Modelling dynamics in protein crystal structures by ensemble refinement
Since the dawn of structural biology there have been experimental observations of dynamic motion in proteins and other biomolecules ( Linderstrøm-Lang and Schellman , 1959 ) . Multiple biophysical methods have firmly established that such atomic ‘wigglings and jigglings’ ( Feynman et al . , 1963 ) play an inherent role in both protein structure and function; and , in conjunction with high-resolution structures insights into dynamics aid the understanding of biomolecular functions in catalysis , ligand or drug binding and macromolecular interactions . Presently X-ray diffraction and NMR spectroscopy are the primary source of data for high-resolution protein structures . Whereas microscopy methods may provide information regarding long-range conformational changes , NMR characterizes fluctuations at atomic detail . However , due to the challenging nature of such experiments the number of dynamics studies is relatively sparse in contrast with the wealth of structural information available in the Protein Data Bank ( PDB ) ( Berman et al . , 2000 ) . The majority of entries in the PDB derived from X-ray diffraction data are presented as static , single , structures , although there is often extensive disorder resulting from protein dynamics and crystal-lattice distortions . Extracting atomic fluctuations from these diffraction data would dramatically increase the scope for dynamics studies of biomolecules and potentially reveal atomic details of structure–function–dynamic mechanisms that have previously been obscured . The diffraction data of proteins are affected by multiple sources of disorder , notably arising from atomic vibrations , concerted motions of protein domains and inter-molecular lattice distortions . Structural models of proteins should account for both anisotropic and anharmonic distributions around the mean atomic positions to reproduce the observed Bragg intensities accurately ( Vitkup et al . , 2002; Furnham et al . , 2006 ) . However , explicit modelling of such distributions in macromolecules using current methods requires extensive parameterization inappropriate for the diffraction quality of a typical protein crystal . Multi-conformer structures represent both anisotropic and anharmonic disorder , but despite numerous attempts at automating the inclusion of minor conformations ( DePristo et al . , 2004; Levin et al . , 2007; Terwilliger et al . , 2007; Korostelev et al . , 2009; van den Bedem et al . , 2009; Lang et al . , 2010 ) , 95% of all protein residues in the Protein Data Bank ( PDB ) ( Berman et al . , 2000 ) derived from diffraction data are modelled with a single conformation ( Lang et al . , 2010 ) . As opposed to multiple discrete models , a MD simulation with time-averaged restraints ( Gros et al . , 1990 ) results in a population of structures in which the individual models are interrelated by a Boltzmann-weighted energy function . This method introduced by Torda et al . ( 1989 ) and implemented in macromolecular crystallography by Gros et al . ( 1990 ) , showed a reduction in R-value . However , cross-validation introduced subsequently ( Brünger , 1992 ) revealed chronically over-fitted models ( Burling and Brunger , 1994; Clarage and Phillips , 1994; Schiffer et al . , 1995 ) . Here , we present an ensemble-refinement method that restricts the number of structures modelled and thereby prevents over-fitting of the data . We model large-scale motions , attributable to , for example , lattice distortions , by an underlying global disorder model . This approach allows MD simulations to sample local atomic fluctuations only , without the need for sampling large-scale global disorder . We show that the method yields reproducible ensembles with improved fit to the X-ray data , as validated by cross validation , Rfree ( Brünger , 1992 ) , and stereochemical analyses . Analyses of the ensembles show that detailed features are observed indicating atomic fluctuations that may be relevant for the biological function of the macromolecules .
We performed MD simulations , in which the model was restrained by a time-averaged X-ray ( Gros et al . , 1990 ) , maximum-likelihood ( Pannu and Read , 1996; Adams et al . , 1997; Murshudov et al . , 1997 ) target function ( see ‘Materials and methods’ ) . The X-ray restraint optimized 〈Fcalc ( hkl ) 〉 against Fobs ( hkl ) , where 〈Fcalc ( hkl ) 〉 are computed as rolling averages from the structures in the MD trajectory , with the length of the averaging window determined by the relaxation time τx . This approach contrasts with the traditional crystallographic refinement approach , where Fcalc ( hkl ) are computed from a single structure and optimized against Fobs ( hkl ) . Prior to the simulations we approximated the large-scale disorder by an overall TLS model derived from the atomic B-factors of the refined single structure . Using one TLS group per protein molecule or domain , we iteratively fitted TLS parameters ( Schomaker and Trueblood , 1968; Winn et al . , 2001 ) to the atomic B-factors of the protein atoms excluding atoms with large deviations in B-factor from the TLS-derived B-factor ( the parameter pTLS described the percentage of atoms included in TLS-fitting; see ‘Materials and methods’ ) . The resulting TLS model was applied to all atoms throughout the simulation . Effectively , this TLS model of the protein core excludes the effects of hyper-flexible surface loops and , hence , describes the global disorder that may be attributed to inter-molecular lattice distortions and overall intra-molecular breathing or domain shifts . Ensemble refinement was tested using 20 diffraction datasets from the PDB and started from either the PDB or PDB_REDO ( Joosten et al . , 2010 ) structures ( ‘Materials and methods’ ) . Upper resolution limits of the datasets ranged from 1 . 1 to 3 . 1 Å resolution and structures had 50 to 1 , 004 amino-acid residues in the asymmetric unit ( Table 1 ) . The simulations were run at an effective temperature of 300 K for the protein atoms , using a temperature bath ( Tbath ) slightly below 300 K to allow for heating due to the non-conservative nature of the time-averaged X-ray restraint modulated by its weight wx-ray ( ‘Materials and methods’ ) . Explicitly modelled solvent atoms were added and/or removed intermittently during the simulation dependent on the corresponding electron-density and difference maps ( ‘Materials and methods’ ) . Bulk solvent effects were accounted for by an averaged Flat Bulk-Solvent Model ( Jiang and Brünger , 1994; Afonine et al . , 2005 ) ( ‘Materials and methods’ ) . The parameters pTLS , τx and the Tbath and wx-ray pair were optimized in a grid search resulting in a shallow optimum scored by Rfree ( Figure 1A ) . After a period of equilibration , the trajectory of structures was acquired over an extensive period of time ( 40 times τx ) . 10 . 7554/eLife . 00311 . 003Table 1 . Ensemble refinement statistics for 20 datasets . Datasets were taken from the PDB or PDB_REDO and were re-refined using ensemble refinement and phenix . refine . The relaxation time τx used , the resulting number of structures in the final ensemble and Rwork and Rfree values are given . The ensemble models yield improved Rfree values for all datasets , ranging in improvement from 0 . 3% to 4 . 9% with a mean improvement of 1 . 8% . The PDB accession numbers are as follows: 1KZK ( Reiling et al . , 2002 ) , 3K0M ( Fraser et al . , 2009 ) , 3K0N ( Fraser et al . , 2009 ) , 2PC0 ( Heaslet et al . , 2007 ) , 1UOY ( Olsen et al . , 2004 ) , 3CA7 ( Klein et al . , 2008 ) , 2R8Q ( Wang et al . , 2007 ) , 3QL0 ( Bhabha et al . , 2011 ) , 1X6P ( Dunlop et al . , 2005 ) , 1F2F ( Kimber et al . , 2000 ) , 3QL3 ( Bhabha et al . , 2011 ) , 1YTT ( Burling et al . , 1996 ) , 3GWH ( Rodríguez et al . , 2009 ) , 1BV1 ( Gajhede et al . , 1996 ) , 1IEP ( Nagar et al . , 2002 ) , 2XFA ( Singh et al . , 2011 ) , 3ODU ( Wu et al . , 2010 ) , 1M52 ( Nagar et al . , 2002 ) , 3CM8 ( He et al . , 2008 ) and 3RZE ( Shimamura et al . , 2011 ) DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 003PDB IDResolution ( Å ) Ensemble refinementphenix . refineEnsemble—phenix . refineτx ( ps ) No . of structuresRworkRfreeRworkRfreeΔRworkΔRfree1KZK1 . 11 . 56000 . 1250 . 1530 . 1360 . 155−0 . 011−0 . 0033K0M1 . 32 . 02500 . 1040 . 1290 . 1160 . 132−0 . 012−0 . 0033K0N1 . 41 . 02090 . 1150 . 1330 . 1190 . 143−0 . 004−0 . 0102PC01 . 40 . 82500 . 1450 . 1880 . 1610 . 193−0 . 016−0 . 0051UOY1 . 51 . 01670 . 1040 . 1370 . 1550 . 185−0 . 051−0 . 0493CA71 . 50 . 8400 . 1490 . 1840 . 1710 . 212−0 . 022−0 . 0292R8Q1 . 51 . 02000 . 1320 . 1620 . 1580 . 178−0 . 026−0 . 0163QL01 . 60 . 5700 . 2040 . 2540 . 2290 . 270−0 . 024−0 . 0171X6P1 . 61 . 04000 . 1210 . 1490 . 1400 . 175−0 . 019−0 . 0261F2F1 . 70 . 81430 . 1280 . 1680 . 1600 . 198−0 . 032−0 . 0313QL31 . 80 . 5800 . 1600 . 2080 . 1700 . 221−0 . 010−0 . 0131YTT1 . 80 . 3840 . 1390 . 1740 . 1660 . 189−0 . 027−0 . 0143GWH2 . 01 . 0390 . 1600 . 2000 . 1870 . 220−0 . 027−0 . 0211BV12 . 00 . 4780 . 1490 . 1820 . 1540 . 205−0 . 005−0 . 0231IEP2 . 10 . 52000 . 1830 . 2380 . 1960 . 245−0 . 012−0 . 0072XFA2 . 11 . 01000 . 1710 . 2170 . 1840 . 244−0 . 013−0 . 0273ODU2 . 50 . 3500 . 2080 . 2690 . 2190 . 281−0 . 010−0 . 0121M522 . 60 . 5500 . 1610 . 2110 . 1680 . 228−0 . 007−0 . 0173CM82 . 90 . 5670 . 1940 . 2350 . 2050 . 248−0 . 011−0 . 0133RZE3 . 10 . 1720 . 2100 . 2800 . 2100 . 2910 . 000−0 . 011Max−0 . 051−0 . 049Min0 . 000−0 . 003Mean−0 . 018−0 . 01810 . 7554/eLife . 00311 . 004Figure 1 . Example of ensemble refinement for dataset 1UOY . ( A ) Optimisation of empirical ensemble refinement parameters ( τx , pTLS and Tbath ) . Simulations are performed independently and in parallel . The plot shows effect of τx , pTLS on Rfree ( each grid point corresponds to the lowest Rfree among all Tbath values ) . Optimum parameters are selected by Rfree . ( B ) R-values obtained during ensemble-refinement simulation , solid lines Rwork and dashed lines Rfree; high values are observed for instantaneous models ( yellow ) contrasting with the rolling average used in the target function ( red ) and the final ensemble ( blue ) . ( C ) R-values are reduced throughout the resolution range for ensemble model ( blue ) compared with phenix . refine re-refined single structure ( black ) ; solid lines Rwork and dashed line Rfree . ( D ) Number of structures in the ensemble , reduced by equidistant selection , versus Rwork ( solid line ) and Rfree ( dashed line ) . Final number of structures is selected as the minimum number required reproducing the Rfree + 0 . 1%; in this case resulting in an ensemble containing 167 structures . ( E ) Density difference maps for the ensemble structure ( mFobs − DFmodel ) exp[iφmodel] , left-hand side , and the single structure right-hand side , contoured at 0 . 34 e/Å3 ( equivalent to 3 . 0 σ for the ensemble model ) , positive and negative densities are coloured green and red respectively . All molecular graphics figures are drawn using PyMol ( The PyMOL Molecular Graphics System , Schrödinger , LLC ) . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 004 Figure 1B shows the R-values as they developed over the simulation time for a structure with PDB code 1UOY ( Olsen et al . , 2004 ) , for which the largest improvement in Rfree was observed among the datasets tested ( possibly due to the high degree of anisotropic and anharmonic side-chain motion for this case ) . The R-values started at a high value and remained high ( ∼35% ) for the individual structures , which is in agreement with the observation that the derived global TLS B-factor model is not optimal for fitting a single structure to the data . Averaging the structure factors over the relaxation time τx of 1 ps ( corresponding to the rolling average structure factors used in the X-ray restraint ) dropped the Rwork and Rfree to ∼11% and ∼15% respectively . The Rwork and Rfree of the collected ensemble of structures ( corresponding to unweighted averaged structure factors ) monotonically decreased to 10 . 3 and 13 . 7% respectively . over the acquisition period of 40 ps . The improvement in R-values from the ensemble model with respect to the single-structure model spanned the entire resolution range of the data ( Figure 1C ) . Acquisition over 40 times τx yielded a highly redundant set of structures . We reduced the number of structures by calculating the minimum number of structures , that is 167 in the case of 1UOY , required to reproduce the R-value of the trajectory ( Figure 1D and ‘Materials and methods’ ) . Analysis of all 20 datasets showed that ensemble refinement improved the Rfree by between 0 . 3 and 4 . 9 percentage points compared to single structures re-refined using the same program package , that is Phenix ( Afonine et al . , 2012 ) , with a mean improvement of 1 . 8% in Rfree values ( Table 1 , Figure 2A ) . The effect of the starting structure on ensemble refinement was assessed by using alternative refinement programs , phenix . refine , Refmac ( Vagin et al . , 2004 ) , and Buster ( Bricogne et al . , 2009 ) , to generate varying input models . No significant differences were observed due to the different starting models ( Tables 3 and 4 ) . The improvement in Rfree , number of structures in the final ensemble and the averaging time τx tended to increase with resolution ( Figure 2A–C ) . The optimum values for the parameters pTLS and Tbath are not correlated with resolution ( Figure 2D , E ) . Concomitant with the reduction in R-values , the ensemble models reduced electron-density differences , decreasing rms fluctuations in difference maps by 0 to 41% with an average of 12% improvement ( Table 2 ) . The difference electron-density maps for the single-structure and ensemble models indicated improvements throughout the asymmetric unit cell , as exemplified in Figure 1E . 10 . 7554/eLife . 00311 . 005Figure 2 . Ensemble refinement parameters and results as function of resolution of the datasets . ( A ) Gain in Rfree of ensemble refinement compared with re-refinement using phenix . refine , ( B ) number of structures in the final ensemble model , ( C ) optimum relaxation time , τx , ( D ) optimum pTLS and ( E ) optimum Tbath plotted as function of resolution of the dataset . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 00510 . 7554/eLife . 00311 . 006Table 2 . Rms ( mFobs − DFmodel ) exp[iφmodel] difference densities obtained from ensemble refinement and re-refinement in phenix . refineDOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 006PDB IDResolution ( Å ) σmFo−DFc ( e/Å3 ) Ensemblephenix . refine1KZK1 . 10 . 1380 . 1613K0M1 . 30 . 0160 . 0183K0N1 . 40 . 0070 . 0082PCO1 . 40 . 0990 . 0991UOY1 . 50 . 1150 . 1623CA71 . 50 . 1320 . 1482R8Q1 . 50 . 1040 . 1183QL01 . 60 . 1240 . 1381X6P1 . 60 . 0980 . 1051F2F1 . 70 . 1040 . 1263QL31 . 80 . 1310 . 1391YTT1 . 80 . 1700 . 2153GWH2 . 00 . 1250 . 1381BV12 . 00 . 1090 . 1191IEP2 . 10 . 0840 . 0912XFA2 . 10 . 0690 . 0743ODU2 . 50 . 1050 . 1131M522 . 60 . 0880 . 0933CM82 . 90 . 0360 . 0363RZE3 . 10 . 0700 . 07010 . 7554/eLife . 00311 . 007Table 3 . Effect of input structure on ensemble refinement . For three datasets ensemble refinement was performed using a starting structure from three different refinement programs . For each structure three random number seed repeats of ensemble refinement were performed and the R-factors are shown to be highly similarDOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 007PDBRe-refinementEnsemble refinementRepeat 1Repeat 2Repeat 3MeanProgramRworkRfreeRworkRfreeRworkRfreeRworkRfreeRworkRfree1UOYBuster0 . 1670 . 1960 . 1080 . 1440 . 1120 . 1450 . 1100 . 1460 . 1100 . 145Refmac0 . 1470 . 1700 . 1040 . 1370 . 1030 . 1400 . 1050 . 1440 . 1040 . 140Phenix0 . 1550 . 1850 . 1090 . 1420 . 1090 . 1470 . 1110 . 1490 . 1100 . 1463CA7Buster0 . 1770 . 2080 . 1370 . 1860 . 1370 . 1920 . 1410 . 1970 . 1380 . 192Refmac0 . 1700 . 2050 . 1390 . 1870 . 1350 . 1890 . 1380 . 1930 . 1370 . 189Phenix0 . 1710 . 2120 . 1380 . 1800 . 1420 . 1890 . 1480 . 1930 . 1420 . 1871BV1Buster0 . 1610 . 2040 . 1370 . 1840 . 1380 . 1850 . 1370 . 1860 . 1380 . 185Refmac0 . 1780 . 2310 . 1400 . 1820 . 1430 . 1840 . 1430 . 1890 . 1420 . 185Phenix0 . 1540 . 2050 . 1390 . 1880 . 1380 . 1890 . 1400 . 1890 . 1390 . 18910 . 7554/eLife . 00311 . 008Table 4 . Fmodel cross-correlation scores for ensembles generated with different input models . Three different refinement programs generated alternative starting structures , see Table 3 . The best ensemble was selected as judged by Rfree . Fmodel cross correlation scores are >0 . 99 for all pairs of ensemble structures for all three datasetsDOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 008PDBEnsemble pairCCRe-refined inputRe-refined input1UOYRefmacBuster0 . 997RefmacPhenix0 . 997BusterPhenix0 . 9993CA7RefmacBuster0 . 993RefmacPhenix0 . 992BusterPhenix0 . 9961BV1RefmacBuster0 . 992RefmacPhenix0 . 990BusterPhenix0 . 992 We used the high-quality experimental phases available to high resolution for 1YTT of mannose-binding protein ( Burling et al . , 1996 ) to validate the ensemble-refinement method . The overall correlation coefficient between the electron-density map from the ensemble model ( obtained without experimental phases ) and the experimentally phased electron-density map was 0 . 903 , compared with 0 . 873 and 0 . 895 for the published and re-refined single structures . These seemingly small improvements in overall quality indicators allow for significant local improvements . Real-space correlation coefficients ( Brändén and Jones , 1990 ) highlighted marked local improvements for flexible residues in particular ( Figure 3A ) with 11 residues improving by more than 0 . 1 in correlation coefficient . This observation was consistent with local improvements in electron-density differences in regions of flexible or disordered side chains ( Figure 3B ) . Moreover , the ensemble model contained structural details previously identified in a multiple-model approach by Burling et al . ( 1996 ) , as shown for the anisotropic distribution for the side chain of Phe121 ( Figure 3C ) and diffuse water shells around hydrophobic residues ( Figure 3D ) . Figure 3E shows that the most occupied water sites in the ensemble correlated with low atomic B-factors for waters in the single-structure model . 10 . 7554/eLife . 00311 . 009Figure 3 . Validation of ensemble refinement using dataset 1YTT with exceptionally high quality experimental phases . ( A ) Real space cross-correlation of experimentally phased electron density map ( |Fobs|exp[iφobs] ) and model map ( |Fmodel|exp[iφmodel] ) for the single-structure ( black ) and ensemble model ( chain A and B , blue and red respectively ) shows improvements particularly for disordered areas ( atomic B-factors from the re-refined single structure are shown in grey dashed lines ) . ( B ) Example of improved vector-difference map ( |Fobs|exp[iφobs] − |Fmodel|exp[iφmodel] ) , contoured at 0 . 71 e/Å3 equivalent to 2 . 5 σ for the single structure for Gln167 , chain A , for single ( left-hand side ) and ensemble structure ( right-hand side ) . ( C ) Conformer distribution of Phe121 ( chain A ) with the experimental phased map ( |Fobs|exp[iφobs] ) contoured at 1 . 4 σ is highly similar to the multi-conformer shown in Figure 1c in Burling et al . ( 1996 ) . ( D ) Partially disordered solvent shell ( red ) around residue Leu203 ( chain A ) as anticipated in Burling et al . ( 1996 ) . Ensemble structure with experimental phased experimental map ( |Fobs|exp[iφobs] ) contoured at 1 . 4 σ ( left side ) and 0 . 7 σ ( right side ) , as shown in Figure 2b in Burling et al . ( 1996 ) . ( E ) Scatter plot showing the anti-correlation between the B-factor of explicit solvent molecules in the re-refined single-structure and the relative occupancy of water molecules at that same position ( within 0 . 5-Å distance ) in the ensemble model . Due to the difficulty in differentiating between disorder ( B-factor ) and occupancy for explicitly modelled water atoms in single structures a high B-factor is likely to correspond to a partially occupied site . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 009 Next , we analysed the stereochemistry of the computed ensemble models . The robustness of the observed atomic distributions was tested by repeating ensemble refinements 10 times using different random starting velocities . Figure 4A shows that the observed distributions are highly reproducible . With data extending to 1 . 5-Å resolution correlations above 0 . 99 were observed between residue distributions from separate runs . At lower resolutions , the majority of residues showed correlations above 0 . 95 , with occasionally correlations dropping below 0 . 8 in very flexible regions ( see Figure 4B , C ) . Clearly , the ensembles contain multiple values for each geometrical term that form a distribution , instead of a single stereochemical value obtained from a single structure; Figure 5A–D presents examples of side-chain distributions ( by χ1 and χ2 angles ) observed in the ensembles along with standard deviations computed from the 10 repeats . Averaged over all 20 cases , the rms deviations from idealized bond lengths , bond angles and dihedral angles for the re-refined single-structures were 0 . 010 Å , 1 . 26° and 15 . 2° respectively . ( Figure 6—source data 1 ) . These deviations decreased for the ensemble models by 0 . 002 Å , 0 . 26° and 6 . 6° respectively , when considering the centroids of the observed stereochemical distributions . Taking all fluctuations around the centroids ( i . e . complete distributions ) into account , these values increased by 0 . 002 Å , 0 . 33° and 4 . 0° respectively compared to the statistics from single structures . This indicates high stereochemical quality for the ensemble model , but that the ensemble of structures contained fluctuations exhibiting larger deviations from ideality . Figure 6A , B shows that high-energy conformations , as indicated by for example non-favourable Ramachandran φ , ψ-angle combinations , occurred transiently and were concentrated in regions of structural flexibility . Counting the most frequent Ramachandran classification for each φ , ψ-angle showed that the ensembles have a similar percentage for ‘allowed’ and an increased number of ‘outliers’ compared to the single structures ( Figure 6C and Figure 6—source data 2 ) . These analyses illustrate that in ensemble refinement conformations were sampled , rather than optimized to a single configuration as in single-structure refinement . Similar to Brünger ( Brünger , 1992 ) , we observe that lower Rfree values correlate with better quality of the Ramachandran statistics ( Figure 6D ) . 10 . 7554/eLife . 00311 . 010Figure 4 . Sampling reproducibility of ensemble refinement . ( A ) Cross-correlations ( CC ) calculated for all pairs from 10 random-number seed repeat ensemble refinements of the 1UOY dataset extending to 1 . 5-Å resolution . ( B ) Cross correlations computed for 1BV1 ( 2 . 0-Å resolution ) ; and , ( C ) for 3CM8 ( 2 . 9-Å resolution ) . Mean CC shown in solid blue ( black error bars indicate ±1 σ ) . Cross correlations were computed from real-space Fmodel electron-density map correlations ( Brändén and Jones , 1990 ) . B-factors from the single structures refined using phenix . refine are shown in dotted grey lines . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01010 . 7554/eLife . 00311 . 011Figure 5 . Reproducibility of side-chain rotamer distributions . Mean χ1 and χ2 distributions of four side-chains from the 10 repeats , with error bars ±1 σ , are shown for 1UOY . The four residues presented are those with the two highest CC values ( see Figure 4A ) , ( A ) Gln11 ( 0 . 9999 ) and ( B ) Arg32 ( 0 . 9999 ) , and the two lowest CC values , ( C ) Lys39 ( 0 . 9976 ) and ( D ) Arg13 ( 0 . 9966 ) . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01110 . 7554/eLife . 00311 . 012Figure 6 . Ramachandran analysis . Distribution of Ramachandran torsion angles classified as outliers ( red ) and allowed ( blue ) for ensemble models , 1UOY ( A ) and 1BV1 ( B ) . Plot shows percentage of classification per residue ( i . e . relative number of times a φ , ψ-torsion angle combination is scored as outlier or allowed as defined by phenix . ramalyze ) . Structure inserts show ( left-hand side ) the location of the non-favourable torsion angles , outliers ( red ) and allowed ( blue ) , and ( right-hand side ) a B-factor putty representation for the single structure refined with phenix . refine . ( C ) Overall Ramachandran statistics for ensemble and re-refined models . The Ramachandran statistics for the ensemble models are calculated in two ways: blue shows the percentage of outliers ( left side ) or allowed ( right side ) from all structures in the ensemble ( cf . ‘whole distribution’ in Figure 6—source data 1 ) , whereas red shows these percentages based on the most frequent occurring classification of each φ , ψ combination ( cf . ‘centroid distribution’ ) . The grey lines show the percentage of allowed ( left side ) and outliers ( right side ) for the re-refined single structures . Ramachandran statistics per re-refined single structure and ensemble are given in Figure 6—source data 2 . ( D ) Correlation of Ramachandran statistics with Rfree values obtained from ensemble refinement . Three ensemble refinements were performed for the dataset 1UOY using different random-number seeds at Tbath values of 220 , 260 , 280 , 290 and 295 K . Shown are the number of Ramachandran outliers ( left side ) and allowed ( right side ) in the ensemble as function of the Rfree value . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01210 . 7554/eLife . 00311 . 013Figure 6—source data 1 . Geometries of single-structure models and ensemble models . Rms deviations ( RMSD ) from ideal bond , angle and dihedral geometries calculated for single structures re-refined using phenix . refine . Geometries for ensemble structures were calculated using two methods , the ‘whole distribution’ , where the RMSD was calculated for each restraint ( averaged over all structures ) , √〈 ( xideal − xmodel ) 2〉 , and ‘centroid’ where the RMSD was calculated using the mean deviation from ideality for each restraint , √〈 ( 〈xideal − xmodel〉 ) 2〉 , which for unimodal functions equals √〈 ( xideal − 〈xmodel〉 ) 2〉 . DOI: http://dx . doi . org/10 . 7554/elife . 00311 . 01310 . 7554/eLife . 00311 . 014Figure 6—source data 2 . Ramachandran statistics for re-refined and ensemble models . The Ramachandran statistics for the ensemble models are calculated in two ways: ‘Ramachandran ( mean ) ’ shows the percentage of outliers , allowed and favoured averaged over all structures in the ensemble ( cf . ‘whole distribution’ in Figure 6—source data 1 ) , whereas ‘Ramachandran ( mode ) ’ shows these percentages based on the most frequent occurring classification of each φ , ψ combination ( cf . ‘centroid distribution’ in Figure 6—source data 1 ) . DOI: http://dx . doi . org/10 . 7554/elife . 00311 . 014 The presence of non-crystallographic symmetry ( NCS ) allowed for crystallographically-independent observations of atomic fluctuations in multiple copies of a protein molecule ( Figure 7A–C ) . In some cases , the applied global TLS models differed significantly between NCS-related copies ( Figure 7B ) . Nevertheless , we observed atomic fluctuations similar both in magnitude and location for related copies in areas not affected by crystal packing ( Figure 7B , C; additional cases of NCS are presented in Figure 7—figure supplement 1–4 ) . Apparently , variations in overall disorder arising from packing differences of NCS copies ( as indicated by different B-factor distributions ) were well accounted for by the applied global TLS models . Similarly , a global increase in disorder present in a dataset collected at ambient temperature vs an isomorphous dataset collected under cryo-conditions was fully accounted for by an increase in global TLS ( Figure 8A ) . These data indicate that the derived atomic fluctuations are molecular traits and that the global TLS model accounts for overall disorder , which includes for example lattice or packing effects . 10 . 7554/eLife . 00311 . 015Figure 7 . Comparison of atomic fluctuations for non-crystallographic symmetry related protein copies for dataset 1M52 . ( A ) Cα trace of the re-refined single structure coloured by B-factor ( from blue to red with increasing B-factor ) for the two chains ( left ) and the B-factors plotted per residue number for protein chain A ( blue ) and B ( red ) ( right ) . ( B ) B-factors from the basal TLS model ( left ) and rms atomic fluctuations ( right ) in the ensemble model averaged per residue . Differences in crystal packing restrict the flexibility of chain B around residue 47 . ( C ) Comparison ( left ) and superposition ( right ) of a region of the protein ( indicated by black box in ( A ) ) of the ensemble of structures observed for protein copy A ( blue ) and B ( red ) . Analogous analyses for 2R8Q , 1YTT , 1IEP and 2XFA are shown in Figure 7—figure supplements 1–4 . The protein copies in 3GWH and 3ODU showed backbone shifts greater than 4 . 5 Å and were left out of this analysis . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01510 . 7554/eLife . 00311 . 016Figure 7—figure supplement 1 . Comparison of atomic fluctuations for NCS related protein copies for dataset 2R8Q . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01610 . 7554/eLife . 00311 . 017Figure 7—figure supplement 2 . Comparison of atomic fluctuations for NCS related protein copies for dataset 1YTT . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01710 . 7554/eLife . 00311 . 018Figure 7—figure supplement 3 . Comparison of atomic fluctuations for NCS related protein copies for dataset 1IEP . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01810 . 7554/eLife . 00311 . 019Figure 7—figure supplement 4 . Comparison of atomic fluctuations for NCS related protein copies for dataset 2XFA . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 01910 . 7554/eLife . 00311 . 020Figure 8 . Ensemble refinement of two isomorphous proline isomerase datasets collected at 100 K and 288 K . ( A ) Left , basal TLS B-factors of ensemble models for 100 K and 288 K datasets ( blue and green , respectively ) . Right , atomic rms fluctuations of ensemble models for 100 K and 288 K datasets ( blue and green , respectively ) . ( B ) Re-refined single-structure ( left ) and ensemble model ( right ) for 100 K dataset . ( C ) Re-refined single-structure and ensemble model for 288 K dataset . In ( B ) and ( C ) atoms are coloured by B-factor ( 5 to 25 Å2 ) . As with the published single structure refinement ( Fraser et al . , 2009 ) alternative conformations were not found for residues Leu98 , Ser99 and Phe113 at 100K . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 020 Inspection of the obtained ensembles showed that most proteins , as expected , are characterized by well-ordered residues in the protein core and flexible residue side chains and loops on the outside ( an example is given in Figure 9A ) . However , three cases exhibited marked flexibility of residue side chains on the inside of the molecule . 1BV1 ( Gajhede et al . , 1996 ) , major birch pollen allergen , has a large forked solvent channel with multiple disordered side chains and a diffuse water network ( Figure 9B ) . The cavity is consistent with its putative role as a general plant steroid carrier ( Marković-Housley et al . , 2003 ) . Presumably , the flexible internal residues play a role in binding the diverse ligands . More surprising are the disordered cores in 1X6P of PAK pilin ( Dunlop et al . , 2005 ) ( Figure 9C ) and 3K0N of the enzyme proline isomerase ( Fraser et al . , 2009 ) ( Figure 9D ) ; in both these cases , the datasets were recorded at ambient temperatures . Multiple ( 16 ) aliphatic and aromatic side chains are highly flexible , forming a molten core in the pilin molecule . These flexible residues , which are extremely well conserved in the type IV pilin family , create the central interface between the characteristic long α-helix and β-sheet of this protein fold ( Hazes et al . , 2000 ) . We hypothesize that this monomeric pilin structure represents an intermediate molten state , which becomes stabilized upon protomer filament formation . The third case with flexible residues on the interior is 3K0N of proline isomerase ( Fraser et al . , 2009 ) . As with the pilin structure , several ( 11 ) aromatic and aliphatic residues showed large side chain fluctuations , yielding a molten core of the protein structure . However , the same protein under cryogenic conditions ( 3K0M ) ( Fraser et al . , 2009 ) showed mostly well-ordered side chains in the ensemble ( Figure 9D , right-hand side ) , indicating that at cryogenic conditions the molten core has been annealed to its ground state configuration . As discussed in more detail in the next paragraph , the observed flexibility of the core residues at ambient temperature is likely of functional relevance for the enzyme . Thus , the computed ensemble models highlighted a hitherto unnoticed phenomenon of molten cores in folded proteins , which are likely relevant for the biological function of these molecules . 10 . 7554/eLife . 00311 . 021Figure 9 . Overview of side-chain dynamics in ensemble structures . Atoms are coloured by their relative probability in the ensemble ( see ‘Materials and methods’ ) , reflecting the degree of disorder ( ranging from well-ordered in blue to disordered in red ) . Bottom left insert shows secondary structure cartoon . Three datasets exhibit disordered interior sides chains forming a molten core region . ( A ) 3CA7 shows an ordered core with disordered hydrophilic side chains on the outside and is typical of the majority of the datasets . ( B ) 1BV1 , the major pollen allergen and putative plant steroid transporter , has a disordered central cavity ( location of cavity show with dotted lines ) . ( C ) 1X6P in the monomeric form of the fibril forming PAK pilin shows multiple disordered aliphatic and aromatic side chains in the interface between the N-terminal α-helix and the four stranded β-sheet domain . ( D ) Proline isomerase exhibits a molten core at 288 K , 3K0N ( left ) ; however , these interior dynamics are frozen-out at 100 K , 3K0M ( right ) . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 021 NMR spectroscopy has previously revealed specific dynamics for active-site residues of proline isomerase ( Eisenmesser et al . , 2005 ) . The solvent-exposed residues Arg55 and Met61 in the active site showed disorder in 3K0M ( Fraser et al . , 2009 ) , where data were collected at 100 K . For 3K0N collected at 288 K , a number of additional residues with multiple conformations were observed ( Figure 8A , B ) . These included Ser99 , Phe113 , which are part of the substrate-binding pocket together with Arg55 and Met61 ( Figure 10A ) , and Leu98 , which neighbours the flexible residue Ser99 but points into the hydrophobic core ( Fraser et al . , 2009 ) . Ensemble refinement of the 288 K data revealed a large number of residue side chains in the core to be flexible . This flexibility in the core appears to be linked to the dynamics of active-site residues through the intervening β-sheet . In particular , the main-chain H-bonding network ( C=O·HN ) of neighbouring β-strands within the sheet was flexible , as indicated by anisotropy in the C=O bonds of residues 55-62-113-98 ( with the largest anisotropy observed for 55 and 62; see Figure 10B ) . Analysis of the side-chain conformations for the active-site residues Arg55 , Met61 , Ser99 and Phe113 showed a 10% minor conformation for the four active-site residues ( Figure 10C ) , which is in good agreement with NMR relaxation data ( see Figure 2 in Eisenmesser et al . , 2005 ) . Mutation of Ser99 to Thr ( >14 Å away from the catalytic Arg55 ) affects the side-chain distributions and lowers the activity ∼300-fold , similar to an Arg55Lys mutation of the catalytic residue ( Eisenmesser et al . , 2005; Fraser et al . , 2009 ) . Thus , the ensemble refinement results support the notion put forward by Eisenmesser et al . and Fraser et al . that side chain dynamics play a critical role in the enzymatic function of proline isomerase and , moreover , expand upon this theme to reveal mechanistic insights arising from the underlying detailed dynamics . 10 . 7554/eLife . 00311 . 022Figure 10 . Dynamics in the binding pocket of proline isomerase at 288 K . ( A ) The location of the binding pocket comprised of residues Arg55 , Met61 , Ser99 and Phe113 . ( B ) Zoom in of binding pocket ( as dotted lines in ( A ) ) showing flexible β-sheet for C=O·HN network of residues 55-62-113-98 in neighbouring β-strands . ( C ) All four residues show a ∼9:1 ratio between major and minor conformations which is in good agreement with NMR relaxation dispersion data collected a similar temperature ( Eisenmesser et al . , 2005 ) . Histograms show mean χ1 angles generated from 10 random number repeats of ensemble refinement ( error bars ±1 σ ) . Inserts show the relevant side chains , coloured by atomic probability ( see ‘Materials and methods’ ) , as observed in the ensemble reported in Table 1 . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 022 Ligand binding to HIV protease is known to have marked effects on the enzyme structure ( Heaslet et al . , 2007 ) . We compared HIV protease in its apo form , 2PC0 ( Heaslet et al . , 2007 ) , and bound to ligand JE-2147 , 1KZK ( Reiling et al . , 2002 ) . As for proline isomerase , HIV protease exhibited flexible , moldable , substrate-binding pockets in the apo state . Enthalpic and entropic binding of the ligand with high affinity ( KD = 41 pM ) ( Velazquez-Campoy et al . , 2001 ) reduced the flexibility in the substrate binding pockets by protein–ligand H-bond interactions and van der Waals stacking ( Figure 11A , B ) . Upon ligand binding , Asp90 became ordered through H-bonding with the ligand in P2 , whereas its dimeric partner lacked a H-bonding partner in P2′ and remained flexible as in the unbound state . The canonical aspartic protease catalytic residues , Asp25 of both monomers , became ordered upon ligand binding . Concomitantly , we observed significant changes in dynamics of specific core residues ( Figure 11C ) . Some residues , most notably Thr26 , ‘froze’ ( Thr26 is part of the conserved Asp25-Thr26-Gly-27 sequence ) . In contrast , the side chains of other residues , most notably Cys95 and Leu97 opposite of Thr26 , became highly disordered in the bound state , whereas they were relatively ordered in the unbound state . This observation supports NMR data that showed that conformational variability increases upon inhibitor binding for Leu97 amongst others ( Torchia and Ishima , 2003 ) . These data suggest that the entropy lost by the catalytic aspartates upon ligand binding is compensated with an increase in disorder of specific core residue side chains . This type of dynamic modulation was also observed for Ca2+ binding to calmodulin , where this effect was dubbed entropy compensation ( Lee et al . , 2000 ) . Similar to the molten core dynamics for proline isomerase , the structure ensembles generated by the ensemble refinement method revealed specific core dynamics for HIV protease , in particular a conformational exchange that is likely functionally relevant . 10 . 7554/eLife . 00311 . 023Figure 11 . Comparison of ensemble structures of bound and unbound forms of HIV protease . ( A ) Residues in the P1 binding sites are disordered in the unbound HIV protease ( 2PC0 ) , left-hand side , with carbon atoms shown in cyan , oxygen red and nitrogen blue . These residues become ordered in HIV protease in complex with a high affinity inhibitor , JE-2147 ( 1KZK ) , right-hand side with carbon atoms of the protease shown in green and of the inhibitor in purple . In 1KZK the two chains of the functional dimer are present in the asymmetric unit , whereas in 2PC0 a monomer is present in the asymmetric unit and the dimer is drawn using the crystallographic twofold axis . ( B ) Shows an alternative orientation showing the P2 binding site . ( C ) The catalytic Asp25 becomes ordered upon binding of the inhibitor , forming a hydrogen bond with the P1 carbonyl and hydroxyl of JE-2147 . In contrast , the distal residues Cys95 and Leu97 at the dimer interface become less ordered upon binding . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 023 The development of new small molecule therapeutics is often supported by the use of macromolecular structure , typically X-ray crystallography of complexes between target proteins and drug candidates . These complexes are typically interpreted as static structures , and the impact of dynamics , if considered at all , is probed using computational methods . Our new ensemble refinement approach makes it possible to study the role of dynamics in drug–target complexes in the context of the experimental data . Therefore , we analysed two structures of Abl kinase in complex with Imatinib ( also known as Gleevec ) , that is 1IEP , and PD173955 , that is 1M52 ( Nagar et al . , 2002 ) . These compounds bind the Abl kinase with high affinity , 37 nM ( Schindler et al . , 2000 ) and 100 nM respectively ( Nagar et al . , 2002 ) . The ensembles provide insights into the flexibility of the protein residues and the ligand moieties in the complex . Figure 12A shows the variation in H-bonding observed in Abl kinase–Imatinib . Variable H-bonding interactions were observed for the hydrophilic N-methylpiperazine moiety with the backbone carbonyl atoms of Ile360 and His361 . In contrast , the ensemble displayed a well-ordered H-bond between the anilino-NH and Thr315 ‘gatekeeper’ side-chain . Moreover , the ordered water network between Glu286 , Lys271 and the pyrimidine moiety of Imatinib ( Nagar et al . , 2002 ) was reproduced in the ensemble model ( Figure 12B ) . We observed that the Abl kinase adopts two different states in these crystal structures . In the Imatinib complex the activation loop , residues 381–402 , is highly disordered ( Figure 12C ) , which was confirmed by comparison to previously published NMR data ( Vajpai et al . , 2008 ) . In general , the ensemble models indicate details of tight and highly ordered drug–target interactions on one side vs disordered interactions elsewhere , which are indicative of less tight interactions , that may suggest which sites to modify in a drug-optimization cycle . 10 . 7554/eLife . 00311 . 024Figure 12 . ABL-kinase Imatinib binding site . ( A ) Imatinib binding site in chain A of the 1IEP dataset showing distribution of the six protein–ligand hydrogen bonds in chain A and chain B ( red and blue respectively ) . ( B ) Hydrogen bond network of ordered water network observed in the re-refined single structure , left , and the ensemble model , right . ( C ) The activation loop ( shown in pink ) is disordered when ABL-kinase is complexed with Imatinib ( shown in cyan ) as observed previously in solution ( Vajpai et al . , 2008 ) . DOI: http://dx . doi . org/10 . 7554/eLife . 00311 . 024
We have shown that far more structural information can be reliably extracted from protein diffraction data than is achieved to date by traditional single-structure modelling methods . Our ensemble refinement method samples distributions that reflect structural details of protein dynamics . The resulting ensemble models provide a more comprehensive description of the molecules and allow interpretation of the molecular function in terms of both the three-dimensional arrangements of the protein residues and their flexibilities . Moreover , ensemble models minimize the risk of structural over-interpretation associated with the seemingly rigid single-structure models . We found comparative analyses of protein molecules in different states to be very useful for identifying detailed changes in structural dynamics that may be mechanistically relevant for the molecular function . Partitioning large-scale disorder into a global model separates intermolecular variations of protein packing in the crystal from the detailed intra-molecular atomic fluctuations . Effectively , the X-ray gradient dictates the MD sampling to yield featureless , ( mFobs−DFmodel ) exp[iφmodel] , electron-density difference maps , while the global disorder model is accounted for by taking BTLS into account when computing the atomic densities . In this way , the ensemble of structures is generated to model the anisotropic and anharmonic electron-density distributions precisely , while being restrained by the bonded and non-bonded energy terms used in the MD simulation . The separation of global disorder and local atomic fluctuations contrasts the original approach by Gros et al . ( 1990 ) , where the MD sampling had to account for both the large scale global disorder and local fluctuations leading to very long relaxation times τx of 16 ps . In the current work much shorter relaxation times of 0 . 25–2 ps can be used , thereby limiting potential over-fitting markedly . The method is applicable to data with a wide range of upper resolution limits . We see marked improvements in Rfree for datasets ranging from 1 . 5 to 2 . 6-Å upper-resolution limit . A detailed interpretation of the ensembles is allowed , supported by the very high local correlations between independent ensemble refinements . However , at lower resolution limits and for highly disordered loops the local correlation between independent runs drops and detailed interpretation is not feasible . Thus , even though the number of independent parameters in an ensemble model is not clearly defined ( and therefore the parameter-to-observation ratio is unclear ) , the gain in Rfree and the very high local correlations between independent runs indicate a high reliability of the ensemble models . However , the method is not a panacea for highly disordered protein regions . In the absence of ordered conformations for a certain region of the protein ( as implicitly defined by the diffraction data ) the ensemble refinement will sample diverse conformations in order to prevent the build up of negative peaks in the electron-density difference map . In other words , if the data ‘says’ that a region is disordered , ensemble refinement will generate diverse conformations for that region . Furthermore , dataset pathologies caused , for example , by radiation damage may have confounded effects that obscure the dynamics inherent to the protein molecule . Thus , perhaps somewhat counter-intuitively , this modelling method that accounts for inherent protein dynamics does not help to resolve structural details of disordered regions , but is particularly suited to resolve dynamical fluctuations in ordered parts of the protein structure . Ensemble refinement of 20 protein datasets highlighted global dynamics features of protein molecules . Surprisingly , in some cases the ensembles indicated the existence of folded protein structures that display molten cores . Most likely , such molten cores may indicate intermediates of protein molecules that function in larger complexes ( such as PAK pilin ) , or alternatively these molten cores support dynamical fluctuations that are needed for ligand binding and enzyme functioning ( as for birch pollen allergen and proline isomerase respectively ) . Furthermore , the ensembles show details of specific order–disorder transitions , or conformational exchanges , between active site and core residues ( as for HIV protease in the unbound and bound state ) that suggest a mechanism of entropy compensation to support the enzymatic activity . The difference in dynamics observed between the ensembles of proline isomerase at cryo and ambient temperatures indicates that flash freezing of a crystal anneals local conformational fluctuations and thereby removes protein dynamics that may be functionally relevant . In conclusion , this new method of modelling X-ray diffraction data reveals a wealth of detailed information about the dynamics of biomolecules that complements the high-resolution structural information already available from the crystallographic experiment . In depth understanding of structure–dynamics in biomolecules will enhance our insights into the molecular mechanisms that underlie biological processes .
The single structure re-refinements used the same starting structure as the ensemble refinements ( alternative conformations were not removed ) and were re-refined using phenix . refine ( version 1 . 7 . 1 ) ( Afonine et al . , 2012 ) and Buster ( version 2 . 10 . 0 ) ( Bricogne et al . , 2009 ) . Standard parameters were used with the exception of optimizing the target weights and increasing the number of macro-cycles to 8 in phenix . refine . Explicit water refinement was performed , anisotropic ADPs were used if present in starting structure and TLS parameters were defined as used in the starting structure . PDB_REDO ( Joosten et al . , 2010 ) models were used as deposited .
Single-structure models derived from X-ray data do not adequately account for the inherent , functionally important dynamics of protein molecules . We generated ensembles of structures by time-averaged refinement , where local molecular vibrations were sampled by molecular-dynamics ( MD ) simulation whilst global disorder was partitioned into an underlying overall translation–libration–screw ( TLS ) model . Modeling of 20 protein datasets at 1 . 1–3 . 1 Å resolution reduced cross-validated Rfree values by 0 . 3–4 . 9% , indicating that ensemble models fit the X-ray data better than single structures . The ensembles revealed that , while most proteins display a well-ordered core , some proteins exhibit a ‘molten core’ likely supporting functionally important dynamics in ligand binding , enzyme activity and protomer assembly . Order–disorder changes in HIV protease indicate a mechanism of entropy compensation for ordering the catalytic residues upon ligand binding by disordering specific core residues . Thus , ensemble refinement extracts dynamical details from the X-ray data that allow a more comprehensive understanding of structure–dynamics–function relationships .
It has been clear since the early days of structural biology in the late 1950s that proteins and other biomolecules are continually changing shape , and that these changes have an important influence on both the structure and function of the molecules . X-ray diffraction can provide detailed information about the structure of a protein , but only limited information about how its structure fluctuates over time . Detailed information about the dynamic behaviour of proteins is essential for a proper understanding of a variety of processes , including catalysis , ligand binding and protein–protein interactions , and could also prove useful in drug design . Currently most of the X-ray crystal structures in the Protein Data Bank are ‘snap-shots’ with limited or no information about protein dynamics . However , X-ray diffraction patterns are affected by the dynamics of the protein , and also by distortions of the crystal lattice , so three-dimensional ( 3D ) models of proteins ought to take these phenomena into account . Molecular-dynamics ( MD ) computer simulations transform 3D structures into 4D ‘molecular movies’ by predicting the movement of individual atoms . Combining MD simulations with crystallographic data has the potential to produce more realistic ensemble models of proteins in which the atomic fluctuations are represented by multiple structures within the ensemble . Moreover , in addition to improved structural information , this process—which is called ensemble refinement—can provide dynamical information about the protein . Earlier attempts to do this ran into problems because the number of model parameters needed was greater than the number of observed data points . Burnley et al . now overcome this problem by modelling local molecular vibrations with MD simulations and , at the same time , using a course-grain model to describe global disorder of longer length scales . Ensemble refinement of high-resolution X-ray diffraction datasets for 20 different proteins from the Protein Data Bank produced a better fit to the data than single structures for all 20 proteins . Ensemble refinement also revealed that 3 of the 20 proteins had a ‘molten core’ , rather than the well-ordered residues core found in most proteins: this is likely to be important in various biological functions including ligand binding , filament formation and enzymatic function . Burnley et al . also showed that a HIV enzyme underwent an order–disorder transition that is likely to influence how this enzyme works , and that similar transitions might influence the interactions between the small-molecule drug Imatinib ( also known as Gleevec ) and the enzymes it targets . Ensemble refinement could be applied to the majority of crystallography data currently being collected , or collected in the past , so further insights into the properties and interactions of a variety of proteins and other biomolecules can be expected .