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Updated: Mar 19, 2026
10:49
Method to Visualize and Analyze Membrane Interacting Proteins by Transmission Electron Microscopy
Published on: March 5, 2017
14.0K
Enumeration of Extended m-Regular Linear Stacks
Qiang-Hui Guo1, Lisa H Sun1, Jian Wang1
1Center for Combinatorics, LPMC-TJKLC, Nankai University , Tianjin, P.R. China .
Summary
This study introduces extended linear stacks to model protein contact maps, showing their generating function relates to standard linear stacks. This allows deriving asymptotic formulas for protein fold structures.
Area of Science:
- Computational Biology
- Statistical Mechanics
- Discrete Mathematics
Background:
- Protein contact maps on 2D square lattices have specific constraints on arc length and vertex degrees.
- Previous work enumerated [Formula: see text]-regular linear stacks with degree bounded by 2.
Purpose of the Study:
- To study extended [Formula: see text]-regular linear stacks that better model real protein contact maps.
- To establish a relationship between the generating functions of standard and extended linear stacks.
Main Methods:
- Mathematical modeling using generating functions for linear stacks.
- Derivation of a rational function relationship between generating functions.
- Elimination of variables to obtain an equation for the extended generating function.
Main Results:
- The generating function of extended [Formula: see text]-regular linear stacks ([Formula: see text]) is a rational function of the generating function for standard [Formula: see text]-regular linear stacks ([Formula: see text]).
- An equation satisfied by [Formula: see text] was derived.
- Asymptotic formulas for the number of [Formula: see text]-regular linear stacks were obtained.
Conclusions:
- The extended linear stack model provides a closer approximation to real protein contact maps.
- The established mathematical framework enables the asymptotic analysis of protein fold structures.
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