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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 and                                eigenmodes.Results are illustrated for aANM steps                                k = 1, 7 and 13                                along the transition R″→T of a single subunit                                (subunit A in the respective PDB structures 1GRU and 1GR5). The left                                ordinate displays the correlation cosine between the distance vector                                    d(k−1)                                and the eigenvectors  for 1≤i≤30 (black                                bars), and the right ordinate shows the corresponding cumulative                                squared cosine (Eq. (5)) (blue curve). The threshold                                        Fmin = 0.5                                for the cumulative square cosine implies the selection of                                        mA(1) = 1,                                        mA(7) = 3,                                and                                mA(13) = 23                                in evaluating vA(k) as indicated by the red                                lines and filled bars. See Table 1 for the complete list of  and  values and associated RMSDs between intermediate                                conformations.
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pcbi-1000360-g003: Correlation cosine between instantaneous distance vector and eigenmodes.Results are illustrated for aANM steps k = 1, 7 and 13 along the transition R″→T of a single subunit (subunit A in the respective PDB structures 1GRU and 1GR5). The left ordinate displays the correlation cosine between the distance vector d(k−1) and the eigenvectors for 1≤i≤30 (black bars), and the right ordinate shows the corresponding cumulative squared cosine (Eq. (5)) (blue curve). The threshold Fmin = 0.5 for the cumulative square cosine implies the selection of mA(1) = 1, mA(7) = 3, and mA(13) = 23 in evaluating vA(k) as indicated by the red lines and filled bars. See Table 1 for the complete list of and values and associated RMSDs between intermediate conformations.

Mentions: Figure 3 illustrates the procedure for selecting mA(k) for the transition R″→T (step E in Figure 1). Results are shown for the aANM iterations k = 1 (top), 7 (middle) and 13 (bottom). The bars displays the correlation cosine as a function of mode number 1≤i≤25 (left ordinate), and the blue curve is the cumulative squared cosine [C(mA(k))]2 (right). For k = 1, the lowest frequency mode (i = 1) alone yields a correlation cosine of 0.82: it suffices, therefore, to take mA(1) = 1 mode at this step to meet the criterion [C(mA(k))]2≥Fmin , if the threshold Fmin = 0.5. For k = 7, on the other hand, the same criterion is met by mA(7) = 3 modes (see the red line), and for k = 13, we need mA(13) = 23 modes.


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 and                                eigenmodes.Results are illustrated for aANM steps                                k = 1, 7 and 13                                along the transition R″→T of a single subunit                                (subunit A in the respective PDB structures 1GRU and 1GR5). The left                                ordinate displays the correlation cosine between the distance vector                                    d(k−1)                                and the eigenvectors  for 1≤i≤30 (black                                bars), and the right ordinate shows the corresponding cumulative                                squared cosine (Eq. (5)) (blue curve). The threshold                                        Fmin = 0.5                                for the cumulative square cosine implies the selection of                                        mA(1) = 1,                                        mA(7) = 3,                                and                                mA(13) = 23                                in evaluating vA(k) as indicated by the red                                lines and filled bars. See Table 1 for the complete list of  and  values and associated RMSDs between intermediate                                conformations.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2664929&req=5

pcbi-1000360-g003: Correlation cosine between instantaneous distance vector and eigenmodes.Results are illustrated for aANM steps k = 1, 7 and 13 along the transition R″→T of a single subunit (subunit A in the respective PDB structures 1GRU and 1GR5). The left ordinate displays the correlation cosine between the distance vector d(k−1) and the eigenvectors for 1≤i≤30 (black bars), and the right ordinate shows the corresponding cumulative squared cosine (Eq. (5)) (blue curve). The threshold Fmin = 0.5 for the cumulative square cosine implies the selection of mA(1) = 1, mA(7) = 3, and mA(13) = 23 in evaluating vA(k) as indicated by the red lines and filled bars. See Table 1 for the complete list of and values and associated RMSDs between intermediate conformations.
Mentions: Figure 3 illustrates the procedure for selecting mA(k) for the transition R″→T (step E in Figure 1). Results are shown for the aANM iterations k = 1 (top), 7 (middle) and 13 (bottom). The bars displays the correlation cosine as a function of mode number 1≤i≤25 (left ordinate), and the blue curve is the cumulative squared cosine [C(mA(k))]2 (right). For k = 1, the lowest frequency mode (i = 1) alone yields a correlation cosine of 0.82: it suffices, therefore, to take mA(1) = 1 mode at this step to meet the criterion [C(mA(k))]2≥Fmin , if the threshold Fmin = 0.5. For k = 7, on the other hand, the same criterion is met by mA(7) = 3 modes (see the red line), and for k = 13, we need mA(13) = 23 modes.

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