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Recent advances in structural biophysics and integrative modelling methods now allow us to decipher the structures of large macromolecular assemblies. Understanding the dynamics and mechanisms involved in their biological function requires rigorous integration of all available data. We have developed a complete modelling pipeline that includes analyses to extract biologically significant information by consistently combining automated and interactive human-guided steps. We illustrate this idea with two examples. First, we describe the ryanodine receptor, an ion channel that controls ion flux across the cell membrane through transitions between open and closed states. The conformational changes associated with the transitions are small compared to the considerable system size of the receptor; it is challenging to consistently track these states with the available cryo-EM structures. The second example involves homologous recombination, in which long filaments of a recombinase protein and DNA catalyse the exchange of homologous DNA strands to reliably repair DNA double-strand breaks. The nucleoprotein filament reaction intermediates in this process are short-lived and heterogeneous, making their structures particularly elusive. The pipeline we describe, which incorporates experimental and theoretical knowledge combined with state-of-the-art interactive and immersive modelling tools, can help overcome these challenges. In both examples, we point to new insights into biological processes that arise from such interdisciplinary approaches.

Protein filaments are dynamic entities that respond to external stimuli by slightly or substantially modifying the internal binding geometries between successive protomers. This results in overall changes in the filament architecture, which are difficult to model due to the helical character of the system. Here, we describe how distortions in RecA nucleofilaments and their consequences on the filament-DNA and bound DNA-DNA interactions at different stages of the homologous recombination process can be modeled using the PTools/Heligeom software and subsequent molecular dynamics simulation with NAMD. Modeling methods dealing with helical macromolecular objects typically rely on symmetric assemblies and take advantage of known symmetry descriptors. Other methods dealing with single objects, such as MMTK or VMD, do not integrate the specificities of regular assemblies. By basing the model building on binding geometries at the protomer-protomer level, PTools/Heligeom frees the building process from a priori knowledge of the system topology and enables irregular architectures and symmetry disruption to be accounted for. Graphical abstract: [Image: see text] Model of ATP hydrolysis-induced distortions in the recombinant nucleoprotein, obtained by combining RecA-DNA and two RecA-RecA binding geometries.

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International audience; Although they play a significant part in the regulation of microtubule structure, dynamics and function, the disordered C-terminal tails of tubulin remain invisible to experimental structural methods and do not appear in the crystallographic structures that are currently available in the Protein Data Bank. Interestingly, these tails concentrate most of the sequence variability between tubulin isotypes, and are the sites of the principal post-translational modifications undergone by this protein. Using homology modeling, we developed two complete models for the human αI/βI and αI/βIII tubulin isotypes that include their C-terminal tails. We then investigated the conformational variability of the two β-tails using long time-scale classical Molecular Dynamics (MD) simulations that revealed similar features, notably the unexpected presence of common anchoring regions on the surface of the tuulin dimer, but also distinctive mobility or interaction patterns, some of which could be related to the tail lengths and charge distributions. We also observed in our simulations that the C-terminal tail from the βI isotype, but not the βIII, formed contacts in the putative binding site of a recently discovered peptide that disrupts microtubule formation in glioma cells. Hindering the binding site in the βI isotype would be consistent with this peptide’s preferential disruption of microtubule formation in glioma, whose cells overexpress βIII, compared to normal glial cells. While these observations need to be confirmed with more intensive sampling, our study opens up new perspectives for the development of isotype-specific chemotherapy drugs.

The number of local minima of the potential energy landscape (PEL) of molecular systems generally grows exponentially with the number of degrees of freedom, so that a crucial property of PEL exploration algorithms is their ability to identify local minima, which are low lying and diverse. In this work, we present a new exploration algorithm, retaining the ability of basin hopping (BH) to identify local minima, and that of transition based rapidly exploring random trees (T-RRT) to foster the exploration of yet unexplored regions. This ability is obtained by interleaving calls to the extension procedures of BH and T-RRT, and we show tuning the balance between these two types of calls allows the algorithm to focus on low lying regions. Computational efficiency is obtained using state-of-the art data structures, in particular for searching approximate nearest neighbors in metric spaces. We present results for the BLN69, a protein model whose conformational space has dimension 207 and whose PEL has been studied exhaustively. On this system, we show that the propensity of our algorithm to explore low lying regions of the landscape significantly outperforms those of BH and T-RRT.

We present novel algorithms and software addressing four core problemsin computational structural biology, namely analyzing a conformationalensemble, comparing two conformational ensembles, analyzing a sampledenergy landscape, and comparing two sampled energy landscapes. Usingrecent developments in computational topology, graph theory, andcombinatorial optimization, we make two notable contributions. First,we a present a generic algorithm analyzing height fields. We then usethis algorithm to perform density based clustering of conformations,and to analyze a sampled energy landscape in terms of basins andtransitions between them. In both cases, topological persistence isused to manage ruggedness. Second, we introduce two algorithms tocompare transition graphs. The first is the classical earth mover distance metric which depends only on local minimum energyconfigurations along with their statistical weights, while the secondincorporates topological constraints inherent to conformationaltransitions.Illustrations are provided on a simplified protein model (BLN69), whosefrustrated potential energy landscape has been thoroughly studied.The software implementing our tools is also made available, and shouldprove valuable wherever conformational ensembles and energy landscapesare used.

The buried surface area (BSA), which measures the size of the interface in a protein-protein complex may differ from the accessible surface area (ASA) lost upon association (which we call DSA), if conformation changes take place. To evaluate the DSA, we measure the ASA of the interface atoms in the bound and unbound states of the components of 144 protein-protein complexes taken from the Protein-Protein Interaction Affinity Database of Kastritis et al. (2011). We observe differences exceeding 20%, and a systematic bias in the distribution. On average, the ASA calculated in the bound state of the components is 3.3% greater than in their unbound state, and the BSA, 7% greater than the DSA. The bias is observed even in complexes where the conformation changes are small. An examination of the bound and unbound structures points to a possible origin: local movements optimize contacts with the other component at the cost of internal contacts, and presumably also the binding free energy.

We compare the changes in side chain conformations that accompany the formation of protein–protein complexes, in residues forming either the interface or the remainder of the solvent-accessible surface of the proteins in the Docking Benchmark 3.0. We find that the interface residues undergo significantly more changes than other surface residues, and these changes are more likely to convert them from a high-energy torsion angle state to a lower-energy one than the reverse. Moreover, in both the unbound proteins and the complexes, the interface residues are more frequently found to be in a high-energy torsion angle state than the noninterface residues. As these differences exist before the binding step, they may be relevant to specificity and help in identifying binding sites for docking predictions. Proteins 2010. © 2010 Wiley-Liss, Inc.

Breaking ties: The antitumour protein, neocarzinostatin (NCS), is one of the few drug-carrying proteins used in human therapeutics. However, the presence of disulfide bonds limits this protein's potential development for many applications. This study describes a generic directed-evolution approach starting from NCS-3.24 (shown in the figure complexed with two testosterone molecules) to engineer stable disulfide-free NCS variants suitable for a variety of purposes, including intracellular applications.The chromoprotein neocarzinostatin (NCS) has been intensively studied for its antitumour properties. It has recently been redesigned as a potential drug-carrying scaffold. A potential limit of this protein scaffold, especially for intracellular applications, is the presence of disulfide bonds. The objective of this work was to create a disulfide-free NCS-derived scaffold. A generic targeted approach was developed by using directed evolution methods. As a starting point we used a previously engineered NCS variant in which a hapten binding site had been created. A library was then generated in which cysteine Cys88 and Cys93 and neighbouring residues were randomly substituted. Variants that preserved the hapten binding function were selected by phage display and further screened by colony filtration methods. Several sequences with common features emerged from this process. The corresponding proteins were expressed, purified and their biophysical properties characterised. How these selected sequences rescued folding ability and stability of the disulfide-free protein was carefully examined by using calorimetry and the results were interpreted with molecular simulation techniques.

In most cases, scratching of the surface of a polymeric glass elicits brittle behavior. Industrial solutions have been successfully used to improve the scratch resistance of polymeric glasses and a common way is to coat the substrate with a thin film. However, one of the limitations of this method is the risk of cracking and chipping. The origin of the success of the coating technique is still of great research interest and further work will be required to explain the improvement in scratch resistance and predict the cracking in anti-scratch coatings. The present study contributes to these aims. Using a single-asperity scratching device allowing in situ observation of the scratch, the fracturing of a thin (3.5 μm) nano-composite coating deposited on a viscoelastic–viscoplastic substrate (polycarbonate) was investigated under different conditions of temperature and scratching speed. Four types of fracture mechanisms were observed, depending on these two variables. The processes involved in deformation of the system were: (i) delamination (blister formation) and fracture (chipping) of the coating and (ii) viscoelastic–viscoplastic deformation of the substrate. Image analyses were performed on video sequences of the different processes leading to damage of the film. The quantitative results are discussed in terms of the damage mechanisms involved.

International audience; Describing biological macromolecular energetics from computer simulations can pose major challenges, and often necessitates enhanced conformational sampling. We describe the calculation of conformational free-energy profiles along carefully chosen collective coordinates: “consensus” normal modes, developed recently as robust alternatives to conventional normal modes. In an application to the HIV-1 protease, we obtain efficient sampling of significant flap opening movements governing inhibitor binding from relatively short simulations, in close correspondence with experimental results.

The number of local minima of the potential energy landscape (PEL) of molecular systems generally grows exponentially with the number of degrees of freedom, so that a crucial property of PEL exploration algorithms is their ability to identify local minima, which are low lying and diverse. In this work, we present a new exploration algorithm, retaining the ability of basin hopping (BH) to identify local minima, and that of transition based rapidly exploring random trees (T-RRT) to foster the exploration of yet unexplored regions. This ability is obtained by interleaving calls to the extension procedures of BH and T-RRT, and we show tuning the balance between these two types of calls allows the algorithm to focus on low lying regions. Computational efficiency is obtained using state-of-the art data structures, in particular for searching approximate nearest neighbors in metric spaces. We present results for the BLN69, a protein model whose conformational space has dimension 207 and whose PEL has been studied exhaustively. On this system, we show that the propensity of our algorithm to explore low lying regions of the landscape significantly outperforms those of BH and T-RRT.

NFL-TBS.40–63 is a 24 amino acid peptide corresponding to the tubulin-binding site located on the light neurofilament subunit, which selectively enters glioblastoma cells, where it disrupts their microtubule network and inhibits their proliferation. We investigated its structural variability and binding modes on a tubulin heterodimer using a combination of NMR experiments, docking, and molecular dynamics (MD) simulations. Our results show that, while lacking a stable structure, the peptide preferentially binds on a specific single site located near the β-tubulin C-terminal end, thus giving us precious hints regarding the mechanism of action of the NFL-TBS.40–63 peptide’s antimitotic activity at the molecular level.

It is still difficult to obtain a precise structural description of the transition between the deoxy T-state and oxy R-state conformations of human hemoglobin, despite a large number of experimental studies. We used molecular dynamics with the Path Exploration with Distance Constraints (PEDC) method to provide new insights into the allosteric mechanism at the atomic level, by simulating the T-to-R transition. The T-state molecule in the absence of ligands was seen to have a natural propensity for dimer rotation, which nevertheless would be hampered by steric hindrance in the "joint" region. The binding of a ligand to the α subunit would prevent such hindrance due to the coupling between this region and the α proximal histidine, and thus facilitate completion of the dimer rotation. Near the end of this quaternary transition, the "switch" region adopts the R conformation, resulting in a shift of the β proximal histidine. This leads to a sliding of the β -heme, the effect of which is to open the β -heme's distal side, increasing the accessibility of the Fe atom and thereby the affinity of the protein. Our simulations are globally consistent with the Perutz strereochemical mechanism.

In order to further characterize the previously observed disruptive effect of the RNA polymerase I promoter sequence (Pol I) from Acanthamoeba castellanii on tandemly repeated 5S rDNA positioning sequences from sea urchin (Lytechinus variegatus), we compared the histone-binding ability of the isolated 199-bp Pol I promoter region to that of the 208-bp 5S rDNA and that of nucleosome core particle sequences isolated from chicken erythocytes. We found the 5S rDNA positioning sequence to be more efficient at forming nucleosomes than the RNA polymerase I promoter sequence. Nevertheless, examination of the free-DNA half-depletion points during the titrations suggested that twice as much histone had bound to RNA polymerase I promoter sequence as to the 5S nucleosome-positioning or core particle sequences. DNA bending analysis suggested two potential DNA bending loci in the RNA polymerase I promoter, whereas only one such locus was predicted for the 5S positioning sequence. Such mixed bending signals on the RNA polymerase I promoter could favor non-nucleosomal deposition of histones on these sequences.

We present novel algorithms and software addressing four core problems in computational structural biology, namely analyzing a conformational ensemble, comparing two conformational ensembles, analyzing a sampled energy landscape, and comparing two sampled energy landscapes. Using recent developments in computational topology, graph theory, and combinatorial optimization, we make two notable contributions. First, we present a generic algorithm analyzing height fields. We then use this algorithm to perform density-based clustering of conformations, and to analyze a sampled energy landscape in terms of basins and transitions between them. In both cases, topological persistence is used to manage (geometric) frustration. Second, we introduce two algorithms to compare transition graphs. The first is the classical earth mover distance metric which depends only on local minimum energy configurations along with their statistical weights, while the second incorporates topological constraints inherent to conformational transitions. Illustrations are provided on a simplified protein model (BLN69), whose frustrated potential energy landscape has been thoroughly studied. The software implementing our tools is also made available, and should prove valuable wherever conformational ensembles and energy landscapes are used.

We derive a series of novel mean-field potentials from statistical analyses of protein-protein contact regions in crystal structures. These potentials are parameterized in terms of the number of contacts made by an atom in an interface region. Such an explicit number dependence avoids the pairwise assumption and is intrinsically softer than distance-based approaches. It appears well suited to protein-protein docking applications, for which detailed interface geometry is generally lacking. In tests including protein complex reconstitution and docking of independently determined protein structures, we show that a hydrophobic potential of this type performs remarkably well, identifying native-like complexes by their favourable potential energies and in several cases demonstrating a recognition energy gap of 4-8 kcal/mol according to the system.

International audience; While proteins and nucleic acids are the fundamental components of an organism, Biology itself is based on the interactions they make with each other. Analyzing macromolecular interactions typically requires handling systems involving from two to hundreds of polypeptide chains. After a brief overview of the modeling challenges faced in computational structural biology, this chapter presents concepts and tools aiming at improving our understanding of the link between the static structures of macromolecular complexes and their biophysical/biological properties. We discuss geometrical approaches suited to atomic-resolution complexes and to large protein assemblies; for each, we also present examples of their successful application in quantifying and interpreting biological data. This methodology includes state-of-the-art geometric analyses of surface area, volume, curvature, and topological properties (isolated components, cavities, voids, cycles) related to Voronoï constructions in the context of structure analysis. On the applied side, we present novel insights into real biological problems gained thanks to these modeling tools.

Base stacking is one of the primary factors stabilizing nucleic acid structure. Yet, methods for locating stacking interactions in DNA and RNA are rare and methods for displaying stacking are rarer still. We present here simple, automated procedures to search nucleic acid molecules for base-base and base-oxygen stacking and to display these interactions graphically in a manner that readily conveys both the location and the quality of the interaction. The method makes no a priori assumptions about relative base positions when searching for stacking, nor does it rely on empirical energy functions. This is a distinct advantage for two reasons. First, the relative contributions of the forces stabilizing stacked bases are unknown. Second, the electrostatic and hydrophobic components of base stacking are both poorly defined by existing potential energy functions.

Unfixed chicken erythrocyte chromatin fibers in very low salt have been imaged with a scanning force microscope operating in the tapping mode in air at ambient humidity. These images reveal a three-dimensional organization of the fibers. The planar "zig-zag" conformation is rare, and extended "beads-on-a-string" fibers are seen only in chromatin depleted of histones H1 and H5. Glutaraldehyde fixation reveals very similar structures. Fibers fixed in 10 mM salt appear somewhat more compacted. These results, when compared with modeling studies, suggest that chromatin fibers may exist as irregular three-dimensional arrays of nucleosomes even at low ionic strength.

International audience; The CAPRI (Critical Assessment of Predicted Interactions) and CASP (Critical Assessment of protein Structure Prediction) experiments have demonstrated the power of community-wide tests of methodology in assessing the current state of the art and spurring progress in the very challenging areas of protein docking and structure prediction. We sought to bring the power of community-wide experiments to bear on a very challenging protein design problem that provides a complementary but equally fundamental test of current understanding of protein-binding thermodynamics. We have generated a number of designed protein-protein interfaces with very favorable computed binding energies but which do not appear to be formed in experiments, suggesting that there may be important physical chemistry missing in the energy calculations. A total of 28 research groups took up the challenge of determining what is missing: we provided structures of 87 designed complexes and 120 naturally occurring complexes and asked participants to identify energetic contributions and/or structural features that distinguish between the two sets. The community found that electrostatics and solvation terms partially distinguish the designs from the natural complexes, largely due to the nonpolar character of the designed interactions. Beyond this polarity difference, the community found that the designed binding surfaces were, on average, structurally less embedded in the designed monomers, suggesting that backbone conformational rigidity at the designed surface is important for realization of the designed function. These results can be used to improve computational design strategies, but there is still much to be learned; for example, one designed complex, which does form in experiments, was classified by all metrics as a nonbinder.

It is now well recognized that receptor flexibility plays an important role in protein-ligand binding. This flexibility can concern not only the mobility and reorganization of side chains in the binding site but also conformational changes of the whole molecule, which makes modeling of ligand docking more challenging. We give here an overview of existing approaches to treating receptor flexibility in protein-ligand docking and virtual screening that range from approximate to more accurate methods, including the use of normal modes in accounting for global conformational changes of the receptor or the use of more precise force fields. In addition, we describe recent successful applications of such approaches that have led to the design or discovery of new lead compounds with therapeutic relevance. These new developments in protein-ligand docking and screening are increasingly applied for better prediction of binding affinities. In view of the ever-increasing power of machine computation, a better accounting of the flexibility of the receptor is justified in order to improve the prediction of ligand binding in the search for new drug candidates by virtual screening.

Background Cathepsin B (catB) is a promising target for anti-cancer drug design due to its implication in several steps of tumorigenesis. catB activity and inhibition are pH-dependent, making it difficult to identify efficient inhibitor candidates for clinical trials. In addition it is known that heparin binding stabilizes the enzyme in alkaline conditions. However, the molecular mechanism of stabilization is not well understood, indicating the need for more detailed structural and dynamic studies in order to clarify the influence of pH and heparin binding on catB stability. Results Our pKa calculations of catB titratable residues revealed distinct protonation states under different pH conditions for six key residues, of which four lie in the crucial interdomain interface. This implies changes in the overall charge distribution at the catB surface, as revealed by calculation of the electrostatic potential. We identified two basic surface regions as possible heparin binding sites, which were confirmed by docking calculations. Molecular dynamics (MD) of both apo catB and catB-heparin complexes were performed using protonation states for catB residues corresponding to the relevant acidic or alkaline conditions. The MD of apo catB at pH 5.5 was very stable, and presented the highest number and occupancy of hydrogen bonds within the inter-domain interface. In contrast, under alkaline conditions the enzyme's overall flexibility was increased: interactions between active site residues were lost, helical content decreased, and domain separation was observed as well as high-amplitude motions of the occluding loop – a main target of drug design studies. Essential dynamics analysis revealed that heparin binding modulates large amplitude motions promoting rearrangement of contacts between catB domains, thus favoring the maintenance of helical content as well as active site stability. Conclusions The results of our study contribute to unraveling the molecular events involved in catB inactivation in alkaline pH, highlighting the fact that protonation changes of few residues can alter the overall dynamics of an enzyme. Moreover, we propose an allosteric role for heparin in the regulation of catB stability in such a manner that the restriction of enzyme flexibility would allow the establishment of stronger contacts and thus the maintenance of overall structure.

International audience; Small G-proteins of the superfamily Ras function as molecular switches, interacting with different cellular partners according to their activation state. G-protein activation involves the dissociation of bound GDP and its replacement by GTP, in an exchange reaction that is accelerated and regulated in the cell by guanine-nucleotide exchange factors (GEFs). Large conformational changes accompany the exchange reaction, and our understanding of the mechanism is correspondingly incomplete. However, much knowledge has been derived from structural studies of blocked or inactive mutant GEFs, which presumably closely represent intermediates in the exchange reaction and yet which are by design incompetent for carrying out the nucleotide exchange reaction. In this study we have used comparative modelling to recreate an exchange-competent form of a late, pre-GDP-ejection intermediate species in Arf1, a well-characterized small G-protein. We extensively characterized three distinct models of this intermediate using molecular dynamics simulations, allowing us to address ambiguities related to the mutant structural studies. We observed in particular the unfavorable nature of Mg 2z associated forms of the complex and the establishment of closer Arf1-GEF contacts in its absence. The results of this study shed light on GEF-mediated activation of this small G protein and on predicting the fate of the Mg ion at a critical point in the exchange reaction. The structural models themselves furnish additional targets for interfacial inhibitor design, a promising direction for exploring potentially druggable targets with high biological specificity.

International audience; Protein flexibility is essential for enzymatic function, ligand binding, and protein–protein or protein–nucleic acid interactions. Normal mode analysis has increasingly been shown to be well suited for studying such flexibility, as it can be used to identify favorable structural deformations that correspond to functional motions. However, normal modes are strictly relevant to a single structure, reflecting a particular minimum on a complex energy surface, and are thus susceptible to artifacts. We describe a new theoretical framework for determining ‘‘consensus’’ normal modes from a set of related structures, such as those issuing from a short molecular dynamics simulation. This approach is more robust than standard normal mode analysis, and provides higher collectivity and symmetry properties. In an application to HIV-1 protease, the low-frequency consensus modes describe biologically relevant motions including flap openingand closing that can be used in interpreting structural changes accompanying the bindingof widely differing inhibitors.

International audience; Recent studies of the mechanisms involved in the regulation of gene expression in eukaryotic organisms depict a highly complex process requiring a coordinated rearrangement of numerous molecules to mediate DNA accessibility. Silencing in Saccharomyces cerevisiae involves the Sir family of proteins. Sir3p, originally described as repressing key areas of the yeast genome through interactions with the tails of histones H3 and H4, appears to have additional roles in that process, including involvement with a DNA binding component. Our in vitro studies focused on the characterization of Sir3p-nucleic acid interactions and their biological functions in Sir3p-mediated silencing using binding assays, EM imaging, and theoretical modeling. Our results suggest that the initial Sir3p recruitment is partially DNA-driven, highly cooperative, and dependent on nucleosomal features other than histone tails. The initial step appears to be rapidly followed by the spreading of silencing using linker DNA as a track.

The pore activity of melittin and several chemically modified derivatives has been investigated using conductance measurements on planar lipid bilayers and marker release from small unilamellar vesicles. The modifications included N-terminal formylation, acetylation, succinylation and modification of the tryptophan residue. All of the compounds showed bilayer permeabilizing properties, though quantitative differences were evident. These comprised changes in the voltage dependence of the conductance, in the single-pore kinetics, in the concentration of aqueous peptide required to induce a given pore activity and in the apparent 'molecularity' reflected by the power law of its concentration dependence. A strong tendency for disrupting bilayers was not always correlated with strong pore activity. For a better understanding of these results, measurements of pore activity were complemented by studying the aggregation behavior in solution and the water-membrane partition equilibrium. Modifications of charged residues gave rise to significant changes in the aggregation properties, had virtually no influence on the partition coefficient. The latter decreased strongly, however, as a result of tryptophan modification. Analysis of the isotherms was consistent with the assumption that the arginine residues in melittin do not contribute very much to charge accumulation at the immediate membrane/water interface.

A straightforward hierarchical statistical-mechanical approach is shown to enable one to describe the stability of the alpha helix in the presence of side-chain interactions. The formulation can be used with even the simple nearest-neighbor models and it is demonstrated explicitly with the popular 2 x 2 Zimm-Bragg model [B. H. Zimm and J. K. Bragg (1959) J. Chem. Physics 31, 526-535]. It involves a conceptual dissection of the polypeptide chain into interacting blocks; the behavior of any block with side-chain interactions is treated then with conventional binding polynomial techniques. This dissection is a manifestation of "nesting," which is a hierarchical framework for the description of the behavior of complex macromolecules [C. H. Robert, H. Decker, B. Richey, S. J. Gill, and J. Wyman (1987) Proc. Natl. Acad. Sci. 84, 1891-1895]. The method is demonstrated through applications to existing, detailed data for the pH and salt dependences of the helix-coil transition in the S peptide and in synthetic peptides.

International audience; In mammals, the olfactory epithelium secretes odorant-binding proteins (OBPs), which are lipocalins found freely dissolved in the mucus layer protecting the olfactory neurons. OBPs may act as passive transporters of predominantly hydrophobic odorant molecules across the aqueous mucus layer, or they may play a more active role in which the olfactory neuronal receptor recognizes the OBP-ligand complex. To better understand the molecular events accompanying the initial steps in the olfaction process, we have performed molecular dynamics studies of rat and pig OBPs with the odorant molecule thymol. These calculations provide an atomic level description of conformational changes and pathway intermediates that remain difficult to study directly. A series of eight independent molecular dynamics trajectories of rat OBP permitted the observation of a consensus pathway for ligand unbinding and the calculation of the potential of mean force (PMF) along this path. Titration microcalorimetry confirmed the specific binding of thymol to this protein with a strong hydrophobic component. In both rat and pig OBPs we observed lipocalin strand pair opening in the presence of ligand, consistent with potential roles of these proteins in olfactive receptor recognition.

The proteins Arno and Gea2 of the Sec7 family can promote GDP–GTP exchange on Arf1, a small GTP-binding protein, which coordinates coated vesicle formation for protein transport within the cell. Crystal structures of the essential Sec7 domain (Sec7d) of Gea2 in the free and Arf1-bound forms suggest that conformational dynamics of the Sec7d as well as those of the G-protein play a role in nucleotide exchange. Starting from a set of complementary crystal structures, we compared the collective movements of unbound Gea2 and Arno Sec7 domains, Arf1-GDP, and the Arf1–Gea2(Sec7d) nucleotide-free complex using normal modes analyses. In all unbound Sec7d analyses, significant low-energy movements were found to lead to closure of the hydrophobic groove towards the form seen in the Arf1–Gea2(Sec7d) complex, suggesting that groove closure is a general feature of the Sec7 family. Low-energy movements in Arf1-GDP implicate critical switch 1 and 2 residues which are coupled to modifications in the myristoylated N-terminal-helix binding site at the other end of the “interswitch” beta hairpin. It is suggested that Sec7d groove closure upon docking of the two molecules may permit extraction of switch 1 from Arf1-GDP and prepare the complex for movement of the interswitch, which is central to the membrane-linked exchange activity. Large-scale collective movements in the Arf1–Sec7d complex appear to participate in the insertion of the Sec7d Glu finger into the GDP binding site to promote actual nucleotide release.

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We present a general mathematical treatment of marker efflux from liposomes or cells mediated by pore formation with the idea of using it in practice to obtain basic information about the underlying rates and mechanism. The approach encompasses permeation of molecules through any kind of pore-like defects in a cell membrane as they are induced by the action of some external agent. The approach broadens an earlier treatment to the more realistic general case in which a distribution of pore lifetimes must be taken into account. We derive a theoretical retention function describing the amount of marker remaining in the cells, formulated in terms of the pore activation and inactivation kinetics. The phenomenological efflux function evaluated directly from experimental data, is directly comparable with this retention function so long as the experimental signal is linearly related to the marker concentration. With the use of self-quenching dyes the relationship between signal and concentration is not, in general, linear, so that a more complicated treatment may be required. Even for these dyes, however, linearity holds under the frequently encountered condition of “all-or-none” release of dye from vesicles, a condition that can itself be verified experimentally.

We discuss the efflux of entrapped marker material from liposomes or cells through pores in the membrane, being monitored by the time course of a certain signal F (e.g., fluorescence emission). This is expressed in terms of an appropriate normalized function of time, the so-called efflux function E(t). Under conditions frequently encountered in practice the measured E(t) can be easily related to the forward rate of pore formation if the liposomes/cells are monodisperse in size. In the basic case of a time-independent rate law it turns out that E(t) must be single exponential. Deviations from such a simple functional behavior might be due to a fairly broad distribution of liposome/cell sizes and/or a more complicated pore formation mechanism. A relevant evaluation of original data is demonstrated making use of experimental results obtained with small unilamellar lipid vesicles where pores are induced by the antibiotic peptide alamethicin. This includes the application of a general method to eliminate the effect of a given liposome/cell size distribution.

Specification of the partition function; computation of average, or thermodynamic, state properties; and applications to calorimetric processes (enthalpy change of ligation of a macromolecule and dissolution of a slightly soluble solid).

A generalization of the allosteric model is presented that incorporates a hierarchy of conformational equilibria. Such a formulation draws upon structural organization already seen in many large macromolecular systems. The functional binding properties of the macromolecule reflect conformational equilibria at each structural level. Appropriate "nested" models are used to interpret structural features and functional aspects of two hemocyanin systems with a large number (12 and 24) of binding sites.

High-precision studies of oxygen binding in hemoglobin (HbA0) solutions at near-physiological concentrations (2-12 mM heme; pHs 7.0-9.1; various buffers) have led to an unanticipated result: an unmeasurably low contribution from the triply ligated species. We have obtained this result from new differential oxygen-binding measurements for human hemoglobin through the use of a thin-layer apparatus, which enables study of solutions at high Hb concentrations. The effect of tetramer dissociation into dimers, which becomes significant at hemoglobin concentrations below 1 mM in heme, is avoided. The analysis of the binding reactions is thus cast in terms of tetramer-binding polynomial written with overall Adair equilibrium constants which directly reflect the contributions of intermediate ligated species. The unmeasurable contribution of the triply ligated species renders the equilibrium constants of the third and fourth stepwise reactions practically undeterminable.

We have examined the competitive binding of oxygen and carbon monoxide to the multisubunit hemocyanin of the tarantula Eurypelma californicum. Employment of high-precision thin-layer methods has enabled detailed characterization of the pure oxygen and pure carbon monoxide binding curves, as well as binding curves performed under mixed-gas conditions. The pure oxygen binding curve and the displacement of oxygen by carbon monoxide at full ligand saturation are highly cooperative, but in the absence of oxygen, carbon monoxide binds noncooperatively. The results were analyzed globally within the framework of a nested allosteric model [Robert, C.H., Decker, H., Richey, B., Gill, S.J., & Wyman, J. (1987) Proc. Natl. Acad. Sci. U.S.A. 84, 1891-1895] which takes into account the hierarchy of subunit structure present in the macromolecule. The use of two ligands enables one to recognize two distinct levels of allosteric interaction functioning in the protein assembly. The binding characteristics of the allosteric states demonstrated for Eurypelma follow a similar pattern as those found earlier for Homarus americanus.

A gas‐solution reaction microcalorimeter has been developed for measuring the heat produced from a macromolecule in solution when the partial pressure of a reacting ligand is changed. The accumulated result of such stepwise heat processes enables the construction of a heat binding curve: namely the enthalpy per mole of reaction site versus the logarithm of the ligand activity [Gill, Richey, Bishop, and Wyman, Biophys. Chem. 21, 1 (1985)]. The high sensitivity (1 μcal) of the calorimeter is achieved by careful twinning and closed‐loop proportional control achieved through continuous computer monitoring. A 15‐μl liquid sample, for example 5‐mM heme hemoglobin, is held in the form of a thin layer by means of a filter paper membrane. This configuration facilitates rapid equilibrium with exposed gases and allows for the completion of a given heat process within the range of 10 min. Gas partial pressures are accurately produced by means of a precision dilution valve incorporated into the calorimeter. The automa...

We have performed high-precision oxygen binding studies on human hemoglobin tetramers in the presence of a series of limited, subsaturating amounts of the effector compounds 2,3-diphosphoglycerate (DPG) and inositol hexaphosphate (IHP). The use of thin-layer optical methods enabled the use of high hemoglobin concentrations, preventing complications arising from the dissociation of the tetramer into dimers. Model-independent, simultaneous analysis of all data for each effector demonstrated that the intrinsic oxygen binding characteristics of the molecule are in agreement with those determined in earlier high-precision studies [e.g., Gill, S. J., Di Cera, E., Doyle, M. L., Bishop, G. A., & Robert, C. H. (1987) Biochemistry 26, 3995-4002] and that the affinity of the tetramer for the tightly binding effector IHP changes most markedly between the second and fourth oxygen binding steps, perhaps indicating a large conformational change. The data were then analyzed by using the truncated allosteric model [Di Cera, E., Robert, C. H., & Gill, S. J. (1987) Biochemistry 26, 4003-4008], which is based on the hypothesis that a quaternary conformational change occurs in the hemoglobin tetramer before the third and fourth oxygen molecules bind.

A quantitative measure of the validity of the MWC description of cooperative binding equilibria has been obtained which uses only the Adair constants. This is accomplished through simple relationships using the zeros of the Adair binding polynomial and unique properties of the zeros of MWC polynomials as described in the accompanying paper (W.E. Briggs, Biophys. Chem. 24 (1986) 311). The method is applied to oxygen binding to a large number of hemoglobins under a wide variety of conditions. In most cases, exemplified by human hemoglobin under a wide range of conditions, the MWC model is allowed and the probability of its suitability is determined. The probability given by this method correlates directly with the deviation between the experimental binding curve and that derived from the theory. In several cases the pattern of the Adair polynomial zeros immediately excludes the MWC model, most notably for carp hemoglobins. A physical picture of cooperative binding site interactions is nevertheless obtained from the patterns of zeros as they relate to the factorization of the binding polynomial.

Differential binding curve measurements for oxygen in the presence of fixed carbon dioxide activities have allowed a detailed determination of the linkage between carbon dioxide and the oxygenated intermediates of human hemoglobin. Model-independent analysis of the data shows that at pH 7.4: (1) the oxygen binding curves are asymmetrical, the population of the triply oxygenated species being negligible; (2) the shape of the oxygen binding curve is invariant with carbon dioxide activity; (3) the maximum linkage is -0.32 moles carbon dioxide per mole oxygen; and (4) the overall carbon dioxide-dependent shift in the oxygen binding curve cannot be explained in terms of carbamino formation alone, the additional influence of bicarbonate being required. An allosteric model that accounts for the low population of triply oxygenated hemoglobin species is employed here as a framework from which to explore the carbon dioxide linkage mechanism at the intermediate stages of oxygenation. Carbon dioxide binding constants are found to be 780 M-1 and 580 M-1 for carbon dioxide binding to the deoxygenated alpha and beta chains, respectively, and 150 M-1 for carbon dioxide binding to the oxygenated form of both chains, as determined by simultaneous fitting of the oxygen binding curves with the model. Finally, by use of the determined binding polynomial for the carbon dioxide-oxygen linkage scheme, we have constructed a series of linkage graphs.

Two high precision techniques, titration microcalorimetry and thin-layer optical binding measurements, have made possible the evaluation of enthalpy changes for the overall oxygenation reactions for human hemoglobin (HbAo). Although the heat of adding three oxygen molecules could not be evaluated due to the indeterminate contribution of this species to the oxygen binding curve of the protein (Gill, S. J., Di Cera, E., Doyle, M. L., Bishop, G. A., and Robert, C. H. (1987) Biochemistry, 26, 3995-4002), the heats for binding two and four oxygen molecules were found to be simple multiples of the first binding heat. A direct consequence of equal stepwise heats is invariance of the shape of the binding curve with temperature, as pointed out by Wyman (Wyman, J. (1939) J. Biol. Chem. 127, 581-599). Titration microcalorimetry was also performed for the binding of carbon monoxide to hemoglobin. While the tight binding of CO precludes high-precision binding measurements, it does allow one to accurately determine the heat of ligation as a function of the CO bound. In these titrations a uniform heat of reaction is not observed, but the heat of binding increases markedly near the end point. This implies that the stepwise binding enthalpy for adding the third CO molecule is anomalously endothermic and for adding the fourth strongly exothermic. A similar phenomenon cannot be ruled out in the case of oxygen because of imprecision intrinsic in the analysis of the weaker ligand binding.

A high precision, two-dimensional study of oxygen and carbon monoxide binding to Panulirus interruptus hemocyanin has been carried out. Global data analysis of three types of experiments, probing the molecule in its various states of CO and O2ligation, revealed the entire hexamer to be the basic allosteric unit involved in a two-state mechnism. The co-operativity and linkage of the two ligands are presented in terms of derivative Hill plot surfaces extended along co-ordinates of CO and O2 activities giving a detailed and comprehensive view of the binding behavior. Among the findings is an apparent high co-operativity of carbon monoxide binding at high oxygen activity. The results are discussed in view of a general mechanism for co-operative behavior found in larger hemocyanin aggregates concerning “nested” allosteric interactions.

We present a general framework for analysis of two closely related problems in biochemical studies: (1) The first is analysis of binding data obtained under conditions in which a second, linked ligand is present in limited total quantity. In such conditions the free activity of the second ligand varies throughout the primary ligand binding curve, and the resultant behavior can be quite complex. Analysis of such curves enables one to quantitatively extract detailed information regarding the linkage of the two ligands at intermediate stages of ligation. The treatment is applied in an accompanying paper to oxygen binding in human hemoglobin in the presence of organic phosphates [Robert, C.H., Fall, L., & Gill, S. J. (1988) Biochemistry (following paper in this issue)]. (2) The second treatment we outline regards the analogous problem of analyzing differential scanning calorimetry (DSC) data obtained for a macromolecule binding a ligand present in limited quantity. A simple model is presented that accounts for dual transitions like those already seen in DSC data for human serum albumin in the presence of nonsaturating amounts of fatty acids [Ross, P., & Shrake, A. (1987) Abstracts of the 42nd Calorimetry Conference, University of Colorado, Boulder, CO].

We have examined common methods of analysis of highly cooperative systems such as oxygen binding by hemoglobin and thermal denaturation. Through extensive simulation of ligand-binding data for a tetrameric macromolecule we show that careful attention must be paid to the formulation of the fitting function and to proper assessment of the number of parameters involved. We conclude that the partition function should be formulated in terms of overall reaction parameters as opposed to stepwise reaction parameters and that bias is introduced by fixing physical parameters such as extrapolated end points.

We examine the effects of concentration (aggregation), buffers, and ligation, under conditions of either constant ligand activity or limited total amount of ligand, upon thermal denaturation of macromolecules as measured by scanning calorimetry. In doing so we utilize and extend an earlier generalized allosteric treatment [S. J. Gill, B. Richey, G. Bishop, and J. Wyman (1985) Biophys. Chem. 21, 1-14], applicable to ligand binding, enthalpy changes, and volume changes in a macromolecular system. The approach is contrasted with formulations based on the idea of structural domains. We show how information from the full scanning calorimetric curves can be utilized in arriving at and testing appropriate models for observed behavior in selected examples.