Resolvability of free energy changes for oxygen binding and subunit association by human hemoglobin

In vitro control analysis of an enzyme system: experimental and analytical developments

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, CLDH and Cpump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.

Analysis of drug-DNA binding isotherms: a Monte Carlo approach

Monte Carlo simulations of neighbor exclusion models have been used to demonstrate the importance of collecting and fitting data over a wide range of saturation. Low saturation data are important for good estimates of the affinity K of a drug or protein for the lattice site. High saturation data are important for distinguishing between negatively cooperative and noncooperative binding modes. Neglect of negative cooperativity (omega < 1) has in general little effect on the estimation of K. The error is mostly absorbed by increasing the value of n. This kind of behavior was previously observed with the fitting of nonideal, monomer-dimer, ultracentrifugation data where variations in B, the second virial coefficient, and K2, the dimerization equilibrium constant, are highly correlated, thus making their individual determination difficult. Within experimental error the distinction between a noncooperative model [Eq. (1)] and a negatively cooperative model [Eq. (3) or (4) with omega < 1] may require additional evidence to justify the choice of one model over another. For example, for homogeneous lattices of synthetic deoxyoligonucleotides, n may be constrained with some validity, thus allowing a more accurate and precise determination of K and omega. In fact, n may be established independently, for example, by nuclear magnetic resonance (NMR) methods. However, the assumption of an integral value of n for natural DNA samples may not be valid because of sequence heterogeneity. Unconstrained fitting of negatively cooperative data to Eq. (4) will thus be a very difficult problem (Table V). At an experimental error of only 2.3%, n and K can be reasonably determined but with a large error in omega. Data from the final 20% of saturation are essential in extracting omega. This may in part explain the absence of more reports of negatively cooperative behavior in the literature. This analysis is independent of the systematic error that may be induced by the transformation of data to the Scatchard plot, or the omission of drug self-association, or the occurrence of wall binding by ligand, or variable point density, or non-Gaussian noise, or the occurrence of another mode of binding distinct from the models of McGhee and von Hippel. Each of these will introduce additional error, possibly biased error, in the parameters estimated; however, this does not obviate our conclusion. Even under these ideal circumstances there are serious limitations that must be considered when fitting neighbor exclusion model data. The direct fitting of absorbance data [to Eq. (2) or functions that incorporate other parameters] will also be sensitive to these considerations.

Evaluation of Adair binding constants from experimental data obtained with an Imai cell. Statistical weighting functions

One group of laboratories uses an 'even-weighted', or unweighted, nonlinear least-squares method for the analysis of experimental oxygen binding data obtained with an Imai oxygenation apparatus. Another group uses an 'end-weighted' nonlinear least-squares analysis. With end weighting each observation is assigned a statistical weight which is proportional to Y(1-Y), where Y is the fractional saturation. In this work we discuss statistical weighting functions as applied to the Imai oxygenation apparatus and then determined what are the best weighting factors for an actual series of published experiments. Based on these calculations, it is concluded that the 'best' weighting for the Imai oxygenation apparatus is a very small amount of end weighting. Furthermore, the amount of end weighting is so small that even weighting, or no weighting at all, is also appropriate.

Consequences of neglecting the hemoglobin concentration on the determination of Adair binding constants

It is commonly believed that the tetrameric Adair constants for oxygen binding to human hemoglobin can be evaluated from a single oxygenation experiment at 'high' hemoglobin concentration without considering the consequence of the presence of alpha beta dimers. We present examples which demonstrate that this is a very dangerous assumption. Without a knowledge of the complete oxygenation-linked dimer-tetramer association reaction (alpha beta Xi----(alpha beta)2Xj), it is impossible to predict a priori how high of a hemoglobin concentration would be required to make this assumption. Furthermore, without a knowledge of the complete oxygenation-linked dimer-tetramer association reaction, it is impossible to predict a priori the direction and magnitude of the systematic errors which are induced by making this assumption.

Analysis of hemoglobin oxygenation from combined equilibrium and kinetic data. Is quaternary enhancement necessary?

An experimental approach based on four independent techniques, in which kinetic and equilibrium measurements of subunit assembly reactions are combined with concentration-dependent oxygen-binding curves, has previously been used to resolve parameters of the linkage system for human hemoglobin over a wide range of conditions [(G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A. 71 (1974) 4312; F.C. Mills et al., Biochemistry 15 (1976) 1093; M.L. Johnson et al., Biochemistry 15 (1976) 5363). Throughout this extensive body of results it has been found that the affinity for binding oxygen to tetramers at the fourth step exceeds the mean affinity of dissociated dimers. The existence of this "quaternary enhancement" effect has recently been questioned by Gibson and Edelstein (J. Biol. Chem. 262 (1987) 516) and by Philo and Lary (J. Biol. Chem. 265 (1990) 139) on the basis of kinetically derived oxygen-binding constants that do not exhibit quaternary enhancement. These authors have also suggested that quaternary enhancement might not be necessary to explain the oxygen-binding data mentioned above. In this study, we have explored the effect of constraining the numerical analysis of oxygen-binding data against the new kinetically derived binding constants. It is found that the sets of linkage constants which are compatible with both the oxygen-binding data and the new kinetically derived dimer binding constant require both quaternary enhancement and substantial dimer cooperativity. Increasing the dimer cooperativity to compensate completely for quaternary enhancement requires both dimeric and tetrameric binding constants that disagree with the kinetically derived values. Thus, the quaternary enhancement effect cannot be eliminated by readjustment of the remaining constants of the linkage system. Possible sources of the discrepancy between the kinetically derived binding constants and the otherwise self-consistent data from the other four techniques are discussed.