A consensus view of protein dynamics Manuel Rueda*†, Carles Ferrer-Costa*†, Tim Meyer*†‡, Alberto Pe´ rez*†, Jordi Camps†§, Adam Hospital*†§, Josep Lluis Gelpi´*†‡, and Modesto Orozco*†‡§¶ *Molecular Modelling and Bioinformatics Unit and §Structural Biology Node, Institut de Recerca Biome`dica, Parc Cientı´ficde Barcelona, Josep Samitier 1-5, 08028 Barcelona, Spain; †Computational Biology Program, Barcelona Supercomputing Center, Jordi Girona 31, Edifici Nexus II, 08028 Barcelona, Spain; and ‡Departament de Bioquı´micai Biologia Molecular, Facultat de Biologia, Universitat de Barcelona, Avgda Diagonal 645, 08028 Barcelona, Spain Edited by Harold A. Scheraga, Cornell University, Ithaca, NY, and approved November 10, 2006 (received for review July 6, 2006) The dynamics of proteins in aqueous solution has been investi- Table 1. Structures representative of protein metafolds gated through a massive approach based on ‘‘state of the art’’ Exp No. of Atoms in molecular dynamics simulations performed for all protein PDB ID code structure disulfide bridges simulation metafolds using the four most popular force fields (OPLS, CHARMM, AMBER, and GROMOS). A detailed analysis of the 1AGI X-ray 3 23,403͞22,734 massive database of trajectories (>1.5 terabytes of data obtained 1BFG X-ray 0 25,212͞24,509 ͞ using Ϸ50 years of CPU) allowed us to obtain a robust-consensus 1BJ7 X-ray 2 19,371 18,518 1BSN NMR 0 33,753͞32,948 picture of protein dynamics in aqueous solution. 1CHN X-ray 0 18,022͞17,282 1CQY X-ray 0 28,856͞28,310 ͉ ͉ ͉ force field molecular dynamics molecular modeling protein structure 1CSP X-ray 0 13,293͞12,949 1CZT X-ray 1 31,072͞30,167 lexibility is a key determinant of the biological functionality of 1EMR X-ray 0 32,808͞31,885 1FAS X-ray 4 15,709͞15,398 Fproteins. A significant percentage of proteins are unfolded in ͞ the absence of ligand, and many others change their conformation 1FVQ NMR 0 16,322 15,921 1GND X-ray 0 68,647͞66,213 as a result of the presence of other molecules or changes in the 1I6F NMR 4 15,837͞15,552 environment (1–4). Experimental representation of flexibility, 1IL6 NMR 4 27,464͞26,486 even aprioripossible, is in general difficult, which makes atomistic 1J5D NMR 0 23,184͞22,682 simulation the only viable alternative to study this important 1JLI NMR 1 36,307͞35,615 phenomenon for many proteins. Among the different theoretical 1K40 X-ray 0 37,686͞36,883 methods available for description of protein flexibility, molecular 1KTE X-ray 1 19,490͞18,869 dynamics is probably the most powerful (5–13). Since it was first 1KXA X-ray 0 24,969͞24,113 ͞ applied to proteins in the late 1970s, molecular dynamics (MD) has 1LIT X-ray 3 26,289 25,651 1LKI X-ray 3 33,388͞32,403 been largely used to study the dynamics of proteins (14, 15). 1NSO NMR 0 31,774͞31,134 Unfortunately, due to the cost of simulations and the diversity of 1OOI X-ray 3 21,754͞21,057 force fields, a consensus view of protein dynamics has not been yet 1OPC X-ray 0 22,833͞22,245 obtained using this technique. In this paper, we present a systematic 1PDO X-ray 0 30,947͞30,199 study of the most populated protein metafolds [see supporting 1PHT X-ray 0 19,995͞19,554 information (SI) Data Set] using state of the art atomistic MD 1SDF NMR 2 32,579͞32,168 simulation conditions and the four most widely used force fields 1SP2 NMR 0 17,093͞16,930 [OPLS (O), CHARMM (C), AMBER (A), and GROMOS (G)] 1SUR X-ray 0 35,945͞34,691 ͞ (16–25). The result of this massive supercomputer effort (Ͼ1.5 2HVM X-ray 3 32,956 31,550 terabytes of data and a computational equivalent to 50 CPU years) For each protein, we quote the number of disulfide bridges, the origin of is a consensus picture of protein dynamics under conditions close experimental structure, and the number of atoms in the simulation box (A, C, to the physiological ones. O͞G). PDB, Protein Data Bank. Results and Discussion Supporting Information. For further details, see SI Data Set and (see Fig. 1). Thus, differences in radii of gyration between MD SI Figs. 5–17 samplings and experimental structures are Ͻ1%, and average differences in solvent accessible surface are Ϸ5%. The average Force Field Convergence. Previous to any dynamic study, we need to backbone rmsds between simulated and experimental structures determine whether force fields are providing a similar picture of are Ϸ2.0 Å (A, 1.9; C, 2.0; O, 1.9; G, 2.5 Å), close to the thermal protein structure and whether such a picture is similar to that noise of MD simulations. Quite surprisingly, the presence or derived experimentally. Analysis of collected samplings indicates an absence of disulfide bridges does not modify the deviation of our average divergence (␣ in Eq. 1)ofϷ2 Å between force fields samplings from experimental structures, which is, however, depen- (slightly larger deviations are found in G simulations), which, dent on the origin of the experimental structure. Thus, proteins considering the thermal noise of the simulations (⍀ in Eq. 2), suggests a similarity of Ϸ70% between the four samplings and an Ϫ1 average ‘‘effective distance (⍀ ) between them of only 1.4 Å Author contributions: M.R., C.F.-C., and T.M. contributed equally to this work; M.R., C.F.-C., (slightly larger values are always obtained for G-simulations; see A.H., J.L.G., and M.O. designed research; M.R., C.F.-C., T.M., A.P., and J.C. performed Table 2). This finding indicates that all simulations are, in fact, research; M.R., C.F.-C., T.M., and A.P. analyzed data; and M.O. wrote the paper. sampling a similar region of the conformational space. This sug- The authors declare no conflict of interest. gestion is supported by the analysis of the radii of gyration and This article is a PNAS direct submission. solvent accessible surface (differences of Ϸ1% in radii of gyration Abbreviations: MD, molecular dynamics; O, OPLS; C, CHARMM; A, AMBER; G, GROMOS. and 2% in solvent-accessible surface between the four force fields; ¶To whom correspondence should be addressed. E-mail: [email protected]. see Fig. 1). This article contains supporting information online at www.pnas.org/cgi/content/full/ Not only are the structures sampled in the four simulations 0605534104/DC1. similar, but they are also close to the experimental conformations © 2007 by The National Academy of Sciences of the USA 796–801 ͉ PNAS ͉ January 16, 2007 ͉ vol. 104 ͉ no. 3 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0605534104 Downloaded by guest on September 28, 2021 BIOPHYSICS Fig. 1. Average values for rmsd (Upper Left), rRMSD (based on TM-score; Upper Right) with respect to experimental structures, radii of gyration (Lower Left), and solvent accessible surface (Lower Right) for A, C, O, and G force fields. COMPUTER SCIENCES showing the largest displacements with experiment correspond intramolecular hydrogen bonds found in experimental structures is always to structures solved by NMR spectroscopy (see Fig. 1 and very well preserved (see Fig. 2), but obviously, hydrogen bond Table 1). The deviations in these cases are due to displacements in donor and acceptors are more promiscuous in MD than inferred regions of large flexibility, where NMR structures are in general from single experimental structures (see below). All MD simula- poorly defined. This is clear when calculations are repeated using tions preserve very well (90%; see Fig. 2) secondary structure the TM-score, a more robust measure that reduces the weight of (␣-helices and ␤-sheets). In summary: (i) different force fields flexible entities in the rms-fit. In this case, no system is found for provide similar picture of protein structure, and (ii) MD simulations which deviation from experimental data are Ͼ2.5 Å (see Fig. 1). sample regions close to experimental structures. Divergences be- Moderate deviations between MD trajectories and experimental tween simulations and experimental structure signal proteins with model might then reflect either lack of quality in some parts of the very flexible moieties whose exact conformation is often not well experimental model, or just the intrinsic differences between defined. The two prerequisites noted above are then fulfilled, and simulation and experimental conditions. Clearly, the commonly we can then safely analyze the dynamics properties of proteins. made assumption that any deviation from experimental structure of B-factors are the simplest method to analyze local deformability MD simulations is always due to simulation errors is not correct and and have the advantage to be accessible from x-ray data, which can ignore important physical characteristics of proteins. provides us with an additional test on the quality of MD- Native protein–protein contacts are well preserved during sim- trajectories. As noted in Fig. 3, there is a very good agreement ulations (in average, 90% correct predictions). The total number of between experimental and MD-derived B-factors (see Fig. 3). Detailed analysis (see SI Fig. 5) show that such an agreement is especially good for A, C, and O simulations, whereas B-factor Table 2. Similarity indexes distribution is slightly displaced to higher values in G trajectories. In AMBER CHARMM OPLS GROMOS all of the cases, ␤-sheet segments are the most rigid, whereas turns AMBER 1.0 0.7 0.7 0.6 are in general the most flexible ones, in good agreement to what is 1.0 1.0 0.8 0.8 deduced from experimental data. In fact, the only significant CHARMM 1.0 0.7 0.6 difference between MD and x-ray B-factors is that, although 1.0 0.8 0.9 experimental B-factors above 60 Å2 are rare, they are not so OPLS 1.0 0.6 uncommon in MD simulations.