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An optimal formulation of the matrix method in statistical mechanics of one‐dimensional interacting units: Efficient iterative algorithmic procedures
Author(s) -
Yeramian E.,
Schaeffer F.,
Caudron B.,
Claverie P.,
Buc H.
Publication year - 1990
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360300502
Subject(s) - partition function (quantum field theory) , statistical mechanics , computer science , matrix (chemical analysis) , range (aeronautics) , sequence (biology) , iterative method , partition (number theory) , ising model , algorithm , statistical physics , mathematical optimization , mathematics , chemistry , physics , materials science , biochemistry , chromatography , quantum mechanics , combinatorics , composite material
Statistical mechanical calculations for one‐dimensional interacting units have undergone great development in many fields of macromolecular science. The partition function is the most rigorous description of an ensemble of molecules in equilibrium. Specific methodological formulations and algorithms were developed to handle numerically the inclusion of long‐range effects (as compared to usual nearest neighbor Ising models) and known sequence‐dependent heterogeneities of biological macromolecules. The most successful approach in formulating these problems in a very general and tractable framework was the so‐called matrix method. Despite several improvements, it was claimed that in practical applications this approach had fundamental limitations inherent to any “matrix” formulation. We show here that a new conceptual formulation allows us to overcome these limitations completely. We propose a general iterative procedure that combines the theoretical advantages of the matrix method with the possibility of highly optimized and efficient numerical algorithms.