Erratum: RNA matrix models with external interactions and their asymptotic behavior [Phys. Rev. E 79 , 061903 (2009)]

2011

Pramana - J Phys

The matrix model of (simplified) RNA folding with an external linear interaction in the action of the partition function is reviewed. The important results for structure combinatorics of the model are discussed and analysed in terms of the already existing models. InstallationThe improved understanding of the role of RNA in biological activities with discoveries and developments in the field of biophysics has highlighted the importance of studying their tertiary (folded 3D) conformations [1]. At the very base of understanding the different levels of structures of these biomolecules, lies the quest for understanding three fundamental problems (given in order): (i) to predict an RNA structure (enumeration), (ii) to find energetically viable structures from the enumerated structures and (iii) to determine kinetics of fold formation [2]. Therefore it is extremely essential to first enumerate and classify all possible types of structures (secondary and tertiary) with a given length, i.e., to know the combinatorics. Secondary structures of RNA have been studied successfully and widely using different statistical and computational models, particularly dynamic programming algorithms [3]. Tertiary structures, owing to their complexity, have been largely unaccessible [4]. Some models have captured the effects of pseudoknotted conformations [5] on the combinatorial and thermodynamic aspects [6]. In particular, a graph theoretic model by Haslinger and Stadler [7] considered bi-secondary structures (secondary structures with non-nested pseudoknots) in addition to the secondary structures and found that the total structures grow asymptotically as β L (where L is the length of RNA chain and β is the constraint-dependent combinatoric factor). Hence, depending upon the different constraining conditions faced by an RNA chain under physiological conditions, the total possible conformations may vary. This very idea springs up the thought of interesting outcomes in the study of the effects of different kinds of perturbations/external interactions/constraints

Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Section: Installationmentioning

confidence: 99%

See 1 more Smart Citation

Matrix models of RNA folding with external interactions: A review

Garg

2011

Pramana - J Phys

“…gives the strength of the external perturbation and i = 1, ..., n in the sum of the interaction term [11]. A L (N ) is the normalization…”

Section: Matrix Model Of Rna With An External Interaction On N ≤ L Numentioning

confidence: 99%

A random matrix approach to RNA folding with interaction

Garg

2009

Pramana - J Phys

Self Cite

In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where n ≤ L and L is the length of the polymer chain. The RNA structures found in the model can be separated into two regimes: (i) 0 ≤ α ≤ 1, n < L and 0 ≤ α < 1, n = L where unpaired and paired base structures exist and (ii) α = 1, n = L with only completely paired base structures. Figures for the genus distribution functions show differences at small lengths. We consider the situation when the strength of external perturbation is different on different bases in the polymer chain.

“…Therefore, the study of the effect of external interaction on RNA is an important area of research. Linear interactions in random matrix models for RNA folding were studied in [12][13][14], and it was established that these interactions have the same effect on RNA molecules as the effect created by a change in temperature and pressure. Recently, a Hermitian matrix model with interaction for RNA complexes (multiple backbone structures) [15] was studied which enumerates the linear cord diagrams of a fixed genus with a given number of chords and backbone.…”

Section: Introductionmentioning

confidence: 99%

Genus distribution and thermodynamics of a random matrix model of RNA with Penner interaction

Bhadola

2013

Phys. Rev. E

Self Cite

The nonlinear Penner external interaction is introduced and studied in the random matrix model of homo RNA. A numerical technique is developed to study the partition function, and a general formula is obtained for all lengths. The genus distribution function for the system is obtained, plotted, and compared with the genus distribution for the real RNA structures found from the protein databank. The genus distribution shows that the nonlinear interaction favors the formation of low genus structures and matches the result for real RNA structures. The distribution of structure with temperature suggests that nonlinear interaction is biased toward the planar structures. The variation of chemical potential with temperature and interaction strength indicates the presence of additional molecules in the system other than the magnesium ions and possibly represents a phase transition. The specific heat has a bump and its derivatives shows a double-peak behavior at a particular temperature. On analyzing the specific heat and derivatives for each genus separately, the planar structure (genus zero) is shown to contribute the most to the bump and double peak. This observation in the nonlinear model is similar to that observed in the unfolding experiments on RNA.