Scaling limit of the disordered generalized Poland-Scheraga model for DNA denaturation

• 成果类型: Article
• 署名作者: Berger, Quentin; Legrand, Alexandre
• 署名单位: Sorbonne Universite; Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS); Institut Universitaire de France; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01304-1
• 发表日期: 2024
• 页码: 179-258
• 关键词: pinning model; critical-behavior; copolymer models; critical curves; polymer; UNIVERSALITY; TRANSITION; relevance; regime; walks

摘要

The Poland-Scheragamodel, introduced in the 1970s, is a reference model to describe the denaturation transition of DNA. More recently, it has been generalized in order to allow for asymmetry in the strands lengths and in the formation of loops: the mathematical representation is based on a bivariate renewal process, that describes the pairs of bases that bond together. Here, we consider a disordered version of the model, in which the two strands interact via a potential ss V ( . i, . j) + h when the ith monomer of the first strand and the j th monomer of the second strand meet. Here, h. Ris a homogeneous pinning parameter, ( .i)i=1 and ( . j) j=1 are two sequences of i.i.d. random variables attached to each DNA strand, V(center dot, center dot) is an interaction function and ss > 0 is the disorder intensity. In our main result, we find some condition on the underlying bivariate renewal so that, if one takes ss, h. 0 at some appropriate (explicit) rate as the length of the strands go to infinity, the partition function of the model admits a non-trivial, disordered, scaling limit. This is known as an intermediate disorder regime and is linked to the question of disorder relevance for the denaturation transition. Interestingly, and unlike any other model of our knowledge, the rate atwhich one has to take ss. 0 depends on the interaction function V(center dot, center dot) and on the distribution of ( .i)i=1, ( . j) j=1. On the other hand, the intermediate disorder limit of the partition function, when it exists, is universal: it is expressed as a chaos expansion of iterated integrals against a Gaussian processM, which arises as the scaling limit of the field (e ss V( . i, . j)) i, j=0 and exhibits correlations on lines and columns.