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1.  A case of structure determination using pseudosymmetry 
When properly applied, pseudosymmetry can be used to improve crystallographic phases through averaging and to facilitate crystal structure determination.
Here, a case is presented of an unusual structure determination which was facilitated by the use of pseudosymmetry. Group A streptococcus uses cysteine protease Mac-1 (also known as IdeS) to evade the host immune system. Native Mac-1 was crystallized in the orthorhombic space group P21212. Surprisingly, crystals of the inactive C94A mutant of Mac-1 displayed monoclinic symmetry with space group P21, despite the use of native orthorhombic Mac-1 microcrystals for seeding. Attempts to solve the structure of the C94A mutant by MAD phasing in the monoclinic space group did not produce an interpretable map. The native Patterson map of the C94A mutant showed two strong peaks along the (1 0 1) diagonal, indicating possible translational pseudosymmetry in space group P21. Interestingly, one-third of the monoclinic reflections obeyed pseudo-orthorhombic P21212 symmetry similar to that of the wild-type crystals and could be indexed and processed in this space group. The pseudo-orthorhombic and monoclinic unit cells were related by the following vector operations: a m = b o − c o, b m = a o and c m = −2c o − b o. The pseudo-orthorhombic subset of data produced good SAD phases, leading to structure determination with one monomer in the asymmetric unit. Subsequently, the structure of the Mac-1 mutant in the monoclinic form was determined by molecular replacement, which showed six molecules forming three translationally related dimers aligned along the (1 0 1) diagonal. Knowing the geometric relationship between the pseudo-orthorhombic and the monoclinic unit cells, all six molecules can be generated in the monoclinic unit cell directly without the use of molecular replacement. The current case provides a successful example of the use of pseudosymmetry as a powerful phase-averaging method for structure determination by anomalous diffraction techniques. In particular, a structure can be solved in a higher pseudosymmetry subcell in which an NCS operator becomes a crystallographic operator. The geometrical relationships between the subcell and parental cell can be used to generate a complete molecular representation of the parental asymmetric unit for refinement.
doi:10.1107/S0907444909039912
PMCID: PMC2789005  PMID: 19966420
pseudosymmetry; structure determination; cysteine proteases; Mac-1
2.  Rigidity analysis of protein biological assemblies and periodic crystal structures 
BMC Bioinformatics  2013;14(Suppl 18):S2.
Background
We initiate in silico rigidity-theoretical studies of biological assemblies and small crystals for protein structures. The goal is to determine if, and how, the interactions among neighboring cells and subchains affect the flexibility of a molecule in its crystallized state. We use experimental X-ray crystallography data from the Protein Data Bank (PDB). The analysis relies on an effcient graph-based algorithm. Computational experiments were performed using new protein rigidity analysis tools available in the new release of our KINARI-Web server http://kinari.cs.umass.edu.
Results
We provide two types of results: on biological assemblies and on crystals. We found that when only isolated subchains are considered, structural and functional information may be missed. Indeed, the rigidity of biological assemblies is sometimes dependent on the count and placement of hydrogen bonds and other interactions among the individual subchains of the biological unit. Similarly, the rigidity of small crystals may be affected by the interactions between atoms belonging to different unit cells.
We have analyzed a dataset of approximately 300 proteins, from which we generated 982 crystals (some of which are biological assemblies). We identified two types of behaviors. (a) Some crystals and/or biological assemblies will aggregate into rigid bodies that span multiple unit cells/asymmetric units. Some of them create substantially larger rigid cluster in the crystal/biological assembly form, while in other cases, the aggregation has a smaller effect just at the interface between the units. (b) In other cases, the rigidity properties of the asymmetric units are retained, because the rigid bodies did not combine.
We also identified two interesting cases where rigidity analysis may be correlated with the functional behavior of the protein. This type of information, identified here for the first time, depends critically on the ability to create crystals and biological assemblies, and would not have been observed only from the asymmetric unit.
For the Ribonuclease A protein (PDB file 5RSA), which is functionally active in the crystallized form, we found that the individual protein and its crystal form retain the flexibility parameters between the two states. In contrast, a derivative of Ribonuclease A (PDB file 9RSA), has no functional activity, and the protein in both the asymmetric and crystalline forms, is very rigid.
For the vaccinia virus D13 scaffolding protein (PDB file 3SAQ), which has two biological assemblies, we observed a striking asymmetry in the rigidity cluster decomposition of one of them, which seems implausible, given its symmetry. Upon careful investigation, we tracked the cause to a placement decision by the Reduce software concerning the hydrogen atoms, thus affecting the distribution of certain hydrogen bonds. The surprising result is that the presence or lack of a very few, but critical, hydrogen bonds, can drastically affect the rigid cluster decomposition of the biological assembly.
Conclusion
The rigidity analysis of a single asymmetric unit may not accurately reflect the protein's behavior in the tightly packed crystal environment. Using our KINARI software, we demonstrated that additional functional and rigidity information can be gained by analyzing a protein's biological assembly and/or crystal structure. However, performing a larger scale study would be computationally expensive (due to the size of the molecules involved). Overcoming this limitation will require novel mathematical and computational extensions to our software.
doi:10.1186/1471-2105-14-S18-S2
PMCID: PMC3817814  PMID: 24564201
3.  Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map 
Robotica  2008;26:419-434.
SUMMARY
A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker–Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.
doi:10.1017/S0263574708004475
PMCID: PMC2865699  PMID: 20454468
State estimation; Lie groups; nonholonomic motion planning; exponential map
4.  Imperfect pseudo-merohedral twinning in crystals of fungal fatty acid synthase 
A case of imperfect pseudo-merohedral twinning in monoclinic crystals of fungal fatty acid synthase is discussed. A space-group transition during crystal dehydration resulted in a Moiré pattern-like interference of the twinned diffraction patterns.
The recent high-resolution structures of fungal fatty acid synthase (FAS) have provided new insights into the principles of fatty acid biosynthesis by large multifunctional enzymes. The crystallographic phase problem for the 2.6 MDa fungal FAS was initially solved to 5 Å resolution using two crystal forms from Thermomyces lanuginosus. Monoclinic crystals in space group P21 were obtained from orthorhombic crystals in space group P212121 by dehydration. Here, it is shown how this space-group transition induced imperfect pseudo-merohedral twinning in the monoclinic crystal, giving rise to a Moiré pattern-like interference of the two twin-related reciprocal lattices. The strategy for processing the twinned diffraction images and obtaining a quantitative analysis is presented. The twinning is also related to the packing of the molecules in the two crystal forms, which was derived from self-rotation function analysis and molecular-replacement solutions using a low-resolution electron microscopy map as a search model.
doi:10.1107/S0907444909000778
PMCID: PMC2631638  PMID: 19171964
imperfect pseudo-merohedral twinning; fungal fatty acid synthase
5.  Crystallization and molecular-replacement studies of the monoclonal antibody mAbR310 specific for the (R)-HNE-modified protein 
Antigen-free Fab fragment of mAbR310, which recognizes (R)-HNE modified protein, has been crystallized. Initial phases have been obtained by molecular replacement.
4-Hydroxy-2-nonenal (HNE), a major racemic product of lipid peroxidation, reacts with histidine to form a stable HNE–histidine Michael addition-type adduct possessing three chiral centres in the cyclic hemiacetal structure. Monoclonal antibodies against HNE-modified protein have been widely used for assessing oxidative stress in vitro and in vivo. Here, the purification, crystallization and preliminary crystallographic analysis of a Fab fragment of novel monoclonal antibody R310 (mAbR310), which recognizes (R)-HNE-modified protein, are reported. The Fab fragment of mAbR310 was obtained by digestion with papain, purified and crystallized. Using hanging-drop vapour-diffusion crystallization techniques, crystals of mAbR310 Fab were obtained. The crystal belongs to the monoclinic space group C2 (unit-cell parameters a = 127.04, b = 65.31, c = 64.29 Å, β = 118.88°) and diffracted X-rays to a resolution of 1.84 Å. The asymmetric unit contains one molecule of mAbR310, with a corresponding crystal volume per protein weight of 2.51 Å3 Da−1 and a solvent content of 51.0%.
doi:10.1107/S1744309106016630
PMCID: PMC2243084  PMID: 16754982
mAbR310; monoclonal antibodies; Fab fragments
6.  Expression, purification, crystallization and structure determination of two glutathione S-transferase-like proteins from Shewanella oneidensis  
The production and purification of recombinant SoGST3 and SoGST6, two GST-like proteins from S. oneidensis, are reported and preliminary crystallographic studies of crystals of the recombinant enzymes are presented.
Genome analysis of Shewanella oneidensis, a Gram-negative bacterium with an unusual repertoire of respiratory and redox capabilities, revealed the presence of six glutathione S-transferase-like genes (sogst1–sogst6). Glutathione S-­transferases (GSTs; EC 2.5.1.18) are found in all kingdoms of life and are involved in phase II detoxification processes by catalyzing the nucleophilic attack of reduced glutathione on diverse electrophilic substrates, thereby decreasing their reactivity. Structure–function studies of prokaryotic GST-like proteins are surprisingly underrepresented in the scientific literature when compared with eukaryotic GSTs. Here, the production and purification of recombinant SoGST3 (SO_1576) and SoGST6 (SO_4697), two of the six GST-like proteins in S. oneidensis, are reported and preliminary crystallographic studies of crystals of the recombinant enzymes are presented. SoGST3 was crystallized in two different crystal forms in the presence of GSH and DTT that diffracted to high resolution: a primitive trigonal form in space group P31 that exhibited merohedral twinning with a high twin fraction and a primitive monoclinic form in space group P21. SoGST6 yielded primitive orthorhombic crystals in space group P212121 from which diffraction data could be collected to medium resolution after application of cryo-annealing protocols. Crystal structures of both SoGST3 and SoGST6 have been determined based on marginal search models by maximum-likelihood molecular replacement as implemented in the program Phaser.
doi:10.1107/S1744309108014589
PMCID: PMC2496851  PMID: 18540073
glutathione S-transferases; Shewanella oneidensis
7.  Expression, purification and crystallization of the ecto-enzymatic domain of rat E-NTPDase1 CD39 
The ecto-enzymatic domain of rat E-NTPDase1 CD39 was expressed and purified and diffraction-quality crystals of the enzyme were obtained.
CD39 is a prototype member of the ecto-nucleoside triphosphate diphospho­hydrolase family that hydrolyzes extracellular nucleoside diphosphates and triphosphates in the presence of divalent cations. Here, the expression, purification and crystallization of the ecto-enzymatic domain of rat CD39, sCD39, are described. The 67 kDa secreted soluble glycoprotein was recombinantly overexpressed in a glycosylation mutant CHO line, Lec.3.2.8.1, and purified from conditioned media. Diffraction-quality crystals of sCD39 were produced by the vapor-diffusion method using PEG 3350 and ammonium dihydrogen phosphate as precipitants. The enzyme crystallized in a primitive trigonal form in space group P32, with unit-cell parameters a = b = 118.1, c = 81.6 Å and with two sCD39 copies in the asymmetric unit. Several low- to medium-resolution diffraction data sets were collected using an in-house X-ray source. Analysis of the intensity statistics showed that the crystals were invariably merohedrally twinned with a high twin fraction. For initial phasing, a molecular-replacement search was performed against the complete 3.2 Å data set using a maximum-likelihood molecular-replacement method as implemented in Phaser. The initial model of the two sCD39 monomers was placed into the P32 lattice and rigid-body refined and position-minimized with PHENIX.
doi:10.1107/S1744309108032569
PMCID: PMC2581708  PMID: 18997343
CD39; ecto-nucleoside triphosphate diphosphohydrolases
8.  Preliminary X-ray crystallographic analysis of β-­carbonic anhydrase psCA3 from Pseudomonas aeruginosa  
Two crystal forms of β-carbonic anhydrase psCA3 from P. aeruginosa were grown. Crystal form A belonged to space group P212121, with unit-cell parameters a = 81.9, b = 84.9, c = 124.2 Å, and diffracted X-rays to 2.9 Å resolution; crystal form B belonged to space group P21212, with unit-cell parameters a = 69.9, b = 77.7, c = 88.5 Å, and diffracted X-rays to 3.0 Å resolution.
Pseudomonas aeruginosa is a Gram-negative bacterium that causes life-threatening infections in susceptible individuals and is resistant to most clinically available antimicrobials. Genomic and proteomic studies have identified three genes, pa0102, pa2053 and pa4676, in P. aeruginosa PAO1 encoding three functional β-carbonic anhydrases (β-CAs): psCA1, psCA2 and psCA3, respectively. These β-CAs could serve as novel antimicrobial drug targets for this pathogen. X-ray crystallographic structural studies have been initiated to characterize the structure and function of these proteins. This communication describes the production of two crystal forms (A and B) of β-CA psCA3. Form A diffracted to a resolution of 2.9 Å; it belonged to space group P212121, with unit-cell parameters a = 81.9, b = 84.9, c = 124.2 Å, and had a calculated Matthews coefficient of 2.23 Å3 Da−1 assuming four molecules in the crystallographic asymmetric unit. Form B diffracted to a resolution of 3.0 Å; it belonged to space group P21212, with unit-cell parameters a = 69.9, b = 77.7, c = 88.5 Å, and had a calculated Matthews coefficient of 2.48 Å3 Da−1 assuming two molecules in the crystallographic asymmetric unit. Preliminary molecular-replacement solutions have been determined with the PHENIX AutoMR wizard and refinement of both crystal forms is currently in progress.
doi:10.1107/S1744309113017594
PMCID: PMC3729167  PMID: 23908036
carbonic anhydrases; β-class carbonic anhydrases; Pseudomonas aeruginosa
9.  Pseudosymmetry, high copy number and twinning complicate the structure determination of Desulfovibrio desulfuricans (ATCC 29577) flavodoxin 
Complications to molecular replacement resulting from a poor starting search model, pseudosymmetry, twinning and a high copy number in the asymmetric unit made the determination of the structure of D. desulfuricans (ATCC 29577) flavodoxin in two crystal forms challenging.
The crystal structure of oxidized flavodoxin from Desulfo­vibrio desulfuricans (ATCC 29577) was determined by molecular replacement in two crystal forms, P3121 and P43, at 2.5 and 2.0 Å resolution, respectively. Structure determination in space group P3121 was challenging owing to the presence of pseudo-translational symmetry and a high copy number in the asymmetric unit (8). Initial phasing attempts in space group P3121 by molecular replacement using a poor search model (46% identity) and multi-wavelength anomalous dispersion were unsuccessful. It was necessary to solve the structure in a second crystal form, space group P43, which was characterized by almost perfect twinning, in order to obtain a suitable search model for molecular replacement. This search model with complementary approaches to molecular replacement utilizing the pseudo-translational symmetry operators determined by analysis of the native Patterson map facilitated the selection and manual placement of molecules to generate an initial solution in the P3121 crystal form. During the early stages of refinement, application of the appropriate twin law, (−h, −k, l), was required to converge to reasonable R-factor values despite the fact that in the final analysis the data were untwinned and the twin law could subsequently be removed. The approaches used in structure determination and refinement may be applicable to other crystal structures characterized by these complicating factors. The refined model shows flexibility of the flavin mononucleotide coordinating loops indicated by the isolation of two loop conformations and provides a starting point for the elucidation of the mechanism used for protein-partner recognition.
doi:10.1107/S0907444909010075
PMCID: PMC2685730  PMID: 19465766
flavodoxins; pseudosymmetry; twinning; high copy number; molecular replacement
10.  Rigid Body Energy Minimization on Manifolds for Molecular Docking 
Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space. We use a canonical parametrization of the manifold, called the exponential parametrization, to map the Euclidean tangent space of the manifold onto the manifold itself. Thus, we locally transform the rigid body optimization to an optimization over a Euclidean space where basic optimization algorithms are applicable. Compared to commonly used methods, this formulation substantially reduces the dimension of the search space. As a result, it requires far fewer costly function and gradient evaluations and leads to a more efficient algorithm. We have selected the LBFGS quasi-Newton method for local optimization since it uses only gradient information to obtain second order information about the energy function and avoids the far more costly direct Hessian evaluations. Two applications, one in protein-protein docking, and the other in protein-small molecular interactions, as part of macromolecular docking protocols are presented. The code is available to the community under open source license, and with minimal effort can be incorporated into any molecular modeling package.
doi:10.1021/ct300272j
PMCID: PMC3561712  PMID: 23382659
11.  Crystallization and preliminary X-ray analysis of the open form of human ecto-5′-nucleotidase (CD73) 
The crystallization of human ecto-5′-nucleotidase (CD73) paves the way for detailed studies of the domain motion between the open and closed forms. It will also enable the structure-based design of inhibitors targeting the open form.
Eukaryotic ecto-5′-nucleotidase (e5NT) catalyses the hydrolysis of extracellular AMP to adenosine and plays a pivotal role in switching on adenosine signalling via the P1 receptors of the purinergic signalling pathway. With such an important regulatory role, e5NT has become an appealing new drug target, with potential applications in the treatment of inflammation, chronic pain, hypoxia and cancer. In order to gain insight into the structure and function of the eukaryotic e5NT enzymes and to assist in structure-based drug design, the crystal structure of human e5NT has been solved. Recombinant human e5NT comprising four asparagine-to-aspartate surface mutations targeting potential glycosylation sites was refolded from bacterial inclusion bodies. Refolded and purified human e5NT crystallized in space group P4332 and a data set to 1.85 Å resolution was obtained. The structure could be solved by molecular replacement using a polyalanine model generated from Thermus thermophilus 5′-nucleotidase (5NT). An anomalous data set revealed the presence of a metal-ion binding site, as well as calcium and chloride ion-binding sites. Structural comparisons with bacterial 5NT homologues showed that the human e5NT crystal structure has an open conformation in which the metal- and substrate-binding sites are distant from each other. Here, the crystallization and preliminary X-ray crystallo­graphic analysis of an open structural conformation of human e5NT are described.
doi:10.1107/S1744309112045447
PMCID: PMC3509985  PMID: 23192044
e5NT; CD73; ecto-enzyme; AMP hydrolysis; membrane proteins
12.  Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes 
PLoS Computational Biology  2008;4(10):e1000191.
Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 Å ligand interface Cα root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.
Author Summary
Protein–protein interactions play a central role in various aspects of the structural and functional organization of the cell, and their elucidation is crucial for a better understanding of processes such as metabolic control, signal transduction, and gene regulation. Genomewide proteomics studies, primarily yeast two-hybrid assays, will provide an increasing list of interacting proteins, but only a small fraction of the potential complexes will be amenable to direct experimental analysis. Thus, it is important to develop computational docking methods that can elucidate the details of specific interactions at the atomic level. Protein–protein docking generally starts with a rigid body search that generates a large number of docked conformations with good shape, electrostatic, and chemical complementarity. The conformations are clustered to obtain a manageable number of models, but the current methods are unable to select the most likely structure among these models. Here we describe a refinement algorithm that, applied to the individual clusters, improves the quality of the models. The better models are suitable for higher-accuracy energy calculation, thereby increasing the chances that near-native structures can be identified, and thus the refinement increases the reliability of the entire docking algorithm.
doi:10.1371/journal.pcbi.1000191
PMCID: PMC2538569  PMID: 18846200
13.  X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals 
Nature Communications  2014;5:3220.
Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.
The structural heterogeneity of a biomolecular crystal structure is typically captured using atomic B-factors, determined during structure refinement. Here, the authors use molecular dynamics to show that this strategy is flawed, and that crystallographic B-factors underestimate structural heterogeneity.
doi:10.1038/ncomms4220
PMCID: PMC3926004  PMID: 24504120
14.  Interconversion of Functional Motions between Mesophilic and Thermophilic Adenylate Kinases 
PLoS Computational Biology  2011;7(7):e1002103.
Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), for which the open/closed transition limits the rate of catalytic turnover. Here, we compare our previously published coarse-grained (double-well Gō) simulation of mesophilic AK from E. coli (AKmeso) to simulations of thermophilic AK from Aquifex aeolicus (AKthermo). In AKthermo, as with AKmeso, the LID domain prefers to close before the NMP domain in the presence of ligand, but LID rigid-body flexibility in the open (O) ensemble decreases significantly. Backbone foldedness in O and/or transition state (TS) ensembles increases significantly relative to AKmeso in some interdomain backbone hinges and within LID. In contact space, the TS of AKthermo has fewer contacts at the CORE-LID interface but a stronger contact network surrounding the CORE-NMP interface than the TS of AKmeso. A “heated” simulation of AKthermo at 375K slightly increases LID rigid-body flexibility in accordance with the “corresponding states” hypothesis. Furthermore, while computational mutation of 7 prolines in AKthermo to their AKmeso counterparts produces similar small perturbations, mutation of these sites, especially positions 8 and 155, to glycine is required to achieve LID rigid-body flexibility and hinge flexibilities comparable to AKmeso. Mutating the 7 sites to proline in AKmeso reduces some hinges' flexibilities, especially hinge 2, but does not reduce LID rigid-body flexibility, suggesting that these two types of motion are decoupled in AKmeso. In conclusion, our results suggest that hinge flexibility and global functional motions alike are correlated with but not exclusively determined by the hinge residues. This mutational framework can inform the rational design of functionally important flexibility and allostery in other proteins toward engineering novel biochemical pathways.
Author Summary
Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), which undergoes chemically rate-limiting domain motions coupled to substrate binding. Since mesophiles and thermophiles often differ in functionally important motions, we compare coarse-grained simulations of AKmeso and AKthermo as well as several proline and glycine mutational variants designed to interconvert the dynamics. As might be expected, both domain motions and local unfolding motions are reduced in AKthermo relative to AKmeso. In AKthermo, both of these types of motions can be partially shifted toward more flexible AKmeso by heating or by mutating hinge prolines. However, only mutation to highly flexible glycine produces motions like those of AKmeso. Thus, the rate-limiting global transition likely depends on a combination of hinge flexibility and stability within the LID and NMP domains. Finally, this mutagenic framework can inform the rational design of flexibility and allostery in other proteins toward engineering novel biological control systems.
doi:10.1371/journal.pcbi.1002103
PMCID: PMC3136430  PMID: 21779157
15.  Conformational Statistics of Semi-Flexible Macromolecular Chains with Internal Joints 
Macromolecules  2006;39(5):1950-1960.
Fluctuations in the bending angles at internal irregularities of DNA and RNA (such as symmetric loops, bulges, and nicks/gaps) have been observed from various experiments. However, little effort has been made to computationally predict and explain the statistical behavior of semi-flexible chains with internal defects. In this paper, we describe the general structure of these macromolecular chains as inextensible elastic chains with one or more internal joints which have limited ranges of rotation, and propose a method to compute the probability density functions of the end-to-end pose of these macromolecular chains. Our method takes advantage of the operational properties of the non-commutative Fourier transform for the group of rigid-body motions in three-dimensional space, SE(3). Two representative types of joints, the hinge for planar rotation and the ball joint for spatial rotation, are discussed in detail. The proposed method applies to various stiffness models of semi-flexible chain-like macromolecules. Examples are calculated using the Kratky-Porod model with specified stiffness, angular fluctuation, and joint locations. Entropic effects associated with internal angular fluctuations of semi-flexible macromolecular chains with internal joints can be computed using this formulation. Our method also provides a potential tool to detect the existence of internal irregularities.
doi:10.1021/ma0512556
PMCID: PMC3019766  PMID: 21243113
16.  Expression, purification and preliminary X-ray diffraction studies of the transcriptional factor PyrR from Bacillus halodurans  
The gene-regulation factor PyrR from B. halodurans has been crystallized in two crystal forms. Preliminary crystallographic analysis showed that the protein forms tetramers in both space groups.
The PyrR transcriptional regulator is widely distributed in bacteria. This RNA-binding protein is involved in the control of genes involved in pyrimidine biosynthesis, in which uridyl and guanyl nucleotides function as effectors. Here, the crystallization and preliminary X-ray diffraction analysis of two crystal forms of Bacillus halodurans PyrR are reported. One of the forms belongs to the monoclinic space group P21 with unit-cell parameters a = 59.7, b = 87.4, c = 72.1 Å, β = 104.4°, while the other form belongs to the orthorhombic space group P22121 with unit-cell parameters a = 72.7, b = 95.9, c = 177.1 Å. Preliminary X-ray diffraction data analysis and molecular-replacement solution revealed the presence of four and six monomers per asymmetric unit; a crystallographic tetramer is formed in both forms.
doi:10.1107/S1744309108018307
PMCID: PMC2494968  PMID: 18678934
Bacillus halodurans; pyrimidine biosynthesis; riboswitch-like element; PyrR; transcriptional/translational factor
17.  Crystallization and preliminary X-ray crystallographic analysis of agkicetin-C from Deinagkistrodon acutus venom 
The crystallization and preliminary crystallographic analysis of agkicetin-C, a well known platelet glycoprotein Ib (GPIb) antagonist from the venom of Deinagkistrodon acutus found in Anhui Province, China is reported.
The crystallization and preliminary crystallographic analysis of agkicetin-C, a well known platelet glycoprotein Ib (GPIb) antagonist from the venom of Deinagkistrodon acutus found in Anhui Province, China is reported. Crystals of agkicetin-C suitable for structure determination were obtained from 1.8 M ammonium sulfate, 40 mM MES pH 6.5 with 2%(v/v) PEG 400. Interestingly, low buffer concentrations of MES seem to be necessary for crystal growth. The crystals of agkicetin-C belong to space group C2, with unit-cell parameters a = 177.5, b = 97.7, c = 106.8 Å, β = 118.5°, and diffract to 2.4 Å resolution. Solution of the phase problem by the molecular-replacement method shows that there are four agkicetin-C molecules in the asymmetric unit, with a V M value of 3.4 Å3 Da−1, which corresponds to a high solvent content of approximately 64%. Self-rotation function calculations show a single well defined non-crystallographic twofold axis with features that may represent additional elements of non-crystallographic symmetry.
doi:10.1107/S1744309104027241
PMCID: PMC1952380  PMID: 16508096
snake venoms; C-type lectins; agkicetin-C
18.  Arginine Kinase. Joint Crystallographic & NMR RDC Analyses link Substrate-Associated Motions to Intrinsic Flexibility 
Journal of molecular biology  2010;405(2):479-496.
The phosphagen kinase family, including creatine and arginine kinases, catalyze the reversible transfer of a “high energy” phosphate between ATP and a phospho-guanidino substrate. They have become a model for the study of both substrate-induced conformational change and intrinsic protein dynamics. Prior crystallographic studies indicated large substrate-induced domain rotations, but differences among a recent set of arginine kinase structures was interpreted as a plastic deformation. Here, the structure of Limulus substrate-free arginine kinase is refined against high resolution crystallographic data and compared quantitatively with NMR chemical shifts and residual dipolar couplings (RDCs). This demonstrates the feasibility of this type of RDC analysis of proteins that are large by NMR standards (42 kDa), and illuminates the solution structure, free from crystal-packing constraints. Detailed comparison of the 1.7 Å resolution substrate-free crystal structure against the 1.2 Å transition state analog complex shows large substrate-induced domain motions which can be broken down into movements of smaller quasi-rigid bodies. The solution state structure of substrate-free arginine kinase is most consistent with an equilibrium of substrate-free and –bound structures, with the substrate-free form dominating, but with varying displacements of the quasi-rigid groups. Rigid-group rotations evident from the crystal structures are about axes previously associated with intrinsic millisecond dynamics using NMR relaxation dispersion. Thus, “substrate-induced” motions are along modes that are intrinsically flexible in the substrate-free enzyme, and likely involve some degree of conformational selection.
doi:10.1016/j.jmb.2010.11.007
PMCID: PMC3017626  PMID: 21075117
Induced-fit; Conformational selection; Protein dynamics; Conformational change; Residual Dipolar Coupling; Crystal
19.  Minimum Free Energy Path of Ligand-Induced Transition in Adenylate Kinase 
PLoS Computational Biology  2012;8(6):e1002555.
Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.
Author Summary
Conformational transitions of proteins have been postulated to play a central role in various protein functions such as catalysis, allosteric regulation, and signal transduction. Among these, the relation between enzymatic catalysis and dynamics has been particularly well-studied. The target molecule in this study, adenylate kinase from Escherichia coli, exists in an open state which allows binding of its substrates (ATP and AMP), and a closed state in which catalytic reaction occurs. In this molecular simulation study, we have elucidated the atomic details of the conformational transition between the open and the closed states. A combined use of the path search method and the free energy calculation method enabled the transition pathways to be traced in atomic detail on micro- to millisecond time scales. Our simulations revealed that two ligand molecules, AMP and ATP, play a distinctive role in the transition scenario. The specific binding of AMP into the hinge region occurs first and creates a bottleneck in the transition. ATP-binding, which requires the dehydration of an occluded water molecule, is completed at a later stage of the transition.
doi:10.1371/journal.pcbi.1002555
PMCID: PMC3369945  PMID: 22685395
20.  Crystallization and preliminary crystallographic analysis of l-asparaginase from Erwinia carotovora  
Er. carotovora l-asparaginase, a potential antileukaemic agent, has been crystallized. Crystals diffract to 2.6 Å using a rotating-anode source and belong to space group P21, with unit-cell parameters a = 78.0, b = 112.3, c = 78.7 Å, β = 101.9° and a homotetramer in the crystallographic asymmetric unit.
Bacterial l-asparaginases have been used as therapeutic agents in the treatment of acute childhood lymphoblastic leukaemia for over 30 y. However, their use is limited owing to the glutaminase activity of the administered enzymes, which results in serious side effects. In contrast, l-asparaginase from Erwinia carotovora exhibits low glutaminase activity at physiological concentrations of l-asparagine and l-glutamine in the blood. Recombinant Er. carotovora l-­asparaginase was crystallized in the presence of l-glutamate by the hanging-drop vapour-diffusion method using 10 mg ml−1 purified enzyme, 16–18%(w/v) PEG 3350 and 0.2 M NaF. X-ray diffraction data were collected to 2.6 Å at 293 K using an in-house rotating-anode generator. The crystals belong to the monoclinic P21 space group, with unit-cell parameters a = 78.0, b = 112.3, c = 78.7 Å, β = 101.9° and a homotetramer in the crystallographic asymmetric unit. A molecular-replacement solution has been found and refinement is currently in progress. The crystal structure may provide leads towards protein-engineering efforts aimed at safer asparaginase administration in leukaemia treatment.
doi:10.1107/S1744309105008249
PMCID: PMC1952439  PMID: 16511054
asparaginase therapy; asparagine; leukaemia; Erwinia carotovora
21.  Preparation, crystallization and preliminary X-ray diffraction studies of the glycosylated form of human interleukin-23 
Interleukin-23 (IL-23), a member of the IL-12 family, is a heterodimeric cytokine composed of p19 and p40 subunits. Human p19 and p40 subunits were cloned and coexpressed in N-acetylglucosaminyltransferase I-negative 293S cells. The glycosylated human IL-23 was purified and crystallized by the hanging-drop vapour-diffusion method.
Interleukin-23 (IL-23), a member of the IL-12 family, is a heterodimeric cytokine composed of p19 and p40 subunits. IL-23 plays crucial roles in the activation, proliferation and survival of IL-17-producing helper T cells which induce various autoimmune diseases. Human p19 and p40 subunits were cloned and coexpressed in N-acetylglucosaminyltransferase I-negative 293S cells, which produce high-mannose-type glycosylated proteins in order to diminish the heterogeneity of modified N-linked glycans. The glycosylated human IL-23 was purified and crystallized by the hanging-drop vapour-diffusion method. X-ray diffraction data were then collected to 2.6 Å resolution. The crystal belonged to space group P61 or P65, with unit-cell parameters a = b = 108.94, c = 83.79 Å, γ = 120°. Assuming that the crystal contains one molecule per asymmetric unit, the calculated Matthews coefficient was 2.69 Å3 Da−1, with a solvent content of 54.2%. The structure was determined by the molecular-replacement method, with an initial R factor of 52.6%. After subsequent rigid-body and positional refinement, the R work and R free values decreased to 31.4% and 38.7%, respectively.
doi:10.1107/S1744309112005295
PMCID: PMC3325813  PMID: 22505413
interleukin-23; cytokines; glycosylation
22.  Pseudo-merohedral twinning and noncrystallographic symmetry in orthorhombic crystals of SIVmac239 Nef core domain bound to different-length TCRζ fragments 
P212121 crystals of SIV Nef core domain bound to a peptide fragment of the T-cell receptor ζ subunit exhibited noncrystallographic symmetry and nearly perfect pseudo-merohedral twinning simulating tetragonal symmetry. For a different peptide fragment, nontwinned tetragonal crystals were observed but diffracted to lower resolution. The structure was determined after assignment of the top molecular-replacement solutions to various twin or NCS domains followed by refinement under the appropriate twin law.
HIV/SIV Nef mediates many cellular processes through interactions with various cytoplasmic and membrane-associated host proteins, including the signalling ζ subunit of the T-­cell receptor (TCRζ). Here, the crystallization strategy, methods and refinement procedures used to solve the structures of the core domain of the SIVmac239 isolate of Nef (Nefcore) in complex with two different TCRζ fragments are described. The structure of SIVmac239 Nefcore bound to the longer TCRζ polypeptide (Leu51–Asp93) was determined to 3.7 Å resolution (R work = 28.7%) in the tetragonal space group P43212. The structure of SIVmac239 Nefcore in complex with the shorter TCRζ polypeptide (Ala63–Arg80) was determined to 2.05 Å resolution (R work = 17.0%), but only after the detection of nearly perfect pseudo-merohedral crystal twinning and proper assignment of the orthorhombic space group P212121. The reduction in crystal space-group symmetry induced by the truncated TCRζ polypeptide appears to be caused by the rearrangement of crystal-contact hydrogen-bonding networks and the substitution of crystallographic symmetry operations by similar noncrystallographic symmetry (NCS) operations. The combination of NCS rotations that were nearly parallel to the twin operation (k, h, −l) and a and b unit-cell parameters that were nearly identical predisposed the P212121 crystal form to pseudo-merohedral twinning.
doi:10.1107/S090744490904880X
PMCID: PMC2815668  PMID: 20124696
pseudo-merohedral twinning; noncrystallographic symmetry; pseudosymmetry; human immunodeficiency virus; Nef; T-cell receptor
23.  Total disc replacement using a tissue-engineered intervertebral disc in vivo: new animal model and initial results  
Study type: Basic science
Introduction: Chronic back pain due to degenerative disc disease (DDD) is among the most important medical conditions causing morbidity and significant health care costs. Surgical treatment options include disc replacement or fusion surgery, but are associated with significant short- and long-term risks.1 Biological tissue-engineering of human intervertebral discs (IVD) could offer an important alternative.2 Recent in vitro data from our group have shown successful engineering and growth of ovine intervertebral disc composites with circumferentially aligned collagen fibrils in the annulus fibrosus (AF) (Figure 1).3
Tissue-engineered composite disc a Experimental steps to generate composite tissue-engineered IVDs3 b Example of different AF formulations on collagen alignment in the AF. Second harmonic generation and two-photon excited fluorescence images of seeded collagen gels (for AF) of 1 and 2.5 mg/ml over time. At seeding, cells and collagen were homogenously distributed in the gels. Over time, AF cells elongated and collagen aligned parallel to cells. Less contraction and less alignment is noted after 3 days in the 2.5 mg/mL gel. c Imaging-based creation of a virtual disc model that will serve as template for the engineered disc. Total disc dimensions (AF and NP) were retrieved from micro-computer tomography (CT) (left images), and nucleus pulposus (NP) dimensions alone were retrieved from T2-weighted MRI images (right images). Merging of MRI and micro-CT models revealed a composite disc model (middle image)—Software: Microview, GE Healthcare Inc., Princeton, NJ; and slicOmatic v4.3, TomoVision, Montreal, Canada. d Flow chart describing the process for generating multi-lamellar tissue engineered IVDs. IVDs are produced by allowing cell-seeded collagen layers to contract around a cell-seeded alginate core (NP) over time
Objective: The next step is to investigate if biological disc implants survive, integrate, and restore function to the spine in vivo. A model will be developed that allows efficient in vivo testing of tissue-engineered discs of various compositions and characteristics.
Methods: Athymic rats were anesthetized and a dorsal approach was chosen to perform a microsurgical discectomy in the rat caudal spine (Fig. 2,Fig. 3). Control group I (n = 6) underwent discectomy only, Control group II (n = 6) underwent discectomy, followed by reimplantation of the autologous disc. Two treatment groups (group III, n = 6, 1 month survival; group IV, n = 6, 6 months survival) received a tissue-engineered composite disc implant. The rodents were followed clinically for signs of infection, pain level and wound healing. X-rays and magnetic resonance imaging (MRI) were assessed postoperatively and up to 6 months after surgery (Fig. 6,Fig. 7). A 7 Tesla MRI (Bruker) was implemented for assessment of the operated level as well as the adjacent disc (hydration). T2-weighted sequences were interpreted by a semiquantitative score (0 = no signal, 1 = weak signal, 2 = strong signal and anatomical features of a normal disc). Histology was performed with staining for proteoglycans (Alcian blue) and collagen (Picrosirius red) (Fig. 4,Fig. 5).
Disc replacement surgery a Operative situs with native disc that has been disassociated from both adjacent vertebrae b Native disc (left) and tissue-engineered implant (right) c Implant in situ before wound closureAF: Annulus fi brosus, nP: nucleus pulposus, eP: endplate, M: Muscle, T: Tendon, s: skin, art: artery, GP: Growth plate, B: Bone
Disc replacement surgery. Anatomy of the rat caudal disc space a Pircrosirius red stained axial cut of native disc space b Saffranin-O stained sagittal cut of native disc space
Histologies of three separate motion segments from three different rats. Animal one = native IVD, Animal two = status after discectomy, Animal three = tissue-engineered implant (1 month) a–c H&E (overall tissue staining for light micrsocopy) d–f Alcian blue (proteoglycans) g–i Picrosirius red (collagen I and II)
Histology from one motion segment four months after implantation of a bio-engineered disc construct a Picrosirius red staining (collagen) b Polarized light microscopy showing collagen staining and collagen organization in AF region c Increased Safranin-O staining (proteoglycans) in NP region of the disc implant d Higher magnification of figure 5c: Integration between implanted tissue-engineered total disc replacement and vertebral body bone
MRI a Disc space height measurements in flash/T1 sequence (top: implant (714.0 micrometer), bottom: native disc (823.5 micrometer) b T2 sequence, red circle surrounding the implant NP
7 Tesla MRI imaging of rat tail IVDs showing axial images (preliminary pilot data) a Diffusion tensor imaging (DTI) on two explanted rat tail discs in Formalin b Higher magnification of a, showing directional alignment of collagen fibers (red and green) when compared to the color ball on top which maps fibers' directional alignment (eg, fibers directing from left to right: red, from top to bottom: blue) c Native IVD in vivo (successful imaging of top and bottom of the IVD (red) d Gradient echo sequence (GE) showing differentiation between NP (light grey) and AF (dark margin) e GE of reimplanted tail IVD at the explantation level f T1Rho sequence demonstrating the NP (grey) within the AF (dark margin), containing the yellow marked region of interest for value acquisition (preliminary data are consistent with values reported in the literature). g T2 image of native IVD in vivo for monitoring of hydration (white: NP)
Results: The model allowed reproducible and complete discectomies as well as disc implantation in the rat tail spine without any surgical or postoperative complications. Discectomy resulted in immediate collapse of the disc space. Preliminary results indicate that disc space height was maintained after disc implantation in groups II, III and IV over time. MRI revealed high resolution images of normal intervertebral discs in vivo. Eight out of twelve animals (groups III and IV) showed a positive signal in T2-weighted images after 1 month (grade 0 = 4, grade 1 = 4, grade 2 = 4). Positive staining was seen for collagen as well as proteoglycans at the site of disc implantation after 1 month in each of the six animals with engineered implants (group III). Analysis of group IV showed positive T2 signal in five out of six animals and disc-height preservation in all animals after 6 months.
Conclusions: This study demonstrates for the first time that tissue-engineered composite IVDs with circumferentially aligned collagen fibrils survive and integrate with surrounding vertebral bodies when placed in the rat spine for up to 6 months. Tissue-engineered composite IVDs restored function to the rat spine as indicated by maintenance of disc height and vertebral alignment. A significant finding was that maintenance of the composite structure in group III was observed, with increased proteoglycan staining in the nucleus pulposus region (Figure 4d–f). Proteoglycan and collagen matrix as well as disc height preservation and positive T2 signals in MRI are promising parameters and indicate functionality of the implants.
doi:10.1055/s-0028-1100918
PMCID: PMC3623095  PMID: 23637671
24.  Crystallization and X-ray data analysis of the 10 kDa C-terminal lid subdomain from Caenorhabditis elegans Hsp70 
Crystals of the C-terminal 10 kDa lid subdomain from the C. elegans chaperone Hsp70 have been obtained that diffract X-rays to ∼3.5 Å and belong to space group I212121. Analysis of X-ray data and initial heavy-atom phasing reveals 24 monomers in the asymmetric unit related by 432 non-crystallographic symmetry.
Hsp70 is an important molecular chaperone involved in the regulation of protein folding. Crystals of the C-terminal 10 kDa helical lid domain (residues 542–640) from a Caenorhabditis elegans Hsp70 homologue have been produced that diffract X-rays to ∼3.4 Å. Crystals belong to space group I212121, with unit-cell parameters a = b = 197, c = 200 Å. The Matthews coefficient, self-rotation function and Patterson map indicate 24 monomers in the asymmetric unit, showing non-crystallographic 432 symmetry. Molecular-replacement studies using the corresponding domain from rat, the only eukaryotic homologue with a known structure, failed and a mercury derivative was obtained. Preliminary MAD phasing using SHELXD and SHARP for location and refinement of the heavy-atom substructure and SOLOMON for density modification produced interpretable maps with a clear protein–solvent boundary. Further density-modification, model-building and refinement are currently under way.
doi:10.1107/S1744309106032064
PMCID: PMC2242859  PMID: 16946485
Hsp70; chaperone; C. elegans
25.  Purification, crystallization and preliminary X-ray diffraction studies of the ATP-binding subunit of an ABC transporter from Geobacillus kaustophilus  
An ABC transporter from G. kaustophilus has been crystallized in space group I222. X-ray diffraction data have been collected to 1.60 Å resolution.
ATP-binding cassette (ABC) transporters, also known as traffic ATPases, form a large family of integral membrane proteins responsible for the translocation of a variety of chemically diverse substrates across the lipid bilayers of cellular membranes of both prokaryotes and eukaryotes by the hydrolysis of ATP. The ATP-binding subunit of an ABC transporter from Geobacillus kaustophilus, a homodimeric enzyme, was overexpressed in Escherichia coli and purified. Crystals were obtained using the microbatch-under-oil method at 291 K. X-ray diffraction data to 1.6 Å resolution were collected on SPring-8 beamline BL26B1. The crystals belonged to the orthorhombic space group I222, with unit-cell parameters a = 54.94, b = 78.63, c = 112.96 Å. Assuming the presence of a dimer in the asymmetric unit gave a crystal volume per protein weight (V M) of 2.32 Å3 Da−1 and a solvent content of 47%; this was consistent with the results of a dynamic light-scattering experiment, which showed a dimeric state of the protein in solution. Molecular-replacement trials using the crystal structure of HisP from the Salmonella typhimurium ATP-binding subunit of an ABC transporter as a search model did not provide a satisfactory solution, indicating that the two ATP-binding subunits of ABC transporters have substantially different structures.
doi:10.1107/S1744309112037918
PMCID: PMC3515392  PMID: 23143260
ATP-binding subunit; ABC transporters; Geobacillus kaustophilus

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