2013/06/06 by Jacques M. Bahi, Christophe Guyeux, Bahi, Jacques M. +5
Biochemistry, Genetics and Molecular Biology · #Biomolecules (q-bio.BM) #FOS: Biological sciences #q-bio.BM
paper · pdf · doi:10.48550/arxiv.1306.1439
Under submission
arxiv created 2013/06/06 · arxiv updated 2013/06/07
Self-avoiding walks (SAW) are the source of very difficult problems in probabilities and enumerative combinatorics. They are also of great interest as they are, for instance, the basis of protein structure prediction in bioinformatics. Authors of this article have previously shown that, depending on the prediction algorithm, the sets of obtained conformations differ: all the self-avoiding walks can be reached using stretching-based algorithms whereas only the folded SAWs can be attained with methods that iteratively fold the straight line. A first study of (un)folded self-avoiding walks is presented in this article. The contribution is majorly a survey of what is currently known about these sets. In particular we provide clear definitions of various subsets of self-avoiding walks related to pivot moves (folded or unfoldable SAWs, etc.) and the first results we have obtained, theoretically or computationally, on these sets. A list of open questions is provided too, and the consequences on the protein structure prediction problem is finally investigated.