Unzipping of two random heteropolymers: Ground-state energy and finite-size effects

Tamm, M. V.; Nechaev, Sergei

doi:10.1103/physreve.78.011903

Cited by 6 publications

(5 citation statements)

References 44 publications

(88 reference statements)

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“…It is not obvious how to do that directly in the frameworks of the dynamic programming approach formalized in the recursion relation ( 7)- (8). To proceed, we exploit some trick (formulated for the first time in [33]), which consists of two consecutive steps.…”

Section: Matching Versus Pairing Of Two Random Linear Heteropolymersmentioning

confidence: 99%

“…In this section, we show how the algorithm used for the computation of the ground state energy of the RNA-like complexes can help to recover the details of the ground state secondary structure. We start with recalling the corresponding procedure for linear matching [28,29,33], and then we pass on to the more complicated RNA-like case.…”

Section: Secondary Structure Recoverymentioning

confidence: 99%

See 1 more Smart Citation

Statistics of noncoding RNAs: alignment and secondary structure prediction

Nechaev¹,

Tamm²,

Valba³

2011

J. Phys. A: Math. Theor.

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A new statistical approach to alignment (finding the longest common subsequence) of two random RNA-type sequences is proposed. We have constructed a generalized ‘dynamic programming’ algorithm for finding the extreme value of the free energy of two noncoding RNAs. In our procedure, we take into account the binding free energy of two random heteropolymer chains which are capable of forming the cloverleaf-like spatial structures typical for RNA molecules. The algorithm is based on two observations: (i) the standard alignment problem can be considered as a zero-temperature limit of a more general statistical problem of binding of two associating heteropolymer chains; (ii) this last problem can be generalized naturally to consider sequences with hierarchical cloverleaf-like structures (i.e. of RNA type). The approach also permits us to perform a ‘secondary structure recovery’. Namely, we can predict the optimal secondary structures of interacting RNAs in a zero-temperature limit knowing only their primary sequences.

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Section: Matching Versus Pairing Of Two Random Linear Heteropolymersmentioning

confidence: 99%

Section: Secondary Structure Recoverymentioning

confidence: 99%

Statistics of noncoding RNAs: alignment and secondary structure prediction

Nechaev¹,

Tamm²,

Valba³

2011

J. Phys. A: Math. Theor.

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“…For example, we could choose ω j taking only two values e AT and e GC and then make a choice for f that reflects the fact that AT bounds are weaker than GC bounds, and that all other possible bounds are even weaker. Even restricting to {ω j } j=1,2,... that is IID, this model is highly non trivial (gPS model with this type of disorder has been considered at a numerical level in [30,31], see also [28,54] for related work). But one could also choose to consider the binding of two sequences that are not complementary (the case considered in [49] goes in this direction, even if only heuristics and numerics are presented): choose for example two independent sequences {ω (1) j } j=1,2,... and {ω…”

Section: Theorem 12 ([35]mentioning

confidence: 99%

Disorder and denaturation transition in the generalized Poland-Scheraga model

Berger¹,

Giacomin²,

Khatib³

2018

Preprint

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We investigate the generalized Poland-Scheraga model, which is used in the bio-physical literature to model the DNA denaturation transition, in the case where the two strands are allowed to be non-complementary (and to have different lengths). The homogeneous model was recently studied from a mathematical point of view in [35,7], via a 2-dimensional renewal approach, with a loop exponent 2+α (α > 0): it was found to undergo a localization/delocalization phase transition of order ν = min(1, α) −1 , together with -in general -other phase transitions. In this paper, we turn to the disordered model, and we address the question of the influence of disorder on the denaturation phase transition, that is whether adding an arbitrarily small amount of disorder (i.e. inhomogeneities) affects the critical properties of this transition. Our results are consistent with Harris' predictions for d-dimensional disordered systems (here d = 2). First, we prove that when α < 1 (i.e. ν > d/2), then disorder is irrelevant: the quenched and annealed critical points are equal, and the disordered denaturation phase transition is also of order ν = α −1 . On the other hand, when α > 1, disorder is relevant: we prove that the quenched and annealed critical points differ. Moreover, we discuss a number of open problems, in particular the smoothing phenomenon that is expected to enter the game when disorder is relevant.

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“…It is not obvious how to do that directly in the frameworks of the dynamic programming approach formalized in the recursion relation (7). To proceed, we exploit the idea (formulated for the first time in [32]), which consists of two consecutive steps:…”

Section: Matching Vs Pairing Of Two Random Rna-type Heteropolymersmentioning

confidence: 99%

Sequence matching algorithms and pairing of noncoding RNAs

Nechaev,

Tamm,

Valba

2010

Preprint

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A new statistical method of alignment of two heteropolymers which can form hierarchical cloverleaf-like secondary structures is proposed. This offers a new constructive algorithm for quantitative determination of binding free energy of two noncoding RNAs with arbitrary primary sequences. The alignment of ncRNAs differs from the complete alignment of two RNA sequences: in ncRNA case we align only the sequences of nucleotides which constitute pairs between two different RNAs, while the secondary structure of each RNA comes into play only by the combinatorial factors affecting the entropc contribution of each molecule to the total cost function. The proposed algorithm is based on two observations: i) the standard alignment problem is considered as a zero-temperature limit of a more general statistical problem of binding of two associating heteropolymer chains; ii) this last problem is generalized onto the sequences with hierarchical cloverleaf-like structures (i.e. of RNA-type).Taking zero-temperature limit at the very end we arrive at the desired "cost function" of the system with account for entropy of side cactus-like loops. Moreover, we have demonstrated in detail how our algorithm enables to solve the "structure recovery" problem. Namely, we can predict in zero-temperature limit the cloverleaflike (i.e. secondary) structure of interacting ncRNAs by knowing only their primary sequences. Contents I. IntroductionA. Binding of noncoding RNAs B. Noncoding RNAs as particular class of associating heteropolymers C. Pairing vs alignment 2 S.K. Nechaev, M.V. Tamm, O.V. Valba II. Theoretical background 5 A. Alignment of linear sequences 5 B. Matching vs pairing of two random linear heteropolymers 6 C. Matching vs pairing of two random RNA-type heteropolymers 8 III. Matching algorithm for two noncoding RNAs A. Matching of linear sequences B. Matching of RNA-type sequences IV. Structure recovery A. Finding the Longest Common Subsequence for linear chains B. Finding the secondary structure for interacting RNA-like chains V. Conclusion A. Temperature dependence of the free energy B. Statistical analysis of a pair of random sequences References I. INTRODUCTION A. Binding of noncoding RNAsAccording to a common definition, the noncoding RNA (ncRNA) is an RNA molecule that is not translated into a protein. The ncRNAs either regulate the gene expression directly, for example by occupying the ribosome binding site, or indirectly providing RNA targeting specificity for a protein-based regulatory mechanism [1]. The class of ncRNAs spreads on regulatory and functional RNAs. In modern classification the term "noncoding RNA" is basically attributed to eucariotic RNAs, sometimes called also "small nonmessenger RNAs". In general, regulatory RNAs act in the cell by one of two basic mechanisms: by base-pairing interactions with other nucleic acids, or by binding to proteins [2]. The base pairing with target molecules constitutes the typical mechanism, by which the ncRNA regulates the gene expression. The base pairing is subdivided in two cl...

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Unzipping of two random heteropolymers: Ground-state energy and finite-size effects

Cited by 6 publications

References 44 publications

Statistics of noncoding RNAs: alignment and secondary structure prediction

Statistics of noncoding RNAs: alignment and secondary structure prediction

Disorder and denaturation transition in the generalized Poland-Scheraga model

Sequence matching algorithms and pairing of noncoding RNAs

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