Unsupervised Learning of Multiple Motifs in Biopolymers Using Expectation Maximization
Machine Learning - Special issue on applications in molecular biology
Approximation algorithms for multiple sequence alignment
Theoretical Computer Science
Combinatorial optimization
On approximation algorithms for local multiple alignment
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
Finding similar regions in many sequences
Journal of Computer and System Sciences - STOC 1999
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies
INFORMS Journal on Computing
A cost-aggregating integer linear program for motif finding
Journal of Discrete Algorithms
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In the motif finding problem one seeks a set of mutually similar subsequences within a collection of biological sequences. This is an important and widely-studied problem, as such shared motifs in DNA often correspond to regulatory elements. We study a combinatorial framework where the goal is to find subsequences of a given length such that the sum of their pairwise distances is minimized. We describe a novel integer linear program for the problem, which uses the fact that distances between subsequences come from a limited set of possibilities. We show how to tighten its linear programming relaxation by adding an exponential set of constraints and give an efficient separation algorithm that can find violated constraints, thereby showing that the tightened linear program can still be solved in polynomial time. We apply our approach to find optimal solutions for the motif finding problem and show that it is effective in practice in uncovering known transcription factor binding sites.