New methods for the colorimetric assay of PIID regulatory protein, uridylyltransferase, and uridylyl-removing enzyme in glutamine synthetase cascade

Adenylylation and deadenylylation of glutamine synthetase (GS) are catalyzed by the same adenylyltransferase (ATase). The ability of ATase to catalyze adenylylation is markedly stimulated by the unmodified form of a regulatory protein, P_IIA, whereas its capacity to catalyze deadenylylation is stimulated by the uridylylated form (P_IID) of the regulatory protein. Interconversion between P_IIA and P_IID is catalyzed by uridylyltransferase (UTase) and uridylylremoving enzyme (UR). New colorimetric methods were developed for the assays of P_IID, UTase, and UR activities. The P_IID activity is monitored by its unique ability to stimulate the ATase catalyzed formation of unadenylylated subunits from adenylylated GS. The inerease of unadenylylated subunits is determined by measuring the γ-glutamyltransferase activity of GS under conditions where the activity of an unadenylylated subunit is about 15 times greater than that of an adenylylated subunit (i.e., at pH 8.0 in the presence of Mn²⁺). Assays for UTase and UR enzyme are derived by coupling the P_IID assay to the UTase and UR reactions. For the UTase reaction, the formation of P_IID from P_IIA is measured, whereas the decrease in P_IID is followed for the UR assay. These assays have been applied to follow the activities of these proteins during their purification procedures, to the mechanistic studies on the deadenylylation reaction, and to determine the activities of these proteins in mutants produced during the genetic study of glutamine synthetase cascade. The problems evolved from these assays are discussed.     

In situ inactivation of E. coli uridylylation cycle is independent of the state of covalent modification of the components of the glutamine synthetase cascade

Permeabilization of nitrogen-starved cells of Escherichia coli W with Lubrol WX leads to a selective inactivation of the uridylyl-removing uridylyltransferase (UR/ UTase) enzyme of the glutamine synthetase (GS) cascade system; whereas similar treatment does not affect activity of UR/UTase in cells grown under conditions of nitrogen excess (10 mm glutamine) (Mura, U., and Stadtman, E. R. (1981) J. Biol. Chem.256, 13014–13021). The possibility that susceptibility to Lubrol inactivation is related to differences in the state of adenylylation of GS and/or in the state of uridylylation of the P_II protein was investigated. Permeabilized cells from nitrogen sufficient as well as from nitrogen-limited growth medium were exposed to Lubrol after prior incubation under conditions that lead to high or low states of GS adenylylation and high or low P_IID/P_IIA ratios. Integrity of UR/UTase was monitored by measuring the capacity of UTP to stimulate the deadenylylation of GS in situ. The results showed that the inactivation of UR/UTase by Lubrol is not affected by the states of GS adenylylation or P_II uridylylation.     

Metabolite regulation of the state of adenylylation of glutamine synthetase

When glutamine synthetase is incubated in a mixture containing adenylyltrans-ferase, the regulatory protein (P_II) and several effectors, including ATP, UTP, P_i, α-ketoglutarate, glutamine, and Mg²⁺ and/or Mn²⁺, it ultimately assumes a constant state of adenylylation. The final state of adenylylation (i.e., the number of adenylylated subunits per mole of enzyme) can vary from 0 to 12 and is specified by the concentrations and ratios of the various effectors and by the extent of uridylylation of P_II (i.e., the P_IIA:P_IID ratio). Under otherwise identical conditions, increasing the concentrations of either UTP, P_i, α-ketoglutarate, Mn²⁺, or P_IID decreases the state of adenylylation finally reached, whereas increasing the concentrations of either glutamine, ATP, or Pua increases the final state of adenylylation. The final state of adenylylation is independent of the concentrations of glutamine synthetase, adenylyltransferase, and P_II (but not of the P_IIA:P_IIDratio), and also of the initial average state of adenylylation of glutamine synthetase. Various lines of evidence show that the final state of adenylylation represents a dynamic steady state in which the rates of adenylylation and deadenylylation of glutamine synthetase are equal. It is concluded that the regulation of glutamine synthetase activity by the adenylylation mechanism utilizes a significant amount of ATP energy, but this amount is less than 0.1% that utilized directly by the glutamine synthetase in the synthesis of glutamine.     

New enzymic assays for glutamine synthetase adenylytransferase and its regulatory protein PIIA.

Glutamine synthetase from some gram-negative bacteria is regulated mainly by a covalent modification cascade. The activity of the enzyme is dependent on its state of adenylylation, which is catalyzed by adenylyltransferase (ATase), whose activity is modulated by a regulatory protein, P_II, which exists in two interconvertible forms, P_IIA and P_IID. In this report, two simple enzymic assays for ATase and P_IIA are described. These methods are based on the knowledge that unadenylylated and adenylylated glutamine synthetase exhibit different pH optima in the γ-glutamyl transferase reaction and that l-alanine, a noncompetitive inhibitor, inhibits them to different extents. These assays have been used in the purification of ATase and P_IIA and in mechanistic studies on adenylylation. The scope and limitations of these assays are discussed.     

Cascade control of E. coli glutamine synthetase. II. Metabolite regulation of the enzymes in the cascade.

Enzymes and regulatory proteins involved in the cascade control of glutamine synthetase activity of Escherichia coli have been separated from one another and the effects of numerous metabolites on each step in the cascade have been determined. The adenylyl transferase (ATase) -catalyzed adenylylation of glutamine synthetase, which requires the presence of the unmodified form of the regulatory protein PII is enhanced by glutamine and is inhibited by either α-ketoglutarate (α-KG) or the uridylylated form (PII·UMP) of the regulatory protein. PII·UMP and α-KG act synergistically to inhibit this activity. In contrast, the PII·UMP-dependent, ATase-catalyzed deadenylylation of glutamine synthetase requires α-KG and ATP and is inhibited by glutamine or PII and synergistically by glutamine plus PII. The capacity of uridylyl transferase (UTase) to catalyze the uridylylation of PII is dependent on the presence of α-KG and ATP and is inhibited by glutamine. The deuridylylation of PII·UMP by the uridylyl removing enzyme (UR) is enhanced by glutamine but is unaffected by α-KG. However, CMP, UMP, and CoA all inhibit activity at 10^?6m. High concentrations of ATase inhibit both UR and UTase activities, presumably by binding the regulatory protein. Of more than 50 substances that alter the activity of at least one enzyme in the cascade, only α-KG and glutamine affect the activity at every step. This accounts for the observation that glutamine synthetase activity in vivo is very sensitive to the intracellular ratio of α-KG to glutamine.     

The effects of point of substitution on the electrochemical behavior of new manganese phthalocyanines, tetra-substituted with diethylaminoethanethiol

The syntheses and comparative studies of the spectral, voltammetry and spectroelectrochemical properties of new manganese phthalocyanine complexes, tetra-substituted with diethylaminoethanethio at the peripheral (complex 3a) and non-peripheral positions (complex 3b) are reported. Solution electrochemistry of complex 3a showed quasi-reversible metal-based (Mn^IIIPc⁻²/Mn^IIPc⁻², E_1/2 = −0.07 V vs. Ag|AgCl) and ring-based (Mn^IIPc⁻²/Mn^IIPc⁻³, E_1/2 = −0.78 V vs. Ag|AgCl) reductions, but no ring-based oxidation. However, complex 3b showed weak irreversible ring-oxidation signal (E_p = +0.86 vs. Ag|AgCl). Reversible metal-based (Mn^IIIPc⁻²/Mn^IIPc⁻², E_1/2 = −0.04 V vs. Ag|AgCl) and ring-based (Mn^IIPc⁻²/Mn^IIPc⁻³, E_1/2 = −0.68 V vs. Ag|AgCl) reductions were also observed for complex 3b. Spectroelectrochemistry was used to confirm these processes. Reduction process involving the metal (Mn^IIIPc⁻²/Mn^IIPc⁻²) was associated with the formation of manganese μ-oxo complex in complex 3a.     

Enzymic procedures for determining the average state of adenylylation of Escherichia coli glutamine synthetase.

Under physiological conditions, the activity of the glutamine synthetase in gram-negative bacteria is inversely proportional to the number of its subunits that are adenylylated [Kingdon, H. S., Shapiro, B. m., and Stadtman, E. R., (1967), Proc. Nat. Acad. Sci. U. S. A.58, 1703 – 1710]. Six different enzymic procedures have been developed for determining the average state of adenylylation, i.e., the average number of adenylylated subunits per enzyme molecule, which can vary from 0 to 12. These methods depend on measurements of the γ-glutamyltransferase activity in assay mixtures containing Mn²⁺ at a pH where adenylylated and unadenylylated subunits are equally active and also under conditions where only unadenylylated subunits are active. The methods can be used to measure the state of adenylylation of glutamine synthetase in crude extracts with an accuracy of ±7%.     

Cascade control of E. coli glutamine synthetase. I. Studies on the uridylyl transferase and uridylyl removing enzyme(s) from E. coli.

The state of adenylylation of glutamine synthetase in Escherichia coli is regulated by the adenylyl transferase, the PII regulatory protein, uridylyl transferase (UTase), and the uridylyl removing enzyme (UR). The regulatory protein exists in an unmodified state (PII) which promotes adenylylation and in a uridylylated form (PII·UMP) which promotes deadenylylation of glutamine synthetase. The UR and UTase enzymes catalyze the interconversion of PII and PII·UMP. The UR and UTase have been partially purified by chromatography over DEAE-cellulose, AH-Sepharose 4B, Sephadex G-200, and gel electrophoresis. The two activities co-purify at all steps in the isolation although preparations containing different ratios of UTase:UR activities have been isolated. These UR·UTase activities have apparent molecular weight of 140,000. Both activities are inactivated by sulfhydryl reagents, both activities are heat inactivated, and both are stabilized by high salt concentrations. Both activities are inhibited in the crude extract by dialyzable inhibitors, but the UR is also inhibited by a nondialyzable inhibitor. This endogenous inhibitor is of molecular weight greater than 100,000 daltons, and binds CMP and UMP which are the apparent inhibitory agents. CMP and UMP are antagonistic in their effects on the UR activity. No effect of the CMP, UMP, or the large inhibitor on the other steps in the cascade could be demonstrated. The Mn²⁺-supported UR activity was also shown to be inhibited by a number of divalent cations, particularly Zn²⁺.     

Manganese(III) complexes of N2O2 donor 5-bromosalicylideneimine ligands: Combined effects of electron withdrawing substituents and chelate ring size variations on electrochemical properties

A series of mononuclear manganese(III) complexes of formulae [Mn(L)(X)(H₂O)] (1-13) and [Mn(L)(X)] (14-17) (X = ClO₄, F, Cl, Br, I, NCS, N₃), derived from the Schiff bases of 5-bromosalicylaldehyde and different types of diamine (1,2-diaminoethane, 1,2-diaminopropane, 1,3-diaminopropane and 1,4-diaminobutane), have been synthesized and characterized by the combination of IR, UV-Vis spectroscopies, cyclic voltammetry and by X-ray crystallography. The redox properties of all the manganese(III) complexes show grossly identical features consisting of a reversible or quasireversible Mn^III/Mn^II reduction. Besides Mn^III/Mn^II reduction, the complexes 4, 5, 10, 13 and 16 also show reversible or quasireversible Mn^III/Mn^IV oxidation. A linear correlation has been found for the complexes 5, 7, 11 and 13 [Mn(L²)(X)(H₂O)] (X = F, Cl, Br, I) when E_1/2 [Mn^III/Mn^II] is plotted against Mulliken electronegativities (χ_M). The effect of the flexibility of the ligand on redox potential has been studied. It has been observed that the manganese(II) state is stabilized with increasing flexibility of the ligand environment. The crystal structure of 6 shows an octahedral geometry.     

Amino acid substitutions in the sugar kinase/hsp70/actin superfamily conserved ATPase core of E. coli glycerol kinase modulate allosteric ligand affinity but do not alter allosteric coupling

IIA^Glc, the glucose-specific phosphocarrier protein of the phosphoenolpyruvate:glycose phosphotransferase system, is an allosteric inhibitor of Escherichia coli glycerol kinase. A linked-functions initial-velocity enzyme kinetics approach is used to define the MgATP-IIA^Glc heterotropic allosteric interaction. The interaction is measured by the allosteric coupling constants Q and W, which describe the mutual effect of the ligands on binding affinity and the effect of the allosteric ligand on V_max, respectively. Allosteric interactions between these ligands display K-type activation and V-type inhibition. The allosteric coupling constant Q is about 3, showing cooperative coupling such that each ligand increases the affinity for binding of the other. The allosteric coupling constant W is about 0.1, showing that the allosteric inhibition is partial such that binding of IIA^Glc at saturation does not reduce V_max to zero. E. coli glycerol kinase is a member of the sugar kinase/heat shock protein 70/actin superfamily, and an element of the superfamily conserved ATPase catalytic core was identified as part of the IIA^Glc inhibition network because it is required to transplant IIA^Glc allosteric control into a non-allosteric glycerol kinase [A.C. Pawlyk, D.W. Pettigrew, Proc. Natl. Acad. Sci. USA 99 (2002) 11115-11120]. Two of the amino acids at this locus of E. coli glycerol kinase are replaced with those from the non-allosteric enzyme to enable determination of its contributions to MgATP-IIA^Glc allosteric coupling. The substitutions reduce the affinity for IIA^Glc by about 5-fold without changing significantly the allosteric coupling constants Q and W. The insensitivity of the allosteric coupling constants to the substitutions may indicate that the allosteric network is robust or the locus is not an element of that network. These possibilities may arise from differences of E. coli glycerol kinase relative to other superfamily members with respect to oligomeric structure and location of the allosteric site in a single domain far from the catalytic site.     

Thymosin β4 in cultured mammalian cell lines

Thymosin β₄, originally isolated from calf thymus [Low et al., Proc. Nat. Acad. Sci. USA78, 1162–1166 (1981)] is present in a number of cell lines unrelated to the reticuloendothelium, including myoblasts and fibroblasts. It is also actively synthesized by these cell lines. Its content and rate of synthesis in the cell lines examined appear to be correlated with their ability to adhere and their motility.     

Synthesis of palladium(II) 3d-metal(II) paddlewheel acetate-bridged heterodimetallic complexes: Unexpected catalysis by water molecules

A study of the reaction kinetics between the trinuclear palladium(II) acetate Pd₃(μ-OOCMe)₆ (1) and the mononuclear 3d-metal (Ni^II, Co^II, Cu^II) acetates in acetic acid under water-specified conditions revealed a fairly complicated reaction mechanism triggered by the primary hydrolytic cleavage of an acetate bridge in molecule 1. The isolated reaction products, as established by X-ray diffraction study, are 1D polymeric complexes {Pd(μ-OOCMe)₄M(OH₂)(HOOCMe)₂}_n (M = Ni^II, Co^II, Cu^II, Mn^II, Zn^II) built of the Pd^II-based paddlewheel units [Pd(μ-OOCMe)₄M] and linked trough the H-bonded H₂O and MeCOOH molecules.     

Coordination polymers of manganese(II) and cobalt(II) of a flexible tetradentate pyridine amide ligand: 1D zigzag network and non-covalent interactions

Synthesis and crystal structure of two coordination polymers of composition [Mn^II(H₂bpbn)_1.5][ClO₄]₂ · 2MeOH · 2H₂O (1) and [Co^II(H₂bpbn)(H₂O)₂]Cl₂ · H₂O (2) [H₂bpbn = N,N′-bis(2-pyridinecarboxamido)-1,4-butane], formed from the reaction between [Mn(H₂O)₆][ClO₄]₂/CoCl₂ · 4H₂O with H₂bpbn in MeCN, are described. In 1 each Mn^II ion is surrounded by three pyridine amide units, providing three pyridine nitrogen and three amide oxygen donors. Each Mn^II center in 1 has distorted MnN₃O₃ coordination. In 2 each Co^II ion is coordinated by two pyridine amide moieties in the equatorial plane and two water molecules provide coordination in the axial positions. Thus, the metal center in 2 has trans-octahedral geometry. In both 1 and 2, the existence of 1D zigzag network structure has been revealed. Owing to π-π stacking of pyridine rings from adjacent layers 1 forms 2D network; 2 forms 2D and 3D network assemblies via N-H?Cl and O-H?Cl secondary interactions. Both the metal centers are high-spin.     

The use of 13C spin lattice relaxation times to study the interaction of alpha-methyl-D-glucopyranoside with concanavalin A

The spin lattice relaxation rates ($\text{1}\text{T}{}_1$) of the natural abundance ¹³C of all seven carbons of α-methyl-d-glucopyranoside were measured in the presence of Mn(II)-concanavalin A. The paramagnetic contribution to the relaxation rates was used to calculate the distance between the Mn(II) site and the saccharide. The results are consistent with the binding of the saccharide in a unique configuration on the surface of the protein with the ?CH₂OH (6 carbon) ~9Å, the ?CH₃ (7 carbon) 14Å, and carbons 1–5 about 10Å from the Mn(II). Notwithstanding the fact that these distances may be 10% or less in error, these data are in disagreement with a value of greater than 10Å between the saccharide and Mn(II) binding sites determined from X-ray diffraction studies by Edelman et al. ((1972) Proc. Nat. Acad. Sci. USA69, 2580–2584) and Hardman and Ainsworth ((1972) Biochemistry11, 4910–4919).     

Seven-coordinate Mn(II) and Co(II) complexes of the pentadentate ligand 2,6-diacetyl-4-carboxymethyl-pyridine bis(benzoylhydrazone): Synthesis, crystal structure and magnetic properties

The metal complexation properties of a functionalized N₃O₂ donor ligand H₂L², where H₂L² stands for 2,6-diacetyl-4-carboxymethyl-pyridine bis(benzoylhydrazone), are investigated by structural and spectroscopic (IR, ESI-MS and EPR) characterization of its Mn(II) and Co(II) complexes. The ligand H₂L² is observed to react essentially in the same fashion as its unmodified parent H₂L¹ producing mixed-ligand [M(H₂L²)(Cl₂)] complexes (M = Mn^II (1), Co^II (3)) upon treatment with MCl₂. Complexes [M(HL²)(H₂O)(EtOH)]BPh₄ (M = Mn 2, M = Co 4), incorporating the supporting ligand in the partially deprotonated form (HL²)⁻, are formed by salt elimination of the [M(H₂L²)(Cl₂)] compounds with NaBPh₄. Compounds 2 and 4 are isostructural featuring distorted pentagonal-bipyramidal coordinated Mn^II and Co^II ions, with the H₂O and EtOH ligands bound in axial positions. Intermolecular hydrogen bonding interactions of the type M-OH₂?O-M involving the H₂O ligands and the carbonyl functions of the supporting ligand assembles the complexes into dimers. Temperature-dependent magnetic susceptibility measurements (2-300 K) show a substantially paramagnetic Curie behavior for the Mn²⁺ compound (2) influenced by zero-field splitting and significant orbital angular momentum contribution for 4 (high-spin Co^II). The exchange coupling across the Mn^II-OH₂?O-Mn^II bridges in 2 was found to be less than 0.1 cm⁻¹, suggesting that no significant intradimer exchange coupling occurs via this path.     

Metal-directed assembly of 1-D and 2-D coordination polymers with fluconazole and dicyanamide co-ligand

The coordination chemistry of a flexible poly(triazolyl)alkane derivative, fluconazole (HFlu), with a series of transition metal ions and dicyanamide (dca) anionic co-ligand has been explored to afford six new metal-organic coordination polymers. Complexes [M(HFlu)₂(dca)₂]_n (M = Mn^II for 1, Fe^II for 2, Co^II for 3, Zn^II for 5, and Cd^II for 6) have the isostructural 1-D double-chain array via bridging fluconazole, whereas [Cu₃(Flu)₂(dca)₄(CH₃OH)₂]_n (4) shows an unusual 2-D layered metal-organic framework with dimeric Cu^II subunits. Notably, both types of coordination patterns are extended into distinct 3-D supramolecular networks via hydrogen-bonding interactions. This result indicates that the choice of metal ion has a significant effect on these polymeric structures as well as the binding modes of the ligands, which is discussed in detail. The Zn^II and Cd^II complexes 5 and 6 display similar fluorescent emissions at 260 nm in the solid state, which essentially are intraligand transitions.     

A source of ultrasensitivity in the glutamine response of the bicyclic cascade system controlling glutamine synthetase adenylylation state and activity in Escherichia coli

Glutamine synthetase (GS) activity in Escherichia coli is regulated by reversible adenylylation, brought about by a bicyclic system comprised of uridylyltransferase/uridylyl-removing enzyme (UTase/UR), its substrate, PII, adenylyltransferase (ATase), and its substrate, GS. The modified and unmodified forms of PII produced by the upstream UTase/UR-PII cycle regulate the downstream ATase-GS cycle. A reconstituted UTase/UR-PII-ATase-GS bicyclic system has been shown to produce a highly ultrasensitive response of GS adenylylation state to the glutamine concentration, but its composite UTase/UR-PII and ATase-GS cycles displayed moderate glutamine sensitivities when examined separately. Glutamine sensitivity of the bicyclic system was significantly reduced when the trimeric PII protein was replaced by a heterotrimeric form of PII that was functionally monomeric, and coupling between the two cycles was different in systems containing wild-type or heterotrimeric PII. Thus, the trimeric nature of PII played a role in the glutamine response of the bicyclic system. We therefore examined regulation of the individual AT (adenylylation) and AR (deadenylylation) activities of ATase by PII preparations with various levels of uridylylation. AR activity was affected in a linear fashion by PII uridylylation, but partially modified wild-type PII activated the AT much less than expected based on the extent of PII modification. Partially modified wild-type PII also bound to ATase less than expected based upon the fraction of modified subunits. Our results suggest that the AT activity is only bound and activated by completely unmodified PII and that this design is largely responsible for ultrasensitivity of the bicyclic system.     

Mimicking the reduced, oxidized and azide inhibited form of manganese superoxide dismutase by mononuclear Mn compounds utilizing tridentate ligands

The manganese complexes [Mn^II(Hbmimpm)₂(NO₃)](NO₃) · Et₂O (1), [Mn^III(bmimpm)₂(OAc)] · 2CH₂Cl₂(2), and [Mn^III(bmiapm)₂(OAc)] · MeOH · H₂O · CH₂Cl₂(3) containing the new ligands Bis(1-methylimidazol-2-yl)-(4-methoxyphen-1-yl)methanol (Hbmimpm) and Bis[(1-methylimidazol-2-yl)](2-aminophenyl)methanol (Hbmiapm) were synthesized. They are good structural models for the reduced (1) and oxidized (2, 3) form of manganese superoxide dismutase. All complexes were characterized by spectroscopic methods and X-ray structure analysis. Compounds 1 and 2 crystallize in the monoclinic space group P2₁/c whereas complex 3 crystallizes in the monoclinic space group P2₁/n. The coordination sphere around the manganese cores is distorted octahedral with two corresponding tridentate ligands representing the protein ligands and one nitrate (1) or acetate (2, 3) ion occupying two cis positions. Similar to the enzyme the Mn(III) complex 2 reacts with sodium azide. The obtained microcrystalline azide adduct was characterized by UV-Vis and IR spectroscopy.     

Structural chemistry of lanthanidedicyclopentadienidehalides. Part 1. Two modifications of gadoliniumdicyclopentadienidebromide, [Gd(C5H5)2Br]2 and 1∞[Gd(C5H5)2Br]

The crystal structures of two modifications of gadoliniumdicyclopentadienidebromide, [Gd(C₅H₅)₂Br]₂ (I) and ¹_∞[Gd(C₅H₅)₂Br] (II) have been determined from X-ray diffraction data. I crystallizes in the [Sc(C₅H₅)₂Cl]₂-type structure, space group P2₁/c, with a=14.110(3), b=16.488(3), c= 13.765(3) Å, β=93.25(2)°, V=3197(2) ų, and D_c= 2.289 g cm⁻³ for Z=6 molecules. II crystallizes in space group P2₁/c with a=5.946(7), b=8.447(5), c=20.239(9) Å, β=90.11(4)°, V=1020(2) ų, D_c=2.392 g cm⁻³ for Z=4 formula units. The structures have been refined by full matrix least-squares techniques to conventional R factors of 0.034 for 3014 (I) and 1964 (II) reflections (with I>2σ(I)). I consists of dimers with two bromine bridges (mean GdBr 2.872 Å). II has a double chain structure with alternating juxtaposition of gadolinium and bromine atoms (GdBr 2.912 Å (once) and 3.133 Å (twice)). The arrangement of the C₅H₅ groups with regard to the metal η⁵ fashion) is nearly identical in I and II (mean GdC 2.63(1) Å (I) and 2.62(1) Å (II)). Single crystals of I and II are obtained by sublimation at different temperatures. The formation of both modifications is discussed as to its dependence on the state of the gaseous phase equilibrium [Gd(C₅H₅)₂Br]₂ ⇄ 2Gd(C₅H₅)₂Br. Obviously, I crystallizes from gaseous phase dimers while II forms from the monomers.     

Analysis of partial assortative mating and sexual selection models for a polygamous species involving a trait based on levels of heterozygosity

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA74, 3476–3479), Wilbur et al. (1978, Evolution32, 264–270), and Singh and Zouros (1978, Evolution32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.