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Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL.

Yang Z, Májek P, Bahar I - PLoS Comput. Biol. (2009)

Bottom Line: Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases.Application to bacterial chaperonin GroEL and comparisons with experimental data, results from action minimization algorithm, and previous simulations support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling potential transition pathways sampled by large complexes/assemblies.An important outcome is the assessment of the critical inter-residue interactions formed/broken near the transition state(s), most of which involve conserved residues.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational Biology, School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.

ABSTRACT
Identification of pathways involved in the structural transitions of biomolecular systems is often complicated by the transient nature of the conformations visited across energy barriers and the multiplicity of paths accessible in the multidimensional energy landscape. This task becomes even more challenging in exploring molecular systems on the order of megadaltons. Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases. Motivated by the utility of elastic network models for describing the collective dynamics of biomolecular systems and by the growing theoretical and experimental evidence in support of the intrinsic accessibility of functional substates, we introduce a new method, adaptive anisotropic network model (aANM), for exploring functional transitions. Application to bacterial chaperonin GroEL and comparisons with experimental data, results from action minimization algorithm, and previous simulations support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling potential transition pathways sampled by large complexes/assemblies. An important outcome is the assessment of the critical inter-residue interactions formed/broken near the transition state(s), most of which involve conserved residues.

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Correlation cosine between instantaneous distance vector andeigenmodes.Results are illustrated for aANM stepsk = 1, 7 and 13along the transition R″→T of a single subunit(subunit A in the respective PDB structures 1GRU and 1GR5). The leftordinate displays the correlation cosine between the distance vectord(k−1)and the eigenvectors  for 1≤i≤30 (blackbars), and the right ordinate shows the corresponding cumulativesquared cosine (Eq. (5)) (blue curve). The thresholdFmin = 0.5for the cumulative square cosine implies the selection ofmA(1) = 1,mA(7) = 3,andmA(13) = 23in evaluating vA(k) as indicated by the redlines and filled bars. See Table 1 for the complete list of  and  values and associated RMSDs between intermediateconformations.
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pcbi-1000360-g003: Correlation cosine between instantaneous distance vector andeigenmodes.Results are illustrated for aANM stepsk = 1, 7 and 13along the transition R″→T of a single subunit(subunit A in the respective PDB structures 1GRU and 1GR5). The leftordinate displays the correlation cosine between the distance vectord(k−1)and the eigenvectors for 1≤i≤30 (blackbars), and the right ordinate shows the corresponding cumulativesquared cosine (Eq. (5)) (blue curve). The thresholdFmin = 0.5for the cumulative square cosine implies the selection ofmA(1) = 1,mA(7) = 3,andmA(13) = 23in evaluating vA(k) as indicated by the redlines and filled bars. See Table 1 for the complete list of and values and associated RMSDs between intermediateconformations.

Mentions: Figure 3 illustrates theprocedure for selectingmA(k) for thetransition R″→T (step E in Figure 1). Results are shown for theaANM iterationsk = 1(top), 7 (middle) and 13(bottom). The bars displays the correlation cosine as a function of mode number1≤i≤25 (left ordinate), andthe blue curve is the cumulative squared cosine[C(mA(k))]2(right). Fork = 1, the lowestfrequency mode (i = 1)alone yields a correlation cosine of 0.82: it suffices, therefore, to takemA(1) = 1mode at this step to meet the criterion[C(mA(k))]2≥Fmin, if the thresholdFmin = 0.5. Fork = 7, on the otherhand, the same criterion is met bymA(7) = 3modes (see the red line), and fork = 13, we needmA(13) = 23modes.


Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL.

Yang Z, Májek P, Bahar I - PLoS Comput. Biol. (2009)

Correlation cosine between instantaneous distance vector andeigenmodes.Results are illustrated for aANM stepsk = 1, 7 and 13along the transition R″→T of a single subunit(subunit A in the respective PDB structures 1GRU and 1GR5). The leftordinate displays the correlation cosine between the distance vectord(k−1)and the eigenvectors  for 1≤i≤30 (blackbars), and the right ordinate shows the corresponding cumulativesquared cosine (Eq. (5)) (blue curve). The thresholdFmin = 0.5for the cumulative square cosine implies the selection ofmA(1) = 1,mA(7) = 3,andmA(13) = 23in evaluating vA(k) as indicated by the redlines and filled bars. See Table 1 for the complete list of  and  values and associated RMSDs between intermediateconformations.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2664929&req=5

pcbi-1000360-g003: Correlation cosine between instantaneous distance vector andeigenmodes.Results are illustrated for aANM stepsk = 1, 7 and 13along the transition R″→T of a single subunit(subunit A in the respective PDB structures 1GRU and 1GR5). The leftordinate displays the correlation cosine between the distance vectord(k−1)and the eigenvectors for 1≤i≤30 (blackbars), and the right ordinate shows the corresponding cumulativesquared cosine (Eq. (5)) (blue curve). The thresholdFmin = 0.5for the cumulative square cosine implies the selection ofmA(1) = 1,mA(7) = 3,andmA(13) = 23in evaluating vA(k) as indicated by the redlines and filled bars. See Table 1 for the complete list of and values and associated RMSDs between intermediateconformations.
Mentions: Figure 3 illustrates theprocedure for selectingmA(k) for thetransition R″→T (step E in Figure 1). Results are shown for theaANM iterationsk = 1(top), 7 (middle) and 13(bottom). The bars displays the correlation cosine as a function of mode number1≤i≤25 (left ordinate), andthe blue curve is the cumulative squared cosine[C(mA(k))]2(right). Fork = 1, the lowestfrequency mode (i = 1)alone yields a correlation cosine of 0.82: it suffices, therefore, to takemA(1) = 1mode at this step to meet the criterion[C(mA(k))]2≥Fmin, if the thresholdFmin = 0.5. Fork = 7, on the otherhand, the same criterion is met bymA(7) = 3modes (see the red line), and fork = 13, we needmA(13) = 23modes.

Bottom Line: Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases.Application to bacterial chaperonin GroEL and comparisons with experimental data, results from action minimization algorithm, and previous simulations support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling potential transition pathways sampled by large complexes/assemblies.An important outcome is the assessment of the critical inter-residue interactions formed/broken near the transition state(s), most of which involve conserved residues.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational Biology, School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.

ABSTRACT
Identification of pathways involved in the structural transitions of biomolecular systems is often complicated by the transient nature of the conformations visited across energy barriers and the multiplicity of paths accessible in the multidimensional energy landscape. This task becomes even more challenging in exploring molecular systems on the order of megadaltons. Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases. Motivated by the utility of elastic network models for describing the collective dynamics of biomolecular systems and by the growing theoretical and experimental evidence in support of the intrinsic accessibility of functional substates, we introduce a new method, adaptive anisotropic network model (aANM), for exploring functional transitions. Application to bacterial chaperonin GroEL and comparisons with experimental data, results from action minimization algorithm, and previous simulations support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling potential transition pathways sampled by large complexes/assemblies. An important outcome is the assessment of the critical inter-residue interactions formed/broken near the transition state(s), most of which involve conserved residues.

Show MeSH