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G K Ackers

Publications and source records attributed to G K Ackers.

At least 19 recordsLinked to original sources

Lack of neighborhood effects from a transcriptionally active phosphoglycerate kinase-neo cassette located between the murine beta-major and beta-minor globin genes.

For the treatment of beta-globin gene defects, a homologous recombination-mediated gene correction approach would provide advantages over random integration-based gene therapy strategies. However, "neighborhood effects" from retained selectable marker genes in the targeted locus are among the key issues that must be taken into consideration for any attempt to use this strategy for gene correction. An Ala-to-Ile mutation was created in the beta6 position of the mouse beta-major globin gene (beta(6I)) as a step toward the development of a murine model system that could serve as a platform for therapeutic gene correction studies. The marked beta-major gene can be tracked at the level of DNA, RNA, and protein, allowing investigation of the impact of a retained phosphoglycerate kinase (PGK)-neo cassette located between the mutant beta-major and beta-minor globin genes on expression of these 2 neighboring genes. Although the PGK-neo cassette was expressed at high levels in adult erythroid cells, the abundance of the beta(6I) mRNA was indistinguishable from that of the wild-type counterpart in bone marrow cells. Similarly, the output from the beta-minor globin gene was also normal. Therefore, in this specific location, the retained, transcriptionally active PGK-neo cassette does not disrupt the regulated expression of the adult beta-globin genes. (Blood. 2001;98:65-73)

Animals↗

Coupled energetics of lambda cro repressor self-assembly and site-specific DNA operator binding II: cooperative interactions of cro dimers.

The bacteriophage lambda relies on interactions of the cI and cro repressors which self assemble and bind the two operators (O(R) and O(L)) of the phage genome to control the lysogenic to lytic switch. While the self assembly and O(R) binding of cI have been investigated in detail, a more complete understanding of gene regulation by phage lambda also requires detailed knowledge of the role of cro repressor as it dimerizes and binds at O(R) sites. Since dimerization and operator binding are coupled processes, a full elucidation of the regulatory energetics in this system requires that the equilibrium constants for dimerization and cooperative binding be determined. The dimerization constant for cro has been measured as a prelude to these binding studies. Here, the energetics of cro binding to O(R) are evaluated using quantitative DNaseI footprint titration techniques. Binding data for wild-type and modified O(R) site combinations have been simultaneously analyzed in concert with the dimerization energetics to obtain both the intrinsic and cooperative DNA binding energies for cro with the three O(R) sites. Binding of cro dimers is strongest to O(R)3, then O(R)1 and lastly, O(R)2. Adjacently bound repressors exhibit positive cooperativity ranging from -0.6 to -1.0 kcal/mol. Implications of these, newly resolved, energetics are discussed in the framework of a dynamic model for gene regulation. This characterization of the DNA-binding properties of cro repressor establishes the foundation on which the system can be explored for other, more complex, regulatory elements such as cI-cro cooperativity.

Allosteric Site↗

Coupled energetics of lambda cro repressor self-assembly and site-specific DNA operator binding I: analysis of cro dimerization from nanomolar to micromolar concentrations.

The cro repressor from bacteriophage lambda is an important and classical transcription regulatory protein that binds DNA operator sites as a dimer. Therefore, a complete understanding of gene regulation by cro requires knowledge of the coupled energetics of its protein dimerization and site-specific DNA binding. A method is described by which cro repressor can be labeled in vivo with [(35)S]methionine to a specific activity of 2 x 10(15) cpm/mol. As a prelude to binding studies, the association equilibrium of cro was determined over the range 10(-)(9)-10(-)(3) M using large-zone analytical gel chromatography with radiolabeled repressor. The data are best described by a monomer-dimer stoichiometry with an equilibrium constant of 3.07 (+/-1.08) x 10(6) M(-)(1) total cro monomer. Stokes radii for monomers and dimers were evaluated from the resolved gel partition coefficients. Under the conditions employed in this study (10 mM Bis-Tris, 200 mM KCl, 2.5 mM MgCl(2), 1 mM CaCl(2), 100 microg/mL BSA, pH 7.0, 20 degrees C), self-association of cro to species with assembly states greater than dimers is not observed.

Bacteriophage lambda↗

Confirmation of a unique intra-dimer cooperativity in the human hemoglobin alpha(1)beta(1)half-oxygenated intermediate supports the symmetry rule model of allosteric regulation.

The contribution of the alpha(1)beta(1)half-oxygenated tetramer [alphabeta:alphaO(2)betaO(2)] (species 21) to human hemoglobin cooperativity was evaluated using cryogenic isoelectric focusing. The cooperative free energy of binding, reflecting O(2)-driven protein structure changes, was measured as (21)DeltaG(c) = 5.1 +/- 0. 3 kcal for the Zn/FeO(2) analog. For the Fe/FeCN analog, (21)DeltaG(c) was estimated as 4.0 kcal after correction for a CN ligand rearrangement artifact, demonstrating that ligand rearrangement does not invalidate previous conclusions regarding this species. In the context of the entire Hb cooperativity cascade, which includes eight intermediate species, the 21 tetramer is highly abundant relative to the other doubly-ligated species, providing strong support for the previously determined consensus partition function of O(2) binding and for the Symmetry Rule model of hemoglobin cooperativity (Ackers et al., Science 1992;255:54-63). Cooperativity of normal human hemoglobin is shown to depend on site-configuration, and not solely the number of O(2) bound, nor the occupancy of alpha vs. beta subunits. Verification of a unique contribution from the alpha(1)beta(1)doubly-oxygenated species to the equilibrium O(2) binding curve strongly reinforces the Symmetry Rule interpretation that the alpha(1)beta(1)dimer acts both as a structural and functional element in cooperative O(2) binding.

Allosteric Regulation↗

Structural and functional properties of human hemoglobins reassembled after synthesis in Escherichia coli.

Human hemoglobin produced in the Escherichia coli coexpression system of Hernan et al. [(1992) Biochemistry 31, 8619-8628] has been transformed into a functionally homogeneous protein whose properties closely approximate those of normal hemoglobin A. Both of the alpha and beta chains of this hemoglobin contain a valine-methionine substitution at position 1 in order to accommodate the difference in specificity of the protein-processing enzymes of procaryotes. Despite extensive purification, functional homogeneity of the E. coli expressed hemoglobin was achieved only by the complete disassembly of the hemoglobin into its component alpha and beta globins and their reassembly in the presence of hemin. The kinetics of CO combination and the thermodynamics of O2 binding and cooperativity of the reassembled alphaV1M-betaV1M hemoglobin closely approximate those of HbA. The alpha globin obtained from the E. coli expressed hemoglobin was also combined with normal human beta chains and hemin to form the alphaV1M variant. The alpha+M variant of HbA, in which the normal N-terminal valine of the alpha chains is preceded by a methionine residue, was prepared by the same procedure. The kinetics of the reactions of CO with the alphaV1M and alpha+M variants are similar to those for HbA. The equilibria of oxygen binding to alphaV1M and HbA are similar whereas alpha+M exhibits a significantly higher oxygen affinity. The three-dimensional structures of alphaV1M and alpha+M offer an explanation for the latter affinity difference. Although the structures of alphaV1M and HbA, which have been determined by X-ray crystallography, are virtually indistinguishable except at the N-terminal residues, that of alpha+M indicates the displacement of a solvent molecule, possibly a chloride ion, from arginine 141alpha. Such an alteration in an anion binding site could result in increased oxygen affinity.

Chemical Fractionation↗

Cooperative non-specific DNA binding by octamerizing lambda cI repressors: a site-specific thermodynamic analysis.

Relationships between dimerization and site-specific binding have been characterized previously for wild-type and mutant cI repressors at the right operator (OR) of bacteriophage lambda DNA. However, the roles of higher-order oligomers (tetramers and octamers) that are also formed from these cI molecules have remained elusive. In this study, a clear correlation has been established between repressor oligomerization and non-specific DNA-binding activity. A modification of the quantitative DNase I footprint titration technique has been used to evaluate the degree of saturation of non-specific, OR-flanking lambda DNA by cI repressor oligomers. With the exception of one mutant, only those repressors capable of octamerizing were found to exhibit non-specific DNA-binding activity. The non-specific interaction was accurately modeled using either a one-dimensional, univalent, site-specific Ising lattice approximation, or a more traditional, multivalent lattice approach. It was found that non-specific DNA-binding by repressor oligomers is highly cooperative and energetically independent from site-specific binding at OR. Furthermore, the coupling free energy resolved for non-specific binding was similar to that of site-specific binding for each repressor, suggesting that similar structural elements may mediate the cooperative component of both binding processes. It is proposed that the state of assembly of the repressor molecule modulates its relative affinity for specific and non-specific DNA sequences. These specificities are allosterically regulated by the transmission of assembly-state information from the C-terminal domain, which mediates self-association and cooperativity, to the N-terminal domain, which primarily mediates DNA-binding. While dimers have a high affinity for their cognate sites within OR, tetramers and octamers may preferentially recognize non-specific DNA sequences. The concepts and findings developed in this study may facilitate quantitative characterization of the relationships between specific, and non-specific binding in other systems that utilize multiple modes of DNA-binding cooperativity.

Bacteriophage lambda↗

A quantitative cryogenic gel-shift technique for analysis of protein-DNA binding.

A cryogenic gel mobility shift technique was developed in which a mixture of protein and DNA samples at equilibrium is rapidly quenched and electrophoresed at -40 degrees C. The rapid and sustained drop in temperature results in almost complete stabilization of the equilibrium species distribution. Autoradiogram analysis of relative abundances for the bound and free DNA sites is carried out over a range of initial binding ratios to yield the binding curve and equilibrium constant as in the usual gel-shift assay. Validity of this technique for determining equilibrium populations of the interacting species is based upon two testable assumptions: (i) The equilibrium species distribution does not change during the cryogenic quench procedure. (ii) This equilibrium distribution is also constant during electrophoresis of the sample. Evidence supporting these assumptions was obtained using lambda cI repressor and a 570-bp DNA fragment containing the repressor binding site OR1. The resolved free energy for this interaction (delta G1) was shown to be independent of the quench procedure, duration of the quench stage, residence time in the gel wells, and duration of low-temperature electrophoresis. The technique yielded a free energy that was in close agreement with those from filter binding and DNAse footprint titration methods. This cryogenic version of the gel-shift method may prove especially useful in cases like that of lambda cI/OR1 binding, for which conventional gel-shift methodology has not been feasible.

Cold Temperature↗

Thermodynamic studies on the equilibrium properties of a series of recombinant betaW37 hemoglobin mutants.

In human hemoglobin (Hb) the beta37 tryptophan residue (betaW37), located at the hinge region of the alpha1beta2 interface, forms many contacts with alpha subunit residues of the opposite dimer, in both the T and R quaternary structures. We have carried out equilibrium O2 binding studies on a series of recombinant Hbs that have mutations at this residue site: betaW37Y, betaW37A, betaW37G, and betaW37E. Binding isotherms measured at high concentrations of these mutants were found to be shifted toward increased affinity and decreased cooperativity from that of the normal HbA0 tetramer. Analysis of these binding isotherms indicated that amino acid substitutions at the beta37 position could both destabilize the tetrameric form of the mutants relative to their constituent dimers and also alter cooperativity of the intact tetrameric species. These alterations from wild-type function are dependent on the particular side chain substituted, with the magnitude of change increasing as Trp is substituted by Tyr, Ala, Gly, and Glu. The dimer to tetramer assembly free energy of deoxy-betaW37E, the most perturbed mutant in the series, was measured using analytical gel chromatography to be 9 kcal/tetramer less favorable than that of deoxy HbA0. Stabilizing the betaW37E tetramer by addition of IHP, or by cross-linking at the alphaK99 positions, does not restore normal O2 binding behavior. Thermodynamic parameters of all the mutants were found to correlate with their CO binding rates and with their high-resolution X-ray crystal structures (see accompanying papers: Kwiatkowski et al. (1998) Biochemistry 37, 4325-4335; Peterson & Friedman (1998) Biochemistry 37, 4346-4357; Kavanaugh et al. (1998) Biochemistry 37, 4358-4373].

Amino Acid Substitution↗

Hydropathic analysis of the non-covalent interactions between molecular subunits of structurally characterized hemoglobins.

The software program, HINT (Hydropathic INTeractions), which characterizes non-polar-non-polar, polar-polar, and non-polar-polar interactions, has been used to examine subunit interface associations involved in the hemoglobin allosteric transition at a residue and atomic level. HINT differs from many other computational programs in that it is based not on a statistical method or a force-field but employs parameters experimentally determined from solvent transfer experiments. The main focus of this study is to compare HINT scores that are based upon experimentally and thermodynamically derived measurements with experimentally determined thermodynamic results. The HINT analysis yields a good first-order approximation of experimentally measured energies for these interactions as determined by free energies of dimer-tetramer assembly for mutant hemoglobins. The results provide a framework for understanding subunit stabilities based upon individual atom interactions and repulsions. HINT, in agreement with previous analyses, indicates that: (1) the alpha1beta1 and alpha2beta2 subunit contacts are stabilized via several polar and many hydrophobic interactions with few repulsive contact areas in both the T (deoxyhemoglobin) and R (oxyhemoglobin) structures; (2) the alpha1alpha2 subunit contacts are primarily stabilized by polar salt bridge linkages in both T and R states; and (3) the alpha1beta2 and alpha2beta1 contacts have both strong positive and negative interactions in both T and R states with few hydrophobic interactions. The HINT scoring methodology provides a quantitative characterization of the major role of the alpha1beta2 and alpha2beta1 interfaces in the T-->R quaternary transition. HINT also confirms the stronger hydrogen bond formation in mutant Hb Rothschild (Trp 37beta-->Arg) with Asp94alpha1 that gives rise to a low-affinity (deoxy) hemoglobin. HINT shows that the stabilization of the alpha1beta2 interface with mutant Hb Ypsilanti (Asp99alpha-->Tyr) produces a high-affinity (oxy) hemoglobin by reducing hydrophobic-polar contacts in the R state. HINT interaction maps also identified specific sites for mutagenesis at the alpha1beta2 interface that can be explored to shift the allosteric equilibrium in either direction. In addition, the HINT program provides useful diagnostic data for checking the quality of refined crystallographic structures.

Crystallography, X-Ray↗

Thermodynamic stability of the asymmetric doubly-ligated hemoglobin tetramer (alpha+CNbeta+CN)(alphabeta): methodological and mechanistic issues.

Free energy contributions to cooperativity by the eight ligation intermediates of human hemoglobin (Hb) have been characterized extensively using six oxygenation analogs [cf. Huang et al. (1996) Biophys. J. 71, 2094-2105, Table 2]. These unprecedented data bses have strongly supported the molecular code mechanism of Hb cooperativity [Ackers et al. (1992) science 255, 54-83]. The present study addresses a recent argument against this work [Shibayama et al. (1997) Biochemistry 36, 4375-4381] based on "free energy" determinations for a doubly-ligated species of the CN-met analog. Shibayama et al. (1997) have claimed that, in the hybridization experiments that have been used to determine free energy of the asymmetric "species[21]" tetramer, a portion of the bound cyanide is allegedly released from CN-met Hb during the incubation with deoxy Hb that is used to achieve hybrid equilibrium. These authors have claimed that cyanide release has resulted in extensive electron exchange between heme sites of the hybridizing sample, leading to incorrect evaluation of the equilibrium species population by the cryogenic techniques that have been employed. In this report, we demonstrate that neither appreciable cyanide loss nor electron exchange occurs with the methods that have been used extensively by our two laboratories for these equilibrium determinations [Perrella et al. (1990) Biophys. Chem. 35, 97-103; Daugherty et al. (1991) Proc. Natl. Acad. Sci. U.S.A. 88, 1110-1114]. An alternative experiment, which Shibayama et al. (1997) have carried out to illustrate their claim, does not evaluate a thermodynamic equilibrium property of the species [21] hybrid. The relevance of their newly-estimated "free energy" is therefore unclear. Nevertheless, Shibayama et al. (1997) have claimed that their proposed "free energy" (which is approximately 1.3 kcal more positive than the free energy of -11.4 kcal found independently by our two laboratories) renders invalid the molecular code mechanism of hemoglobin cooperativity. This representation is utterly without foundation since a free energy even more positive than suggested by Shibayama et al. (1997) would be fully consistent with the molecular code mechanism.

Animals↗

Effects of NaCl on the linkages between O2 binding and subunit assembly in human hemoglobin: titration of the quaternary enhancement effect.

Oxygen binding by human hemoglobin (Hb) and the coupled reactions of dimer-tetramer assembly were studied over a range of NaCl concentrations (from 0.08 M to 1.4 M) at pH 7.4 and 21.5 degrees C. A strategy of multi-dimensional analysis was employed [G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A., 91, (1974) 4312] to optimize the resolution of the contributions to cooperativity and their heterotropic salt linkages at each stoichiometric degree of O2 binding. A wide range of Hb concentration was utilized at each [NaCl] in which O2-linked subunit assembly reactions contributed significantly to the positions and shapes of the binding isotherms. Kinetic determinations yielded forward and reverse rate constants for assembly of the unligated species. Amplitudes for the assembly rate data had concentration dependences in agreement with the independently determined dimer-tetramer assembly constants of oxyhemoglobin. Concentration-dependent binding isotherms were analyzed, in combination with the kinetically determined equilibrium constants, to yield salt-linked components of cooperativity at the four stages of oxygenation. The principal results of this study were as follows. (i) Assembly of fully oxygenated Hb tetramers is opposed by NaCl: the dimer-to-tetramer equilibrium constant becomes two orders of magnitude less favorable over the [NaCl] range 0.08 M to 1.4 M. By contrast, for deoxy-Hb the assembly equilibrium constant is reduced only two-fold. (ii) Oxygen binding to dimers is non-cooperative over the entire salt range, whereas dimer affinity is slightly favored by increasing the NaCl concentration. (iii) Overall affinity of tetramers for O2 is opposed by NaCl, becoming an order of magnitude less favorable over the range employed. Most of this decrease occurs at the fourth binding step, which shows a large, salt-mediated quaternary enhancement effect; i.e., the assembly of dimers into tetramers at 0.08 M NaCl is accompanied by an eight-fold increase in O2 affinity. (iv) The quaternary enhancement effect at the last O2-binding step is titrated progressively by salt until it reaches a negligible value near the highest [NaCl] of this study. The lowest [NaCl] condition (0.08 M) elicits the greatest tetramer cooperativity with the largest maximal Hill coefficient and the greatest suppression of intermediates. Possible origins and mechanistic implications of these phenomena are considered.

Hemoglobins↗

Tertiary and quaternary chloride effects of the partially ligated (CN-met) hemoglobin intermediates.

Heterotropic effects of NaCl were studied using CN-met hemoglobin, which has been found to follow the same rules of homotropic cooperativity as CO-Hb and O2-Hb [Huang and Ackers, Biochemistry, 35 (1996) 704; Huang et al., Biophys. J., 71 (1996) 2094]. Modulation of heme site cooperativity by NaCl was determined in this study for all partially ligated CN-met intermediates by measuring their dimer-to-tetramer assembly free energies as a function of NaCl concentration (0.08-1.4 M; pH 7.4, T = 21.5 degrees C). Thermodynamic linkage analysis yielded the contributions to heme site binding cooperativity for all 16 reactions of the binding cascade, and also their apparent changes in bound salt. The principal findings were as follows: (i) At each [NaCl] the ten tetrameric species exhibited three discrete cooperative free energy levels; (ii) positional isomers of the doubly ligated tetramers were distributed among two of these levels according to their specific configurations of ligated sites, in conformity with the symmetry rule mechanism of hemoglobin cooperativity [Ackers et al., Science 255 (1992) 54]; (iii) the apparent moles of NaCl release followed the same configuration-specific distribution as that of heme site cooperativity, i.e., this parameter was synchronized according to the same response clusters. The system thus manifests both a "tertiary chloride effect" and a "quaternary chloride effect", which parallel the tertiary and quaternary Bohr effects [Daugherty et al., Biochemistry, 33 (1994) 10345; Perrella et al., Biochemistry, 33 (1994) 10358] and the tertiary and quaternary enthalpy effects [Huang and Ackers, Biochemistry, 34 (1995) 6316]. Comparison with findings on the stoichiometric O2-binding linkages over an identical range of conditions [Doyle et al., Biophys. Chem., 64 (1997)] revealed that the overall NaCl release upon ligating all four hemes is identical for O2 and CN-met, whereas the detailed distributions of apparent chloride release showed variations between the two ligands, i.e., CN-met Hb showed only a negligible quaternary enhancement at all [NaCl] conditions and a larger tertiary chloride effect compared with O2-Hb. Possible origins of these variations are considered.

Allosteric Regulation↗

The Gibbs conference on biothermodynamics: origins and evolution.

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

Journal Article↗

Heterometallic hybrids of homometallic human hemoglobins.

Hybridization experiments between normal Hb tetramers (Fe2+ Hb) and those with four metal-substituted hemes (i.e., replacement of Fe2+ by Co2+, Mg2+, Mn2+, Mn3+, Ni2+, or Zn2+) have revealed unexpected behavior. These homometallic Hbs have previously served as models that mimic the deoxy or oxy properties of normal Fe2+ Hb. In this study, hybrids were composed of one alpha 1 beta 1 dimer that is metal-substituted at both hemes, in association with a second dimer alpha 2 beta 2 that has normal Fe2+ hemes. Both metal-substituted subunits are unligated, whereas the two Fe2+ subunits either are both unligated or both ligated with O2, CO, or CN. It was found that four of the metal-substituted Hbs (Mg2+ Hb, Mn2+ Hb, Ni2+ Hb, and Zn2+ Hb) did not form detectable amounts of heterometallic hybrids with normal Fe2+ Hb even though (i) their homometallic parents formed tight tetrameric complexes with stabilities similar to that of Fe2+ Hb and (ii) hybrids with metal substitution at both alpha sites or both beta sites are known to form readily. This striking positional effect was independent of whether the normal Fe2+ hemes were ligated and of which ligand was used. These findings indicate that surprisingly large changes in tetramer behavior can arise from small and subtle perturbations at the heme sites. Possible origins of these effects are considered.

Binding Sites↗

Cooperativity mutants of bacteriophage lambda cI repressor: temperature dependence of self-assembly.

Analytical ultracentrifugation was used to study higher order self-assembly of lambda cI repressors, including eight mutants whose monomer to dimer reactions were recently characterized [Burz et al. (1994) Biochemistry 33, 8399]. Six of the mutants were found to remain dimeric up to 50 microM total protein; the remaining mutants (EK102 and PT158) were found to undergo higher order oligomerization, as does wild-type cI. For these three repressors, we determined the stoichiometries and energetics of higher order assembly over the temperature range 5-40 degrees C. Weak dimerization exhibited by two other mutants, SN228 and SR228, was also evaluated by sedimentation equilibrium over this same temperature range. The end-state for higher order assembly of wild-type cI was determined to be octameric, in agreement with Senear et al. [(1993) Biochemistry 32, 6179-6189]. The assembly free energies resolved by the sedimentation analysis program NONLIN [Johnson, M. L., et al. (1981) Biophys. J. 36, 575-588] leads to the prediction that tetramers may contribute significantly to the intermediate populations during assembly. This analysis of the species populations is in accord with recent conclusions from fluorescence anisotropy studies [Banik et al. (1993) J. Biol. Chem. 268, 3938]. It was found that two of the mutant repressors (EK102 and PTI58) assemble into octamers, but with differing possible intermediates. PT158 satisfies the stoichiometry 8M1 <--> 2M4 <--> M8, while the EK102 data conforms to a 4M2 <--> 2M4 <--> M8 model, similar to WT (both the EK102 and WT data could also be described by a dimer-octamer model with no intermediates). Of the six repressors found in this study to remain dimeric, three exhibit non-cooperative DNA binding (GD147, KN192, YH210), two express intermediate cooperativity (EK188, SR228), and one is fully cooperative (SN228). The three octamerizing repressors are fully cooperative [Burz & Ackers (1994) Biochemistry 33, 8399], suggesting a correlation between their ability to form higher order assemblies and to engage in cooperative DNA binding. Linear van't Hoff plots were obtained for overall assembly of wild-type and EK102 dimers, while that of PT158 monomers was curved, indicating a negative heat capacity change. The van't Hoff analyses of dimerization constants for SN228 and SR228 were distinctly different from each other and also from that of wild type; such differences might be related to the disparate cooperative behavior found previously for these mutants (Burz & Ackers, 1994).

Centrifugation, Isopycnic↗