scholarly journals A new entropy model for RNA: part IV, The Minimum Free Energy (mFE) and the thermodynamically most-probable folding pathway (TMPFP)

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Wayne Dawson ◽  
Gota Kawai
Keyword(s):  
Free Energy ◽  
Dynamic Programming ◽  
Secondary Structure ◽  
Dynamic Programming Algorithm ◽  
Minimum Free Energy ◽  
Programming Algorithm ◽  
Folding Pathway ◽  
Rna Sequences ◽  
Entropy Model ◽  
Suboptimal Structure

Here we discuss four important questions (1) how can we be sure that the thermodynamically most-probable folding-pathway yields the minimum free energy for secondary structure using the dynamic programming algorithm (DPA) approach, (2) what are its limitations, (3) how can we extend the DPA to find the minimum free energy with pseudoknots, and finally (4) what limitations can we expect to find in a DPA approach for pseudoknots. It is our supposition that some structures cannot be fit uniquely by the DPA, but may exist in real biology situations when disordered regions in the biomolecule are necessary. These regions would be identifiable by using suboptimal structure analysis. This grants us some qualitative tools to identify truly random RNA sequences, because such are likely to have greater degeneracy in their thermodynamically most-probable folding-pathway.

PSRna: Prediction of small RNA secondary structures based on reverse complementary folding method

2016 ◽  
Vol 14 (04) ◽  
pp. 1643001 ◽  
Author(s):  
Jin Li ◽  
Chengzhen Xu ◽  
Lei Wang ◽  
Hong Liang ◽  
Weixing Feng ◽  
...  
Keyword(s):  
Free Energy ◽  
Secondary Structure ◽  
Small Rna ◽  
Small Rnas ◽  
Dynamic Programming Algorithm ◽  
Real Data ◽  
Secondary Structures ◽  
Minimum Free Energy ◽  
Programming Algorithm ◽  
Rna Secondary Structures

Prediction of RNA secondary structures is an important problem in computational biology and bioinformatics, since RNA secondary structures are fundamental for functional analysis of RNA molecules. However, small RNA secondary structures are scarce and few algorithms have been specifically designed for predicting the secondary structures of small RNAs. Here we propose an algorithm named “PSRna” for predicting small-RNA secondary structures using reverse complementary folding and characteristic hairpin loops of small RNAs. Unlike traditional algorithms that usually generate multi-branch loops and 5[Formula: see text] end self-folding, PSRna first estimated the maximum number of base pairs of RNA secondary structures based on the dynamic programming algorithm and a path matrix is constructed at the same time. Second, the backtracking paths are extracted from the path matrix based on backtracking algorithm, and each backtracking path represents a secondary structure. To improve accuracy, the predicted RNA secondary structures are filtered based on their free energy, where only the secondary structure with the minimum free energy was identified as the candidate secondary structure. Our experiments on real data show that the proposed algorithm is superior to two popular methods, RNAfold and RNAstructure, in terms of sensitivity, specificity and Matthews correlation coefficient (MCC).

RANKING VALID TOPOLOGIES OF THE SECONDARY STRUCTURE ELEMENTS USING A CONSTRAINT GRAPH

2011 ◽  
Vol 09 (03) ◽  
pp. 415-430 ◽  
Author(s):  
KAMAL AL NASR ◽  
DESH RANJAN ◽  
MOHAMMAD ZUBAIR ◽  
JING HE
Keyword(s):  
Dynamic Programming ◽  
Secondary Structure ◽  
Protein Complexes ◽  
Dynamic Programming Algorithm ◽  
Weighted Graph ◽  
Minimum Cost ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Constraint Graph ◽  
Density Maps

Electron cryo-microscopy is a fast advancing biophysical technique to derive three-dimensional structures of large protein complexes. Using this technique, many density maps have been generated at intermediate resolution such as 6–10 Å resolution. Although it is challenging to derive the backbone of the protein directly from such density maps, secondary structure elements such as helices and β-sheets can be computationally detected. Our work in this paper provides an approach to enumerate the top-ranked possible topologies instead of enumerating the entire population of the topologies. This approach is particularly practical for large proteins. We developed a directed weighted graph, the topology graph, to represent the secondary structure assignment problem. We prove that the problem of finding the valid topology with the minimum cost is NP hard. We developed an O(N2 2N) dynamic programming algorithm to identify the topology with the minimum cost. The test of 15 proteins suggests that our dynamic programming approach is feasible to work with proteins of much larger size than we could before. The largest protein in the test contains 18 helical sticks detected from the density map out of 33 helices in the protein.

scholarly journals Mathematical and Biological Modelling of RNA Secondary Structure and Its Effects on Gene Expression

2006 ◽  
Vol 7 (1) ◽  
pp. 37-43 ◽  
Author(s):  
T. A. Hughes ◽  
J. N. McElwaine
Keyword(s):  
Gene Expression ◽  
Free Energy ◽  
Secondary Structure ◽  
Structure Prediction ◽  
Secondary Structure Prediction ◽  
Secondary Structures ◽  
Minimum Free Energy ◽  
Messenger Rnas ◽  
Rna Sequences ◽  
Translational Machinery

Secondary structures within the 5′ untranslated regions of messenger RNAs can have profound effects on the efficiency of translation of their messages and thereby on gene expression. Consequently they can act as important regulatory motifs in both physiological and pathological settings. Current approaches to predicting the secondary structure of these RNA sequences find the structure with the global-minimum free energy. However, since RNA folds progressively from the 5′ end when synthesised or released from the translational machinery, this may not be the most probable structure. We discuss secondary structure prediction based on local-minimisation of free energy with thermodynamic fluctuations as nucleotides are added to the 3′ end and show that these can result in different secondary structures. We also discuss approaches for studying the extent of the translational inhibition specified by structures within the 5′ untranslated region.

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