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. 2009 Nov 25;131(46):16968-75.
doi: 10.1021/ja907476w.

Toward a unified representation of protein structural dynamics in solution

Phineus R L Markwick  1 , Guillaume Bouvignies, Loic Salmon, J Andrew McCammon, Michael Nilges, Martin Blackledge
Affiliations
Free PMC article

Toward a unified representation of protein structural dynamics in solution

Phineus R L Markwick et al. J Am Chem Soc. .
Free PMC article

Abstract

An atomic resolution description of protein flexibility is essential for understanding the role that structural dynamics play in biological processes. Despite the unique dependence of nuclear magnetic resonance (NMR) to motional averaging on different time scales, NMR-based protein structure determination often ignores the presence of dynamics, representing rapidly exchanging conformational equilibria in terms of a single static structure. In this study, we use the rich dynamic information encoded in experimental NMR parameters to develop a molecular and statistical mechanical characterization of the conformational behavior of proteins in solution. Critically, and in contrast to previously proposed techniques, we do not use empirical energy terms to restrain a conformational search, a procedure that can strongly perturb simulated dynamics in a nonpredictable way. Rather, we use accelerated molecular dynamic simulation to gradually increase the level of conformational sampling and to identify the appropriate level of sampling via direct comparison of unrestrained simulation with experimental data. This constraint-free approach thereby provides an atomic resolution free-energy weighted Boltzmann description of protein dynamics occurring on time scales over many orders of magnitude in the protein ubiquitin.

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Figures

Figure 1
Figure 1
Effect of increasing the acceleration level on N−HN order parameters in ubiquitin. (A) Order parameters are shown after performing a free energy weighting correction, and are averaged over the trajectories. From top to bottom, the boost energy is 0 (standard 5 ns MD control set), 100, 150, 200, 250, 300, 350, 400, and 450 kcal/mol. The acceleration parameter, α, was fixed at a value of 60 kcal/mol. (B) Change in the trajectory-averaged cumulative R-values for RDCs as a function of the acceleration level. In all cases, the acceleration parameter α = 60 kcal/mol. The boost energy of 0 represents the control set of 5 ns standard MD simulations starting from the X-ray crystal structure(47) using a different random seed generator. (C) Change in the trajectory-averaged cumulative R-values for J-couplings as a function of the acceleration level. In all cases the acceleration parameter α = 60 kcal/mol.
Figure 2
Figure 2
Experimental vs theoretical RDCs for four representative alignment media out of the 23 alignment media. The trajectory averaged cumulative R-factors for the shown alignment media are respectively 0.096, 0.098, 0.100, and 0.111. The trajectory averaged cumulative R-factors across all alignment media varied from 0.090 to 0.129.
Figure 3
Figure 3
Residue specific trajectory averaged RDC cumulative R-factors. The optimal extended conformational space molecular ensemble [(Eboost − Vdih) = 250 kcal/mol] is shown in red and compared to a “control set” of standard 5 ns MD simulations shown in blue. Cumulative R-factors for the extended conformational space molecular ensemble are in general lower than those for the control set, confirming the observation of a global improvement in the theoretical RDC data.
Figure 4
Figure 4
(A) Experimental vs theoretical scalar J-couplings for the optimized extended conformational space molecular ensemble [(Eboost − Vdih) = 250 kcal/mol]. The three scalar J-couplings are 3JHN-Hα [black circles], 3JHN-Cβ [red circles], and 3JNH-C′ [blue circles]. (B) NH−Hα Karplus Curves. Red: optimal Karplus curve for ′. Black: optimal Karplus curve for standard 5 ns MD simulation. Blue: optimal Karplus curve for optimal AMD result. Cyan: DFT Karplus curve for NMe-Ala-Ace.
Figure 5
Figure 5
Order parameters for ubiquitin. The 15N spin relaxation experimental data are represented by the blue line.(45) The theoretical fast time-scale (ps−ns) order parameters are shown as black circles and the slow time-scale (RDC-optimized) order parameters are shown in red. The error bars depict the variation in the magnitude of the order parameters for the different molecular ensembles generated from the 20 AMD simulations at the same acceleration level (Eboost − Vdih = 250 kcal/mol).
Figure 6
Figure 6
Twenty-four representative structures taken from an RDC-optimized molecular ensemble. The residues are color-coded according to the value of the RDC order parameters (blue: 1.0, red: 0.0).
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