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.

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, R_free (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 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, (mF_obs−DF_model)exp[iφ_model], electron-density difference maps, while the global disorder model is accounted for by taking B_TLS 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 τ_x 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 R_free 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 R_free 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 method of ensemble refinement was implemented in the Phenix software (Adams et al., 2010). Adaptations and new procedures developed for ensemble refinement are given in section ‘Ensemble refinement methods’. Simulations were performed as described in section ‘Ensemble refinement protocol’. Details of the single-structure re-refinements used for comparison with the ensemble models are given in section ‘Single structure re-refinements’. Validation of the global disorder TLS model, the dependency of ensemble refinement on the starting structure and additional ensemble refinement calculations are given in ‘Additional ensemble refinement calculations’.

Ensemble refinement was performed using phenix.ensemble_refinement, as will be made available in the next release of Phenix.

Ensemble refinement methods

Time-averaged restraints

View detailed protocol

The overall model structure factors are calculated as (1), defined by Afonine et al. (2005), incorporating overall anisotropic scaling (Sheriff and Hendrickson, 1987) and bulk solvent contributions (Jiang and Brünger, 1994).

(1) ${\mathit{F}}_{\mathit{model}}=k{e}^{\left(-\frac{{\mathit{h}}^T{\mathit{A}}^{-1}{\mathit{B}}_{\mathit{cart}}{\left({\mathit{A}}^{-1}\right)}^T\mathit{h}}{4}\right)}\left({\mathit{F}}_{calc}+k_{\mathit{sol}}{e}^{\left(-\frac{B_{\mathit{sol}}{s}^2}{4}\right)}{\mathit{F}}_{\mathit{mask}}\right),$

where, k is the overall scale factor, h is the column vector with Miller indices, A is the orthogonalisation matrix, B_cart is the anisotropic scale matrix, F_calc is the structure factors calculated from atomic model, k_sol and B_sol are the parameters for the flat bulk solvent model and F_mask are the structure factors calculated from bulk solvent mask.

In order to restrain the instantaneous structures produced during the MD simulation with time and spatially averaged X-ray data, time-averaged restraints are used (Gros et al., 1990). This produces time-averaged (or rolling-average) structure factors such that (1) becomes (2).

(2) ${\mathit{F}}_{\mathit{model}}^t=k{e}^{\left(-\frac{{\mathit{h}}^{\text{T}}{\mathit{A}}^{-1}{\mathit{B}}_{\mathit{cart}}{\left({\mathit{A}}^{-1}\right)}^T\mathit{h}}{4}\right)}\left({\langle {\mathit{F}}_{\mathit{calc}}\rangle }_t+k_{\mathit{sol}}{e}^{\left(-\frac{B_{\mathit{sol}}{s}^2}{4}\right)}{\langle {\mathit{F}}_{\mathit{mask}}\rangle }_t\right).$

This is a time-dependent memory function, that is a ‘rolling’ average, where the size of the averaging window is controlled by the τ_x parameter (typically 1 ps). This averaging function is updated with the current individual structure every 10 time-steps (∆t) during the simulation and is implemented as in (3).

(3) ${\langle {\mathit{F}}_{\mathit{calc}}\rangle }_t=e^{-\mathit{\Delta t}/{\tau }_x}{\langle {\mathit{F}}_{\mathit{calc}}\rangle }_{t-\mathit{\Delta t}}+\left(1-e^{-\mathit{\Delta t}/{\tau }_x}\right){\mathit{F}}_{\mathit{calc}}^t.$

Dual explicit-bulk solvent model

Request a detailed protocol

Due to the stochastic behaviour of solvent molecules and the number of partially disordered or low occupancy sites, explicitly modelled solvent atoms are repositioned every 250 time-steps. Electron-density and difference density maps are generated using F_model^t, excluding reflections in the free R set. Water oxygen atoms with an electron-density peak >1.0 σ in the 2mF_obs − DF_model map or a peak >3.0 σ in the mF_obs − DF_model map are preserved, otherwise the atom is removed. New water atoms are added for positions which have a 2mF_obs − DF_model peak >1.0 σ and a mF_obs − DF_model peak >3.0 σ, and are between 1.8–3.0 Å in distance to an existing atom. For high-resolution cases these criteria are adjusted to include mF_obs − DF_model map peaks >2.5 σ. Newly positioned atoms are assigned a random, Boltzmann-weighted, velocity. Explicitly modelled solvent atoms contribute to the atomic model (F_calc).

Bulk solvent is modelled using a solvent mask (Afonine et al., 2005). The mask structure factors (F_mask) are averaged in the same manner as the atomic model (F_calc) (4).

(4) ${\langle {\mathit{F}}_{\mathit{mask}}\rangle }_t=e^{-\mathit{\Delta t}/{\tau }_x}{\langle {\mathit{F}}_{\mathit{mask}}\rangle }_{t-\mathit{\Delta t}}+\left(1-e^{-\mathit{\Delta t}/{\tau }_x}\right){\mathit{F}}_{\mathit{mask}}^t.$

The k_sol and B_sol bulk solvent parameters and B_cart scaling parameters used for the duration of the simulation are calculated from the starting structure as described previously (Afonine et al., 2005), they are re-optimized for the final ensemble.

Constrained target functions

Request a detailed protocol

The overall scale factor, k, is constrained during the simulation. For the maximum-likelihood target function, as shown for acentric reflections, (5) during normalisation (6), the sum of the rolling-average structure factor array (2) is scaled to the sum of the structure factor array from the starting model (F_ref) as shown in (7).

(5) $P_{\mathit{x-ray}}=\frac{2E_{\mathit{obs}}}{1-{\mathrm{\sigma }}_A^2}\text{exp}\left(-\frac{E_{\mathit{obs}}^2+{\mathrm{\sigma }}_A^2{E}_{\mathit{model}}^t}{1-{\mathrm{\sigma }}_A^2}\right)I_0\left(\frac{2E_{\mathit{obs}}{\mathrm{\sigma }}_A{E}_{\mathit{model}}^t}{1-{\mathrm{\sigma }}_A^2}\right),$

(6) $E_{\mathit{model}}^t=\frac{k{\mathit{F}}_{\mathit{model}}^t}{\sqrt{\epsilon {\Sigma }_N}},$

(7) $k=\frac{\underset{\mathit{hkl}}{\Sigma }{\mathit{F}}_{\mathit{ref}}}{\underset{\mathit{hkl}}{\Sigma }{\mathit{F}}_{\mathit{model}}^t},$

where, E_obs and E_model are the normalised structure factors, σ_A is the Sigma-A weighting factor, I₀ is a modified Bessel function of order 0 and ε is the expected intensity factor.

Temperature bath and X-ray weight

Request a detailed protocol

The simulations are performed such that the non-solvent atoms are at a target temperature (T_target) of 300 K, where the simulation is coupled to a velocity-scaled temperature-bath (Berendsen et al., 1984). The temperature bath is set to a value less than 300 K, typically 295–298 K. Because the X-ray restraints are computed from a time-dependent memory function, the X-ray energy term is non-conservative and thus heating occurs. During the equilibration phase the X-ray weight (w_x-ray) is modulated by the temperature of the protein atoms (T_protein) every 10 time-steps (∆t), such that the non-solvent atoms sample consistently at the target temperature (8).

(8) $w_{\mathit{x-ray}}^t=w_{\mathit{x-ray}}^{t-\mathit{\Delta t}}\frac{T_{\mathit{target}}}{T_{\mathit{protein}}}.$

Thus, the thermostat offset controls the X-ray weight in a system independent manner whilst maintaining the target temperature. In the acquisition phase the X-ray weight is fixed to the averaged value used in the equilibration phase.

TLS approximation of the global disorder

Request a detailed protocol

The partitioning of inter-molecular disorder is performed before the start of the simulation using ADPs from the traditionally refined starting structure. TLS groups are assigned per molecule or domain as appropriate to model global packing disorder. For each group, TLS parameters are fitted to the ADPs of the starting structure for all non-solvent, non-hydrogen atoms. The agreement of the isotropic equivalents for the fitted TLS ADPs (B_tls) and the reference ADPs (B_ref) is scored as (9) for all non-solvent, non-hydrogen atoms.

(9) $R_i=\left|B_{\mathit{ref}}^i-B_{\mathit{tls}}^i\right|.$

A percentile of atoms with the poorest fitting ADPs (p_TLS) are excluded from the next round of TLS parameter fitting and repeated until the fitted TLS parameters converge. The converged TLS parameters are then applied to all atoms within that group for the duration of the simulation. Solvent atoms are assigned to the TLS group of the closest non-water atom, this assignment is updated every 250 time-steps. This TLS model produced lower R-values than using the ADP values from the re-refined single structure or using the one overall isotropic B-factor for all atoms in the model (Table 5).

Table 5

PDB	Resolution (Å)	Global isotropic B-factor				Refined ADPs			Fitted TLS ADPs
		Rwork	Rfree	Wilson B-factor (Å2)	Global B-factor (Å2)	Rwork	Rfree	Scale factor	Rwork	Rfree	pTLS
3K0M	1.3	0.117	0.147	12.0	12.0	0.125	0.146	0.9	0.103	0.130	0.3
3K0N	1.4	0.121	0.153	19.1	19.1	0.126	0.153	0.9	0.114	0.133	0.1
1UOY	1.5	0.103	0.148	10.4	9.4	0.107	0.144	0.9	0.101	0.136	0.3
3CA7	1.5	0.129	0.194	16.8	13.4	0.142	0.192	0.9	0.142	0.190	0.5
1X6P	1.6	0.108	0.158	15.9	12.7	0.113	0.152	0.8	0.121	0.150	0.8
1F2F	1.7	0.116	0.184	15.6	14.8	0.123	0.167	0.8	0.126	0.167	0.7
1BV1	2.0	0.125	0.192	22.6	18.1	0.135	0.191	0.8	0.145	0.182	0.6
Mean	-	0.117	0.168	-	-	0.125	0.164	-	0.122	0.155	-

Generation of the final ensemble

Request a detailed protocol

Structure factors for the final ensemble are calculated from the population of collected structure as in (2) where F_calc and F_mask are defined as (10) and (11).

(10) ${\langle {\mathit{F}}_{\mathit{calc}}\rangle }_{\mathit{final}}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\mathit{F}}_{\mathit{calc}}^i,}$

(11) ${\langle {\mathit{F}}_{\mathit{mask}}\rangle }_{\mathit{final}}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\mathit{F}}_{\mathit{mask}}^i.}$

The acquisition phase is split into several time blocks, in each of which 250 structures are typically stored. The R-values of all possible contiguous time blocks are calculated and the periods with the lowest R_work are selected. This selection reduces the R_work by 0–1.0% (mean improvement in 0.3%). For the 1YTT dataset with high quality experimental phases, the block selection for lowest R_work corresponds well with the overall map correlation coefficient computed between the experimentally phased map and the map derived from the ensemble model (Figure 13). Next, to reduce the redundancy in the number of structures in the final ensemble (during the simulation thousands of structures are collected), we calculate the smallest number of structures that reproduce the R_free within 0.1%. This is performed by iteratively parsing the stored structures with increasing time spacing (see Figure 1D). The overall and bulk-solvent scale factors are optimised for the final ensemble. The ensembles of structures are stored using the standard PDB format for multiple models, with B-factors listed as computed from the TLS model and overall B-factor scaling contributions.

Figure 13

Download asset Open asset

Calculation of atomic positional probability

Request a detailed protocol

All atoms comprising the ensemble are assigned a probability (P_i) based on the positional likelihood of atom i in a given model relative to the complete ensemble of models. F_calc electron-density maps are calculated for each model in the ensemble and 〈F_calc〉 electron-density map is calculated for the complete ensemble as (10). P_i is calculated as (12).

(12) $P_i=\frac{{\rho }_{\langle {\mathit{F}}_{\mathit{calc}}\rangle }^i}{{\rho }_{{\mathit{F}}_{\mathit{calc}}}^i}.$

Calculating from an electron-density function allows for non-Gaussian distributions unlike RMSF, which is calculated from mean atomic position. These probabilities aid the visual inspection of the ensemble models and allow the observer to control the level of detail displayed (Figure 14).

Figure 14

Download asset Open asset

1. 1. Burnley BT
   2. Afonine PV
   3. Adams PD
   4. Gros P

   (2012) Data from: Modelling dynamics in protein crystal structures by ensemble refinement

   Available at Dryad Digital Repository.

   http://dx.doi.org/10.5061/dryad.5n01h

1. 1. Reiling KK
   2. Endres NF
   3. Dauber DS
   4. Craik CS
   5. Stroud RM

   (2002) JE-2147-HIV Protease Complex

   ID 1KZK. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
2. 1. Fraser JS
   2. Clarkson MW
   3. Degnan SC
   4. Erion R
   5. Kern D
   6. Alber T

   (2009) Cryogenic structure of CypA

   ID 3K0M. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
3. 1. Fraser JS
   2. Clarkson MW
   3. Degnan SC
   4. Erion R
   5. Kern D
   6. Alber T

   (2009) Room temperature structure of CypA

   ID 3K0N. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
4. 1. Heaslet H
   2. Rosenfeld R
   3. Giffin M
   4. Lin YC
   5. Tam K
   6. Torbett BE
   7. Elder JH
   8. McRee DE
   9. Stout CD

   (2007) Apo Wild-type HIV Protease in the open conformation

   ID 2PC0. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
5. 1. Olsen JG
   2. Flensburg C
   3. Olsen O
   4. Bricogne G
   5. Henriksen A

   (2004) The Bubble Protein from Penicillium brevicompactum Dierckx Exudate

   ID 1UOY. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
6. 1. Klein DE
   2. Stayrook SE
   3. Shi F
   4. Narayan K
   5. Lemmon MA

   (2008) High Resolution Crystal Structure of the EGF domain of spitz

   ID 3CA7. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
7. 1. Wang H
   2. Yan Z
   3. Geng J
   4. Kunz S
   5. Seebeck T
   6. Ke H

   (2007) Structure of LmjPDEB1 in complex with IBMX

   ID 2R8Q. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
8. 1. Bhabha G
   2. Lee J
   3. Ekiert DC
   4. Gam J
   5. Wilson IA
   6. Dyson HJ
   7. Benkovic SJ
   8. Wright PE

   (2011) Crystal structure of N23PP/S148A mutant of E. coli dihydrofolate reductase

   ID 3QL0. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
9. 1. Dunlop KV
   2. Irvin RT
   3. Hazes B

   (2005) Structure 4; room temperature crystal structure of truncated pak pilin from Pseudomonas aeruginosa at 1.63A resolution

   ID 1X6P. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

   http://www.rcsb.org/pdb/
10. 1. Kimber MS
    2. Nachman J
    3. Cunningham AM
    4. Gish GD
    5. Pawson T
    6. Pai EF

    (2000) SRC SH2 ThrEF1Trp Mutant

    ID 1F2F. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
11. 1. Bhabha G
    2. Lee J
    3. Ekiert DC
    4. Gam J
    5. Wilson IA
    6. Dyson HJ
    7. Benkovic SJ
    8. Wright PE

    (2011) Re-refined coordinates for PDB entry 1RX2

    ID 3QL3. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
12. 1. Burling FT
    2. Weis WI
    3. Flaherty KM
    4. Brunger AT

    (1996) Yb substituted subtilisin fragment of mannose binding protein A (Sub-MBP-A), MAD structure at 110K

    ID 1YTT. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
13. 1. Rodriguez DD
    2. Grosse C
    3. Himmel S
    4. Gonzalez C
    5. de Ilarduya IM
    6. Becker S
    7. Sheldrick GM
    8. Uson I

    (2009) Crystallographic Ab Initio protein solution far below atomic resolution

    ID 3GWH. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
14. 1. Gajhede M
    2. Osmark P
    3. Poulsen FM
    4. Ipsen H
    5. Larsen JN
    6. Joost van Neerven RJ
    7. Schou C
    8. Lowenstein H
    9. Spangfort MD

    (1996) Birch pollen allergen Bet V 1

    ID 1BV1. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
15. 1. Nagar B
    2. Bornmann W
    3. Pellicena P
    4. Schindler T
    5. Veach DR
    6. Miller WT
    7. Clarkson B
    8. Kuriyan J

    (2002) Crystal structure of the C-Abl Kinase domain in complex with STI-571

    ID 1IEP. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
16. 1. Singh BK
    2. Sattler JM
    3. Chatterjee M
    4. Huttu J
    5. Schuler H
    6. Kursula I

    (2011) Crystal structure of Plasmodium berghei actin depolymerization Factor 2

    ID 2XFA. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
17. 1. Wu B
    2. Chien EY
    3. Mol CD
    4. Fenalti G
    5. Liu W
    6. Katritch V
    7. Abagyan R
    8. Brooun A
    9. Wells P
    10. Bi FC
    11. Hamel DJ
    12. Kuhn P
    13. Handel TM
    14. Cherezov V
    15. Stevens RC

    (2010) The 2.5 A structure of the CXCR4 chemokine receptor in complex with small molecule antagonist IT1t

    ID 3ODU. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
18. 1. Nagar B
    2. Bornmann W
    3. Pellicena P
    4. Schindler T
    5. Veach DR
    6. Miller WT
    7. Clarkson B
    8. Kuriyan J

    (2002) Crystal Structure of the c-Abl Kinase domain in complex with PD173955

    ID 1M52. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
19. 1. He X
    2. Zhou J
    3. Bartlam M
    4. Zhang R
    5. Ma J
    6. Lou Z
    7. Li X
    8. Li J
    9. Joachimiak A
    10. Zeng Z
    11. Ge R
    12. Rao Z
    13. Liu Y

    (2008) A RNA polymerase subunit structure from virus

    ID 3CM8. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/
20. 1. Shimamura T
    2. Shiroishi M
    3. Weyand S
    4. Tsujimoto H
    5. Winter G
    6. Katritch V
    7. Abagyan R
    8. Cherezov V
    9. Liu W
    10. Han GW
    11. Kobayashi T
    12. Stevens RC
    13. Iwata S

    (2011) Structure of the human histamine H1 receptor in complex with doxepin

    ID 3RZE. Publically available at the RCSB Protein Data Bank (http://www.rcsb.org/pdb/).

    http://www.rcsb.org/pdb/

1. 1. Adams PD
   2. Afonine PV
   3. Bunkóczi G
   4. Chen VB
   5. Davis IW
   6. Echols N

   et al. (2010) PHENIX: a comprehensive Python-based system for macromolecular structure solution

   Acta Crystallogr D Biol Crystallogr 66:213–221.

   https://doi.org/10.1107/S0907444909052925

   • Google Scholar
2. 1. Adams PD
   2. Pannu NS
   3. Read RJ
   4. Brünger AT

   (1997)

   Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

   Proc Natl Acad Sci USA 94:5018–5023.

   • Google Scholar
3. 1. Afonine PV
   2. Grosse-Kunstleve RW
   3. Adams PD

   (2005) A robust bulk-solvent correction and anisotropic scaling procedure

   Acta Crystallogr D Biol Crystallogr 61:850–855.

   https://doi.org/10.1107/S0907444905007894

   • Google Scholar
4. 1. Afonine PV
   2. Grosse-Kunstleve RW
   3. Echols N
   4. Headd JJ
   5. Moriarty NW
   6. Mustyakimov M

   et al. (2012) Towards automated crystallographic structure refinement with phenix.refine

   Acta Crystallogr D Biol Crystallogr 68:352–367.

   https://doi.org/10.1107/S0907444912001308

   • Google Scholar
5. 1. Berendsen HJC
   2. Postma JPM
   3. van Gunsteren WF
   4. DiNola A
   5. Haak JR

   (1984) Molecular dynamics with coupling to an external bath

   The Journal of Chemical Physics 81:3684.

   https://doi.org/10.1063/1.448118

   • Google Scholar
6. 1. Berman HM
   2. Westbrook J
   3. Feng Z
   4. Gilliland G
   5. Bhat TN
   6. Weissig H

   et al. (2000) The protein data bank

   Nucleic Acids Res 28:235–242.

   https://doi.org/10.1093/nar/28.1.235

   • Google Scholar
7. 1. Bhabha G
   2. Lee J
   3. Ekiert DC
   4. Gam J
   5. Wilson IA
   6. Dyson HJ

   et al. (2011) A dynamic knockout reveals that conformational fluctuations influence the chemical step of enzyme catalysis

   Science 332:234–238.

   https://doi.org/10.1126/science.1198542

   • Google Scholar
8. 1. Brändén CI
   2. Jones TA

   (1990) Between objectivity and subjectivity

   Nature 343:687–689.

   https://doi.org/10.1038/343687a0

   • Google Scholar
9. 1. Bricogne G
   2. Blanc E
   3. Brandi M
   4. Flensburg C
   5. Keller P
   6. Paciorek W

   et al. (2009)

   BUSTER, version 2.8.0. Retrieved from about:home

   BUSTER, version 2.8.0. Retrieved from about:home.

   • Google Scholar
10. 1. Brünger AT

    (1992) Free R value: a novel statistical quantity for assessing the accuracy of crystal structures

    Nature 355:472–475.

    https://doi.org/10.1038/355472a0

    • Google Scholar
11. 1. Burling FT
    2. Brunger AT

    (1994)

    Thermal motion and conformational disorder in protein crystal structures: comparison of multi-conformer and time-averaging models

    Israel Journal of Chemistry 34:165–175.

    • Google Scholar
12. 1. Burling FT
    2. Weis WI
    3. Flaherty KM
    4. Brünger AT

    (1996) Direct observation of protein solvation and discrete disorder with experimental crystallographic phases

    Science 271:72–77.

    https://doi.org/10.1126/science.271.5245.72

    • Google Scholar
13. 1. Burnley BT
    2. Afonine PV
    3. Adams PD
    4. Gros P

    (2012) Data from: modelling dynamics in protein crystal structures by ensemble refinement

    Dryad Digital Repository.

    https://doi.org/10.5061/dryad.5n01h

    • Google Scholar
14. 1. Clarage JB
    2. Phillips GN Jr

    (1994) Cross-validation tests of time-averaged molecular dynamics refinements for determination of protein structures by X-ray crystallography

    Acta Crystallogr D Biol Crystallogr 50:24–36.

    https://doi.org/10.1107/S0907444993009515

    • Google Scholar
15. 1. DePristo MA
    2. de Bakker PI
    3. Blundell TL

    (2004) Heterogeneity and inaccuracy in protein structures solved by X-ray crystallography

    Structure 12:831–838.

    https://doi.org/10.1016/j.str.2004.02.031

    • Google Scholar
16. 1. Dunlop KV
    2. Irvin RT
    3. Hazes B

    (2005) Pros and cons of cryocrystallography: should we also collect a room-temperature data set?

    Acta Crystallogr D Biol Crystallogr 61:80–87.

    https://doi.org/10.1107/S0907444904027179

    • Google Scholar
17. 1. Eisenmesser EZ
    2. Millet O
    3. Labeikovsky W
    4. Korzhnev DM
    5. Wolf-Watz M
    6. Bosco DA

    et al. (2005) Intrinsic dynamics of an enzyme underlies catalysis

    Nature 438:117–121.

    https://doi.org/10.1038/nature04105

    • Google Scholar
18. Book

    1. Feynman RP
    2. Leighton RB
    3. Sands ML

    (1963)

    The Feynman lectures on physics, Vol 1: Mainly mechanics, radiation, and heat

    Reading: Addison-Wesley.

    • Google Scholar
19. 1. Fraser JS
    2. Clarkson MW
    3. Degnan SC
    4. Erion R
    5. Kern D
    6. Alber T

    (2009) Hidden alternative structures of proline isomerase essential for catalysis

    Nature 462:669–673.

    https://doi.org/10.1038/nature08615

    • Google Scholar
20. 1. Furnham N
    2. Blundell TL
    3. DePristo MA
    4. Terwilliger TC

    (2006) Is one solution good enough?

    Nat Struct Mol Biol 13:184–185.

    https://doi.org/10.1038/nsmb0306-184

    • Google Scholar
21. 1. Gajhede M
    2. Osmark P
    3. Poulsen FM
    4. Ipsen H
    5. Larsen JN
    6. Joost van Neerven RJ

    et al. (1996) X-ray and NMR structure of Bet v 1, the origin of birch pollen allergy

    Nat Struct Mol Biol 3:1040–1045.

    https://doi.org/10.1038/nsb1296-1040

    • Google Scholar
22. 1. Gros P
    2. van Gunsteren WF
    3. Hol WG

    (1990)

    Inclusion of thermal motion in crystallographic structures by restrained molecular dynamics

    Science 249:1149–1152.

    • Google Scholar
23. 1. Grosse-Kunstleve RW
    2. Afonine PV
    3. Adams PD

    (2004)

    Cctbx news: geometry restraints and other new features

    Newsletter of the IUCr Commission on Crystallographic Computing 4:19–36.

    • Google Scholar
24. 1. Hazes B
    2. Sastry PA
    3. Hayakawa K
    4. Read RJ
    5. Irvin RT

    (2000) Crystal structure of Pseudomonas aeruginosa PAK pilin suggests a main-chain-dominated mode of receptor binding

    J Mol Biol 299:1005–1017.

    https://doi.org/10.1006/jmbi.2000.3801

    • Google Scholar
25. 1. He X
    2. Zhou J
    3. Bartlam M
    4. Zhang R
    5. Ma J
    6. Lou Z

    et al. (2008) Crystal structure of the polymerase PAC–PB1N complex from an avian influenza H5N1 virus

    Nature 454:1123–1126.

    https://doi.org/10.1038/nature07120

    • Google Scholar
26. 1. Heaslet H
    2. Rosenfeld R
    3. Giffin M
    4. Lin YC
    5. Tam K
    6. Torbett BE

    et al. (2007) Conformational flexibility in the flap domains of ligand-free HIV protease

    Acta Crystallogr D Biol Crystallogr 63:866–875.

    https://doi.org/10.1107/S0907444907029125

    • Google Scholar
27. 1. Jiang JS.
    2. Brünger AT

    (1994) Protein hydration observed by X-ray diffraction. Solvation properties of penicillopepsin and neuraminidase crystal structures

    J Mol Biol 243:100–115.

    https://doi.org/10.1006/jmbi.1994.1633

    • Google Scholar
28. 1. Joosten RP
    2. te Beek TA
    3. Krieger E
    4. Hekkelman ML
    5. Hooft RW
    6. Schneider R

    et al. (2010) A series of PDB related databases for everyday needs

    Nucleic Acids Res 39:D411–D419.

    https://doi.org/10.1093/nar/gkq1105

    • Google Scholar
29. 1. Kimber MS
    2. Nachman J
    3. Cunningham AM
    4. Gish GD
    5. Pawson T
    6. Pai EF

    (2000)

    Structural basis for specificity switching of the Src SH2 domain

    Mol Cell 5:1043–1049.

    • Google Scholar
30. 1. Klein DE
    2. Stayrook SE
    3. Shi F
    4. Narayan K
    5. Lemmon MA

    (2008) Structural basis for EGFR ligand sequestration by Argos

    Nature 453:1271–1275.

    https://doi.org/10.1038/nature06978

    • Google Scholar
31. 1. Korostelev A
    2. Laurberg M
    3. Noller HF

    (2009) Multistart simulated annealing refinement of the crystal structure of the 70S ribosome

    Proc Natl Acad Sci USA 106:18195–18200.

    https://doi.org/10.1073/pnas.0909287106

    • Google Scholar
32. 1. Lang PT
    2. Ng HL
    3. Fraser JS
    4. Corn JE
    5. Echols N
    6. Sales M

    et al. (2010)

    Automated electron-density sampling reveals widespread conformational polymorphism in proteins

    Protein Sci 19:1420–1431.

    • Google Scholar
33. 1. Lee AL
    2. Kinnear SA
    3. Wand AJ

    (2000) Redistribution and loss of side chain entropy upon formation of a calmodulin-peptide complex

    Nat Struct Biol 7:72–77.

    https://doi.org/10.1038/71280

    • Google Scholar
34. 1. Levin EJ
    2. Kondrashov DA
    3. Wesenberg GE
    4. Phillips GN Jr

    (2007) Ensemble refinement of protein crystal structures: validation and application

    Structure 15:1040–1052.

    https://doi.org/10.1016/j.str.2007.06.019

    • Google Scholar
35. 1. Linderstrøm-Lang K
    2. Schellman J

    (1959)

    The Enzymes

    The Enzymes, Vol 1, New York, Academic Press.

    • Google Scholar
36. 1. Marković-Housley Z
    2. Degano M
    3. Lamba D
    4. von Roepenack-Lahaye E
    5. Clemens S
    6. Susani M

    et al. (2003)

    Crystal structure of a hypoallergenic isoform of the major birch pollen allergen Bet v 1 and its likely biological function as a plant steroid carrier

    J Mol Biol 325:123–133.

    • Google Scholar
37. 1. Murshudov GN
    2. Vagin AA
    3. Dodson EJ

    (1997) Refinement of macromolecular structures by the maximum-likelihood method

    Acta Crystallogr D Biol Crystallogr 53:240–255.

    https://doi.org/10.1107/S0907444996012255

    • Google Scholar
38. 1. Nagar B
    2. Bornmann WG
    3. Pellicena P
    4. Schindler T
    5. Veach DR
    6. Miller WT

    et al. (2002)

    Crystal structures of the kinase domain of c-Abl in complex with the small molecule inhibitors PD173955 and imatinib (STI-571)

    Cancer Res 62:4236–4243.

    • Google Scholar
39. 1. Olsen JG
    2. Flensburg C
    3. Olsen O
    4. Bricogne G
    5. Henriksen A

    (2004) Solving the structure of the bubble protein using the anomalous sulfur signal from single-crystal in-house Cu Kalpha diffraction data only

    Acta Crystallogr D Biol Crystallogr 60:250–255.

    https://doi.org/10.1107/S0907444903025927

    • Google Scholar
40. 1. Pannu NS
    2. Read RJ

    (1996) Improved structure refinement through maximum likelihood

    Acta Crystallogr Sect A Found Crystallogr 52:659–668.

    https://doi.org/10.1107/S0108767396004370

    • Google Scholar
41. 1. Reiling KK
    2. Endres NF
    3. Dauber DS
    4. Craik CS
    5. Stroud RM

    (2002)

    Anisotropic dynamics of the JE-2147-HIV protease complex: drug resistance and thermodynamic binding mode examined in a 1.09 A structure

    Biochemistry 41:4582–4594.

    • Google Scholar
42. 1. Rodríguez DD
    2. Grosse C
    3. Himmel S
    4. Gonzalez C
    5. de Ilarduya IM
    6. Becker S

    et al. (2009) Crystallographic ab initio protein structure solution below atomic resolution

    Nat Methods 6:651–653.

    https://doi.org/10.1038/nmeth.1365

    • Google Scholar
43. 1. Schiffer CA
    2. Gros P
    3. van Gunsteren WF

    (1995) Time-averaging crystallographic refinement: possibilities and limitations using alpha-cyclodextrin as a test system

    Acta Crystallogr D Biol Crystallogr 51:85–92.

    https://doi.org/10.1107/S0907444994007158

    • Google Scholar
44. 1. Schindler T
    2. Bornmann W
    3. Pellicena P
    4. Miller WT
    5. Clarkson B
    6. Kuriyan J

    (2000)

    Structural mechanism for STI-571 inhibition of abelson tyrosine kinase

    Science 289:1938–1942.

    • Google Scholar
45. 1. Schomaker V
    2. Trueblood KN

    (1968) On the rigid-body motion of molecules in crystals

    Acta Crystallogr B 24:63–76.

    https://doi.org/10.1107/S0567740868001718

    • Google Scholar
46. 1. Sheriff S
    2. Hendrickson WA

    (1987) Description of overall anisotropy in diffraction from macromolecular crystals

    Acta Crystallogr A 43:118–121.

    https://doi.org/10.1107/S010876738709977X

    • Google Scholar
47. 1. Shimamura T
    2. Shiroishi M
    3. Weyand S
    4. Tsujimoto H
    5. Winter G
    6. Katritch V

    et al. (2011) Structure of the human histamine H1 receptor complex with doxepin

    Nature 475:65–70.

    https://doi.org/10.1038/nature10236

    • Google Scholar
48. 1. Singh BK
    2. Sattler JM
    3. Chatterjee M
    4. Huttu J
    5. Schuler H
    6. Kursula I

    (2011) Crystal structures explain functional differences in the two actin depolymerization factors of the malaria parasite

    J Biol Chem 286:28256–28264.

    https://doi.org/10.1074/jbc.M111.211730

    • Google Scholar
49. 1. Terwilliger TC
    2. Grosse-Kunstleve RW
    3. Afonine PV
    4. Adams PD
    5. Moriarty NW
    6. Zwart P

    et al. (2007) Interpretation of ensembles created by multiple iterative rebuilding of macromolecular models

    Acta Crystallogr D Biol Crystallogr 63:597–610.

    https://doi.org/10.1107/S0907444907009791

    • Google Scholar
50. 1. Torchia DA
    2. Ishima R

    (2003) Molecular structure and dynamics of proteins in solution: insights derived from high-resolution NMR approaches

    Pure and Applied Chemistry 75:1371–1381.

    https://doi.org/10.1351/pac200375101371

    • Google Scholar
51. 1. Torda A
    2. Scheek R
    3. van Gunsteren WF

    (1989) Time-dependent distance restraints in molecular dynamics simulations

    Chemical Physics Letters 157:289–294.

    https://doi.org/10.1016/0009-2614(89)87249-5

    • Google Scholar
52. 1. Vagin AA
    2. Steiner RA
    3. Lebedev AA
    4. Potterton L
    5. McNicholas S
    6. Long F

    et al. (2004) REFMAC5 dictionary: organization of prior chemical knowledge and guidelines for its use

    Acta Crystallogr D Biol Crystallogr 60:2184–2195.

    https://doi.org/10.1107/S0907444904023510

    • Google Scholar
53. 1. Vajpai N
    2. Strauss A
    3. Fendrich G
    4. Cowan-Jacob SW
    5. Manley PW
    6. Grzesiek S

    et al. (2008) Solution conformations and dynamics of ABL kinase-inhibitor complexes determined by NMR substantiate the different binding modes of imatinib/nilotinib and dasatinib

    J Biol Chem 283:18292–18302.

    https://doi.org/10.1074/jbc.M801337200

    • Google Scholar
54. 1. van den Bedem H
    2. Dhanik A
    3. Latombe JC
    4. Deacon AM

    (2009) Modeling discrete heterogeneity in X-ray diffraction data by fitting multi-conformers

    Acta Crystallogr D Biol Crystallogr 65:1107–1117.

    https://doi.org/10.1107/S0907444909030613

    • Google Scholar
55. 1. Velazquez-Campoy A.
    2. Kiso Y
    3. Freire E

    (2001) The binding energetics of first- and second-generation HIV-1 protease inhibitors: implications for drug design

    Arch Biochem Biophys 390:169–175.

    https://doi.org/10.1006/abbi.2001.2333

    • Google Scholar
56. 1. Vitkup D
    2. Ringe D
    3. Karplus M
    4. Petsko GA

    (2002)

    Why protein R-factors are so large: a self-consistent analysis

    Proteins 46:345–354.

    • Google Scholar
57. 1. Wang H
    2. Yan Z
    3. Geng J
    4. Kunz S
    5. Seebeck T
    6. Ke H

    (2007) Crystal structure of the Leishmania major phosphodiesterase LmjPDEB1 and insight into the design of the parasite-selective inhibitors

    Mol Microbiol 66:1029–1038.

    https://doi.org/10.1111/j.1365-2958.2007.05976.x

    • Google Scholar
58. 1. Winn MD
    2. Isupov MN
    3. Murshudov GN

    (2001)

    Use of TLS parameters to model anisotropic displacements in macromolecular refinement

    Acta Crystallogr D Biol Crystallogr 57:122–133.

    • Google Scholar
59. 1. Wu B
    2. Chien EYT
    3. Mol CD
    4. Fenalti G
    5. Liu W
    6. Katritch V

    et al. (2010) Structures of the CXCR4 chemokine GPCR with small-molecule and cyclic peptide antagonists

    Science 330:1066–1071.

    https://doi.org/10.1126/science.1194396

    • Google Scholar

Author details

1. B Tom Burnley

   Crystal and Structural Chemistry, Bijvoet Center for Biomolecular Research, Department of Chemistry, Faculty of Science, Utrecht University, Utrecht, The Netherlands

   Contribution

   BTB: developed the method, programmed the method in PHENIX, analysed the data and wrote the manuscript

   Competing interests

   The authors have declared that no competing interests exist

2. Pavel V Afonine

   Lawrence Berkeley National Laboratory, Berkeley, United States

   Contribution

   PVA: helped program the method in PHENIX and assisted in the writing of the manuscript

   Competing interests

   The authors have declared that no competing interests exist

3. Paul D Adams

   1. Lawrence Berkeley National Laboratory, Berkeley, United States
   2. Department of Bioengineering, University of California Berkeley, Berkeley, United States

   Contribution

   PDA: helped program the method in PHENIX and assisted in the writing of the manuscript

   Competing interests

   The authors have declared that no competing interests exist

4. Piet Gros

   Crystal and Structural Chemistry, Bijvoet Center for Biomolecular Research, Department of Chemistry, Faculty of Science, Utrecht University, Utrecht, The Netherlands

   Contribution

   PG: developed the method, analysed the data and wrote the manuscript

   For correspondence

   p.gros@uu.nl

   Competing interests

   The authors have declared that no competing interests exist

• 5,099

  views

• 878

  downloads

• 244

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.