Disequilibrium among several linked neutral genes in finite population I. Mean changes in disequilibrium

Formulae are developed for computing changes in expected values in a finite population of linkage disequilibrium among neutral genes from more than two loci, although the exact analysis is taken up to only six loci. An essentially haploid model is used. As with two loci, the three-locus disequilibrium declines exponentially at all generations, but for m > 3 loci a matrix has to be constructed to give joint changes in the m-locus disequilibrium and products of disequilibria with fewer loci, for example of two m/2-locus disequilibria. The asymptotic rates of change in multilocus disequilibria depend on the arrangement of genes on the chromosome as well as its total length, but the initial rate of breakdown of disequilibrium from a line cross base is less dependent on the arrangement. With equally spaced loci the asymptotic rate of breakdown of m locus disequilibrium is roughly proportional to m. Although mutation and interference are excluded from the main analysis, it is shown how they can be incorporated.     

Multivariate Analysis of Gametic Disequilibrium in the Yanomama

The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. Thirty-two of the fifty villages departed significantly from multiple-locus gametic equilibrium. The largest contributions to the departure from multiple-locus equilibrium were due to the disequilibria between MN and Ss and between Rh(Cc) and Rh(Ee), indicating the effects of tight linkage. After removing the effects of these obvious sources of disequilibrium, sixteen of the fifty villages still remained significantly out of equilibrium. The disequilibrium between any particular pair of loci was highly erratic from village to village, and (with the exception of the MN-Ss and Cc-Ee disequilibria) averaged out very close to zero overall, suggesting a lack of systematic forces (epistatic selection). The departure from equilibrium in any one village is in excess of that expected from random sampling alone, and is attributed primarily to the fission-fusion mode of village formation operative in the Yanomama and the fact that a single village consists of a few extended lineages. Village allele frequencies are highly correlated across loci, and most of the non-independence is accounted for by large correlations in the average allelic frequencies of different loci for related villages. It is suggested that these correlations also are due to territorial expansion and population growth. For the tribe as a whole, all but the tightly linked markers of the MNSs and Rh complexes are approximately uncorrelated, and large departures from multiple-locus Hardy-Weinberg expectation are primarily due to substantial Wahlund variance within the tribe. There is no need to postulate a role for selection in these disequilibria.     

An allosteric pore model for sugar transport in human erythrocytes

Glucose transport in human erythrocytes is characterized by a marked asymmetry in the $\text{V}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for entry and for exit. In addition, they show a high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and a high $\text{V}$ for equilibrium exchange but low $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for infinite cis and for infinite trans exit and entry. An allosteric pore model has been proposed to account for these characteristics. In this model, substrate-induced conformational changes destabilize the interfaces between protein subunits (the pore gates).Pores doubly occupied from inside destabilize the transport gates and result in high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and high $\text{V}$ transport parameters. This effect is less marked when pores are doubly occupied from outside and therefore transport asymmetry results.     

Genetic structure of five susceptibility gene regions for coronary artery disease: disequilibria within and among regions

We analyzed two-locus disequilibria for 16 polymorphic loci of seven susceptibility genes for coronary artery disease located in five chromosomal regions distributed across four chromosomes. Included were the genes coding for apolipoprotein B (ApoB, chromosome 2, four marker loci), lipoprotein lipase (LPL, chromosome 8, three marker loci), apolipoproteins AI, CIII, AIV (ApoAI–CIII–AIV, chromosome 11, three marker loci), apolipoprotein E (ApoE, chromosome 19, two marker loci), and the low density lipoprotein receptor (LDLR, chromosome 19, four marker loci). Our sample included 540 unrelated individuals from the Rochester, Minn. population. There were no statistically significant deviations of single-locus genotypes from Hardy-Weinberg equilibrium. The strongest associations within genes were for composite diallelic disequilibria; 17/19 were significant (13 at Pr <0.001, 1 at Pr <0.01, 3 at Pr <0.05). These observations suggest marker alleles within genes have a shared evolutionary history reflected by disequilibria that have not been dissipated by recombination. Disequilibrium was not generally concordant with the physical orderings of markers. Only two significant higher-order disequilibria were observed although 12 triallelic disequilibria were at maximum possible values. We observed 19 statistically significant disequilibria (Pr <0.05; 4 composite diallelic, 13 triallelic, and 2 quadriallelic) between 101 pairs of marker loci, where each locus in a pair was from a different unlinked region. These unexpected results are most likely explained by recent historical factors, including worldwide population expansion and amalgamation with continuous admixture, that influence the genetic structure (organization of alleles and non-alleles into genotypes) of a population. We conclude that disequilibria between loci from unlinked regions may be more extensive than is commonly assumed. Our findings also suggest that it is, on average, at least 15 times more likely to not detect significant disequilibrium among unlinked loci when it is really present than to make a false positive inference. Disequilibria between functional loci within or between regions will impact estimates of genetic variance associated with particular functional mutations within a susceptibility gene region. Received: 15 January 1998 / Accepted: 24 June 1998     

Kinetics of active and passive components of water exchange between the air and a mite, Dermatophagoides farinae

Female North American house dust mites were found to exchange water with the ambient air from two compartments. At humidities above the critical equilibrium activity (CEA), transpiration out of a single large compartment was observed using HTO as a tracer for water. Total sorption into this compartment was also observed by following changes in the specific radioactivity. The sorption data required that an active process or pump be present. The water in this pump is the second compartment above the CEA. Below the CEA the large compartment could be identified as a compartment characterized by a small transpiration rate constant. The pump below the CEA becomes a rapidly transpiring fast compartment. By separating the water pool into two compartments, it was possible to relate a_v to k and $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$. The major effect of a_v on k was related to its effect on the permeability of the cuticle. The influence of a_v on $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$ was different for active and passive sorption. Above the CEA the pump operated at full capacity and active $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$ was directly proportional to a_v. Passive sorption was influenced by a_v in two ways. The driving force for $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$ was further reduced below saturation by the effect of a_v on the permeability of the exchange surface.     

Evolution of the three overlapping gene systems in G4 and phi X174.

Bacteriophage G4 has the same $\text{A}\text{B}$ and $\text{D}\text{E}$ overlapping gene systems as φX174 and together with the A and $\text{C}\text{K}$ overlapping gene system (Shaw et al., 1978), 7 of the 11 G4 and φX174 genes are involved in overlaps. The nucleotide differences between G4 and φX174 in the overlapping portions of the A, C and D genes are 23%, 27% and 21%, respectively, compared with 32%, 36% and 34% in the non-overlapping portions of the same genes. The amino acid differences between the G4 and φX174 overlapping B, K and E proteins, are 44%, 39% and 44%, respectively, compared with 28%, 26% and 16% in the regions of genes A, A and C, and D which contain genes B, K and E. These results suggest that the nucleotide sequences of overlapping genes evolve at almost the same rate as in non-overlapping genes, and that this is made possible by a lower amino acid sequence stringency of one of the pairs of proteins. The overlapping $\text{D}\text{E}$ and A and $\text{C}\text{K}$ gene systems may have originated by taking advantage of a high incidence of T nucleotides in the second codon position to produce a hydrophobic protein and the $\text{A}\text{B}$ gene system may have evolved by read-through of the A gene into the B gene. From the nucleotide sequences, other overlapping genes appear to be possible in these bacteriophages.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.     

Activation of the β-galactoside transport system in escherichia coli ML-308 by n-alkanols. Modification of lipid-protein interaction by a change in bilayer fluidity

The net rate of transport of $\text{o-}\text{nitrophenyl}\text{-β-}\text{d}\text{-}\text{galactopyranoside}$ by Escherichia coli ML-308 is increased at temperatures below the apparent phase transition of the lipid bilayer in the presence of n-alkanols. The degree of activation produced is determined both by the concentration and chain length of the n-alkanol used. At low concentrations n-alkanols “activate” transport, but do not cause either cell lysis or denaturation of β-galactosidase.Arrhenius plots of the kinetic constants for transport indicate the K_m shows discontinuity with increasing temperature, while the slope for V changes only gradually. The presence of 10.5 mM n-hexanol increases the value of both K_m and V at low temperature. A comparison of these data to those obtained at a single substrate concentration (1.85 mM o-nitrophenyl-β-d-galactopyranoside) suggests the biphasic behavior of Arrhenius plots at that concentration may be attributed to changes in the K_m for the transport process.     

A convective mass transfer model for determining intestinal wall permeabilities: laminar flow in a circular tube

A convective mass transfer model as analyzed and developed for use in determining intestinal wall permeabilities from external perfusion experiments. Analysis of the model indicates that the ratio of the exit to inlet concentration $\text{C}{}_{\mathrm{m}}\text{C}{}_0$ is a function of only two dimensionless independent variables, the wall permeability, $\text{P}{}_{\mathrm{w}}{}^1$ and Graetz number, Gz = πDL/2Q. The Graetz number contains the independent variables of interest, length, diflusivity, and flow rate. The radius of the intestine is included implicitly in the flow rate. Since $\text{C}{}_{\mathrm{m}}\text{C}{}_0$ and Gz are the experimental quantities, and the solution to the model system contains P_ω¹ implicitly, a convenient approximate method is developed which allows a direct calculation of P_ω¹. This method is in error by 10–20% in the worst cases. The approach is illustrated by application to the determination of the wall permeabilities for two non polar compounds.     

Disequilibrium among several linked neutral genes in finite population. II. Variances and covariances of disequilibria

A method is derived for computing the variances and covariances of linkage disequilibria between neutral genes in finite populations, which is based on a linear transformation of results given previously for the mean values of disequilibria. The formulae obtained are limited to moments of sixth order or less, such as the variance of the three-locus disequilibrium. It is shown that there is no covariance between any pair of disequilibria in populations starting equilibrium. The pattern of change with time in variance of the three-locus disequilibrium from populations initially in equilibrium is similar to that for two loci, except that the highest values are achieved rather earlier and are smaller.     

The concept of high- and low-affinity reactions in bovine cytochrome c oxidase steady-state kinetics

(1) Analysis of the data from steady-state kinetic studies shows that two reactions between cytochrome c and cytochrome c oxidase sufficed to describe the concave Eadie-Hofstee plots ($\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 1 · 10}{}^{\mathrm{?8}}\text{M}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 2 · 10}{}^{\mathrm{?5}}\text{M}$). It is not necessary to postulate a third reaction of $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 10}{}^{\mathrm{?6}}\text{M}$. (2) Change of temperature, type of detergent and type of cytochrome c affected both reactions to the same extent. The presence of only a single catalytic cytochrome c interaction site on the oxidase could explain the kinetic data. (3) Our experiments support the notion that, at least under our conditions (pH 7.8, low-ionic strength), the dissociation of ferricytochrome c from cytochrome c oxidase is the rate-limiting step in the steady-state kinetics. (4) A series of models, proposed to describe the observed steady-state kinetics, is discussed.     

Genetic Coadaptation in the Chromosomal Polymorphism of DROSOPHILA SUBOBSCURA. I. Seasonal Changes of Gametic Disequilibrium in a Natural Population

Seasonal changes in gene arrangement and allozyme frequencies have been investigated in Drosophila subobscura for several years. Some arrangements (O_st and O₃₊₄₊₇) show seasonal variation, which suggests that chromosomal polymorphism is flexible in this species. Seasonal changes in allozyme frequencies for Lap and Pept-1 loci, both located within the same inversions of chromosome O, are significant only inside the O_st arrangement, but not inside O₃₊₄ arrangement. This arrangement-dependent response of allozyme generates variation in arrangement-allozyme disequilibrium. The historical hypothesis on the maintenance of disequilibria cannot explain these seasonal changes, and some kind of natural selection must be invoked. Association between Lap and Pept-1 is also seasonal inside O_st but not inside O₃₊₄. We propose that O_st probably consists of a finite array of supergenes that are differentially favored in each season by natural selection. The present evidence on this supergene selection and other genetic, biogeographic and phylogenetic data points to O₃₊₄ as the most primitive gene order among the present arrangements.     

Sucrose transport by Streptococcus mutans. Evidence for multiple transport systems

The transport of sucrose by selected mutant and wild-type cells of Streptococcus mutans was studied using washed cocci harvested at appropriate phases of growth, incubated in the presence of fluoride and appropriately labelled substrates. The rapid sucrose uptake observed cannot be ascribed to possible extracellular formation of hexoses from sucrose and their subsequent transport, formation of intracellular glycogen-like polysaccharide, or binding of sucrose or extracellular glucans to the cocci. Rather, there are at least three discrete transport systems for sucrose, two of which are $\text{phospho}\text{enol}\text{pyruvate-dependent}$ phosphotransferases with relatively low apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values and the other a non-phosphotransferase (non-PTS) third transport system (termed TTS) with a relatively high apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$. For strain 6715-13 mutant 33, the $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values are 6.25·10^?5 M, 2.4·10^?4 M, and 3.0·10^?3 M, respectively; for strain NCTC-10449, the $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values are 7.1·10^?5 M, 2.5·10^?4 M and 3.3·10^?3 M, respectively. The two lower $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ systems could not be demonstrated in mid-log phase glucose-adapted cocci, a condition known to repress sucrose-specific phosphotransferase activity, but under these conditions the highest $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ system persists. Also, a mutant devoid of sucrose-specific phosphotransferase activity fails to evidence the two high affinity (low apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$) systems, but still has the lowest affinity (highest $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$) system. There was essentially no uptake at 4°C indicating these processes are energy dependent. The third transport system, whose nature is unknown, appears to function under conditions of sucrose abundance and rapid growth which are known to repress $\text{phospho}\text{enol}\text{pyruvate-dependent}$ sucrose-specific phosphotransferase activity in S. mutans. These multiple transport systems seem well-adapted to S. mutans which is faced with fluctuating supplies of sucrose in its natural habitat on the surfaces of teeth.     

Involvement of the proton electrochemical gradient in genetic transformation in Escherichia coli

Plasmid pIY2 DNA which encodes for ampicillin-resistance was used to study the energetics of Ca⁺⁺-induced transformation in Escherichia coli. When cells are exposed to DNA in the presence of carbonylcyanide-m-chlorophenylhydrazone or 2,4-dinitrophenol, two protonophores that collapse the proton electrochemical gradient across the cell membrane ($\text{Δ}\text{μ}{}_{\mathrm{H}}\text{+}$), transformation to ampicillin-resistance is drastically reduced with little or no effect on viability. Furthermore, when the components of $\text{Δ}\text{μ}{}_{\mathrm{H}}\text{+}$ are altered by varying ambient pH or by performing transformation in the presence of valinomycin or nigericin, the efficiency of transformation is directly correlated with the magnitude of the membrane potential and changes in the pH gradient have no significant effect. It is concluded that $\text{Δ}\text{μ}{}_{\mathrm{H}}\text{+}$, more specifically the membrane potential, plays a critical role in Ca⁺⁺-induced transformation.     

The composition-dependence of the extent of reaction between a multivalent acceptor and a bivalent ligand: Implications of self-interaction of the ligand in precipitin effects

Theory is presented relating to the reversible interaction of an f-valent acceptor, A, with a bivalent ligand, B, which leads to the formation of a series of complexes comprising networks of alternating A and B molecules. An explicit expression is derived for the overall extent of reaction in terms of the total molar concentrations of reactants $\text{(}\text{m}{}_{\mathrm{A}}$ and $\text{m}{}_{\mathrm{B}}\text{)}$, the valency of the acceptor and the site-binding constant, k, governing the equilibria. It is shown by differentiation of this expression holding $\text{m}{}_{\mathrm{A}}$ (or $\text{m}{}_{\mathrm{B}}$) fixed that relations are available for the independent evaluation of f and k from a combination of precipitin and radioimmunoassay experiments. Moreover, it is established that dilution with solvent ($\text{m}{}_{\mathrm{A}}\text{/}\text{m}{}_{\mathrm{B}}$ fixed) cannot lead to the appearance of a precipitate with this type of crosslinking system. The latter observation forms the background for the development of theory pertaining to the joint operation of ligand dimerization, 2B?B₂, and crosslinking of the multivalent acceptor with bivalent B₂. The theoretical examination of this system is developed in terms of site-probability functions and involves the delineation of unique solutions for the extent of crosslinking reaction aided by the definition of the extent of binding in defined limits. It is shown with the use of numerical examples that the system involving self-associating ligand may result in the appearance of a precipitate on dilution with solvent and the conditions for the operation of this phenomenon are elucidated. It is noted that other types of ligand self-interaction may lead to similar effects in crosslinking systems, and the general principles emerging from this study are discussed in terms of systems in which antibody ligands are known to be involved in association reactions or are suspected to be so involved on the basis of precipitation effects observed on dilution with solvent.     

On the stereochemistry of 2,3-dihydroxy fatty acids. The single crystal structure of potassium d-erythro-2,3-dihydroxyoctadecanoate

The erythro-2,3-dihydroxyoctadecanoic acid studied is a synthetic homologue of a natural occurring constituent of sphingolipids. The potassium salt of the acid crystallizes in the monoclinic space group P2, with the unit cell dimension: $\text{a = 5.39, b = 7.06, c = 26.26}\text{A}\text{?}\text{and}\text{β = 94.9°}$. The crystal structure was solved by direct methods and was refined to R = 0.062. The absolute configuration of the compound was determined by means of anomalous scattering effects, showing that the natural fatty acid has d-erythro configuration. The compound packs tail to tail in an unusual bilayer arrangement. The hydrocarbon chains have an extreme tilt of 60° and opposite inclination in the two halves of the bilayer. Laterally the hydrocarbon chains are arranged according to the monoclinic M∥ packing mode. The carbon chain makes a perpendicular bent at carbon atom 2. This places the 2-hydroxyl group in a preferred co-planar conformation towards the carboxylate group and at hydrogen bond distance to one of the carboxylate oxygens. The carboxylate group and the two hydroxyl groups are co-ordinated to K⁺ ions and together account for a large molecular cross-ection of 38 Ų. Monolayer studies show that the acid forms a phase with this spacious molecular area also in contact with water. On compression above 10 mN m^?1 transition to a more condensed state ($\text{S = 27}\text{A}\text{?}{}^2$) takes place accompanied by marked changes of the surface potential.     

Kinetic parameters for the binding of p-nitrophenyl alpha-d-mannopyranoside to concanavalin A.

Binding of the chromogenic ligand p-nitrophenyl α-d-mannopyranoside to concanavalin A was studied in a stopped-flow spectrometer. Formation of the protein-ligand complex could be represented as a simple one-step process. No kinetic evidence could be obtained for a ligand-induced change in the conformation of concanavalin A, although the existence of such a conformational change was not excluded. The entire change in absorbance produced on ligand binding occurred in the monophasic process monitored in the stopped-flow spectrometer. The value of the apparent second-order rate constant (k_a) for complex formation (k_a = 54,000 s^?1m^? at 25 °C, pH 5.0, Γ/2 0.5) was independent of the protein concentration when the protein was in the range of 233–831 μm in combining sites and in excess of the ligand. The apparent first-order rate constant (k_?a) for dissociation of the complex was obtained from the rate constant for the decomposition of the complex upon the addition of excess methyl α-d-mannopyranoside (k_?a = 6.2 s^?1 at 25 °C, pH 5.0, Γ/2 0.5). The ratio $\text{k}{}_{\mathrm{<mtext>a</mtext>}}{}_{\mathrm{<mtext>?</mtext><mtext>a</mtext>}}$ (0.9 × 10₄m^?1) was in reasonable agreement with value of 1.1 ± 0.1 × 10⁴m^?1 determined for the equilibrium constant for complex formation by ultraviolet difference spectrometry. Plots of ln($\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{T}$) and ln($\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{T}$) vs $\text{1}\text{T}$ were linear (T is temperature) and were used to evaluate activation parameters. The enthalpies of activation for formation and dissociation of the complex are 9.5 ± 0.3 and 16.8 ± 0.2 kcal/mol, respectively. The unitary entropies of activation for formation and dissociation of the complex are 2.8 ± 1.1 and 1.3 ± 0.7 entropy units, respectively. These entropy changes are much less than those usually associated with substantial changes in the conformation of proteins.     

Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.