Conformational flexibility of pyruvate dehydrogenase complexes: a computational analysis by quantized elastic deformational model

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0

New computational biophysics pipelines for analysing the global dynamics of structural ensembles and large, dynamic complexes resolved by cryoEM are reviewed.

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth of structural data arising from cryoEM and other structural biology methods, has driven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.

State-dependent sequential allostery exhibited by chaperonin TRiC/CCT revealed by network analysis of Cryo-EM maps

The eukaryotic chaperonin TRiC/CCT plays a major role in assisting the folding of many proteins through an ATP-driven allosteric cycle. Recent structures elucidated by cryo-electron microscopy provide a broad view of the conformations visited at various stages of the chaperonin cycle, including a sequential activation of its subunits in response to nucleotide binding. But we lack a thorough mechanistic understanding of the structure-based dynamics and communication properties that underlie the TRiC/CCT machinery. In this study, we present a computational methodology based on elastic network models adapted to cryo-EM density maps to gain a deeper understanding of the structure-encoded allosteric dynamics of this hexadecameric machine. We have analysed several structures of the chaperonin resolved in different states toward mapping its conformational landscape. Our study indicates that the overall architecture intrinsically favours cooperative movements that comply with the structural variabilities observed in experiments. Furthermore, the individual subunits CCT1-CCT8 exhibit state-dependent sequential events at different states of the allosteric cycle. For example, in the ATP-bound state, subunits CCT5 and CCT4 selectively initiate the lid closure motions favoured by the overall architecture; whereas in the apo form of the heteromer, the subunit CCT7 exhibits the highest predisposition to structural change. The changes then propagate through parallel fluxes of allosteric signals to neighbours on both rings. The predicted state-dependent mechanisms of sequential activation provide new insights into TRiC/CCT intra- and inter-ring signal transduction events.

A Coarse-Grained Methodology Identifies Intrinsic Mechanisms That Dissociate Interacting Protein Pairs

We address the problem of triggering dissociation events between proteins that have formed a complex. We have collected a set of 25 non-redundant, functionally diverse protein complexes having high-resolution three-dimensional structures in both the unbound and bound forms. We unify elastic network models with perturbation response scanning (PRS) methodology as an efficient approach for predicting residues that have the propensity to trigger dissociation of an interacting protein pair, using the three-dimensional structures of the bound and unbound proteins as input. PRS reveals that while for a group of protein pairs, residues involved in the conformational shifts are confined to regions with large motions, there are others where they originate from parts of the protein unaffected structurally by binding. Strikingly, only a few of the complexes have interface residues responsible for dissociation. We find two main modes of response: In one mode, remote control of dissociation in which disruption of the electrostatic potential distribution along protein surfaces play the major role; in the alternative mode, mechanical control of dissociation by remote residues prevail. In the former, dissociation is triggered by changes in the local environment of the protein, e.g., pH or ionic strength, while in the latter, specific perturbations arriving at the controlling residues, e.g., via binding to a third interacting partner is required for decomplexation. We resolve the observations by relying on an electromechanical coupling model which reduces to the usual elastic network result in the limit of the lack of coupling. We validate the approach by illustrating the biological significance of top residues selected by PRS on select cases where we show that the residues whose perturbation leads to the observed conformational changes correspond to either functionally important or highly conserved residues in the complex.

Structural and Functional Analyses of the Human PDH Complex Suggest a "Division-of-Labor" Mechanism by Local E1 and E3 Clusters

The pseudo-atomic structural model of human pyruvate dehydrogenase complex (PDHc) core composed of full-length E2 and E3BP components, calculated from our cryoelectron microscopy-derived density maps at 6-Å resolution, is similar to those of prokaryotic E2 structures. The spatial organization of human PDHc components as evidenced by negative-staining electron microscopy and native mass spectrometry is not homogeneous, and entails the unanticipated formation of local clusters of E1:E2 and E3BP:E3 complexes. Such uneven, clustered organization translates into specific duties for E1-E2 clusters (oxidative decarboxylation and acetyl transfer) and E3BP-E3 clusters (regeneration of reduced lipoamide) corresponding to half-reactions of the PDHc catalytic cycle. The addition of substrate coenzyme A modulates the conformational landscape of PDHc, in particular of the lipoyl domains, extending the postulated multiple random coupling mechanism. The conformational and associated chemical landscapes of PDHc are thus not determined entirely stochastically, but are restrained and channeled through an asymmetric architecture and further modulated by substrate binding.

Interconversion of inactive to active conformation of MARK2: Insights from molecular modeling and molecular dynamics simulation

The Ser/Thr protein kinase MARK2, also known as Par1b, belongs to the highly-conserved family of PAR proteins which regulate cell polarity and partitioning through the animal kingdom. In the current study, inactive and active structures of human MARK2 were constructed by modeling and molecular dynamics simulation, based on available incomplete crystal structures in Protein Data Bank, to investigate local structural changes through which MARK2 switches from inactive to active state. None of the MARK2 wild type inactive crystal structures represent the position of activation segment. So, the contribution of this loop to the formation of inactive state is not clear. In the modeled structure of inactive MARK2, activation segment occludes the enzyme active site and assumes a relatively stable position. We also presented a detailed description of the major structural changes occur through the activation process and proposed a framework on how these deviations might be affected by the phosphorylation of Thr208 or existence of the UBA domain. Inspection of protein active state in the presence of Mg-ATP, demonstrated the precise arrangement of the various parts of enzyme around Mg-ATP and the importance of their stability in localization of the resulting complex. The results also confirmed the alleged mild auto-inhibitory role of the UBA domain and suggested a reason for the necessity of this role, based on structural similarities to other related kinases.

The Pyruvate Dehydrogenase Complex and Related Assemblies in Health and Disease

The family of 2-oxoacid dehydrogenase complexes (2-OADC), typified by the pyruvate dehydrogenase multi-enzyme complex (PDC) as its most prominent member, are massive molecular machines (M_r, 4-10 million) controlling key steps in glucose homeostasis (PDC), citric acid cycle flux (OGDC, 2-oxoglutarate dehydrogenase) and the metabolism of the branched-chain amino acids, leucine, isoleucine and valine (BCOADC, branched-chain 2-OADC). These highly organised mitochondrial arrays, composed of multiple copies of three separate enzymes, have been widely studied as paradigms for the analysis of enzyme cooperativity, substrate channelling, protein-protein interactions and the regulation of activity by phosphorylation . This chapter will highlight recent advances in our understanding of the structure-function relationships, the overall organisation and the transport and assembly of PDC in particular, focussing on both native and recombinant forms of the complex and their individual components or constituent domains. Biophysical approaches, including X-ray crystallography (MX), nuclear magnetic resonance spectroscopy (NMR), cryo-EM imaging, analytical ultracentrifugation (AUC) and small angle X-ray and neutron scattering (SAXS and SANS), have all contributed significant new information on PDC subunit organisation, stoichiometry, regulatory mechanisms and mode of assembly. Moreover, the recognition of specific genetic defects linked to PDC deficiency, in combination with the ability to analyse recombinant PDCs housing both novel naturally-occurring and engineered mutations, have all stimulated renewed interest in these classical metabolic assemblies. In addition, the role played by PDC, and its constituent proteins, in certain disease states will be briefly reviewed, focussing on the development of new and exciting areas of medical and immunological research.

PIM: phase integrated method for normal mode analysis of biomolecules in a crystalline environment

In this study, a normal mode analysis, named phase integrated method (PIM), is developed for computing modes of biomolecules in a crystalline environment. PIM can calculate low-frequency modes on one or a few asymmetric units (AUs) and generate exact modes of a whole unit cell according to space group symmetry, while the translational symmetry between unit cells is maintained via the periodic boundary condition. Therefore, the method can dramatically reduce computational cost in mode calculation in the presence of crystal symmetry. PIM also has an option to map modes onto a single AU to form an orthonormalized mode set, which can be directly applied to normal-mode-based thermal parameter refinement in X-ray crystallography. The performance of PIM was tested on all 65 space groups available in protein crystals (one protein for each space group) and on another set of 83 ultra-high-resolution X-ray structures. The results showed that considering space group symmetry in mode calculation is crucial for accurately describing vibrational motion in a crystalline environment. Moreover, the optimal inter-AU packing stiffness was found to be about 60% of that of intra-AU interactions (non-bonded interaction only).

Functional motions of Candida antarctica lipase B: a survey through open-close conformations

Candida antarctica lipase B (CALB) belongs to psychrophilic lipases which hydrolyze carboxyl ester bonds at low temperatures. There have been some features reported about cold-activity of the enzyme through experimental methods, whereas there is no detailed information on its mechanism of action at molecular level. Herein, a comparative molecular dynamics simulation and essential dynamics analysis have been carried out at three temperatures (5, 35 and 50°C) to trace the dominant factors in the psychrophilic properties of CALB under cold condition. The results clearly describe the effect of temperature on CALB with meaningful differences in the flexibility of the lid region (α5 helix), covering residues 141–147. Open- closed conformations have been obtained from different sets of long-term simulations (60 ns) at 5°C gave two reproducible distinct forms of CALB. The starting open conformation became closed immediately at 35 and 50°C during 60 ns of simulation, while a sequential open-closed form was observed at 5°C. These structural alterations were resulted from α5 helical movements, where the closed conformation of active site cleft was formed by displacement of both helix and its side chains. Analysis of normal mode showed concerted motions that are involved in the movement of both α5 and α10 helices. It is suggested that the functional motions needed for lypolytic activity of CALB is constructed from short-range movement of α5, accompanied by long-range movement of the domains connected to the lid region.

Atomic resolution cryo electron microscopy of macromolecular complexes

Single-particle cryo electron microscopy (cryoEM) is a technique for determining three-dimensional (3D) structures from projection images of molecular complexes preserved in their "native," noncrystalline state. Recently, atomic or near-atomic resolution structures of several viruses and protein assemblies have been determined by single-particle cryoEM, allowing ab initio atomic model building by following the amino acid side chains or nucleic acid bases identifiable in their cryoEM density maps. In particular, these cryoEM structures have revealed extended arms contributing to molecular interactions that are otherwise not resolved by the conventional structural method of X-ray crystallography at similar resolutions. High-resolution cryoEM requires careful consideration of a number of factors, including proper sample preparation to ensure structural homogeneity, optimal configuration of electron imaging conditions to record high-resolution cryoEM images, accurate determination of image parameters to correct image distortions, efficient refinement and computation to reconstruct a 3D density map, and finally appropriate choice of modeling tools to construct atomic models for functional interpretation. This progress illustrates the power of cryoEM and ushers it into the arsenal of structural biology, alongside conventional techniques of X-ray crystallography and NMR, as a major tool (and sometimes the preferred one) for the studies of molecular interactions in supramolecular assemblies or machines.

Solution structure and characterisation of the human pyruvate dehydrogenase complex core assembly

Mammalian pyruvate dehydrogenase complex (PDC) is a key multi-enzyme assembly that is responsible for glucose homeostasis maintenance and conversion of pyruvate into acetyl-CoA. It comprises a central pentagonal dodecahedral core consisting of two subunit types (E2 and E3BP) to which peripheral enzymes (E1 and E3) bind tightly but non-covalently. Currently, there are two conflicting models of PDC (E2+E3BP) core organisation: the 'addition' model (60+12) and the 'substitution' model (48+12). Here we present the first ever low-resolution structures of human recombinant full-length PDC core (rE2/E3BP), truncated PDC core (tE2/E3BP) and native bovine heart PDC core (bE2/E3BP) obtained by small-angle X-ray scattering and small-angle neutron scattering. These structures, corroborated by negative-stain and cryo electron microscopy data, clearly reveal open pentagonal core faces, favouring the 'substitution' model of core organisation. The native and recombinant core structures are all similar to the truncated bacterial E2 core crystal structure obtained previously. Cryo-electron microscopy reconstructions of rE2/E3BP and rE2/E3BP:E3 directly confirm that the core has open pentagonal faces, agree with scattering-derived models and show density extending outwards from their surfaces, which is much more structurally ordered in the presence of E3. Additionally, analytical ultracentrifugation characterisation of rE2/E3BP, rE2 (full-length recombinant E2-only) and tE2/E3BP supports the substitution model. Superimposition of the small-angle neutron scattering tE2/E3BP and truncated bacterial E2 crystal structures demonstrates conservation of the overall pentagonal dodecahedral morphology, despite evolutionary diversity. In addition, unfolding studies using circular dichroism and tryptophan fluorescence spectroscopy show that the rE2/E3BP is less stable than its rE2 counterpart, indicative of a role for E3BP in core destabilisation. The architectural complexity and lower stability of the E2/E3BP core may be of benefit to mammals, where sophisticated fine-tuning is required for cores with optimal catalytic and regulatory efficiencies.

X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution

Crystallography supplies unparalleled detail on structural information critical for mechanistic analyses; however, it is restricted to describing low energy conformations of macromolecules within crystal lattices. Small angle X-ray scattering (SAXS) offers complementary information about macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, but without the size limitations inherent in NMR and electron microscopy studies. Together these techniques can allow multi-scale modeling to create complete and accurate images of macromolecules for modeling allosteric mechanisms, supramolecular complexes, and dynamic molecular machines acting in diverse processes ranging from eukaryotic DNA replication, recombination and repair to microbial membrane secretion and assembly systems. This review addresses both theoretical and practical concepts, concerns and considerations for using these techniques in conjunction with computational methods to productively combine solution scattering data with high-resolution structures. Detailed aspects of SAXS experimental results are considered with a focus on data interpretation tools suitable to model protein and nucleic acid macromolecular structures, including membrane protein, RNA, DNA, and protein-nucleic acid complexes. The methods discussed provide the basis to examine molecular interactions in solution and to study macromolecular flexibility and conformational changes that have become increasingly relevant for accurate understanding, simulation, and prediction of mechanisms in structural cell biology and nanotechnology.

Structures of the human pyruvate dehydrogenase complex cores: a highly conserved catalytic center with flexible N-terminal domains

Dihydrolipoyl acetyltransferase (E2) is the central component of pyruvate dehydrogenase complex (PDC), which converts pyruvate to acetyl-CoA. Structural comparison by cryo-electron microscopy (cryo-EM) of the human full-length and truncated E2 (tE2) cores revealed flexible linkers emanating from the edges of trimers of the internal catalytic domains. Using the secondary structure constraints revealed in our 8 A cryo-EM reconstruction and the prokaryotic tE2 atomic structure as a template, we derived a pseudo atomic model of human tE2. The active sites are conserved between prokaryotic tE2 and human tE2. However, marked structural differences are apparent in the hairpin domain and in the N-terminal helix connected to the flexible linker. These permutations away from the catalytic center likely impart structures needed to integrate a second component into the inner core and provide a sturdy base for the linker that holds the pyruvate dehydrogenase for access by the E2-bound regulatory kinase/phosphatase components in humans.

Thorough validation of protein normal mode analysis: a comparative study with essential dynamics

The deformation patterns of a large set of representative proteins determined by essential dynamics extracted from atomistic simulations and coarse-grained normal mode analysis are compared. Our analysis shows that the deformational space obtained with both approaches is quite similar when taking into account a representative number of modes. The results provide not only a comprehensive validation of the use of a low-frequency modal spectrum to describe protein flexibility, but also a complete picture of normal mode limitations.

DFprot: a webtool for predicting local chain deformability

DFprot is a web-based server for predicting main-chain deformability from a single protein conformation. The server automatically performs a normal-mode analysis (NMA) of the uploaded structure and calculates its capability to deform at each of its residues. Non-specialists can easily and rapidly obtain a quantitative first approximation of the flexibility of their structures with a simple and efficient interface.

AVAILABILITY

http://sbg.cib.csic.es/Software/DFprot.

An expanded conformation of single-ring GroEL-GroES complex encapsulates an 86 kDa substrate

Electron cryomicroscopy reveals an unprecedented conformation of the single-ring mutant of GroEL (SR398) bound to GroES in the presence of Mg-ATP. This conformation exhibits a considerable expansion of the folding cavity, with approximately 80% more volume than the X-ray structure of the equivalent cis cavity in the GroEL-GroES-(ADP)(7) complex. This expanded conformation can encapsulate an 86 kDa heterodimeric (alphabeta) assembly intermediate of mitochondrial branched-chain alpha-ketoacid dehydrogenase, the largest substrate ever observed to be cis encapsulated. The SR398-GroES-Mg-ATP complex is found to exist as a mixture of standard and expanded conformations, regardless of the absence or presence of the substrate. However, the presence of even a small substrate causes a pronounced bias toward the expanded conformation. Encapsulation of the large assembly intermediate is supported by a series of electron cryomicroscopy studies as well as the protection of both alpha and beta subunits of the substrate from tryptic digestion.

Packing regularities in biological structures relate to their dynamics

The high packing density inside proteins leads to certain geometric regularities and also is one of the most important contributors to the high extent of cooperativity manifested by proteins in their cohesive domain motions. The orientations between neighboring nonbonded residues in proteins substantially follow the similar geometric regularities, regardless of whether the residues are on the surface or buried, a direct result of hydrophobicity forces. These orientations are relatively fixed and correspond closely to small deformations from those of the face-centered cubic lattice, which is the way in which identical spheres pack at the highest density. Packing density also is related to the extent of conservation of residues, and we show this relationship for residue packing densities by averaging over a large sample or residue packings. There are three regimes: (1) over a broad range of packing densities the relationship between sequence entropy and inverse packing density is nearly linear, (2) over a limited range of low packing densities the sequence entropy is nearly constant, and (3) at extremely low packing densities the sequence entropy is highly variable. These packing results provide important justification for the simple elastic network models that have been shown for a large number of proteins to represent protein dynamics so successfully, even when the models are extremely coarse grained. Elastic network models for polymeric chains are simple and could be combined with these protein elastic networks to represent partially denatured parts of proteins. Finally, we show results of applications of the elastic network model to study the functional motions of the ribosome, based on its known structure. These results indicate expected correlations among its components for the step-wise processing steps in protein synthesis, and suggest ways to use these elastic network models to develop more detailed mechanisms, an important possibility because most experiments yield only static structures.

Interpreting Correlated Motions Using Normal Mode Analysis

With the increased popularity of normal mode analyses in structural biology, it is important to carefully consider how to best utilize the results for gaining biological insights without over interpretation. The discussion in this article argues that for the purpose of identifying correlated motions in biomolecules, a case separate from concomitant conformational changes of structural motifs, it is generally important to use a large number of normal modes. This is illustrated through three increasingly complex examples. The simplest case includes two bilinearly coupled harmonic oscillators and serves as a straightforward problem where the important considerations are explicit and transparent. The argument is then generalized to include a system of N-coupled harmonic oscillators and finally to a realistic biomolecule. Although a small number of normal modes are useful for probing structural flexibility, it is clear that a much larger number of modes are required for properly investigating correlated motions in biomolecules.

A New Method for Coarse-Grained Elastic Normal-Mode Analysis

In this paper, we report a new method for coarse-grained elastic normal-mode analysis. The purpose is to overcome a long-standing problem in the conventional analysis called the tip effect that makes the motional patterns (eigenvectors) of some low-frequency modes irrational. The new method retains the merits of a conventional method such as not requiring lengthy initial energy minimization, which always distorts structures, and also delivers substantially more accurate low-frequency modes with no tip effect for proteins of any size. This improvement of modes is crucial for certain types of applications such as structural refinement or normal-mode-based sampling.

The Allosteric Mechanism of Yeast Chorismate Mutase: A Dynamic Analysis

The effector-regulated allosteric mechanism of yeast chorismate mutase (YCM) was studied by normal mode analysis and targeted molecular dynamics. The normal mode analysis shows that the conformational change between YCM in the R state and in the T state can be represented by a relatively small number of low-frequency modes. This suggests that the transition is coded in the structure and is likely to have a low energetic barrier. Quantitative comparisons (i.e. frequencies) between the low-frequency modes of YCM with and without effectors (modeled structures) reveal that the binding of Trp increases the global flexibility, whereas Tyr decreases global flexibility. The targeted molecular dynamics simulation of substrate analog release from the YCM active site suggests that a series of residues are critical for orienting and "recruiting" the substrate. The simulation led to the switching of a series of substrate-release-coupled salt-bridge partners in the ligand-binding domain; similar changes occur in the transition between YCM R-state and T-state crystal structures. Thus, the normal mode analysis and targeted molecular dynamics results provide evidence that the effectors regulate YCM activity by influencing the global flexibility. The change in flexibility is coupled to the binding of substrate to the T state and release of the product from the R state, respectively.

Can conformational change be described by only a few normal modes?

We suggest a simple method to assess how many normal modes are needed to map a conformational change. By projecting the conformational change onto a subspace of the normal-mode vectors and using root mean square deviation as a test of accuracy, we find that the first 20 modes only contribute 50% or less of the total conformational change in four test cases (myosin, calmodulin, NtrC, and hemoglobin). In some allosteric systems, like the molecular switch NtrC, the conformational change is localized to a limited number of residues. We find that many more modes are necessary to accurately map this collective displacement. In addition, the normal-mode "spectra" can provide useful information about the details of the conformational change, especially when comparing structures with different bound ligands, in this case, calmodulin. Indeed, this approach presents normal-mode analysis as a useful basis in which to capture the mechanism of conformational change, and shows that the number of normal modes needed to capture the essential collective motions of atoms should be chosen according to the required accuracy.

Combining electron microscopy and comparative protein structure modeling

Recently, advances have been made in methods and applications that integrate electron microscopy density maps and comparative modeling to produce atomic structures of macromolecular assemblies. Electron microscopy can benefit from comparative modeling through the fitting of comparative models into electron microscopy density maps. Also, comparative modeling can benefit from electron microscopy through the use of intermediate-resolution density maps in fold recognition, template selection and sequence-structure alignment.

Usefulness and limitations of normal mode analysis in modeling dynamics of biomolecular complexes

Various types of large-amplitude molecular deformation are ubiquitously involved in the functions of biological macromolecules, especially supramolecular complexes. They can be very effectively analyzed by normal mode analysis with well-established procedures. However, despite its enormous success in numerous applications, certain issues related to the applications of normal mode analysis require further discussion. In this review, the author addresses some common issues so as to raise the awareness of the usefulness and limitations of the method in the general community of structural biology.

The role of shape in determining molecular motions

We examined the role of molecular shape in determining the patterns of low-frequency deformational motions of biological macromolecules. The low-frequency subspace of eigenvectors in normal mode analysis was found to be robustly similar upon randomization of the Hessian matrix elements as long as the structure of the matrix is maintained, which indicates that the global shape of molecules plays a more dominant role in determining the highly anisotropic low-frequency motions than the absolute values of stiffness and directionality of local interactions. The results provided a quantitative foundation for the validity of elastic normal mode analysis.

A structural perspective on protein-protein interactions

Structures of macromolecular complexes are necessary for a mechanistic description of biochemical and cellular processes. They can be solved by experimental methods, such as X-ray crystallography, NMR spectroscopy and electron microscopy, as well as by computational protein structure prediction, docking and bioinformatics. Recent advances and applications of these methods emphasize the need for hybrid approaches that combine a variety of data to achieve better efficiency, accuracy, resolution and completeness.

Theoretical analysis of twist/bend ratio and mechanical moduli of bacterial flagellar hook and filament

Certain motile bacteria employ rotating flagella for propulsion. The relative flexibility of two key components of the flagellum, filament and hook, is partially responsible for the mechanistic workings of this motor. A new computational method, the quantized elastic deformational model, was employed in this article to calculate the dimensionless twist/bend ratio (EI/GJ) of the filament and hook, providing a quantitative means to compare their relative stiffness. Both ratios were much <1.0, an average of 0.0440 for the filament and 0.0512 for the hook, indicating that within each structure bending is favored over twisting. These two ratios, along with previous experimental measurements, allowed us to propose a theoretical Young's modulus (E) between 10(6) and 10(7) dyn/cm(2) for the hook. This value is orders of magnitude smaller than experimentally determined Young's moduli of the filament, hence in agreement with empirical evidence linking compliance in the flagellum mainly to the hook.

New advances in normal mode analysis of supermolecular complexes and applications to structural refinement

Normal mode analysis is an effective computational method for studying large-amplitude low-frequency molecular deformations that are ubiquitously involved in the functions of biological macromolecules, especially supermolecular complexes. The recent years have witnessed a substantial advance in methodology development in the field. This review is intended to summarize some of the important advances that enable one to simulate deformations of supermolecular complexes at expended resolution- and length-scales, with particular emphasis on the implications in structural refinement against low- to intermediate-resolution structural data such as those from electron cryomicroscopy and fibre diffraction.

The crystal structure of murine p97/VCP at 3.6A

p97/VCP is a member of the AAA ATPase family and has roles in both membrane fusion and ubiquitin dependent protein degradation. Here, we present a 3.6A crystal structure of murine p97 in which D2 domain has been modelled as poly-alanine and the remaining approximately 100 residues are absent. The resulting structure illustrates a head-to-tail packing arrangement of the two p97 AAA domains in a natural hexameric state with D1 ADP bound and D2 nucleotide free. The head-to-tail packing arrangement observed in this structure is in contrast to our previously predicted tail-to-tail packing model. The linker between the D1 and D2 domains is partially disordered, suggesting a flexible nature. Normal mode analysis of the crystal structure suggests anti-correlated motions and distinct conformational states of the two AAA domains.

Conformational sampling for the impatient

Several new methods for sampling conformations of biomolecules have appeared recently. A brief review thereof is presented, with particular emphasis on applications that have been published, and suitability for different kinds of systems. Four methods (namely: RESPA, replica-exchange molecular dynamics, CONCOORD and Gaussian network method) are readily applicable for biomolecular systems.

Organization of the cores of the mammalian pyruvate dehydrogenase complex formed by E2 and E2 plus the E3-binding protein and their capacities to bind the E1 and E3 components

The subunits of the dihydrolipoyl acetyltransferase (E2) component of mammalian pyruvate dehydrogenase complex can form a 60-mer via association of the C-terminal I domain of E2 at the vertices of a dodecahedron. Exterior to this inner core structure, E2 has a pyruvate dehydrogenase component (E1)-binding domain followed by two lipoyl domains, all connected by mobile linker regions. The assembled core structure of mammalian pyruvate dehydrogenase complex also includes the dihydrolipoyl dehydrogenase (E3)-binding protein (E3BP) that binds the I domain of E2 by its C-terminal I' domain. E3BP similarly has linker regions connecting an E3-binding domain and a lipoyl domain. The composition of E2.E3BP was thought to be 60 E2 plus approximately 12 E3BP. We have prepared homogenous human components. E2 and E2.E3BP have s(20,w) values of 36 S and 31.8 S, respectively. Equilibrium sedimentation and small angle x-ray scattering studies indicate that E2.E3BP has lower total mass than E2, and small angle x-ray scattering showed that E3 binds to E2.E3BP outside the central dodecahedron. In the presence of saturating levels of E1, E2 bound approximately 60 E1 and maximally sedimented 64.4 +/- 1.5 S faster than E2, whereas E1-saturated E2.E3BP maximally sedimented 49.5 +/- 1.4 S faster than E2.E3BP. Based on the impact on sedimentation rates by bound E1, we estimate fewer E1 (approximately 12) were bound by E2.E3BP than by E2. The findings of a smaller E2.E3BP mass and a lower capacity to bind E1 support the smaller E3BP substituting for E2 subunits rather than adding to the 60-mer. We describe a substitution model in which 12 I' domains of E3BP replace 12 I domains of E2 by forming 6 dimer edges that are symmetrically located in the dodecahedron structure. Twelve E3 dimers were bound per E248.E3BP12 mass, which is consistent with this model.