Dynamics of Ca2+-saturated calmodulin D129N mutant studied by multiple molecular dynamics simulations

Fifteen independent 1-nsec MD simulations of fully solvated Ca(2+) saturated calmodulin (CaM) mutant D129N were performed from different initial conditions to provide a sufficient statistical basis to gauge the significance of observed dynamical properties. In all MD simulations the four Ca(2+) ions remained in their binding sites, and retained a single water ligand as observed in the crystal structure. The coordination of Ca(2+) ions in EF-hands I, II, and III was sevenfold. In EF-hand IV, which was perturbed by the mutation of a highly conserved Asp129, an anomalous eightfold Ca(2+) coordination was observed. The Ca(2+) binding loop in EF-hand II was observed to dynamically sample conformations related to the Ca(2+)-free form. Repeated MD simulations implicate two well-defined conformations of Ca(2+) binding loop II, whereas similar effect was not observed for loops I, III, and IV. In 8 out of 15 MD simulations Ca(2+) binding loop II adopted an alternative conformation in which the Thr62 >C=O group was displaced from the Ca(2+) coordination by a water molecule, resulting in the Ca(2+) ion ligated by two water molecules. The alternative conformation of the Ca(2+) binding loop II appears related to the "closed" state involved in conformational exchange previously detected by NMR in the N-terminal domain fragment of CaM and the C-terminal domain fragment of the mutant E140Q. MD simulations suggest that conformations involved in microsecond exchange exist partially preformed on the nanosecond time scale.     

Molecular dynamics study of water penetration in staphylococcal nuclease

The ionization properties of Lys and Glu residues buried in the hydrophobic core of staphylococcal nuclease (SN) suggest that the interior of this protein behaves as a highly polarizable medium with an apparent dielectric constant near 10. This has been rationalized previously in terms of localized conformational relaxation concomitant with the ionization of the internal residue, and with contributions by internal water molecules. Paradoxically, the crystal structure of the SN V66E variant shows internal water molecules and the structure of the V66K variant does not. To assess the structural and dynamical character of interior water molecules in SN, a series of 10-ns-long molecular dynamics (MD) simulations was performed with wild-type SN, and with the V66E and V66K variants with Glu66 and Lys66 in the neutral form. Internal water molecules were identified based on their coordination state and characterized in terms of their residence times, average location, dipole moment fluctuations, hydrogen bonding interactions, and interaction energies. The locations of the water molecules that have residence times of several nanoseconds and display small mean-square displacements agree well with the locations of crystallographically observed water molecules. Additional, relatively disordered water molecules that are not observed crystallographically were found in internal hydrophobic locations. All of the interior water molecules that were analyzed in detail displayed a distribution of interaction energies with higher mean value and narrower width than a bulk water molecule. This underscores the importance of protein dynamics for hydration of the protein interior. Further analysis of the MD trajectories revealed that the fluctuations in the protein structure (especially the loop elements) can strongly influence protein hydration by changing the patterns or strengths of hydrogen bonding interactions between water molecules and the protein. To investigate the dynamical response of the protein to burial of charged groups in the protein interior, MD simulations were performed with Glu66 and Lys66 in the charged state. Overall, the MD simulations suggest that a conformational change rather than internal water molecules is the dominant determinant of the high apparent polarizability of the protein interior.     

Backbone and side chain dynamics of mutant calmodulin-peptide complexes

The mechanism of long-range coupling of allosteric sites in calcium-saturated calmodulin (CaM) has been explored by characterizing structural and dynamics effects of mutants of calmodulin in complex with a peptide corresponding to the smooth muscle myosin light chain kinase calmodulin-binding domain (smMLCKp). Four CaM mutants were examined: D95N and D58N, located in Ca2+-binding loops; and M124L and E84K, located in the target domain-binding site of CaM. Three of these mutants have altered allosteric coupling either between Ca2+-binding sites (D58N and D95N) or between the target- and Ca2+-binding sites (E84K). The structure and dynamics of the mutant calmodulins in complex with smMLCKp were characterized using solution NMR. Analysis of chemical shift perturbations was employed to detect largely structural perturbations. 15N and 2H relaxation was employed to detect perturbations of the dynamics of the backbone and methyl-bearing side chains of calmodulin. The least median squares method was found to be robust in the detection of perturbed sites. The main chain dynamics of calmodulin are found to be largely unresponsive to the mutations. Three mutants show significantly perturbed dynamics of methyl-bearing side chains. Despite the pseudosymmetric location of Ca2+-binding loop mutations D58N and D95N, the dynamic response of CaM is asymmetric, producing long-range perturbation in D58N and almost none in D95N. The mutations located at the target domain-binding site have quite different effects. For M124L, a local perturbation of the methyl dynamics is observed, while the E84K mutation produces a long-range propagation of dynamic perturbations along the target domain-binding site.     

Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

Importance of the CMAP correction to the CHARMM22 protein force field: dynamics of hen lysozyme

The recently developed CMAP correction to the CHARMM22 force field (C22) is evaluated from 25 ns molecular dynamics simulations on hen lysozyme. Substantial deviations from experimental backbone root mean-square fluctuations and N-H NMR order parameters obtained in the C22 trajectories (especially in the loops) are eliminated by the CMAP correction. Thus, the C22/CMAP force field yields improved dynamical and structural properties of proteins in molecular dynamics simulations.     

Molecular dynamics simulations of lignin peroxidase in solution

The dynamical and structural properties of lignin peroxidase and its Trp171Ala mutant have been investigated in aqueous solution using molecular dynamics (MD) simulations. In both cases, the enzyme retained its overall backbone structure and all its noncovalent interactions in the course of the MD simulations. Very interestingly, the analysis of the MD trajectories showed the presence of large fluctuations in correspondence of the residues forming the heme access channel; these movements enlarge the opening and facilitate the access of substrates to the enzyme active site. Moreover, steered molecular dynamics docking simulations have shown that lignin peroxidase natural substrate (veratryl alcohol) can easily approach the heme edge through the access channel.     

Collective dynamics of EcoRI-DNA complex by elastic network model and molecular dynamics simulations

Anisotropic network model (ANM) is used to analyze the collective motions of restriction enzyme EcoRI in free form and in complex with DNA. For comparison, three independent molecular dynamics (MD) simulations, each of 1.5 ns duration, are also performed for the EcoRI-DNA complex in explicit water. Although high mobility (equilibrium fluctuations) of inner and outer loops that surround the DNA is consistent in both methods and experiments, MD runs sample different conformational subspaces from which reliable collective dynamics cannot be extracted. However, ANM employed on different conformations from MD simulations indicates very similar collective motions. The stems of the inner loops are quite immobile even in the free enzyme and form a large, almost fixed, pocket for DNA binding. As a result, the residues that make specific and non-specific interactions with the DNA exhibit very low fluctuations in the free enzyme. The vibrational entropy difference between the EcoRI complex and free protein + unkinked DNA is positive (favorable), which may partially counteract the unfavorable enthalpy difference of DNA kink formation. Dynamic domains in EcoRI complex and cross-correlations between residue fluctuations indicate possible means of communication between the distal active sites.     

Anisotropic atomic motions in high-resolution protein crystallography molecular dynamics simulations

Molecular dynamics (MD) simulations using empirical force fields are popular for the study of proteins. In this work, we compare anisotropic atomic fluctuations in nanosecond-timescale MD simulations with those observed in an ultra-high-resolution crystal structure of crambin. In order to make our comparisons, we have developed a compact graphical technique for assessing agreement between spatial atomic distributions determined by MD simulations and observed anisotropic temperature factors.     

Molecular dynamics study of conformational changes in human serum albumin by binding of fatty acids

Human serum albumin (HSA) binds with fatty acids under normal physiologic conditions. To date, there is little published information on the tertiary structure of HSA-fatty acid complex in aqueous solution. In the present study, we used molecular dynamics (MD) simulations to elucidate possible structural changes of HSA brought about by the binding of fatty acids. Both unliganded HSA and HSA-fatty acid complex models for MD calculations were constructed based on the X-ray crystal structures. Five myristates (MYRs) were bound in the HSA-fatty acid complex model. In the present MD study, the motion of domains I and III caused by the binding of MYR molecules increased the radius of gyration of HSA. Root-mean-square fluctuations from the MD simulations revealed that the atomic fluctuations of the specific amino acids at drug-binding site I that can regulate the drug-binding affinity were increased by the binding of MYR molecules. Primary internal motions, characterized by the first three principal components, were observed mainly at domains I and III in the principal component analysis for trajectory data. The directional motion projected on the first principal component of unliganded HSA was conserved in HSA-MYR complex as the third principal directional motion with higher frequency. However, the third principal directional motion in unliganded HSA turned into the first principal directional motion with lower frequency in the HSA-MYR complex. Thus, the present MD study provides insights into the possible conformational changes of HSA caused by the binding of fatty acids.     

Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: application to alpha-amylase inhibitor

The dynamics of alpha-amylase inhibitors has been investigated using molecular dynamics (MD) simulations and two analytical approaches, the Gaussian network model (GNM) and anisotropic network model (ANM). MD simulations use a full atomic approach with empirical force fields, while the analytical approaches are based on a coarse-grained single-site-per-residue model with a single-parameter harmonic potential between sufficiently close (r 相似文献   

Stability and fluctuations of amide hydrogen bonds in a bacterial cytochrome c: a molecular dynamics study

Molecular dynamics (MD) simulations on a bacterial cytochrome c were performed to investigate the lifetime and fluctuations of backbone hydrogen bonds and to correlate these data with protection factors for hydrogen exchange measured by NMR spectroscopy (Bartalesi et al. in Biochemistry, 42:10923–10930, 2003). The MD simulations provide a consistent pattern in that long lifetimes of hydrogen bonds go along with small amplitude fluctuations. In agreement with experiments, differences in stability were found with a rather flexible N-terminal segment as compared with a more rigid C-terminal part. Protection factors of backbone hydrogen exchange correlate strongly with the number of contacts but also with hydrogen-bond occupancy, hydrogen-bond survival times, as well as the inverse of fluctuations of backbone atoms and hydrogen-bond lengths derived from MD simulation data. We observed a conformational transition in the C-terminal loop, and significant motion in the N-terminal loop, which can be interpreted as being the structural units involved in the onset of the protein unfolding process in agreement with experimental evidence on mitochondrial cytochrome c. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users. Gernot Kieseritzky and Giulia Morra both contributed equally to this work.     

Molecular dynamics and molecular docking studies on E166A point mutant,R274N/R276N double mutant,and E166A/R274N/R276N triple mutant forms of class A β-lactamases

Bacterial resistance to β-lactams antibiotics is a serious threat to human health. The most common cause of resistance to the β-lactams is the production of β-lactamase that inactivates β-lactams. Specifically, class A extended-spectrum β-lactamase produced by antibiotic resistant bacteria is capable of hydrolyzing extended-spectrum Cephalosporins and Monobactams. Mutations in class A β-lactamases play a crucial role in substrate and inhibitor specificity. In this present study, the E166A point mutant, R274N/R276N double mutant, and E166A/R274N/R276N triple mutant class A β-lactamases are analyzed. Molecular dynamics (MD) simulations are done to understand the consequences of mutations in class A β-lactamases. Root mean square deviation, root mean square fluctuation, radius of gyration, solvent accessibility surface area, hydrogen bond, and essential dynamics analysis results indicate notable loss in stability for mutant class A β-lactamases. MD simulations of native and mutant structures clearly confirm that the substitution of alanine at the position of 166, Asparagine at 274 and 276 causes more flexibility in 3D space. Molecular docking results indicate the mutation in class A β-lactamases which decrease the binding affinity of Cefpirome and Ceftobiprole which are third and fifth generation Cephalosporins, respectively. MD simulation of Ceftobiprole-native and mutant type Class A β-lactamases complexes reveal that E166A/R274N/R276N mutations alter the structure and notable loss in the stability for Ceftobirole-mutant type Class A β-lactamases complexes. Ceftobiprole is currently prescribed for patients with serious bacterial infections; this phenomenon is the probable cause for the effectiveness of Ceftobiprole in controlling bacterial infections.     

Molecular dynamics simulation studies on structural and conformational changes in tyrosine-67 nitrated cytochrome c

Protein tyrosine nitration is well-established post-translational modification occurring in a number of diseases, viz. neurodegenerative, cardiovascular diseases, ageing, etc. Tyrosine-67 (Tyr-67) nitration of cytochrome c (cyt c) was observed under oxidative stress affecting its structure and electron transfer properties. Hence, in this study, molecular dynamics (MD) simulations were carried out at room temperature to investigate the structural and conformational changes in the nitrated cyt c's. MD results revealed that the bond between FE (Heme-105) and S (Met-80) considerably weakened, radius of gyration, backbone and Cα root-mean-square deviations decreased and hydrogen bonding increased in the nitrated cyt c's relative to wild type (WT) cyt c. Ramachandran plot analysis revealed that N- and C-terminal helices also affected by nitration at CE2 carbon atom. Furthermore, essential dynamics analysis showed that amplitude of concerted motion decreased in the nitrated cyt c's, perhaps due to the increase in the hydrogen bonding interaction. Taken together, the structural and conformational changes in the active site Tyr-67 nitrated cyt c may have implications in the loss of electron/proton transfer and gain of apoptotic properties.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Combining NMR ensembles and molecular dynamics simulations provides more realistic models of protein structures in solution and leads to better chemical shift prediction

While chemical shifts are invaluable for obtaining structural information from proteins, they also offer one of the rare ways to obtain information about protein dynamics. A necessary tool in transforming chemical shifts into structural and dynamic information is chemical shift prediction. In our previous work we developed a method for 4D prediction of protein ¹H chemical shifts in which molecular motions, the 4th dimension, were modeled using molecular dynamics (MD) simulations. Although the approach clearly improved the prediction, the X-ray structures and single NMR conformers used in the model cannot be considered fully realistic models of protein in solution. In this work, NMR ensembles (NMRE) were used to expand the conformational space of proteins (e.g. side chains, flexible loops, termini), followed by MD simulations for each conformer to map the local fluctuations. Compared with the non-dynamic model, the NMRE+MD model gave 6–17% lower root-mean-square (RMS) errors for different backbone nuclei. The improved prediction indicates that NMR ensembles with MD simulations can be used to obtain a more realistic picture of protein structures in solutions and moreover underlines the importance of short and long time-scale dynamics for the prediction. The RMS errors of the NMRE+MD model were 0.24, 0.43, 0.98, 1.03, 1.16 and 2.39 ppm for ¹Hα, ¹HN, ¹³Cα, ¹³Cβ, ¹³CO and backbone ¹⁵N chemical shifts, respectively. The model is implemented in the prediction program 4DSPOT, available at .     

Retention of Conformational Entropy upon Calmodulin Binding to Target Peptides Is Driven by Transient Salt Bridges

Calmodulin (CaM) is a highly flexible calcium-binding protein that mediates signal transduction through an ability to differentially bind to highly variable binding sequences in target proteins. To identify how binding affects CaM motions, and its relationship to conformational entropy and target peptide sequence, we have employed fully atomistic, explicit solvent molecular dynamics simulations of unbound CaM and CaM bound to five different target peptides. The calculated CaM conformational binding entropies correlate with experimentally derived conformational entropies with a correlation coefficient R² of 0.95. Selected side-chain interactions with target peptides restrain interhelical loop motions, acting to tune the conformational entropy of the bound complex via widely distributed CaM motions. In the complex with the most conformational entropy retention (CaM in complex with the neuronal nitric oxide synthase binding sequence), Lys-148 at the C-terminus of CaM forms transient salt bridges alternating between Glu side chains in the N-domain, the central linker, and the binding target. Additional analyses of CaM structures, fluctuations, and CaM-target interactions illuminate the interplay between electrostatic, side chain, and backbone properties in the ability of CaM to recognize and discriminate against targets by tuning its conformational entropy, and suggest a need to consider conformational dynamics in optimizing binding affinities.     

Conformational properties of a cyclic peptide bradykinin B2 receptor antagonist using experimental and theoretical methods.

The solution conformation of the cyclic peptide J324 (cyclo0,6-[Lys0,Glu6,D-Phe7]BK), an antagonist targeted at the bradykinin (BK) B2 receptor, has been investigated using experimental and theoretical methods. In order to gain insight into the structural requirements essential for BK antagonism, we carried out molecular dynamics (MD) simulations using simulated annealing as the sampling protocol. Following a free MD simulation we performed simulations using nuclear Overhauser enhancement (NOE) distance constraints determined by NMR experiments. The low-energy structures obtained were compared with each other, grouped into families and analyzed with respect to the presence of secondary structural elements in their backbone. We also introduced new ways of plotting structural data for a more comprehensive analysis of large conformational sets. Finally, the relationship between characteristic backbone conformations and the spatial arrangement of specific pharmacophore centers was investigated.     

Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories.

This paper explores the dependence of the molecular dynamics (MD) trajectory of a protein molecule on the titration state assigned to the molecule. Four 100-ps MD trajectories of bovine pancreatic trypsin inhibitor (BPTI) were generated, starting from two different structures, each of which was held in two different charge states. The two starting structures were the X-ray crystal structure and one of the solution structures determined by NMR, and the charge states differed only in the ionization state of N terminus. Although it is evident that the MD simulations were too short to sample fully the equilibrium distribution of structures in each case, standard Poisson-Boltzmann titration state analysis of the resulting configurations shows general agreement between the overall titration behavior of the protein and the charge state assumed during MD simulation: at pH 7, the total net charge of the protein resulting from the titration analysis is consistently lower for the protein with the N terminus assumed to be neutral than for the protein with the N terminus assumed to be charged. For most of the ionizable residues, the differences in the calculated pKaS among the four trajectories are statistically negligible and remain in good agreement with the data obtained by crystal structure titration and by experiment. The exceptions include the N terminus, which responds directly to the change of its imposed charge; the C terminus, which in the NMR structure interacts strongly with the former; and a few other residues (Arg 1, Glu 7, Tyr 35, and Arg 42) whose pKaS reflect the initial structure and the limited trajectory lengths. This study illustrates the importance of the careful assignment of protonation states at the start of MD simulations and points to the need for simulation methods that allow for the variation of the protonation state in the calculation of equilibrium properties.     

Arrhythmogenic Calmodulin Mutations Affect the Activation and Termination of Cardiac Ryanodine Receptor-mediated Ca2+ Release

The intracellular Ca²⁺ sensor calmodulin (CaM) regulates the cardiac Ca²⁺ release channel/ryanodine receptor 2 (RyR2), and mutations in CaM cause arrhythmias such as catecholaminergic polymorphic ventricular tachycardia (CPVT) and long QT syndrome. Here, we investigated the effect of CaM mutations causing CPVT (N53I), long QT syndrome (D95V and D129G), or both (CaM N97S) on RyR2-mediated Ca²⁺ release. All mutations increased Ca²⁺ release and rendered RyR2 more susceptible to store overload-induced Ca²⁺ release (SOICR) by lowering the threshold of store Ca²⁺ content at which SOICR occurred and the threshold at which SOICR terminated. To obtain mechanistic insights, we investigated the Ca²⁺ binding of the N- and C-terminal domains (N- and C-domain) of CaM in the presence of a peptide corresponding to the CaM-binding domain of RyR2. The N53I mutation decreased the affinity of Ca²⁺ binding to the N-domain of CaM, relative to CaM WT, but did not affect the C-domain. Conversely, mutations N97S, D95V, and D129G had little or no effect on Ca²⁺ binding to the N-domain but markedly decreased the affinity of the C-domain for Ca²⁺. These results suggest that mutations D95V, N97S, and D129G alter the interaction between CaM and the CaMBD and thus RyR2 regulation. Because the N53I mutation minimally affected Ca²⁺ binding to the C-domain, it must cause aberrant regulation via a different mechanism. These results support aberrant RyR2 regulation as the disease mechanism for CPVT associated with CaM mutations and shows that CaM mutations not associated with CPVT can also affect RyR2. A model for the CaM-RyR2 interaction, where the Ca²⁺-saturated C-domain is constitutively bound to RyR2 and the N-domain senses increases in Ca²⁺ concentration, is proposed.     

Molecular dynamics of sickle and normal hemoglobins

Molecular dynamics (MD) simulations have been carried out for 62.5 ps on crystal structures of deoxy sickle cell hemoglobin (HbS) and normal deoxy hemoglobin (HbA) using the CHARMM MD algorithm, with a time step of 0.001 ps. In the trajectory analysis of the 12.5–62.5 (50 ps) simulation, oscillations of the radius of gyration and solvent-accessible surface area were calculated. HbS exhibited a general contraction during the simulation, while HbA exhibited a nearly constant size. The average deviations of simulated structures from the starting structures were found to be 1.8 Å for HbA and 2.3 Å for HbS. The average rms amplitudes of atomic motions (atomic flexibility) were about 0.7 Å for HbA and about 1.0 Å for HbS. The amplitudes of backbone motion correlate well with temperature factors derived from x-ray crystallography. A comparison of flexibility between the α- and β-chains in both HbA and HbS indicates that the β-chains generally exhibited greater flexibility than the α-chains, and that the HbS β-chains exhibit greater flexibility in the N-terminal and D- and F-helix regions than do those of HbA. The average amplitude of backbone torsional oscillations was about 9°, a value comparable with that of other simulations, with enhanced torsional oscillation occurring primarily at the ends of helices or in loop regions between helices. Comparison of atomic flexibility and torsional oscillation results suggests that the increased β-chain flexibility results from relatively concerted motions of secondary structure elements. The increased flexibility may play an important role in HbS polymerization. Time course analysis of conformational energy of association, hydrogen bonding and hydrophobic bonding (as calculated from solvent accessibility) shows that all three of these factors contribute to the stability of subunit association for both hemoglobins. © 1993 John Wiley & Sons, Inc.