Hemoglobins with multiple reactive sulphydryl groups: The reaction of dog hemoglobin with 5,5′-dithiobis (2-nitrobenzoate)

Dog hemoglobin has four sulphydryl groups per (tetramer) molecule located at the G18(111)a and F9(93)β positions. The two sulphydryls at the G18(111)a positions are unreactive toward nonmercurial sulphydryl reagents, but those at the F9(93)β positions are reactive toward these reagents. We have studied the kinetics of the reaction of dog hemoglobin with 5,5′-dithiobis (2-nitrobenzoic acid) as a function ofpH. At allpH values studied, the reaction is kinetically monophasic. Quantitative analysis of thepH dependence of the apparent second-order rate constant shows that two ionizable groups are linked to the reaction of the sulphydryl group. TheirpK _a values are 5.57 and 9.0. These values are assigned to HisHC3(146)β and to the CysF9(93)β sulphydryl. We find that dog carbonmonoxyhemoglobin is significantly—almost an order of magnitude—less reactive than the aquomet, azidomet, and oxy derivatives. This result may be due to a greater tendency (at acidpH) for the salt bridge between HisHC3(146)β and AspFG1(94)β to form in the carbonmonoxy than in the other derivatives. Formation of this salt bridge is known to hinder access to the CysF9(93)β sulphydryl [Perutz, M. F. (1970),Nature 228, 734–739].     

Transition of hemoglobin between two tertiary conformations: determination of equilibrium and thermodynamic parameters from the reaction of 5,5'-dithiobis(2-nitrobenzoate) with the CysF9[93]beta sulfhydryl group

The equilibrium constant of the reaction of 5,5'-dithiobis(2-nitrobenzoate) with the CysF9[93]beta sulfhydryl group of hemoglobin decreases by 2 to 3 orders of magnitude between pH 5.6 and 9. The reaction is coupled to the ionizations of two groups on the protein. At 25 degrees C one group has a pK(a) of 5.31+/-0.2 when hemoglobin is in its (tertiary) r conformation, typified by the thiolate anion form of CysF9[93]beta; this changes to 7.73+/-0.4 in the (tertiary) t conformation, typified by the mixed disulfide form of the sulfhydryl. The second group ionizes with a pK(a) of 7.11+/-0.4 in the r conformation; this changes to 8.38+/-0.2 in the t conformation. K(rt), the equilibrium constant for the r<-->t isomerization process, is 0.22+/-0.06. The standard enthalpy and entropy changes for the isomerization are DeltaH(o)(rt)=24.2 kJ mol(-1) and DeltaS(o)(rt)=68.8 JK(-1)mol(-1), respectively.     

Reversible reaction of 5,5'-dithiobis(2-nitrobenzoate) with the hemoglobins of the domestic cat: acetylation of NH3+ terminal group of the beta chain transforms the complex pH dependence of the forward apparent second order rate constant to a simple form

We demonstrate kinetically that the reaction of 5,5'-dithiobis(2-nitrobenzoate) with the CysF9[93]beta sulfhydryl group of domestic cat hemoglobins is a reversible process. In the major hemoglobin, in which the NH3+ terminal group of GlyNA1[1]beta is free, kf, the apparent forward second order rate constant, has a complex pH dependence profile. In the minor hemoglobin, the NH3+ terminal group of SerNA1[1]beta is acetylated, and the pH dependence profile of kf is simple. These results support the proposal that the positively charged groups at the organic phosphate binding site are electrostatically linked to CysF9[93]beta. Quantitative analyses of the complex profiles enabled us to estimate pKas of 7.47 +/- 0.3; 6.53 +/- 0.03 and 8.49 +/- 0.3 for GlyNA1[1]beta, HisH21[143]beta and other histidines within 2 nm of the sulfhydryl, and CysF9[93]beta, respectively, of the major hemoglobin. Analyses of the simple profiles gave pKas of 6.33 +/- 0.17 and 8.54 +/- 0.5 for HisH21[143]beta and other histidines within a distance of 2 nm of the sulfhydryl, and CysF9[93]beta of the minor hemoglobin, respectively.     

The pH-dependent binding of NADH and subsequent enzyme isomerization of human liver beta 3 beta 3 alcohol dehydrogenase

Human class I beta 3 beta 3 is one of the alcohol dehydrogenase dimers that catalyzes the reversible oxidation of ethanol. The beta 3 subunit has a Cys substitution for Arg-369 (beta 369C) in the coenzyme-binding site of the beta1 subunit. Kinetic studies have demonstrated that this natural mutation in the coenzyme-binding site decreases affinity for NAD+ and NADH. Structural studies suggest that the enzyme isomerizes from an open to closed form with coenzyme binding. However, the extent to which this isomerization limits catalysis is not known. In this study, stopped-flow kinetics were used from pH 6 to 9 with recombinant beta 369C to evaluate rate-limiting steps in coenzyme association and catalysis. Association rates of NADH approached an apparent zero-order rate with increasing NADH concentrations at pH 7.5 (42 +/- 1 s-1). This observation is consistent with an NADH-induced isomerization of the enzyme from an open to closed conformation. The pH dependence of apparent zero-order rate constants fit best a model in which a single ionization limits diminishing rates (pKa = 7.2 +/- 0.1), and coincided with Vmax values for acetaldehyde reduction. This indicates that NADH-induced isomerization to a closed conformation may be rate-limiting for acetaldehyde reduction. The pH dependence of equilibrium NADH-binding constants fits best a model in which a single ionization leads to a loss in NADH affinity (pKa = 8.1 +/- 0. 2). Rate constants for isomerization from a closed to open conformation were also calculated, and these values coincided with Vmax for ethanol oxidation above pH 7.5. This suggests that NADH-induced isomerization of beta 369C from a closed to open conformation is rate-limiting for ethanol oxidation above pH 7.5.     

Transition of hemoglobin between two tertiary conformations: The transition constant differs significantly for the major and minor hemoglobins of the Japanese quail (Cortunix cortunix japonica)

We demonstrate that 5,5'-dithiobis(2-nitrobenzoate) - DTNB - reacts with only CysF9[93]beta and CysB5[23]beta among the multiple sulfhydryl groups of the major and minor hemoglobins of the Japanese quail (Cortunix cortunix japonica). K(equ), the equilibrium constant for the reaction, does not differ very significantly between the two hemoglobins. It decreases 430-fold between pH approximately 5.6 and pH approximately 9: from a mean of 7+/-1 to a mean of 0.016+/-0.003. Quantitative analyses of the K(equ) data based on published X-ray and temperature-jump evidence for a tertiary structure transition in liganded hemoglobin enable the calculation of K(rt), the equilibrium constant for the r<---->t tertiary structure transition. K(rt) differs significantly between the two hemoglobins: 0.744+/-0.04 for the major, 0.401+/-0.01 for the minor hemoglobin. The mean pK(a)s of the two groups whose ionizations are coupled to the DTNB reaction are about the same as previously reported for mammalian hemoglobins.     

Varying apparent rate constant: determination of uptake and release of protons during tetramer-dimer dissociation in human hemoglobin A

The effect of association-dissociation on the sulphydryl reactivity of human hemoglobin A is reported. The reactivity of CysF9(93)beta towards the sulphydryl reagent, 5,5'-dithiobis(2-nitrobenzoate), is higher at lower concentrations of hemoglobin at all pH values. This is because hemoglobin dimers have higher sulphydryl reactivity than tetramers and it is known that the proportion of dimers increases as the hemoglobin concentration decreases. This study takes advantage of this observation to determine the tetramer-dimer dissociation constant, K(4,2), of hemoglobin A and subsequently the proton uptake and the proton release during this process. The concentration dependence profiles of the apparent second-order rate constants, k(app), show that (between 2 and 20 microM heme) k(app) decreases with increasing hemoglobin concentration. Above 30 M heme k(app) remains fairly constant for all hemoglobin derivatives (oxy, carbonmonoxy and aquomethemoglobin) used. The pH dependence of the negative logarithm of tetramer-dimer dissociation constant, pK(4,2), for oxy- (and for carbonmonoxy-) hemoglobin exhibits a biphasic character with a maximum near pH 7.4 (and 6.6). For aquomethemoglobin, pK(4,20 decreases with increasing pH. The tetramer-dimer dissociation of human oxyhemoglobin A at an ionic strength of 200 mM uptakes 0.87 +/- 0.09 mole of protons between pH 6.2 to 7.4 phase and releases 0.84 0.09 mole of protons between pH 7.4 and 9.0 phase. Under a similar condition carbonmonoxyhemoglobin uptakes 0.54 +/- 0.05 mole of protons between pH 5.8 and 6.6 phase and releases 0.48 +/- 0.05 mole of protons between pH 6.6 and 9.0 phase. Aquomethemoglobin has only a single phase, it releases 0.39 +/- 0.05 mole of protons during tetramer-dimer dissociation.     

Immune response in dog. 3. Antibody formation in dogs and rabbits to human serum proteins and keyhole limpet haemocyanin.

Antibody formation in dogs and rabbits to human serum proteins and keyhole limpet haemocyanin (KLH) following primary, secondary and multiple stimulation was analysed. Primary injection of human serum stimulates the formation of precipitin antibodies to beta2 lipoprotein in dogs, beta2 lipoprotein and beta globulin in rabbits. After a secondary dose the rabbits formed precipitins to a whole range of human serum proteins, while the dogs to beta2 lipoprotein, albumin, beta globulin. When the primary dose of antigen was divided over a period of 8 weeks, the dog produced precipitins to beta2 lipoprotein while the rabbit to a wide range of serum proteins. Secondary stimulation of these animals did not increase the number of precipitins formed. Quantitative analysis of the antibody produced show that the best response was with beta2 lipoprotein followed by albumin and beta globulin. As the immunogenicity of the antigen was greater the differences between the two species were narrow. These differences were less pronounced following the primary injection than after the secondary and multiple stimulations. The primary response to KLH (which represents mainly IgM) is better in the dog than in the rabbit, while the secondary response (IgG) was better in the rabbit. The poorer IgG response in the dog compared to the rabbit, observed in all the experiments, is discussed.     

Hemoglobins with multiple reactive sulphydryl groups: The reaction of pigeon hemoglobin with 5,5′-dithiobis (2-nitrobenzoic acid)

Pigeon hemoglobin has eight reactive sulphydryl groups per (tetramer) molecule, as determined by Boyer titration with p-chloromercuribenzoate. However, only four of these are titra-table with 5,5′-dithiobis(2-nitrobenzoate) under the same experimental conditions. The time course of the reaction of pigeon hemoglobin with 5,5′-dithiobis(2-nitrobenzoate) is biphasic. In thepH range 6–9, the fast phase is between one and two orders of magnitude faster than the slow phase. For the fast phase,k _app, the apparent second-order rate constant, increases monotonously withpH. Quantitative analysis reveals that the reactionof the sulphydryl group responsible for this phase is coupled to the ionization of two groups with pK _a values of 6.15±0.1 and 8.5±0.1. These pK _a values are assigned to HisHC3(146)β and to the CysF9(93)β sulphydryl group, respectively. For the slow phase thek _app vs.pH profiles are bowl-shaped. Analysis reveals that the reaction of the sulphydryl group to which this phase may be attributed is coupled to the ionization of two groups with mean pK _a values of 6.53±0.1 and 8.25±0.1. Examination of the structure of hemoglobin allows us to assign these values to HisG19(117)β and CysB5(23)β, respectively. The CysB5(23)β sulphydryl is in the region of the molecule where amino acid substitutions have been found to give rise to significant changes in the oxygen affinity of hemoglobin [Huanget al. (1990),Biochemistry 29, 7020–7023.     

Temperature-jump studies on hemoglobin. Kinetic evidence for a non-quaternary isomerization process in deoxy- and carbonmonoxyhemoglobin

Temperature jumps on mixtures of hemoglobin and pH indicators give rise to relaxation signals in the microsecond range. The pH and concentration dependences of the reciprocal relaxation time, 1/tau, may be rationalized on the basis of a reaction scheme in which a slow isomerization process in the protein moiety is coupled to a rapid co-operative ionization of two protons. At 11 degrees C the rate constants of the isomerization are kr = 4.2(+/- 1.8) x 10(4) s-1 and kf = 1.3(+/- 0.1) x 10(4) s-1 in deoxyhemoglobin; in carbonmonoxyhemoglobin they are kr = 3.9(+/- 1.3) x 10(4) s-1 and kf = 5.3(+/- 1.8) x 10(3) s-1. The pKa values of the coupled ionizing groups are 5.3 in deoxy- and 6.0 in carbonmonoxyhemoglobin. Modification of the CysF9(93) beta sulfhydryl group with iodoacetamide abolishes the pH dependence of 1/tau, suggesting that this sulfhydryl is involved in the isomerization process. Consideration of the X-ray structure of oxyhemoglobin allows a structural interpretation of the results. It is concluded that the isomerization may be important for the physiological function of hemoglobin, but that it is not identical with the quaternary structure transition.     

Analysis of cloned mRNA sequences encoding subfragment 2 and part of subfragment 1 of alpha- and beta-myosin heavy chains of rabbit heart

Two cardiac myosin heavy chain cDNA clones, pMHC alpha 252 and pMHC beta 174, were constructed using rabbit ventricular mRNA isolated from adult thyrotoxic and normal hearts, respectively. The complete DNA sequences of the 2.2- and 1.4-kilobase inserts of pMHC beta 174 and pMHC alpha 252, respectively, were obtained. The 736 amino acids specified by pMHC beta 174 begin 439 (1.3 kilobases) residues from the heavy chain NH2 terminus and include a 400-amino acid segment of subfragment 1 and the entire subfragment 2 region. Clone pMHC alpha 252 encodes 465 amino acids encompassing all of subfragment 2 and a portion of light meromyosin. Comparison of these two clones revealed extensive sequence overlap which included 1107 nucleotides specifying a 369-amino acid segment corresponding to subfragment 2. Within this region 78 (7%) base and 32 (8.7%) amino acid mismatches were noted. These differences were clustered within discrete regions, with the subfragment 1/subfragment 2 junctional region being particularly divergent. Structural differences between pMHC alpha 252 and pMHC beta 174 indicate that these two clones represent two similar but distinct myosin heavy chain genes whose expression is responsible for ventricular myosin heavy chain isoforms alpha and beta, respectively. The derived amino acid sequences of both clones exhibit extensive homology (greater than 81%) with sequences obtained by direct analysis of adult rabbit skeletal muscle myosin heavy chain protein. The sequences corresponding to the subfragment 2 region are consistent with an alpha-helical conformation with a characteristic 7-residue periodicity in the linear distribution of nonpolar amino acids. Conversely, subfragment 1 sequences specified by pMHC beta 174 suggest a folded highly irregular structure.     

Contribution of the gamma-carboxyl group of Glu-43(beta) to the alkaline Bohr effect of hemoglobin A.

Glu-43(beta) of hemoglobin A exhibits a high degree of chemical reactivity around neutral pH for amidation with nucleophiles in the presence of carbodiimide. Such a reactivity is unusual for the side-chain carboxyl groups of proteins. In addition, the reactivity of Glu-43(beta) is also sensitive to the ligation state of the protein [Rao, M. J., & Acharya, A. S. (1991) J. Protein Chem. 10, 129-138]. The influence of deoxygenation of hemoglobin A on the chemical reactivity of the gamma-carboxyl group of Glu-43(beta) has now been investigated as a function of pH (from 5.5 to 7.5). The chemical reactivity of Glu-43(beta) for amidation increases upon deoxygenation only when the modification reaction is carried out above pH 6.0. The pH-chemical reactivity profile of the amidation of hemoglobin A in the deoxy conformation reflects an apparent pKa of 7.0 for the gamma-carboxyl group of Glu-43(beta). This pKa is considerably higher than the pKa of 6.35 for the oxy conformation. The deoxy conformational transition mediated increase in the pKa of the gamma-carboxyl group of Glu-43(beta) implicates this carboxyl group as an alkaline Bohr group. The amidated derivative of hemoglobin A with 2 mol of glycine ethyl ester covalently bound to the protein was isolated by CM-cellulose chromatography.(ABSTRACT TRUNCATED AT 250 WORDS)     

The interplay between basicity, conformation, and enzymatic reduction in biliverdins.

Biliverdins with extended conformations are reduced by biliverdin reductase (BvR) at higher rates than biliverdins with helical conformations. To find out the molecular basis for this important feature of BvR mechanism, helical and extended biliverdins were titrated for their acid-base equilibria in a protic solvent (methanol). It was found that the basicity of biliverdins increases with the stretching of the conformation. Biliverdin IX gamma (all-syn) has a pKa = 3.6; 5,10,15-syn,syn,anti-biliverdin has a pKa = 3.7; 5,10,15-syn,anti,syn-biliverdin has a pKa = 6.1; 5,10,15-syn,anti,anti-biliverdin has a pKa = 6.4; and 5,10,15-all-anti-biliverdin has a pKa = 7.9. The increase in basicity with progressive stretching of conformations closely parallels the increase in the reduction rates by BvR. A biliverdin constrained by a four carbon chain to a helical conformation and which is a very weak base (pKa = 0.4) is not reduced by BvR. Nucleophilic additions of 2-mercaptoethanol at the C10 in biliverdins closely parallel their basicities, as can be expected if the formation of a positive mesomeric species at C10 is linked to the basicity (i.e., the ease of protonation) of the N23 on the pyrrolenine ring.     

A study of conformational changes in two beta-93 modified hemoglobin A's using a triphosphate spin label.

The binding of oxygen and 1-oxyl-2,2,6,6-tetramethylpiperidine 4-triphosphate (spin-labeled triphosphate) to normal adult human hemoglobin (HbA) covalently labeled at the beta-93 sulfhydryl groups with N-(2,2,6,6-tetramethyl-4-piperidinyl)iodoacetamide (I) was studied. HbA-I was used as a model for HbA labeled at the beta-93 SH groups with N-(1-oxyl-2,2,6,6-tetramethyl-4-piperidinyl)iodoacetamide (II) since the binding of SLTP to HbA-II could not be measured conveniently, in the presence of the paramagnetic resonance signal of II. Both HbA-I and HbA-II can be treated as variant hemoglobins with abnormal beta chains. The oxygen and SLTP binding data from HbA-I and oxygen binding data from HbA-II are consistent with a concerted transition model for cooperativity which assumes nonequivalence between alpha and beta subunits (GCT model). The distribution of environments "seen" by conformation sensitive probes such as II and trifluoracetone (19F NMR probe) attached to the beta-93 sulfhydryl groups of HbA can also be accounted for by the GCT model. It is proposed that the beta-93 probes sense the dramatic change in beta subunit structure resulting from the quaternary structure change (T leads to R) upon heme saturation as well as tertiary structure changes at the alpha1-beta2 contact region resulting from ligand binding to the beta-heme group. Structural changes caused by ligation of the alpha-hemes are not discussed.     

Limits of diffusion in the hydrolysis of substrates by the phosphotriesterase from Pseudomonas diminuta.

The catalytic mechanism for the enzymatic hydrolysis of a series of paraoxon analogues by the phosphotriesterase from Pseudomonas diminuta has been determined. The Br?nsted plots relating the pKa of the leaving group to the observed kinetic parameters, Vmax and V/Km, are both nonlinear. This observation is consistent with a change in the rate-limiting step from chemical to physical events as the pKa of the leaving group is decreased. This conclusion is confirmed by the effects of solvent viscosity on Vmax and V/Km for the same series of analogues. The data were fitted to the scheme E k1A in equilibrium k2 EA k3----EP k7----E'P k9----E + products where EA is the enzyme-substrate complex, EP is the enzyme-product complex, E'P is the enzyme-product complex after a viscosity-independent unimolecular reaction, and the values for k1, k2, k7, and k9 are 4.1 X 10(7) M-1 s-1, 2550 s-1, 3370 s-1, and 5940 s-1, respectively. The magnitude of the chemical step, represented by k3, is dependent on the pKa of the leaving group phenol as predicted by the Br?nsted equation (log k3 = beta pKa + C) where beta = -1.8 and the constant (C) = 17.7. The magnitude of beta indicates that the transition state for substrate hydrolysis is very product-like.     

Isometric force generated by locust skeletal muscle: responses to single stimuli

A mathematical model of the locust hind leg extensor muscle is described. The model accounts for the force response of the muscle to well-separated input stimuli under isometric conditions. Experimental data was collected by stimulating the extensor muscle and measuring the force generated at the tibia. In developing a model it was assumed that the response to a single isolated stimulus was linear. A linear model was found to fit well to the response to an isolated stimulus. No assumptions were made about the model order and models of various order were fitted to data in the frequency domain, using a least squares fit. The stimulus can be approximated as an impulse, with the response to each stimulus well described by a linear second-order system. Using a third-order model provided a better fit to data, but the improvement in fit was marginal and the model uses one extra parameter. A fourth-order model, which is often used to describe the behaviour of isometric muscle was found to overfit the data. Using a second-order model provides a simpler way of describing the behaviour of an isometric twitch.     

Structure of human oxyhaemoglobin at 2.1 A resolution

The structure of human oxyhaemoglobin was determined by single crystal X-ray analysis at 2.1 A resolution. Data were collected on an Arndt-Wonacott camera at -2 degrees C. The structure was refined to an R factor of 0.223 by the Jack-Levitt method, starting from Baldwin's model of human carbon monoxide haemoglobin. The active sites in the alpha and beta subunit are distinct. The iron atoms are 0.16(8) A and 0.00(8) A from the mean plane of the porphyrin carbons and nitrogens (0.12(8) A and -0.11(8) A from the mean plane of the porphyrin nitrogens) in the alpha and beta subunit, respectively, in correlation with the orientation of HisF8 relative to the porphyrin nitrogens. The haem group appears to be nearly planar in the alpha subunit but ruffled in the beta subunit. The Fe-O(1)-O(2) angles are 153(7) degrees and 159(12) degrees in the alpha and beta subunit, respectively. The oxygen molecule forms a hydrogen bond to N epsilon of HisE7 in the alpha, but either none or a weak one in the beta subunit. The following bond lengths were found: Fe-N epsilon (HisF8) = 1.94(9) A (alpha) and 2.07(9) A (beta); Fe-O(1) = 1.66(8) A (alpha) and 1.87(13) A (beta); Fe-Nporph (mean = 1.99(5) A (alpha) and 1.96(6) A (beta). These dimensions agree with the values obtained in oxymyoglobin and model compounds. The C-terminal residues, ArgHC3(141 alpha) and HisHC3(146 beta), are relatively delocalized, and their positions do not enable them to form the intersubunit salt bridges in which they are involved in deoxyhaemoglobin. The penultimate tyrosine residues, TyrHC2 140 alpha and 145 beta, are relatively localized and maintain the hydrogen bonds to the carbonyl oxygens of ValFG5 (93 alpha and 98 beta), with only minor variations compared to their geometry in deoxyhaemoglobin. TyrHC2(145 beta), however, alternates between a major and a minor site, in conjunction with CysF9(93 beta), both sharing the internal pocket between the F and H helices while in the major conformation. This suggests that the role of the penultimate tyrosines in the allosteric mechanism may differ from that previously proposed by Perutz. The overall quaternary structure of oxyhaemoglobin is identical, within experimental error, to that of carbon monoxide haemoglobin, and thus confirms the applicability of the allosteric mechanisms proposed by Perutz and Baldwin & Chothia to the process of oxygen binding.     

Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.     

Characteristics of the upper airway pressure-flow relationship during sleep

In examining the mechanical properties of the respiratory system during sleep in healthy humans, we observed that the inspiratory pressure-flow relationship of the upper airway was often flow limited and too curvilinear to be predicted by the Rohrer equation. The purposes of this study were 1) to describe a mathematical model that would better define the inspiratory pressure-flow relationship of the upper airway during sleep and 2) to identify the segment of airway responsible for the sleep-related flow limitation. We measured nasal and total supralaryngeal pressure and flow during wakefulness and stage 2 sleep in five healthy male subjects lying supine. A right rectangular hyperbolic equation, V = (alpha P)/(beta + P), where V is flow, P is pressure, alpha is an asymptote for peak flow, and beta is pressure at a flow of alpha/2, was used in its linear form, P/V = (beta/alpha) + (P/alpha). The goodness of fit of the new equation was compared with that for the linearized Rohrer equation P/V = K1 + K2V. During wakefulness the fit of the hyperbolic equation to the actual pressure-flow data was equivalent to or significantly better than that for the Rohrer equation. During sleep the fit of the hyperbolic equation was superior to that for the Rohrer equation. For the whole supralaryngeal airway during sleep, the correlation coefficient for the hyperbolic equation was 0.90 +/- 0.50, and for the Rohrer equation it was 0.49 +/- 0.25. The flow-limiting segment was located within the pharyngeal airway, not in the nose.(ABSTRACT TRUNCATED AT 250 WORDS)