Evaluation of Hill slopes and Hill coefficients when the saturation binding or velocity is not known.

1. The Hill coefficient (nH), an often-used measure of deviations from hyperbolic behaviour (nonhyperbolicity) in kinetic and binding systems, is usually estimated from the maximum or minimum slope of the Hill plot. The method depends strongly on the assumed magnitude of the asymptotic velocity (V) or binding (P) whose evaluation may be difficult in nonlinear/co-operative systems. Therefore, alternative procedures were devised for the estimation nH which do not require the prior knowledge of V or P. 2. When pairs of velocity/binding readings (v and w) are obtained at concentrations of c and alpha c, respectively (where alpha is a fixed constant), then the relation between w and v is described by a hyperbola, provided that Hill's equation is valid. In this case, linearizing plots, v/w versus v, w versus, w/v, and 1/w versus 1/v, can be used for estimation of the degree of the equation. However, if the Hill expression is applicable, these methods are not efficient and traditional procedures, particularly nonlinear regression, should be used. 3. The 'linearizing' plots of the Hill equation can be applied advantageously for the evaluation of the Hill slope and of nH also in the general case, when the Hill expression is actually not valid, provided that deviations from hyperbolic behaviour are positive. Appropriately extrapolated intercepts of the first two plots estimate alphanH. Furthermore, the slope of the third plot yields, similarly to the method of Kurganov et al., a continuous measure of the Hill slope (including its maximum) at all concentrations. The agreement is, at positive nonhyperbolicities, excellent theoretical values of Hill slopes and coefficients and those estimated by the proposed methods. 4. A coefficient of nonhyperbolicity (theta) is defined for 2nd-degree rate equations which provides a quantitative measure of positive or negative deviation from first-degree, hyperbolic characteristics. It is closely related to the Hill coefficient.     

Ligand interaction energies and molecular recognition by chloramphenicol acetyltransferase.

The apparent binding energy for the interaction of the 3-hydroxyl group of chloramphenicol (CM) with the proposed general base (His-195) in chloramphenicol acetyltransferase (CAT) was determined by comparison of the dissociation constants of CM and 3-deoxyCM with CAT. The delta Gapp for this hydrogen bond to the N-3 of the imidazole ring is 1.5 kcal mol-1. Extending the use of modified ligands, in an approach which is complementary to that of site-directed mutagenesis, the binding affinity of each of a family of 3-halo-3-deoxychloramphenicol derivatives was observed to increase in the series F less than Cl less than Br less than I and is dominated by hydrophobic considerations. There is a linear free energy relationship between the dissociation constants for binding to CAT and an empirical hydrophobicity scale derived from reverse-phase HPLC retention times. The existence of such a relationship allows a true estimate of the total energetic contribution of interactions between the 3-hydroxyl group of CM and its contacts at the active site of CAT to be made on the basis of a regression analysis. The calculated value of delta Gbind (2.7 kcal mol-1) must include not only the hydrogen bond but also some favorable van der Waals interactions. The results demonstrate some of the advantages of an analysis of the energetics of ligand binding using modified ligands, in an approach that is formally analogous with and complementary to the use of site-directed mutations.(ABSTRACT TRUNCATED AT 250 WORDS)     

On the relationship between the Hill coefficients for steady-state and transient kinetic data: A criterion for concerted transitions in allosteric proteins

A frequently used measure for the extent of cooperativity in ligand binding by allosteric proteins is the Hill coefficient. Hill coefficients can be measured for steady-state kinetic data and also for transient kinetic data. Here, the relationship between the two types of Hill coefficients is analysed. It is shown that a value of 1 for the ratio of the two Hill coefficients is a test for a concerted ligand-induced transition between two conformations of the protein, in accordance with the Monod-Wyman-Changeux model. A value of 1 for this ratio has recently been observed for a series of chaperonin GroEL mutants suggesting that ATP-induced allosteric transitions in this protein are concerted.     

Lipoplex thermodynamics: determination of DNA-cationic lipoid interaction energies

An experimental study of the cationic lipid-DNA binding affinity is presented. The binding free energy was determined by monitoring lipoplex dissociation under conditions of increasing salt concentration. The primary procedure was based on the extent of quenching by energy transfer of fluorophores on DNA molecules by fluorophore on a lipid as these molecules came into close association in the lipoplex. Titration calorimetry on the Dickerson dodecamer was also done, with results that were in agreement with the fluorescence data. Measurements on short oligonucleotides allowed estimation of the binding energy per nucleotide. The binding free energy is approximately 0.6 kcal/mole nucleotide for the Dickerson dodecamer and declines for longer oligonucleotides. The entropy gained upon complex formation is approximately 1 entropy unit per released counterion. The method was applied to long DNA molecules (herring and lambda-phage DNA) and revealed that complete dissociation occurs at 750 mM NaCl. Likely contributions of macromolecular desolvation and DNA flexibility to the binding energy are discussed.     

Lectin-sugar interaction. Calculated versus experimental binding energies.

Although a steadily increasing number of protein--ligand docking experiments have been performed successfully, there are only few studies concerning protein--sugar interactions. In this study, we investigate the interaction of wheat germ agglutinin (WGA) with N-acetylglucosamine and a number of its derivatives and predict the binding free energies using flexible docking techniques. To assess the quality of our predictions, we also determined those binding free energies experimentally in cell-binding studies. The predicted binding site, ligand orientation, and details of the binding mode are in perfect agreement with the known crystal structure of WGA with a sialoglycopeptide. Furthermore, we obtained an excellent linear correlation of our predicted binding free energies with both our own data and experimental data from the literature [Monsigny, M., Roche, A.C., Sene, C., Maget Dana, R. & Delmotte, F. (1980) Eur. J. Biochem. 104, 147-153.]. In both cases, predicted energies were within 1.0 kJ x mol(-1) of the experimental value. These results illustrate the usefulness of docking-based methods for the qualitative and quantitative prediction of protein--carbohydrate interactions. The insights gained from such theoretical studies may be used to complement the results from the still scarce crystal structures.     

DNA-binding activity and subunit interaction of the mariner transposase

Mos1 is a member of the mariner/Tc1 family of transposable elements originally identified in Drosophila mauritiana. It has 28 bp terminal inverted repeats and like other elements of this type it transposes by a cut and paste mechanism, inserts at TA dinucleotides and codes for a transposase. This is the only protein required for transposition in vitro. We have investigated the DNA binding properties of Mos1 transposase and the role of transposase–transposase interactions in transposition. Purified transposase recognises the terminal inverted repeats of Mos1 due to a DNA-binding domain in the N-terminal 120 amino acids. This requires a putative helix–turn–helix motif between residues 88 and 108. Binding is preferentially to the right hand end, which differs at four positions from the repeat at the left end. Cleavage of Mos1 by transposase is also preferentially at the right hand end. Wild-type transposase monomers interact with each other in a yeast two-hybrid assay and we have used this to isolate mutations resulting in reduced interaction. These mutations lie along the length of the protein, indicating that transposase–transposase interactions are not due to a single interaction domain. One such mutation which retains both DNA-binding and catalytic activity has greatly reduced ability to excise Mos1 from plasmid DNA through coordinate cleavage of the two ends and transposition in vitro is lowered to a level 20-fold below that of the wild-type. This suggests that transposase–transposase interaction is required to form a synaptic complex necessary for coordinate cleavage at the ends of Mos1 during transposition. This mutant enzyme allows insertion at dinucleotides other than TA, including sequences with GC base pairs. This is the first example of a mariner/Tc1 transposase with altered target specificity.     

A simple method to identify supramolecules in action: Hill coefficients for exergonic self-assembly

Precise supramolecular architecture is often essential for significant function. Simple methods to reliably and rapidly demonstrate the existence of such supramolecular structure and function at relevant concentrations in complex systems are badly needed. Hill plots, describing the dependence of a signal on the n-th power of the monomer concentration, are compatible only with the identification of supramolecules that do not really exist, that is, endergonic self-assembly (Litvinchuk et al., J Am Chem Soc 2004;126:10067). Here, we show that the artificial increase in monomer concentration by chemical denaturation restores compatibility of Hill plots with exergonic self-assembly and affords Hill coefficients n > 1 for stable supramolecules. Recent rigid-rod pi-stack architecture with photosynthetic and ion channel activity is used as timely example, circular dichroism (CD) spectroscopy as method of choice for both sensitive and selective detection under relevant conditions.     

Functional interaction between Epstein-Barr virus DNA polymerase catalytic subunit and its accessory subunit in vitro.

The Epstein-Barr virus (EBV) DNA polymerase catalytic subunit (BALF5 protein) and its accessory subunit (BMRF1 protein) have been independently overexpressed and purified (T. Tsurumi, A. Kobayashi, K. Tamai, T. Daikoku, R. Kurachi, and Y. Nishiyama, J. Virol. 67:4651-4658, 1993; T. Tsurumi, J. Virol. 67:1681-1687, 1993). In an investigation of the molecular basis of protein-protein interactions between the subunits of the EBV DNA polymerase holoenzyme, we compared the DNA polymerase activity catalyzed by the BALF5 protein in the presence or absence of the BMRF1 polymerase accessory subunit in vitro. The DNA polymerase activity of the BALF5 polymerase catalytic subunit alone was sensitive to high ionic strength on an activated DNA template (80% inhibition at 100 mM ammonium sulfate). Addition of the polymerase accessory subunit to the reaction greatly enhanced DNA polymerase activity in the presence of high concentrations of ammonium sulfate (10-fold stimulation at 100 mM ammonium sulfate). Optimal stimulation was obtained when the molar ratio of BMRF1 protein to BALF5 protein was 2 or more. The DNA polymerase activity of the BALF5 protein along with the BMRF1 protein was neutralized by a monoclonal antibody to the BMRF1 protein, whereas that of the BALF5 protein alone was not, suggesting a specific interaction between the BALF5 protein and the BMRF1 protein in the reaction. The processivity of nucleotide polymerization of the BALF5 polymerase catalytic subunit on singly primed M13 single-stranded DNA circles was low (approximately 50 nucleotides). Addition of the BMRF1 polymerase accessory subunit resulted in a strikingly high processive mode of deoxynucleotide polymerization (> 7,200 nucleotides). These findings strongly suggest that the BMRF1 polymerase accessory subunit stabilizes interaction between the EBV DNA polymerase and primer template and functions as a sliding clamp at the growing 3'-OH end of the primer terminus to increase the processivity of polymerization.     

Perturbation of ribosome subunit interaction by glutaraldehyde fixation

Ultracentrifugal analysis of ribosomal purity is complicated by the rapid reequilibration of ribosomes with their subunits, and this is further enhanced by the effects of hydrostatic pressure. Fixation of the ribosome system prior to ultracentrifugal analysis supposedly freezes the reequilibration, and thus tends to obviate these difficulties. However, no redistribution of the ribosome-subunit population must be allowed to occur during fixation. Thus, it is necessary that fixation be extremely rapid compared to the ribosome-subunit reequilibration, in order to avoid errors in analysis. It was the purpose of this investigation to make a direct experimental comparison of the rates of these two processes, fixation and ribosome-subunit reequilibration, using the stopped-flow technique with a light-scattering detector, under a variety of buffer environment readjustments. The following findings resulted from this study: (1) Fixation in Tris buffers could not be followed by light scattering because of interaction of glutaraldehyde with Tris, leading to continuous production of high molecular weight contaminants. (2) Polymerization of glutaraldehyde leads to increased ultraviolet absorption, which must not be confused with scattering changes. (3) Undialyzed ribosome solutions prepared by dissolving stock suspensions stored at high levels of magnesium and univalent electrolyte into a known standard buffer produced solutions having free Mg2+ levels lower than those of original buffer, complicating kinetic observations and threatening ribosome stability. (4) Addition of malonic acid as a buffer for Mg2+ largely eliminated this problem. (5) The kinetics of glutaraldehyde were measured quantitatively by studying the perturbation of ribosome association and dissociation kinetics produced during shifts of Mg2+ levels. (6) At fixative levels not producing coagulation, fixation kinetics can be competitive with those of association-dissociation. (7) Mass action effects like those of dilution can be caused by fixation, and can give rise to excess subunits, which may be mistaken for loose couples in original ribosome preparations.     

Noncovalent interaction energies in covalent complexes: TEM-1 beta-lactamase and beta-lactams

The class A beta-lactamase TEM-1 is a key bacterial resistance enzyme against beta-lactam antibiotics, but little is known about the energetic bases for complementarity between TEM-1 and its inhibitors. Most inhibitors form a covalent adduct with the catalytic Ser70, making the measurement of equilibrium constants, and hence interaction energies, technically difficult. This study evaluates noncovalent interactions within covalent complexes by examining the differential stability of TEM-1 and its inhibitor adducts. The thermal denaturation of TEM-1 follows a two-state, reversible model with a melting temperature (T(m)) of 51.6C and a van't Hoff enthalpy of unfolding (DeltaH(VH)) of 146.2 kcal/mol at pH 7.0. The stability of the enzyme changes on forming an inhibitor adduct. As expected, some inhibitors stabilize TEM-1; transition-state analogues increase the T(m) by up to 3.7C (1.7 kcal/mol). Surprisingly, all beta-lactam covalent acyl--enzyme complexes tested destabilize TEM-1 significantly relative to the apo-enzyme. For instance, the clinically used inhibitor clavulanic acid and the beta-lactamase-resistant beta-lactams moxalactam and imipenem destabilize TEM-1 by over 2.6C (1.2 kcal/mol) in their covalent adducts. Based on the structure of the TEM-1/imipenem complex (Maveyraud et al., J Am Chem Soc 1998;120:9748--52), destabilization by moxalactam and imipenem is thought to be caused by a steric clash between the side-chain of Asn132 and the 6(7)-alpha group of these beta-lactams. To test this hypothesis, the mutant enzyme N132A was made. In contrast with wild-type, the covalent complexes between N132A and both imipenem and moxalactam stabilize the enzyme, consistent with the hypothesis. To investigate the structural bases of this dramatic change in stability, the structure of N132A/imipenem was determined by X-ray crystallography. In the complex with N132A, imipenem adopts a very different conformation from that observed in the wild-type complex, and the putative destabilizing interaction with residue 132 is relieved. Studies of several enzymes suggest that beta-lactams, and covalent inhibitors in general, can have either net favorable or net unfavorable noncovalent interaction energies within the covalent complex. In the case of TEM-1, such unfavorable interactions convert substrate analogues into very effective inhibitors.     

The anomalous variation of successive molecular ionization energies and the electron-vibrational interaction

In this work we point out the conditions which determine the anomalous variation of successive molecular ionization energies. It is shown that this variation arises when the strong electronvibrational interaction coming from the change of the number of electrons in a molecule exceeds the Coulomb electronic repulsion. The interrelation between this effect and the mechanism of the disproportionation reaction is discussed.     

Inferring topology from clustering coefficients in protein-protein interaction networks

Background  

Although protein-protein interaction networks determined with high-throughput methods are incomplete, they are commonly used to infer the topology of the complete interactome. These partial networks often show a scale-free behavior with only a few proteins having many and the majority having only a few connections. Recently, the possibility was suggested that this scale-free nature may not actually reflect the topology of the complete interactome but could also be due to the error proneness and incompleteness of large-scale experiments.     

Can interaction coefficients be determined from cencus data?

Summary The method of estimating interactions proposed independently by Pimm and Schoener is studied using field data from the community of rodents which lives in the arid, rocky habitats of Israel. One important problem the method addresses is how to remove the effects of habitat heterogeneity on the estimate. We tried six different variations of the analysis scheme outlined by Crowell and Pimm, and found their results qualitatively inconsistent. This was especially true when we compared the results produced from separate habitat variables with those produced from the principal components of the habitat variation.Another problem, this one not previously addressed, is great variation in the average abundance of the different species. We discovered that the ratio of the average abundances of two species is the best predictor of the value of their coefficients of interaction. Common species appear to have weak influence on rare ones; rare ones appear to have strong influence on common ones. The statistical mechanism which produces this relationship is clear, indicating that the relationship is an artifact.     

On the interaction of mitochondrial complex III with the Rieske iron-sulfur protein (subunit V).

Limited proteolysis of solubilized beef heart mitochondrial complex III with trypsin yields a product previously identified as fragment V" (González-Halphen, D., Lindorfer, M. A., and Capaldi, R. A. (1988) Biochemistry 27, 7021-7031). In this work, fragment V" was generated by trypsin treatment of both the intact complex III and the purified Rieske iron-sulfur protein. Thus, in its bound or isolated form, the same sites of subunit V are sensitive to protease action. Fragment V" was a soluble protein that retained its iron-sulfur moiety. It was purified by exclusion from a hydrophobic phenyl-Sepharose CL-4B column followed by gel filtration. In contrast to the pure, intact subunit V, fragment V" did not reconstitute oxidoreductase activity when combined with complex III devoid of subunit V. However, a 20-amino acid synthetic peptide carrying the sequence between amino acids Lys33 and Lys52 of the Rieske iron-sulfur protein competed with intact subunit V in reconstitution assays. The results obtained suggest that the iron-sulfur protein binds to complex III by hydrophobic protein-protein interactions, and that a nontransmembrane 18-amino acid amphipathic stretch accounts for the association of this subunit to the rest of the complex.     

A contribution to the theory of preferential interaction coefficients

A simple and complete derivation of the relation between concentration-based preferential interaction coefficients and integrals over the relevant pair correlation functions is presented for the first time. Certain omissions from the original treatment of pair correlation functions in multicomponent thermodynamics are also addressed. Connections between these concentration-based quantities and the more common molality-based preferential interaction coefficients are also derived. The pair correlation functions and preferential interaction coefficients of both solvent (water) and cosolvent (osmolyte) in the neighborhood of a macromolecule contain contributions from short-range repulsions and generic long-range attractions originating from the macromolecule, as well as from osmolyte-solvent exchange reactions beyond the macromolecular surface. These contributions are evaluated via a heuristic analysis that leads to simple insightful expressions for the preferential interaction coefficients in terms of the volumes excluded to the centers of the water and osmolyte molecules and a sum over the contributions of exchanging sites in the surrounding solution. The preferential interaction coefficients are predicted to exhibit the experimentally observed dependence on osmolyte concentration. Molality-based preferential interaction coefficients that were reported for seven different osmolytes interacting with bovine serum albumin are analyzed using the this formulation together with geometrical parameters reckoned from the crystal structure of human serum albumin. In all cases, the excluded volume contribution, which is the volume excluded to osmolyte centers minus that excluded to water centers in units of V1, exceeds in magnitude the contribution of the exchange reactions. Under the assumption that the exchange contribution is dominated by sites in the first surface-contiguous layer, the ratio of the average exchange constant to its neutral random value is determined for each osmolyte. These ratios all lie in the range 1.0 +/- 0.15, which indicates rather slight deviations from random occupation near the macromolecular surface. Finally, a mechanism is proposed whereby the chemical identity of an osmolyte might be concealed from partially ordered multilayers of water in clefts, grooves, and pits, and its consequences are noted.     

A calorimetric study of subunit interaction in immunoglobulin G

The non covalent interaction of the heavy and light chains of immuno-globulin G has been studied in a batch calorimeter and shown to be exothermic. The enthalpy of association ranged from ?5.6 to ?112.5 kJ/mole of heavy-light chain pairs formed at 25° for subunits derived from eight myeloma proteins. The values for kappa and lambda chains were not significantly different. The enthalpy showed a marked temperature dependance giving changes in heat capacity near -9kJ/deg/mole between 25° and 35° suggesting the involvement of apolar bonds in the association. However the large negative enthalpy of association suggests the presence of additional types of bonding.     

Computational estimation of specific side chain interaction energies in alpha helices

We have used a structure energy-based computer program developed for protein design, Perla, to provide theoretical estimates of all specific side chain-side chain interaction energies occurring in alpha helices. The computed side chain-side chain interaction energies were used as substitutes for the corresponding values used by the helix/coil transition algorithm, AGADIR. Predictions of peptide helical contents were nearly as successful as those obtained with the originally calibrated set of parameters; a correlation to experimentally observed alpha-helical populations of 0.91 proved that our theoretical estimates are reasonably correct for amino acid pairs that are frequent in our database of peptides. Furthermore, we have determined experimentally the previously uncharacterized interaction energies for Lys-Ile, Thr-Ile, and Phe-Ile amino acid pairs at i,i + 4 positions. The experimental values compare favorably with the computed theoretical estimates. Importantly, the computed values for Thr-Ile and Phe-Ile interactions are better than the energies based on chemical similarity, whereas for Lys-Ile they are similar. Thus, computational techniques can be used to provide precise energies for amino acid pairwise interactions, a fact that supports the development of structure energy-based computational tools for structure predictions and sequence design.