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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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Comparison with the results from steepest descent pathway (SDP)                                based on action minimization.(A) Fragmentation of the SDP pathway for the transition                                1GRU←→1GR5 of a subunit into nine macrosteps,                                consisting each of five frames. Same color scheme is adopted in                                panels B and C. (B) Correlation between SDP macrosteps and ANM modes                                accessible to the original conformation . (C) Same as panel B, for the right portion of the                                trajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using the                                eigenvectors  generated for 1GRU_A. Note that the early                                macrosteps from both directions are accounted for by a few slowest                                ANM modes, while increasingly higher modes are being recruited as                                the molecule proceeds away from its original conformation,                                consistent with the results found by aANM (see                                    Table 1).                                (D) RMSD values between the intermediate conformations sampled by                                the aANM and SDP methods. The aANM                                results refer to the trajectory                                Fmin = 0.5.                                The RMSDs between pairs of intermediates remain lower than 2.0                                Å at all steps (see the color-coded scale on the                            right).
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pcbi-1000360-g005: Comparison with the results from steepest descent pathway (SDP) based on action minimization.(A) Fragmentation of the SDP pathway for the transition 1GRU←→1GR5 of a subunit into nine macrosteps, consisting each of five frames. Same color scheme is adopted in panels B and C. (B) Correlation between SDP macrosteps and ANM modes accessible to the original conformation . (C) Same as panel B, for the right portion of the trajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using the eigenvectors generated for 1GRU_A. Note that the early macrosteps from both directions are accounted for by a few slowest ANM modes, while increasingly higher modes are being recruited as the molecule proceeds away from its original conformation, consistent with the results found by aANM (see Table 1). (D) RMSD values between the intermediate conformations sampled by the aANM and SDP methods. The aANM results refer to the trajectory Fmin = 0.5. The RMSDs between pairs of intermediates remain lower than 2.0 Å at all steps (see the color-coded scale on the right).

Mentions: Toward a more critical analysis of the modes that contribute to the SDP, we reorganized the SDP trajectory (consisting of 46 frames) into a series of k = 9 (macro)steps by collapsing each set of five consecutive frames into a macrostep (Figure 5A) and we calculated the deformation vector ΔRkSDP = Rn+5SDP−RnSDP for each macrostep. The following questions were raised: Which ANM modes effectively contribute to these macrosteps? Do SDP macrosteps exhibit the same tendency as aANM to originally proceed via softer modes and gradually recruit increasingly larger subsets of modes? How similar are the conformations visited along the aANM and the SDP? To this aim, we evaluated the correlation cosine between ΔRkSDP and the ANM modes uiA(1) and uiB(1) accessible to original states RA(0) and RB(0). The results are shown as a function of mode index i in the respective panels B and C of Figure 5. The correlation cosines represent the relative contributions of the intrinsically accessible ANM modes to the SDP macrosteps. In accord with the results from aANM, only very few modes at the low frequency end of the spectrum contribute to the SDP macrosteps in the close neighborhood of the original states (red plots). The slow modes contribute by almost by the same amount as those observed in aANM at the successive stages of the transition pathway. The contribution of higher frequency modes, which is negligibly small at early stages, gradually increases, consistent with the aANM.


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

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

Comparison with the results from steepest descent pathway (SDP)                                based on action minimization.(A) Fragmentation of the SDP pathway for the transition                                1GRU←→1GR5 of a subunit into nine macrosteps,                                consisting each of five frames. Same color scheme is adopted in                                panels B and C. (B) Correlation between SDP macrosteps and ANM modes                                accessible to the original conformation . (C) Same as panel B, for the right portion of the                                trajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using the                                eigenvectors  generated for 1GRU_A. Note that the early                                macrosteps from both directions are accounted for by a few slowest                                ANM modes, while increasingly higher modes are being recruited as                                the molecule proceeds away from its original conformation,                                consistent with the results found by aANM (see                                    Table 1).                                (D) RMSD values between the intermediate conformations sampled by                                the aANM and SDP methods. The aANM                                results refer to the trajectory                                Fmin = 0.5.                                The RMSDs between pairs of intermediates remain lower than 2.0                                Å at all steps (see the color-coded scale on the                            right).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2664929&req=5

pcbi-1000360-g005: Comparison with the results from steepest descent pathway (SDP) based on action minimization.(A) Fragmentation of the SDP pathway for the transition 1GRU←→1GR5 of a subunit into nine macrosteps, consisting each of five frames. Same color scheme is adopted in panels B and C. (B) Correlation between SDP macrosteps and ANM modes accessible to the original conformation . (C) Same as panel B, for the right portion of the trajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using the eigenvectors generated for 1GRU_A. Note that the early macrosteps from both directions are accounted for by a few slowest ANM modes, while increasingly higher modes are being recruited as the molecule proceeds away from its original conformation, consistent with the results found by aANM (see Table 1). (D) RMSD values between the intermediate conformations sampled by the aANM and SDP methods. The aANM results refer to the trajectory Fmin = 0.5. The RMSDs between pairs of intermediates remain lower than 2.0 Å at all steps (see the color-coded scale on the right).
Mentions: Toward a more critical analysis of the modes that contribute to the SDP, we reorganized the SDP trajectory (consisting of 46 frames) into a series of k = 9 (macro)steps by collapsing each set of five consecutive frames into a macrostep (Figure 5A) and we calculated the deformation vector ΔRkSDP = Rn+5SDP−RnSDP for each macrostep. The following questions were raised: Which ANM modes effectively contribute to these macrosteps? Do SDP macrosteps exhibit the same tendency as aANM to originally proceed via softer modes and gradually recruit increasingly larger subsets of modes? How similar are the conformations visited along the aANM and the SDP? To this aim, we evaluated the correlation cosine between ΔRkSDP and the ANM modes uiA(1) and uiB(1) accessible to original states RA(0) and RB(0). The results are shown as a function of mode index i in the respective panels B and C of Figure 5. The correlation cosines represent the relative contributions of the intrinsically accessible ANM modes to the SDP macrosteps. In accord with the results from aANM, only very few modes at the low frequency end of the spectrum contribute to the SDP macrosteps in the close neighborhood of the original states (red plots). The slow modes contribute by almost by the same amount as those observed in aANM at the successive stages of the transition pathway. The contribution of higher frequency modes, which is negligibly small at early stages, gradually increases, consistent with the aANM.

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
Related in: MedlinePlus