Weighting functions and parameter resolvability for oxygenation data subject to error in the independent variable.

Parameter resolvability and bias has been investigated for weighted nonlinear regression of data where the independent variable is subject to instrumental uncertainty. The specific example of cooperative oxygenation of hemoglobin was studied, where fractional saturation is determined spectrophotometrically and the oxygen activity is measured with a Clark polarographic electrode. For this system the instrumental uncertainty in the oxygen electrode was measured directly and the influence of the uncertainties on resolution of oxygen binding parameters was determined by Monte Carlo simulations. Four weighting functions were tested for their ability to minimize parameter uncertainty and bias: (1) uniform weighting; (2) "propagated weighting" whereby uncertainties in the independent variable are propagated into and added to uncertainties of the dependent variable; (3) Hill plot transform, or "end weighting"; and (4) maximum likelihood analysis, where deviations between fitting function and data are minimized as weighted horizontal and vertical distance vectors. Results of the Monte Carlo simulations favor the use of either uniform weighting, propagated weighting, or maximum likelihood weighting methods. Use of the Hill transform as a weighting function produced poorer parameter resolvability and inaccurate representation of the data in general. Bias error was negligible for all weighting functions.     

Regulation of oxygen affinity by quaternary enhancement: Does hemoglobin ypsilanti represent an allosteric intermediate?

Recent crystallographic studies on the mutant human hemoglobin Ypsilanti (beta 99 Asp-->Tyr) have revealed a previously unknown quaternary structure called "quaternary Y" and suggested that the new structure may represent an important intermediate in the cooperative oxygenation pathway of normal hemoglobin. Here we measure the oxygenation and subunit assembly properties of hemoglobin Ypsilanti and five additional beta 99 mutants (Asp beta 99-->Val, Gly, Asn, Ala, His) to test for consistency between their energetics and those of the intermediate species of normal hemoglobin. Overall regulation of oxygen affinity in hemoglobin Ypsilanti is found to originate entirely from 2.6 kcal of quaternary enhancement, such that the tetramer oxygenation affinity is 85-fold higher than for binding to the dissociated dimers. Equal partitioning of this regulatory energy among the four tetrameric binding steps (0.65 kcal per oxygen) leads to a noncooperative isotherm with extremely high affinity (pmedian = .14 torr). Temperature and pH studies of dimer-tetramer assembly and sulfhydryl reaction kinetics suggest that oxygenation-dependent structural changes in hemoglobin Ypsilanti are small. These properties are quite different from the recently characterized allosteric intermediate, which has two ligands bound on the same side of the alpha 1 beta 2 interface (see ref. 1 for review). The combined results do, however, support the view that quaternary Y may represent the intermediate cooperativity state of normal hemoglobin that binds the last oxygen.     

Cooperative oxygen binding, subunit assembly, and sulfhydryl reaction kinetics of the eight cyanomet intermediate ligation states of human hemoglobin.

Correlations between the energetics of cooperativity and quaternary structural probes have recently been made for the intermediate ligation states of Hb [Daugherty et al. (1991) Proc. Natl. Acad. Sci. US 88, 1110-1114]. This has led to a "molecular code" which translates configurations of the 10 ligation states into switch points of quaternary transition according to a "symmetry rule"; T-->R quaternary structure change is governed by the presence of at least one heme-site ligand on each of the alpha beta dimeric half-molecules within the tetramer [see Ackers et al. (1992) Science 255, 54-63, for summary]. In order to further explore this and other features of the cooperative mechanism, we have used oxygen binding to probe the energetics and cooperativities for the vacant sites of the cyanomet ligation species. We have also probed structural aspects of all eight cyanomet ligation intermediates by means of sulfhydryl reaction kinetics. Our oxygen binding results, obtained from a combination of direct and indirect methods, demonstrate the same combinatorial aspect to cooperativity that is predicted by the symmetry rule. Overall oxygen affinities of the two singly-ligated species (alpha +CN beta)(alpha beta) and (alpha beta +CN)(alpha beta) were found to be identical (pmedian = 2.4 Torr). In contrast, the doubly-ligated species exhibited two distinct patterns of oxygen equilibria: the asymmetric species (alpha +CN beta +CN)(alpha beta) showed very high cooperativity (nmax = 1.94) and low affinity (pmedian = 6.0 Torr), while the other three doubly-ligated species showed diminished cooperativity (nmax = 1.23) and considerably higher oxygen affinity (pmedian = 0.4 Torr). Extremely high oxygen affinities were found for the triply-ligated species (alpha +CN beta +CN)(alpha beta +CN) and (alpha +CN beta +CN)(alpha +CN beta) (pmedian = 0.2 Torr). Their oxygen binding free energies are considerably more favorable than those of the alpha and beta subunits within the dissociated alpha beta dimer, demonstrating directly the quaternary enhancement effect, i.e., enhanced oxygen affinity at the last binding step of tetramer relative to the dissociated protomers. Oxygen binding free energies measured for the alpha subunit within the isolated (alpha beta +CN) dimer and for the beta subunit within the isolated (alpha +CN beta) dimer sum to the free energy for binding two oxygens to normal hemoglobin dimers (-16.3 +/- 0.2 versus -16.7 +/- 0.2, respectively), arguing against cooperativity in the isolated dimer. Correlations were established between cooperative free energies of the 10 cyanomet ligation microstates and the kinetics for reacting their free sulfhydryl groups.(ABSTRACT TRUNCATED AT 400 WORDS)     

Heterotropic effects of chloride on the ligation microstates of hemoglobin at constant water activity.

Dimer-tetramer assembly reactions of the 10 CN-met ligation microstates of hemoglobin (Hb) were analyzed as a function of NaCl concentration while maintaining constant water activity by the addition of compensating sucrose. The assembly free energy for fully ligated cyanomet Hb and for fully oxygenated Hb becomes less favorable by 1.8 kcal when [NaCl] is increased from 0.08 to 0.7 M, whereas that of unligated Hb is practically insensitive to changes in [NaCl]. Values of 1.6 and 0.3 mol chloride release were found for the assembly of fully ligated and deoxy Hb, respectively; i.e., a net release of 1.3 mol chloride is coupled to the ligation of tetramers for both oxygen and cyanomet ligation. The ligation-linked salt component at constant water activity was evaluated to be 1.0 mol for the full oxygenation of the Hb tetramer in agreement with the overall value previously reported. When the detailed salt linkages accompanying all 16 stepwise cyanomet ligation reactions were experimentally resolved, only two "chloride" effects were found. The first chloride effect correlates with the ligation steps, which create tertiary constraint, and the second effect is coupled to the six switchpoints of quaternary T-->R transition. The distribution of these chloride effects agrees closely with predictions of the "symmetry rule mechanism." The total chloride release for CN-met ligation is in good agreement with that for oxygenation. Free energy contributions to assembly and cooperativity arising from the osmotic effects of chloride were found to be small for all ligation species.     

Cooperative protein-DNA interactions: effects of KCl on lambda cI binding to OR.

The effects of monovalent salt activity on the site-specific and cooperative interactions of cI repressor with its three operator sites OR were studied by using quantitative DNase I footprint titration methods. Individual-site binding isotherms were obtained for binding repressor dimers to each site of wild-type OR and to mutant operator templates in which binding to one or two sites has been eliminated. The standard Gibbs energies for intrinsic binding, delta G1, delta G2, and delta G3, and cooperative interactions, delta G12 and delta G23, were determined at each condition (range 50-200 mM KCl). It is found that the dimer affinity for each of the three sites increases as [KCl] decreases, a striking result given that the monomer-dimer equilibrium shifts toward monomer formation under identical solution conditions [Koblan, K. S., & Ackers, G. K. (1991) Biochemistry (preceding paper in this issue)]. The magnitudes of ion-linked effects are found to differ at the three operator sites, while the intrinsic interaction binding free energies for sites OR1 and OR3 change in parallel over the entire range of [KCl]. The KCl dependencies at OR1 and OR3 represent the average release of 3.7 +/- 0.6 and 3.8 +/- 0.6 apparent ions, respectively. By contrast, the KCl dependency of OR2 binding corresponds to the displacement of 5.2 +/- 0.7 apparent ions. The ability of cI repressor to discriminate between the three operator sites thus appears linked to ion binding/release reactions.     

Analysis of calorimetric data for isodesmic self-associating systems.

ATP and respiration (NADH)-driven NAD(P)⁺ transhydrogenase (EC 1.6.1.1) activities are low in membranes from Escherichia coli cultured on yeast extract medium (17 and 21 nmol/min × mg) but high on glucose (82 and 142 nmol/min × mg). The ATPase and respiratory activities in both cases appeared comparable. Growth of the bacteria in yeast extract medium followed by washing and replacement into a glucose medium showed that after 3 h the energy-linked and energy-independent NAD(P)⁺ transhydrogenase (reduction of acetylpyridine NAD⁺ by NADPH) activities had appeared simultaneously. Incorporation of chloramphenicol or omission of glucose in the induction medium resulted in no increase in these activities indicating that de novo protein synthesis is required for the induction of energy-linked and -independent NAD(P)⁺ transhydrogenase. It was found that the K_m values for acetylpyridine NAD⁺ and NADPH for the energy-independent reaction in membranes from glucose grown cells (143 and 62 μm) were similar to those in membranes from cells grown on glucose-yeast extract (135 and 45 μm), respectively, but the maximum velocity at infinite acetyl pyridine NAD⁺ and NADPH increased from 353 to 2175 nmol/min × mg. Furthermore, the membrane-bound NAD(P)⁺ transhydrogenase in glucose-yeast extract grown cells showed substrate inhibition at high NADPH and low acetyl pyridine NAD⁺ levels. Further kinetic data demonstrate that the mechanism of the energy-independent NAD(P)⁺ transhydrogenase in E. coli is similar to that of the mitochondrial enzyme and exhibits similar responses to competitive inhibitors at the NAD⁺ and NADPH sites.     

The Gibbs conference on biothermodynamics: origins and evolution

The Gibbs conference on biothermodynamics arose in the late 1980's as a 'self-organized' endeavor by researchers at eleven institutions of the US. Over a period of 10 years these annual conferences have grown steadily in size. They have fostered the development of new thermodynamic approaches and their applications in biochemistry. By emphasizing participation by students and postdoctoral fellows they have contributed significantly to the career development of young scientists in this field.     

The OR control system of bacteriophage lambda. A physical-chemical model for gene regulation

A quantitative model has been developed for processes in the bacteriophage lambda that control the switchover from lysogenic to lytic modes of growth. These processes include the interactions of cI repressor and cro proteins at the three DNA sites of the right operator, OR, the binding of RNA polymerase at promoters PR and PRM, the synthesis of cI repressor and cro proteins, and the degradative action of recA during induction of lysis. The model is comprised of two major physical-chemical components: a statistical thermodynamic theory for relative probabilities of the various molecular configurations of the control system; and a kinetic model for the coupling of these probabilities to functional events, including synthesis of regulatory proteins cI and cro. Using independently evaluated interaction constants and rate parameters, the model was found capable of predicting essential physiological characteristics of the system over an extended time. Sufficiency of the model to predict known physiological properties lends credence to the physical-chemical assumptions used in its construction. Several major physiological characteristics were found to arise as "system properties" through the non-linear, time-dependent, feedback-modulated combinations of molecular interactions prescribed by the model. These include: maintenance of the lysogenic state in the absence of recA-mediated cI repressor degradation; induction of lysis and the phenomenon of subinduction; and autogenous negative control of cro. We have used the model to determine the roles, within the composite system, of several key molecular processes previously characterized by studies in vitro. These include: co-operativity in cI repressor binding to DNA; interactions between repressors and RNA polymerase (positive control); and the monomer-dimer association of cI repressor molecules. A major role of cI repressor co-operativity is found to be that of guaranteeing stability of the lysogenic state against minor changes in cI repressor levels within the cell. The role of positive control seems to be that of providing for a peaked, rather than monotonic, dependence of PRM activity on cI repressor level, while permitting PR activity to be a step function. The model correlates an immense body of studies in vivo and in vitro, and it makes testable predictions about molecular phenomena as well as physiological characteristics of bacteriophage lambda. The approach developed in this study can be extended to include more features of the lambda system and to treat other systems of gene regulation.