Regular Simple Queues of Protein Contact Maps

A protein fold can be viewed as a self-avoiding walk in certain lattice model, and its contact map is a graph that represents the patterns of contacts in the fold. Goldman, Istrail, and Papadimitriou showed that a contact map in the 2D square lattice can be decomposed into at most two stacks and one...

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Vydáno v:Bulletin of mathematical biology Ročník 79; číslo 1; s. 21 - 35
Hlavní autoři: Guo, Qiang-Hui, Sun, Lisa Hui, Wang, Jian
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2017
Springer Nature B.V
Témata:
Algorithms
Cell Biology
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Molecular
Nucleic Acid Conformation
Original Article
Protein Folding
Protein Interaction Mapping - statistics & numerical data
Protein Interaction Maps
Proteins - chemistry
RNA - chemistry
Motzkin path
92B05
Contact map
Queue
05A15
Stack
ISSN:0092-8240, 1522-9602, 1522-9602
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Shrnutí:A protein fold can be viewed as a self-avoiding walk in certain lattice model, and its contact map is a graph that represents the patterns of contacts in the fold. Goldman, Istrail, and Papadimitriou showed that a contact map in the 2D square lattice can be decomposed into at most two stacks and one queue. In the terminology of combinatorics, stacks and queues are noncrossing and nonnesting partitions, respectively. In this paper, we are concerned with 2-regular and 3-regular simple queues, for which the degree of each vertex is at most one and the arc lengths are at least 2 and 3, respectively. We show that 2-regular simple queues are in one-to-one correspondence with hill-free Motzkin paths, which have been enumerated by Barcucci, Pergola, Pinzani, and Rinaldi by using the Enumerating Combinatorial Objects method. We derive a recurrence relation for the generating function of Motzkin paths with k i peaks at level i , which reduces to the generating function for hill-free Motzkin paths. Moreover, we show that 3-regular simple queues are in one-to-one correspondence with Motzkin paths avoiding certain patterns. Then we obtain a formula for the generating function of 3-regular simple queues. Asymptotic formulas for 2-regular and 3-regular simple queues are derived based on the generating functions.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-016-0212-y