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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 transition1GRU←→1GR5 of a subunit into nine macrosteps,consisting each of five frames. Same color scheme is adopted inpanels B and C. (B) Correlation between SDP macrosteps and ANM modesaccessible to the original conformation . (C) Same as panel B, for the right portion of thetrajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using theeigenvectors  generated for 1GRU_A. Note that the earlymacrosteps from both directions are accounted for by a few slowestANM modes, while increasingly higher modes are being recruited asthe molecule proceeds away from its original conformation,consistent with the results found by aANM (seeTable 1).(D) RMSD values between the intermediate conformations sampled bythe aANM and SDP methods. The aANMresults refer to the trajectoryFmin = 0.5.The RMSDs between pairs of intermediates remain lower than 2.0Å at all steps (see the color-coded scale on theright).
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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 transition1GRU←→1GR5 of a subunit into nine macrosteps,consisting each of five frames. Same color scheme is adopted inpanels B and C. (B) Correlation between SDP macrosteps and ANM modesaccessible to the original conformation . (C) Same as panel B, for the right portion of thetrajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using theeigenvectors generated for 1GRU_A. Note that the earlymacrosteps from both directions are accounted for by a few slowestANM modes, while increasingly higher modes are being recruited asthe molecule proceeds away from its original conformation,consistent with the results found by aANM (seeTable 1).(D) RMSD values between the intermediate conformations sampled bythe aANM and SDP methods. The aANMresults refer to the trajectoryFmin = 0.5.The RMSDs between pairs of intermediates remain lower than 2.0Å at all steps (see the color-coded scale on theright).

Mentions: Toward a more critical analysis of the modes that contribute to the SDP, wereorganized the SDP trajectory (consisting of 46 frames) into a series ofk = 9(macro)steps by collapsing each set offive consecutive frames into a macrostep (Figure 5A) and we calculated thedeformation vector ΔRkSDP = Rn+5SDP−RnSDP for each macrostep. The following questions wereraised: Which ANM modes effectively contribute to these macrosteps? Do SDPmacrosteps exhibit the same tendency as aANM to originallyproceed via softer modes and gradually recruit increasingly larger subsetsof modes? How similar are the conformations visited along theaANM and the SDP? To this aim, we evaluated the correlationcosine 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 indexi in the respective panels B and C of Figure 5. The correlationcosines represent the relative contributions of the intrinsically accessibleANM modes to the SDP macrosteps. In accord with the results fromaANM, only very few modes at the low frequency end of thespectrum contribute to the SDP macrosteps in the close neighborhood of theoriginal states (red plots). The slow modes contribute by almost by the sameamount as those observed in aANM at the successive stagesof the transition pathway. The contribution of higher frequency modes, whichis negligibly small at early stages, gradually increases, consistent withthe 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 transition1GRU←→1GR5 of a subunit into nine macrosteps,consisting each of five frames. Same color scheme is adopted inpanels B and C. (B) Correlation between SDP macrosteps and ANM modesaccessible to the original conformation . (C) Same as panel B, for the right portion of thetrajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using theeigenvectors  generated for 1GRU_A. Note that the earlymacrosteps from both directions are accounted for by a few slowestANM modes, while increasingly higher modes are being recruited asthe molecule proceeds away from its original conformation,consistent with the results found by aANM (seeTable 1).(D) RMSD values between the intermediate conformations sampled bythe aANM and SDP methods. The aANMresults refer to the trajectoryFmin = 0.5.The RMSDs between pairs of intermediates remain lower than 2.0Å at all steps (see the color-coded scale on theright).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
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 transition1GRU←→1GR5 of a subunit into nine macrosteps,consisting each of five frames. Same color scheme is adopted inpanels B and C. (B) Correlation between SDP macrosteps and ANM modesaccessible to the original conformation . (C) Same as panel B, for the right portion of thetrajectory, i.e. the reconfiguration from 1GR5_A to 1GRU_A using theeigenvectors generated for 1GRU_A. Note that the earlymacrosteps from both directions are accounted for by a few slowestANM modes, while increasingly higher modes are being recruited asthe molecule proceeds away from its original conformation,consistent with the results found by aANM (seeTable 1).(D) RMSD values between the intermediate conformations sampled bythe aANM and SDP methods. The aANMresults refer to the trajectoryFmin = 0.5.The RMSDs between pairs of intermediates remain lower than 2.0Å at all steps (see the color-coded scale on theright).
Mentions: Toward a more critical analysis of the modes that contribute to the SDP, wereorganized the SDP trajectory (consisting of 46 frames) into a series ofk = 9(macro)steps by collapsing each set offive consecutive frames into a macrostep (Figure 5A) and we calculated thedeformation vector ΔRkSDP = Rn+5SDP−RnSDP for each macrostep. The following questions wereraised: Which ANM modes effectively contribute to these macrosteps? Do SDPmacrosteps exhibit the same tendency as aANM to originallyproceed via softer modes and gradually recruit increasingly larger subsetsof modes? How similar are the conformations visited along theaANM and the SDP? To this aim, we evaluated the correlationcosine 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 indexi in the respective panels B and C of Figure 5. The correlationcosines represent the relative contributions of the intrinsically accessibleANM modes to the SDP macrosteps. In accord with the results fromaANM, only very few modes at the low frequency end of thespectrum contribute to the SDP macrosteps in the close neighborhood of theoriginal states (red plots). The slow modes contribute by almost by the sameamount as those observed in aANM at the successive stagesof the transition pathway. The contribution of higher frequency modes, whichis negligibly small at early stages, gradually increases, consistent withthe 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