Life and expectations post-kidney transplant: a qualitative analysis of patient responses

BACKGROUND

The effect of a kidney transplant on a recipient extends beyond the restoration of kidney function. However, there is limited qualitative analysis of recipient perspectives on life following transplantation, particularly in the United States. To understand the full patient experience, it is necessary to understand recipient views on life adjustments after kidney transplantation, medical management, and quality of life. This could lead to improvements in recipient care and sense of well-being.

METHODS

We conducted a paper-based survey from March 23 to October 1, 2015 of 476 kidney transplant recipients at the University of Michigan Health System in Ann Arbor, Michigan. We analyzed their open-ended responses using qualitative research methods. This is a companion analysis to a previous quantitative report on the closed-ended responses to that survey.

RESULTS

Common themes relating to changes following transplantation included: improvements in quality of life, a return to normalcy, better health and more energy. Concerns included: duration of graft survival, fears about one day returning to dialysis or needing to undergo another kidney transplant, comorbidities, future quality of life, and the cost and quality of their healthcare. Many recipients were grateful for their transplant, but some were anxious about the burdens transplantation placed on their loved ones.

CONCLUSIONS

While most recipients reported meaningful improvements in health and lifestyle after kidney transplantation, a minority of participants experienced declines in energy or health status. Worries about how long the transplant will function, future health, and cost and quality of healthcare are prevalent. Future research could study the effects of providing additional information, programs, and interventions following transplantation that target these concerns. This may better prepare and support kidney recipients and lead to improvements in the patient experience.

Comparison of patient and provider goals, expectations, and experiences following kidney transplantation

OBJECTIVE

This study examined whether kidney transplant recipients' post-transplant goals and expectations align with those as perceived by their healthcare providers.

METHODS

Post-transplant goals and expectations across four domains were assessed via a descriptive survey of healthcare providers (N=72) and kidney transplant recipients (N=476) at the University of Michigan from March 23 - October 1, 2015. Demographic and transplant-related data were collected via a retrospective review of medical records, and survey responses were compared using Chi-square tests, Wilcoxon two-sample tests, and logistic regression.

RESULTS

Patients expressed higher quality of life (mean Neuro-QOL T-score 60.2 vs. 52.7), were less likely to report that they were currently experiencing complications (11% vs. 24%), and anticipated their transplants to last longer (median 25 vs. 15 years) and to live longer (median 80 vs. 71 years) than providers expected for their typical patient. However, provider perceptions of patients' future ability to feel well, perform daily activities and work were significantly higher than those expressed by patients (all p<0.05).

CONCLUSION

Kidney transplant patient and provider expectations differ in significant ways.

PRACTICE IMPLICATIONS

Identified areas of discordance may provide opportunities for patients and providers to better evaluate treatment option tradeoffs in post-transplant clinical interactions.

An equation of state describing hydrophobic interactions

Several thermodynamic properties for the process of dissolution of pure hydrocarbons into water are found to be linearly related to the number of hydrogens on the hydrocarbon molecule. From the correlations found for the Gibbs energy change, enthalpy change, and heat capacity change, along with the use of an average minimum solubility temperature, an equation of state for the hydrophobic effect is derived. The entropy change upon dissolution per hydrocarbon hydrogen atom is close to -R ln 2. A model based upon a "tetrahedrally" localized water molecule with one corner defined by a carbon-hydrogen group and the other three corners defined by water molecules is used to estimate the observed entropy and heat capacity changes.

Partial molar heat capacities of the side chains of some amino acid residues in aqueous solution. The influence of the neighboring charges

Partial molar heat capacities of the side chains of some amino acid residues (Ala, Val, Leu, Ile, Ser) have been determined over a broad temperature range from calorimetric heat capacity measurements of the corresponding tripeptides and cyclodipeptides. The data obtained are compared with those determined earlier from the heat capacities of analog compounds. It is shown that in amino acids and even tripeptides of the Gly-X-Gly type, the influence of the end charges on the heat capacity of the side chain is rather significant even in buffered solutions of high ionic strength.

Ethanol-conditioned place preference is reduced in dopamine D2 receptor-deficient mice

Pharmacological blockade studies have supported a role of the dopamine system in ethanol reward for many years, but receptor subtype specificity has been difficult to establish. Recently, genetically engineered mice lacking functional dopamine D2 receptors have been shown to drink less ethanol in a two-bottle choice task. To determine whether reduced ethanol intake reflects a reduction in ethanol reward, D2 receptor-deficient [knockout (KO)] mice were compared to heterozygous (HET) and wild-type (WT; C57BL/6xDBA/2 F2 hybrid) mice in a place conditioning task. Under conditions that produced reliable place preference in both WT and HET mice, KO mice showed no evidence of place conditioning, suggesting that D2 receptor gene inactivation reduced ethanol reward or the ability to learn about ethanol reward. Consistent with previous findings, this mutation also produced a gene dose-related reduction in basal activity levels. Moreover, KO and HET mice showed enhancement of ethanol-stimulated activity relative to WT mice. However, differences in basal and ethanol-stimulated activity did not explain the differences in place conditioning. Overall, this study strongly supports the conclusion that dopamine D2 receptors normally influence ethanol reward in mice.

Nasopharyngeal rhabdomyosarcoma

Nasopharyngeal Rhabdomyosarcama, a common soft tissue sarcoma in children, is a rare identity, only four cases so far have been reported as per the review of literature. Ours is the fifth case presented exclusively in the nasopharynx, which is reported, hereby. The prognosis of this clinical entity is always gloomy and the modality of thr treatment is always surgery, chemotherapy and radiotherapy.

Determination of the carbon monoxide binding constants of myoglobin mutants: comparison of kinetic and equilibrium methods

The carbon monoxide (CO) binding constants of human myoglobin (Mb) and several single-site mutants have been determined using two different methods. In the kinetic method, which is commonly used for this ligand, the overall association (k(on)) and dissociation (k(off)) rates of CO were measured by flash photolysis and NO replacement, respectively, and the ratio k(on)/k(off) was calculated. In the equilibrium method, the binding constant Keq was measured directly using a thin-layer technique. These two measurements yield similar results for human wild-type Mb but differ significantly for some of the mutants. Possible reasons for these discrepancies are analyzed. A model assuming the presence of interconverting conformers with different association and dissociation rates is considered in light of infrared measurements on the CO stretching frequency in the MbCO forms of the same proteins [Balasubramanian et al. (1993a) Proc. Natl. Acad. Sci, U.S.A. 90, 4718]. It is suggested that in the case of some mutants which exhibit multiple conformations, this model may lead to nonequilibrium kinetics, which could produce the observed discrepancies between the kinetic and equilibrium determinations of the binding constant. These results suggest that both equilibrium and kinetic data should be obtained, even for a monomeric protein such as Mb, before the relative stabilities of mutants can be meaningfully compared.

Peptide-urea interactions as observed in diketopiperazine-urea cocrystal

In order to develop a more complete understanding of urea induced protein denaturation we have investigated the crystal structure of urea with the cyclic dipeptide diketopiperazine. This structure, determined to an R factor of 8.1%, shows extensive hydrogen bonding between urea and the peptide groups of diketopiperazine. These studies support a model where hydrogen bonding plays an important contribution in urea-induced protein denaturation. In the companion paper we present thermodynamic data for urea-peptide interactions in aqueous solution that further support this model.

A thin-layer gas-solution microcalorimeter for the determination of heat binding curves

A thin-layer gas-solution microcalorimeter has been developed to study the binding reactions of gaseous ligands with ligand binding macromolecules in solution. Gas partial pressures are accurately changed logarithmically by means of a precision dilution valve allowing for the stepwise determination of reaction heats. Heat binding curves are constructed in which the enthalpy per mole of reaction site is plotted versus the logarithm of the ligand activity. MicroJoule sensitivity is achieved through closed loop proportion computer control and precisely twinned highly isolated sample and reference geometry. The sample, typically 50 microliters and 1 to 4 mM heme protein, is placed on a filter paper membrane which acts as a matrix of support. This orientation allows for the rapid equilibrium of reacting ligand in approximately 10 min while not significantly altering the ligand activity. The system is controlled by computer measuring the heat of reaction as the partial pressure is changed automatically, typically by flushing the system with reacting ligand then reducing its partial pressure logarithmically with a nonreacting gas such as nitrogen. Binding curves can be constructed with as little as 20 nmol of oxygen binding sites.

Thin-layer microcalorimetric studies of oxygen and carbon monoxide binding to hemoglobin and myoglobin

A thin-layer gas-solution microcalorimeter has been developed to study the binding reactions of gaseous ligands with ligand binding macromolecules. We have measured the enthalpy of binding oxygen and carbon monoxide to horse myoglobin, human hemoglobin A0 and sperm whale myoglobin in phosphate buffer at pH 7.6, with the enzyme reducing system of Hayashi. Reactions of human hemoglobin were also done under various buffer conditions in order to elucidate the Bohr effect. These binding reactions were found not to exhibit a detectable enthalpy change over the temperature range of 10 degrees C to 25 degrees C. The enzyme reducing system was shown to react with oxygen in a manner that releases a substantial amount of heat. This problem was corrected by using a minimum amount and by placing the buffer and enzyme system in the reference cell effectively cancelling the oxygen enzyme reaction heat as well as the heat of gas dissolution. It was also demonstrated that glucose-6-phosphate, one of the reducing system components, in 50 mM concentrations can influence the heat of binding oxygen and carbon monoxide to hemoglobin. This effect was shown to be absent in the myoglobins and also with hemoglobin at glucose-6-phosphate concentrations less than 5 mM.

Oxygen binding constants and stepwise enthalpies for human and bovine hemoglobin at pH 7.6

A high-precision thin-layer gas-solution microcalorimeter has been developed to study the binding reactions of gaseous ligands with ligand-binding macromolecules in a manner analogous to that of the Gill thin-layer optical apparatus [Doleman & Gill (1976) Anal. Biochem. 87, 127]. We have generated differential heat-binding curves of oxygen binding to human and bovine hemoglobin in phosphate buffer at pH 7.6, with the enzyme-reducing system of Hayashi et al. [(1973) Biochim. Biophys. Acta 310, 309]. Experiments were conducted at a number of different temperatures in order to expand the data field, allowing for separation of enthalpy and free energy parameters. This type of experimental analysis makes no assumptions of optical linearity between the various heme groups and reveals that the triply ligated species is measurably significant for both human and bovine hemoglobin. It was also determined that the concentration of doubly ligated species of bovine hemoglobin is relatively low. The experiments indicate that the reactions for both hemoglobins are enthalpy-driven for oxygen stepwise additions 1, 2, and 4 while being entropy-driven for step 3. Human hemoglobin oxygen-binding experiments were also performed with the Gill thin-layer optical apparatus under solution conditions identical to those used in the calorimeter. The experiments revealed that if optical linearity is assumed, the overall third equilibrium constant is negative or near zero. This indicated that either the optical cell's performance is much poorer than the thin-layer calorimeter or there is an appreciable nonlinear optical effect.

Hydrogen exchange measurement of the free energy of structural and allosteric change in hemoglobin

The inability to localize and measure the free energy of protein structure and structure change severely limits protein structure-function investigations. The local unfolding model for protein hydrogen exchange quantitatively related the free energy of local structural stability with the hydrogen exchange rate of concerted sets of structurally related protons. In tests with a number of modified hemoglobin forms, the loss in structural free energy obtained locally from hydrogen exchange results matches the loss in allosteric free energy measured globally by oxygen-binding and subunit dissociation experiments.

Solid model compounds and the thermodynamics of protein unfolding

Analysis of thermodynamic data on the dissolution of solid cyclic dipeptides into water in terms of group additivity provides a rationale for the enthalpy and entropy convergence temperatures observed for small globular protein denaturation and the dissolution of model compounds into water. Convergence temperatures are temperatures at which the extrapolated enthalpy or entropy changes for a series of related compounds take on a common value. At these temperatures (TH* and TS*) the apolar contributions to the corresponding thermodynamic values (delta H degrees and delta S degrees) are shown to be zero. Other contributions such as hydrogen bonding and configurational effects can then be evaluated and their quantitative effects on the stability of globular proteins assessed. It is shown that the denaturational heat capacity is composed of a large positive contribution from the exposure of apolar groups and a significant negative contribution from the exposure of polar groups in agreement with previous results. The large apolar contribution suggests that a liquid hydrocarbon model of the hydrophobic effect does not accurately represent the apolar contribution to delta H degrees of denaturation. Rather, significant enthalpic stabilizing contributions are found to arise from peptide groups (hydrogen bonding). Combining the average structural features of globular proteins (i.e. number of residues, fraction of buried apolar groups and fraction of hydrogen bonds) with their specific group contributions permits a first-order prediction of the thermodynamic properties of proteins. The predicted values compare well with literature values for cytochrome c, myoglobin, ribonuclease A and lysozyme. The major thermodynamic features are described by the number of peptide and apolar groups in a given protein.

A dodecamer of globin chains is the principal functional subunit of the extracellular hemoglobin of Lumbricus terrestris

Repeated dissociation of the approximately 3600-kDa hexagonal bilayer extracellular hemoglobin of Lumbricus terrestris in 4 M urea followed by gel filtration at neutral pH produces a subunit that retains the oxygen affinity of the native molecule (approximately 12 torr), but only two-thirds of the cooperativity (nmax = 2.1 +/- 0.2 versus 3.3 +/- 0.3). The mass of this subunit was estimated to be 202 +/- 15 kDa by gel filtration and 202 +/- 26 kDa from mass measurements of unstained freeze-dried specimens by scanning transmission electron microscopy. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis of this subunit showed that it consists predominantly of the heme-containing subunits M (chain I, 17 kDa) and T (disulfide-bonded chains II-IV, 50 kDa). Mixing of subunits M and T isolated concurrently with the 200-kDa subunit resulted in partial association into particles that had a mass of 191 +/- 13 kDa determined by gel filtration and 200 +/- 38 kDa determined by scanning transmission electron microscopy and whose oxygen affinity and cooperativity were the same as those of the 200-kDa subunit. The results imply that the 200-kDa subunit is a dodecamer of globin chains, consisting of three copies each of subunits M and T (3 x chains (I + II + III + IV], in good agreement with the mass of 209 kDa calculated from the amino acid sequences of the four chains, and represents the largest functional subunit of Lumbricus hemoglobin. Twelve copies of this subunit would account for two-thirds of the total mass of the molecule, as suggested earlier (Vinogradov, S. N., Lugo, S. L., Mainwaring, M. G., Kapp, O. H., and Crewe, A. V. (1986) Proc. Natl. Acad. Sci. U. S. A. 83, 8034-8038). The retention of only partial cooperativity by the 200-kDa subunit implies that full cooperativity is dependent on the presence of a complete hexagonal bilayer structure, wherein 12 200-kDa subunits are linked together by approximately 30-kDa heme-deficient chains.

Nonlinear optical effects in oxygen-binding reactions of hemoglobin A0

Optical spectra have been taken in the Soret band (440-400 nm) under different oxygen partial pressures for hemoglobin (Hb) A0 at pH 7.0, 15 degrees C, 2-3 mM heme, 30 mM inositol hexaphosphate, 0.1 Hepes and 0.1 M NaCl. Application of the matrix method of singular value decomposition (SVD) to the difference spectra for different oxygen pressures shows the presence of at least two distinct optical transitions. From this result one concludes that the optical response to oxygen binding is nonlinear in the Soret band. The degree of nonlinearity has been determined by fitting the data at different wavelengths to the four-step reaction Adair equation with the inclusion of optical parameters that describe the intermediate oxygenated species. It is found that the data are well-represented by two optical parameters at each wavelengths, one which represents the optical change for the addition of the first and second oxygen molecules and the other which corresponds to the change for the addition of the third and fourth oxygen molecules. The ratio of these optical parameters depends only moderately upon wavelength with an average value of 0.8 over the Soret band. Thus, there is an approx. 20% smaller optical response for the first two ligated species than that for the last two ligated species. The overall Adair equilibrium constants are evaluated as follows: beta 1 = 0.081 +/- 0.003 Torr-1, beta 2 = 2.53 x 10(-3) +/- 2.4 x 10(-4) Torr-2, beta 3 = 1.25 x 10(-5) +/- 1.0 x 10(-6) Torr-3, beta 4 = 1.77 x 10(-6) +/- 1.5 x 10(-7) Torr-4.

Analysis of parameter resolution from derivatives of binding isotherms

Examination of binding information in the form of derivative (or finite difference) measurements is explored (1) experimentally by a thin-layer optical procedure (Dolman, D. & Gill, S. J. (1978) Anal. Biochem. 87, 127-134) and (2) theoretically by simulation in order to determine the influence of the number of data points and their standard error upon the resolvability of binding parameters in cooperative and non-cooperative systems. The data is described by the difference in optical absorbance divided by the change in the logarithm of the ligand activity and each data point is assumed to be influenced by a random error with a given variance. It is found that increasing the number of data points, which in turn effectively reduces the magnitude of the observed absorbance changes, results in an increase in the uncertainty of the resolved parameters of the system. The effect is verified by both experimental and simulation studies. Thus one is led to suggest that fewer measurements for the change of absorbance with larger magnitudes produces the most favorable situation for parameter resolution when the data is in the form of finite difference measurements.

Oxygenation properties of the two co-occurring hemoglobins of the tube worm Riftia pachyptila

Riftia pachyptila vascular blood and coelomic fluid contain two hemoglobin molecules that differ in their distribution and physical properties. The present study of the two isolated hemoglobins shows that both have an extremely high affinity for oxygen, but differ in their oxygenation characteristics. FI, the larger molecular weight (Mr) fraction (1,700,000), has a lower oxygen affinity, a well defined pH Bohr effect, and high cooperativity of oxygen binding. FII, the lower Mr fraction (400,000) has a higher oxygen affinity, no pH Bohr effect, and reduced cooperativity of oxygen binding. Both hemoglobins show marked effects of temperature on oxygen binding, and no effect of heme concentration or the presence of sulfide on oxygen affinity. The differences in the oxygenation properties and distribution of the two hemoglobins in the body fluids of Riftia pachyptila may allow them to play different roles in oxygen transport and storage for the animal which lives in the variable environment of the hydrothermal vents.

Common features of protein unfolding and dissolution of hydrophobic compounds

Protein unfolding and the dissolution of hydrophobic compounds (including solids, liquids, and gases) in water are characterized by a linear relation between entropy change and heat capacity change. The same slope is found for various classes of compounds, whereas the intercept depends on the particular class. The feature common to these processes is exposure of hydrophobic groups to water. These observations make possible the assignment of the heat capacity change to hydrophobic solvation and lead to the description of protein stability in terms of a hydrophobic and a nonhydrophobic contribution. A general representation of protein stability is given by the heat capacity change and the temperature.

Stabilization of the T-state of hemoglobin

The effect of inositol hexaphosphate and bezafibrate on binding of O2 and CO to HbAO at high concentrations (1 mM) has been evaluated using thin layer optical techniques. Data analysis shows 1) the occurrence of greatly reduced ligand dependent cooperativity (Hill slope of 2.23 for CO and 1.51 for O2), and 2) the presence of significant triply ligated species. The data fits a nested allosteric two-state MWC model in which the T state consists of two allosteric substrates, Tt and Tr, where Tt binds only to the alpha chains and Tr binds to both alpha and beta chains. The model indicates that the triply ligated species consists of a predominant amount of T form, agreeing with kinetic observations of CO ligated hemoglobin. The maximum amount of triply ligated R molecules (CO or O2) implicated is less than 1%, a result similar to that found previously for binding studies made in the absence of BZF and IHP.

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.

Information theory and the analysis of ligand-binding data

The phenomenological principles of information theory are used in the analysis of ligand-binding phenomena in biological macromolecules. Information maps are constructed to visualize regions of ligand chemical potential with maximum amount of information and to devise suitable experimental strategies therefrom. Extensive simulation studies and analysis of experimental data also point out the properties of information used as a weighting procedure in nonlinear least-squares analyses.

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.

Temperature- and pH-dependence of the oxygen-binding reaction of human fetal haemoglobin

O2 binding to human haemoglobin F0 was studied at high haem concentrations (3 mM) in the temperature range 15-35 degrees C and in the pH range 6.8-8.7 at 25 degrees C. Comparison with O2 binding to human adult haemoglobin A0 under identical solution conditions reveals striking similarities in the Bohr effect and the enthalpy of oxygenation between the two haemoglobins.

Carbon monoxide and oxygen binding to human hemoglobin F0

Differential binding curve measurements of carbon monoxide and oxygen binding to human hemoglobin F0 under near-physiological conditions (0.1 M NaCl and 15 mM 2,3-diphosphoglyceric acid, pH 7.35, and 37 degrees C) have allowed a detailed description of the binding and linkage between these two gaseous ligands. Comparison with human hemoglobin A0 under identical solution conditions shows that fetal hemoglobin F0 binds oxygen and carbon monoxide with higher affinity than human hemoglobin A0, but with the same cooperativity. Construction of the partition coefficient surface for carbon monoxide and oxygen binding reveals a failure of Haldane's laws for both hemoglobins. Linkage graphs are used to explore the phenomenological properties of the system. The graphs provide a quantitative description of the mechanism of carbon monoxide toxicity on oxygen transport by hemoglobin in vivo and demonstrate striking similarities between the functional properties of fetal and adult hemoglobins.

Identical linkage and cooperativity of oxygen and carbon monoxide binding to Octopus dofleini hemocyanin

Employment of high-precision thin-layer methods has enabled detailed functional characterization of oxygen and carbon monoxide binding for (1) the fully assembled form with 70 binding sites and (2) the isolated chains with 7 binding sites of Octopus dofleini hemocyanin. The striking difference in the cooperativities of the two ligands for the assembled decamer is revealed through an examination of the binding capacities and the partition coefficient, determined as functions of the activities of both ligands. A global analysis of the data sets supported a two-state allosteric model assuming an allosteric unit of 7. Higher level allosteric interactions were not indicated. This contrasts to results obtained for arthropod hemocyanins. Oxygen and carbon monoxide experiments performed on the isolated subunit chain confirmed the presence of functional heterogeneity reported previously [Miller, K. (1985) Biochemistry 24, 4582-4586]. The analysis shows two types of binding sites in the ratio of 4:3.

A new method for the determination of equilibrium constants through binding capacity measurements

The recent discovery of the negligible contribution of the triply ligated species to the oxygenation process of human hemoglobin A0 (S.J. Gill, E. Di Cera, M.L. Doyle, G.A. Bishop and C.H. Robert, Biochemistry 26 (1987) 3995) has pointed out the high precision of differential binding measurements. These measurements closely approximate the binding capacity (E. Di Cera, S.J. Gill and J. Wyman, Proc. Natl. Acad. Sci. U.S.A. 85 (1988) 449) of the system and can be used to calculate higher derivatives of the binding curve. We develop here a new method for the determination of equilibrium constants through binding capacity measurements by which the physical parameters expressing the optical properties of the system are eliminated in the data analysis.

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.

Canonical formulation of linkage thermodynamics

The canonical structure of the group of thermodynamic potentials obtained from the energy of a physico-chemical system removes any possible distinction between physical and chemical binding phenomena. Transformations of these potentials by means of Jacobians give linkage relations for equilibrium thermodynamics. Linkage matrices are introduced to explore the functional properties of a biological macromolecule. They provide a quantitative basis for a broader approach and understanding of generalized binding phenomena.

Inhibition of bacterial ice nucleators by fish antifreeze glycoproteins

Certain bacteria promote the formation of ice in super-cooled water by means of ice nucleators which contain a unique protein associated with the cell membrane. Ice nucleators in general are believed to act by mimicking the structure of an ice crystal surface, thus imposing an ice-like arrangement on the water molecules in contact with the nucleating surface and lowering the energy necessary for the initiation of ice formation. Quantitative investigation of the bacterial ice-nucleating process has recently been made possible by the discovery of certain bacteria that shed stable membrane vesicles with ice nucleating activity. The opposite effect, inhibition of ice formation, has been described for a group of glycoproteins found in different fish and insect species. This group of substances, termed antifreeze glycoproteins (AFGPs), promotes the supercooling of water with no appreciable effect on the equilibrium freezing point or melting temperature. Substantial evidence now indicates that AFGPs act by binding to a growing ice crystal and slowing crystal growth. As the ice-nucleating protein surface is believed to have a structure similar to an embryonic ice crystal, AFGPs might be predicted to interact directly with a bacterial ice-nucleating site. We report here that AFGPs from the antarctic fish Dissostichus mawsoni inhibit the ice-nucleating activity of membrane vesicles from the bacterium Erwinia herbicola. The inhibition effect shows saturation at high concentration of AFGP and conforms to a simple binding reaction between the AFGP and the nucleation centre.

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.

Alkaline Bohr effect of human hemoglobin Ao

Differential oxygen binding measurements obtained over the pH range 6.95 to 9.10 at 25 degrees C have allowed a detailed description of the alkaline Bohr effect of human hemoglobin Ao. Phenomenological analysis of the data in terms of the Adair equation shows that: (1) the oxygen binding curves are asymmetrical with the population of the triply oxygenated species being negligible throughout the pH range studied: (2) the shape of the oxygen binding curve is affected by pH, especially at low saturation; and (3) the maximum O2-proton linkage is -0.52 mole of proton per mole of oxygen at pH 7.4. A possible molecular mechanism of the Bohr effect is proposed within the framework of an allosteric model which accounts for the low population of triply oxygenated hemoglobin species. At least three Bohr groups are necessary for a quantitative description of the alkaline Bohr effect. Two of these groups titrate in the range of the His146 beta and Vall alpha residues, which have long been identified as the main alkaline Bohr groups, and altogether contribute 84% of the alkaline Bohr effect at physiological pH. A third ionizable group, linked to oxygenation presumably at the beta chains, is implicated and is titrated in a pH range characteristic of a surface histidyl residue.

On the determination of species fractions from ligand-binding data. Application to human hemoglobin

A method outlined in a previous study (S.J. Gill, H.T. Gaud, J. Wyman and G. Barisas, Biophys. Chem. 8 (1978) 53) is applied for the determination of species fractions from ligand-binding data for the oxygen reaction with human hemoglobin. The results obtained by this alternative approach, which is based on the solution of a system of linear equations, are consistent with those obtained using nonlinear least-squares analysis.

Effect of differences in optical properties of intermediate oxygenated species of hemoglobin A0 on Adair constant determination

Careful evaluation of the so-called isosbestic properties of oxygenated and deoxygenated hemoglobin spectra demonstrates that the spectral changes are not strictly linear with respect to the degree of saturation. In order to quantify the extent of nonlinearity, optical measurements of O2 binding to human hemoglobin were made at different wavelengths in the Soret region approaching the presumed isosbestic point. The results indicate that the extinction coefficient of intermediate oxygenated hemoglobin is 1% less than that of the fully oxygenated hemoglobin, with a resulting 3% (+/- 0.15%) nonlinearity effect on measurements taken at the peak of the oxygenated hemoglobin spectrum (414 nm). The lack of isosbestic conditions allows one to investigate the functional properties of the oxygenated intermediates directly. The small difference in the absorbance of different oxygenated species has practically no influence on the determination of Adair constants at wavelengths removed from the critical isosbestic region.

Binding capacity: cooperativity and buffering in biopolymers

The group of linkage potentials resulting from the energy of a physicochemical system expressed per mol of a reference component, say a polyfunctional macromolecule, leads to the concept of binding capacity. This concept applies equally to both chemical and physical ligands and opens the way to consideration of higher-order linkage relationships. It provides a means of exploring the consequences of thermodynamic stability on generalized binding phenomena in biopolymers.

Thermodynamics of carbon monoxide binding to monomeric cytochrome c'

The thermodynamic parameters for carbon binding to monomeric Rhodopseudomonas palustris cytochrome c' are determined. An enthalpy change for CO(aq) binding to the cytochrome is measured directly by titration calorimetry as -6.7 +/- 0.2 kcal/mol of heme, the CO binding equilibrium constant is measured at 35 degrees C as (1.96 +/- 0.05) X 10(5) M-1, and the binding equilibrium constant at 25 degrees C is calculated from the van't Hoff equation as (2.8 +/- 0.1) X 10(5) M-1. Comparison of the results to the known energetics of CO binding to dimeric cytochrome c', where the CO binding site is buried in the protein interior, indicates that the heme binding site on the monomer form is, in contrast, more exposed.

Carbon monoxide binding to human hemoglobin A0

The carbon monoxide binding curve to human hemoglobin A0 has been measured to high precision in experimental conditions of 600 microM heme, 0.1 M N-(2-hydroxyethyl)piperazine-N'-2-ethanesulfonic acid, 0.1 M NaCl, 10 mM inositol hexaphosphate, 1 mM disodium ethylenediaminetetraacetic acid, pH 6.94, and 25 degrees C. Comparison to the oxygen binding curve in the same experimental conditions demonstrates that the two curves are not parallel. This result invalidates Haldane's two laws for the partitioning between carbon monoxide and oxygen to human hemoglobin. The partition coefficient is found to be 263 +/- 27 at high saturation, in agreement with previous studies, but is lowered substantially at low saturation. Although the oxygen and carbon monoxide binding curves are not parallel, both show the population of the triply ligated species to be negligible. The molecular mechanism underlying carbon monoxide binding to hemoglobin is consistent with the allosteric model [Di Cera, E., Robert, C. H., & Gill, S. J. (1987) Biochemistry 26, 4003-4008], which accounts for the negligible contribution of the triply ligated species in the oxygen binding reaction to hemoglobin [Gill, S. J., Di Cera, E., Doyle, M. L., Bishop, G. A., & Robert, C. H. (1987) Biochemistry 26, 3995-4002]. The nature of the different binding properties of carbon monoxide stems largely from the lower partition coefficient of the T state (123 +/- 34), relative to the R state (241 +/- 19).(ABSTRACT TRUNCATED AT 250 WORDS)

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.