Tripeptide loop closure: a detailed study of reconstructions based on Ramachandran distributions

Tripeptide loop closure (TLC) is a standard procedure to reconstruct protein backbone conformations, by solving a zero dimensional polynomial system yielding up to 16 solutions. In this work, we first show that multiprecision is required in a TLC solver to guarantee the existence and the accuracy of solutions. We then compare solutions yielded by the TLC solver against tripeptides from the Protein Data Bank. We show that these solutions are geometrically diverse (up to 3å RMSD with respect to the data), and sound in terms of potential energy. Finally, we compare Ramachandran distributions of data and reconstructions for the three amino acids. The distribution of reconstructions in the second angular space (φ2 , ψ2) stands out, with a rather uniform distribution leaving a central void. We anticipate that these insights, coupled to our robust implementation in the (https://sbl.inria.fr/doc/Tripeptide_loop_closure-user-manual.html), will help understanding the properties of TLC reconstructions, with potential applications to the generation of conformations of flexible loops in particular. This article is protected by copyright. All rights reserved.

Pore formation kinetics in membranes, determined from the release of marker molecules out of liposomes or cells

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.

A soft, mean-field potential derived from crystal contacts for predicting protein-protein interactions

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.

Finding and visualizing nucleic acid base stacking

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.

Estimating friction coefficients of mixed globular/chain molecules, such as protein/DNA complexes

Existing methods for predicting translational friction properties of complex molecules start by explicitly building up their three-dimensional shape with spherical subunits. This treatment has been used especially for two types of systems: rigid assemblies and flexible chain molecules. However, many protein/DNA complexes such as chromatin consist of a small number of globular, relatively rigid, bound protein interspersed by long stretches of flexible DNA chain. I present a higher level of treatment of such macromolecules that avoids explicit subunit modeling as much as possible. An existing analytical formulation of the hydrodynamics equations is shown to be accurate when used with the present treatment. Thus the approach is fast and can be applied to hydrodynamic studies of highly degenerate multiple equilibria, such as those encountered in problems of the regulation of chromatin structure. I demonstrate the approach by predicting the effect of a hypothetical unwinding process in dinucleosomes and by simulating the distribution of sedimentation coefficients for cooperative and random models for a chromatin saturation process.

Significance of bound water to local chain conformations in protein crystals

We examine how the polypeptide chain in protein crystal structures exploits the multivalent hydrogen-bonding potential of bound water molecules. This shows that multiple interactions with a single water molecule tend to occur locally along the chain. A distinctive internal-coordinate representation of the local water-binding segments reveals several consensus conformations. The fractional water occupancy of each was found by comparison of the total number of conformations in the database regardless of the presence or absence of bound water. The water molecule appears particularly frequently in type II beta-turn geometries and an N-terminal helix feature. This work constitutes a first step into assessing not only the generality but also the significance of specific water binding in globular proteins.

Kinetics of pore-mediated release of marker molecules from liposomes or cells

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.

A combined study of aggregation, membrane affinity and pore activity of natural and modified melittin

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 hierarchical "nesting" approach to describe the stability of alpha helices with side-chain interactions

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.

Allosteric formulation of thermal transitions in macromolecules, including effects of ligand binding and oligomerization

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.

Binding of oxygen and carbon monoxide to the hemocyanin from the spiny lobster

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 O2 ligation, revealed the entire hexamer to be the basic allosteric unit involved in a two-state mechanism. 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.

Quantitative analysis of linkage in macromolecules when one ligand is present in limited total quantity

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].

Linkage of organic phosphates to oxygen binding in human hemoglobin at high concentrations

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.

Nested allosteric interaction in tarantula hemocyanin revealed through the binding of oxygen and carbon monoxide

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.

Analysis and parameter resolution in highly cooperative systems

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.

Carbon dioxide and oxygen linkage in human hemoglobin tetramers

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.

Calorimetric studies of oxygen and carbon monoxide binding to human hemoglobin. Sequential binding heats for oxygen

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.

Allosteric interpretation of the oxygen-binding reaction of human hemoglobin tetramers

An allosteric model is presented that provides a simple explanation for the low population of triply ligated species, relative to the other species, in the oxygenation of human hemoglobin tetramers as found in high-concentration studies [Gill, S. J., Di Cera, E., Doyle, M. L., Bishop, G. A., & Robert, C. H. (1987) Biochemistry (preceding paper in this issue)]. The model is a quantitative interpretation of the Perutz mechanism [Perutz, M. F. (1970) Nature (London) 228, 726-739] and is based on a number of structural and thermodynamic findings so far reported in the analysis of hemoglobin properties. Human hemoglobin is assumed to exist in two quaternary states: the T or low-affinity state and the R or high-affinity state. An extreme chain heterogeneity in the T state is postulated so that oxygen binds only to the alpha chains. Nearest-neighbor interactions between the alpha chains may lead to cooperativity within the T state. The R state is noncooperative, and both the alpha and beta chains have equal oxygen affinity.

Oxygen binding constants for human hemoglobin tetramers

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.

Nesting: hierarchies of allosteric interactions

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.

Cooperative free energies for nested allosteric models as applied to human hemoglobin

A model is developed for ligand binding to human hemoglobin that describes the detailed cooperative free-energies for each of the ten different ligated (cyanomet) species as observed by Smith and Ackers (Smith, F.R., and G.K. Ackers. 1985. Proc. Natl. Acad. Sci. USA.82:5347-5351). The approach taken here is an application of the general principle of hierarchical levels of allosteric control, or nesting, as suggested by Wyman (Wyman, J. 1972. Curr. Top. Cell. Reg. 6:207-223). The model is an extension of the simple two-state MWC model (Monod, J., J. Wyman, and J.P. Changeux. 1965. J. Mol. Biol. 12:88-118) using the idea of cooperative binding within the T (deoxy) form of the macromolecule, and has recently been described as a "cooperon" model (Di Cera, E. 1985. Ph.D. thesis). The T-state cooperative binding is described using simple interaction rules first devised by Pauling (Pauling, L. 1935. Proc. Natl. Acad. Sci. USA. 21:186-191). In this application three parameters suffice to describe the cooperative free-energies of the 10 ligated species of cyanomet hemoglobin. The redox process in the presence of cyanide, represented as a Hill plot, is simulated from Smith and Ackers' cooperative free-energies and is compared with available electrochemical binding measurements.

Analysis of zeros of binding polynomials for tetrameric hemoglobins

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.