced which comprises existing ones as special cases.