A Dynamic Programming Algorithm for Finding the Optimal Placement of a Secondary Structure Topology in Cryo-EM Data

2015 ◽  
Vol 22 (9) ◽  
pp. 837-843 ◽  
Author(s):  
Abhishek Biswas ◽  
Desh Ranjan ◽  
Mohammad Zubair ◽  
Jing He
Keyword(s):  
Dynamic Programming ◽  
Secondary Structure ◽  
Dynamic Programming Algorithm ◽  
Optimal Placement ◽  
Programming Algorithm ◽  
Structure Topology ◽  
Secondary Structure Topology

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 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.

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