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Entropy
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Loop Entropy
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Loop Entropy

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (20 December 2012) | Viewed by 54349

Special Issue Editor

Prof. Dr. Gregory S. Chirikjian

E-Mail Website
Guest Editor
Department of Mechanical Engineering, Johns Hopkins University, 223 Latrobe Hall, 3400 North Charles Street, Baltimore, MD 21218-2682, USA
Interests: computational structural biology (in particular, computational mechanics of large proteins); conformational statistics of biological macromolecules; developed theory for "hyper-redundant" (snakelike) robot motion planning; designs and builds hyper-redundant robotic manipulator arms; applied mathematics (applications of group theory in engineering); self-replicating robotic systems

Special Issue Information

Dear Colleagues,

Macromolecules such as polypeptides and nucleic acids form the basis for all living things. These molecules typically fold into tertiary structures that have highly ordered regions. However, it is often the case that some aspects of these tertiary structures remain underdetermined when viewed as a static object. This underdetermination manifests itself in the form of hinge and breathing motions, allosteric reorganization, intrinsically disordered regions, and loop motions. In this special issue of Entropy, models of the various aspects of conformational variability in biological macromolecules are examined. Concepts from polymer theory, statistical thermodynamics, computer science, molecular dynamics simulation, stochastic modeling, and information theory will be used to model the conformational disorder of biomolecules both in their denatured and folded states.

Gregory S. Chirikjian
Guest Editor

Keywords

  • entropy
  • statistical mechanics
  • RNA
  • DNA
  • loops
  • conformation
  • molecular simulation
  • stochastic models
  • Brownian motion
  • protein folding
  • polymer theory

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Published Papers (6 papers)

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Research

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15 pages, 2378 KiB  
Article
Substrate Effect on Catalytic Loop and Global Dynamics of Triosephosphate Isomerase
by Zeynep Kurkcuoglu and Pemra Doruker
Entropy 2013, 15(3), 1085-1099; https://doi.org/10.3390/e15031085 - 18 Mar 2013
Cited by 4 | Viewed by 6276
Abstract
The opening/closure of the catalytic loop 6 over the active site in apo triosephosphate isomerase (TIM) has been previously shown to be driven by the global motions of the enzyme, specifically the counter-clockwise rotation of the subunits. In this work, the effect of [...] Read more.
The opening/closure of the catalytic loop 6 over the active site in apo triosephosphate isomerase (TIM) has been previously shown to be driven by the global motions of the enzyme, specifically the counter-clockwise rotation of the subunits. In this work, the effect of the substrate dihydroxyacetone phosphate (DHAP) on TIM dynamics is assessed using two apo and two DHAP-bound molecular dynamics (MD) trajectories (each 60 ns long). Multiple events of catalytic loop opening/closure take place during 60 ns runs for both apo TIM and its DHAP-complex. However, counter-clockwise rotation observed in apo TIM is suppressed and bending-type motions are linked to loop dynamics in the presence of DHAP. Bound DHAP molecules also reduce the overall mobility of the enzyme and change the pattern of orientational cross-correlations, mostly those within each subunit. The fluctuations of pseudodihedral angles of the loop 6 residues are enhanced towards the C-terminus, when DHAP is bound at the active site. Full article
(This article belongs to the Special Issue Loop Entropy)
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14 pages, 493 KiB  
Article
Protein Loop Dynamics Are Complex and Depend on the Motions of the Whole Protein
by Michael T. Zimmermann and Robert L. Jernigan
Entropy 2012, 14(4), 687-700; https://doi.org/10.3390/e14040687 - 10 Apr 2012
Cited by 10 | Viewed by 7392
Abstract
We investigate the relationship between the motions of the same peptide loop segment incorporated within a protein structure and motions of free or end-constrained peptides. As a reference point we also compare against alanine chains having the same length as the loop. Both [...] Read more.
We investigate the relationship between the motions of the same peptide loop segment incorporated within a protein structure and motions of free or end-constrained peptides. As a reference point we also compare against alanine chains having the same length as the loop. Both the analysis of atomic molecular dynamics trajectories and structure-based elastic network models, reveal no general dependence on loop length or on the number of solvent exposed residues. Rather, the whole structure affects the motions in complex ways that depend strongly and specifically on the tertiary structure of the whole protein. Both the Elastic Network Models and Molecular Dynamics confirm the differences in loop dynamics between the free and structured contexts; there is strong agreement between the behaviors observed from molecular dynamics and the elastic network models. There is no apparent simple relationship between loop mobility and its size, exposure, or position within a loop. Free peptides do not behave the same as the loops in the proteins. Surface loops do not behave as if they were random coils, and the tertiary structure has a critical influence upon the apparent motions. This strongly implies that entropy evaluation of protein loops requires knowledge of the motions of the entire protein structure. Full article
(This article belongs to the Special Issue Loop Entropy)
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20 pages, 878 KiB  
Article
Quantitative Comparison of Conformational Ensembles
by Kevin C. Wolfe and Gregory S. Chirikjian
Entropy 2012, 14(2), 213-232; https://doi.org/10.3390/e14020213 - 10 Feb 2012
Cited by 11 | Viewed by 6509
Abstract
A number of measures have been used in the structural biology literature to compare the shapes or conformations of biological macromolecules. However, the issue of how to compare two ensembles of conformations has received far less attention. Herein, the problem of how to [...] Read more.
A number of measures have been used in the structural biology literature to compare the shapes or conformations of biological macromolecules. However, the issue of how to compare two ensembles of conformations has received far less attention. Herein, the problem of how to quantitatively compare two such ensembles is addressed in several different ways using concepts from probability and information theory. Ultimately, such metrics could be used in the evaluation of structure-prediction algorithms and the analysis of how conformational mobility is inhibited by bound ligands. Full article
(This article belongs to the Special Issue Loop Entropy)
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9 pages, 119 KiB  
Article
Loop Entropy Assists Tertiary Order: Loopy Stabilization of Stacking Motifs
by Daniel P. Aalberts
Entropy 2011, 13(11), 1958-1966; https://doi.org/10.3390/e13111958 - 24 Nov 2011
Cited by 1 | Viewed by 6709
Abstract
The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of [...] Read more.
The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of forming multibranch and other RNA loops is derived with a polymer-physics based theory. We also derive a formula for the free energy of coaxial stacking in the context of a loop. Simulations support the analytic formulas. The effects of stacking of unpaired bases are also studied with simulations. Full article
(This article belongs to the Special Issue Loop Entropy)
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Review

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18 pages, 1541 KiB  
Review
Application of Solution NMR Spectroscopy to Study Protein Dynamics
by Christoph Göbl and Nico Tjandra
Entropy 2012, 14(3), 581-598; https://doi.org/10.3390/e14030581 - 22 Mar 2012
Cited by 19 | Viewed by 11924
Abstract
Recent advances in spectroscopic methods allow the identification of minute fluctuations in a protein structure. These dynamic properties have been identified as keys to some biological processes. The consequences of this structural flexibility can be far‑reaching and they add a new dimension to [...] Read more.
Recent advances in spectroscopic methods allow the identification of minute fluctuations in a protein structure. These dynamic properties have been identified as keys to some biological processes. The consequences of this structural flexibility can be far‑reaching and they add a new dimension to the structure-function relationship of biomolecules. Nuclear Magnetic Resonance (NMR) spectroscopy allows the study of structure as well as dynamics of biomolecules in a very broad range of timescales at atomic level. A number of new NMR methods have been developed recently to allow the measurements of time scales and spatial fluctuations, which in turn provide the thermodynamics associated with the biological processes. Since NMR parameters reflect ensemble measurements, structural ensemble approaches in analyzing NMR data have also been developed. These new methods in some instances can even highlight previously hidden conformational features of the biomolecules. In this review we describe several solution NMR methods to study protein dynamics and discuss their impact on important biological processes. Full article
(This article belongs to the Special Issue Loop Entropy)
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39 pages, 3695 KiB  
Review
Modeling Structures and Motions of Loops in Protein Molecules
by Amarda Shehu and Lydia E. Kavraki
Entropy 2012, 14(2), 252-290; https://doi.org/10.3390/e14020252 - 13 Feb 2012
Cited by 47 | Viewed by 14677
Abstract
Unlike the secondary structure elements that connect in protein structures, loop fragments in protein chains are often highly mobile even in generally stable proteins. The structural variability of loops is often at the center of a protein’s stability, folding, and even biological function. [...] Read more.
Unlike the secondary structure elements that connect in protein structures, loop fragments in protein chains are often highly mobile even in generally stable proteins. The structural variability of loops is often at the center of a protein’s stability, folding, and even biological function. Loops are found to mediate important biological processes, such as signaling, protein-ligand binding, and protein-protein interactions. Modeling conformations of a loop under physiological conditions remains an open problem in computational biology. This article reviews computational research in loop modeling, highlighting progress and challenges. Important insight is obtained on potential directions for future research. Full article
(This article belongs to the Special Issue Loop Entropy)
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