On the within-sibship variance

An approximate formula for the expected within-sibship genotypic variance of a polygenic, diallelic, additive character is obtained for arbitrary recombination between the loci affecting the character. The formula is exact, when there is no recombination, or when the recombination is free. It is also shown that, if the value of $\text{1}\text{2}\text{V}{}_{\mathrm{k}}$ (one-half of the parental genotypic variance) is assigned to the within-sibship genotypic variance, as in the model of Cavalli-Sforza and Feldman (1976, Proc. Natl. Acad. Sci. USA73, 1689–1692), it implies the assumptions of random mating and of the perfect linkage. If, on the other hand, the value of $\text{1}\text{2}\text{V}{}^0$ (one-half of the linkage equilibrium genotypic variance) is assigned to the within-sibship variance, as in the model of Rice, Cloninger, and Reich (1978, Amer. J. Hum. Genet.30, 618–643), it implies the assumptions of random mating and either of the free recombination, or of the linkage equilibrium, if the recombination is not free.     

Purification of antibodies against biotin on lipoic acid-sepharose

The use of a “hapten-analog” affinity column, lipoyl-Sepharose, is described for the purification of antibodies directed against biotin. The antibodies bind to biotin very tightly ($\text{K}{}_{\mathrm{d}}\text{? 10}{}^{\mathrm{?8}}$m) (M. Berger, 1975, Biochemistry14, 2338–2342), and elution of antibody from biotin-Sepharose requires harsh conditions (1–1.5 m acetic acid) and results in a poor yield of antibody, which, upon storage, loses much of its capacity to inhibit the biotin-containing enzyme, transcarboxylase. With lipoyl-Sepharose, the antibody can be eluted in good yield and with high efficacy using 0.1 m acetic acid. In addition, antibody-biotin complexes or complexes of the antibody with biotin enzyme can be eluted directly from antibody-bound lipoyl-Sepharose using solutions of biotin or of biotin-containing enzyme.     

Regulation of coenzyme utilization by the dual nucleotide-specific glucose 6-phosphate dehydrogenase from Leuconostoc mesenteroids.

The dual wavelength assay technique (H. R. Levy, and G. H. Daouk, 1979, J. Biol. Chem.254, 4843–4847) is used to examine the rates of the NADP- and NAD-linked reactions of Leuconostoc mesenteroides glucose 6-phosphate dehydrogenase simultaneously under various conditions. Inhibition by ATP, MgATP^2?, acetyl-CoA, and palmitoyl-CoA is greatly diminished at high glucose 6-P concentration which favors the NAD-linked reaction. Increasing $\text{NADPH}\text{NADP}{}^{\mathrm{+}}$ concentration ratios inhibit the NADP-linked, but stimulate the NAD-linked reaction. The selective effects of glucose 6-P and the $\text{NADPH}\text{NADP}{}^{\mathrm{+}}$ concentration ratio, which cannot be detected by conventional assays, are explained in terms of the differing kinetic mechanisms for the NADP-linked and NAD-linked reactions previously described (C. Olive, M. E. Geroch, and H. R. Levy, 1971, J. Biol. Chem.246, 2047–2057). It is proposed that these effects constitute the mechanism whereby the nucleotide specificity of the amphibolic glucose 6-phosphate dehydrogenase from Leuconostoc mesenteroides is regulated.     

Enzymic and physicochemical characterization of ribulose 1,5-bisphosphate carboxylase/oxygenase from diploid and tetraploid cultivars of perennial ryegrass

Homogeneous preparations of ribulose 1,5-bisphosphate carboxylase/oxygenase (EC 4.1.1.39) were isolated from several diploid and tetraploid cultivars of perennial ryegrass (Lolium perenne L.) by three different purification protocols. The apparent K_m values for substrate CO₂ were essentially identical for the fully $\text{CO}{}_2\text{Mg}{}^{\mathrm{2+}}$-activated diploid and tetraploid enzymes, as were the kinetics for deactivation and activation of the $\text{CO}{}_2\text{Mg}{}^{\mathrm{2+}}$ activated and -depleted carboxylases, respectively. Similarly, virtually indistinguishable electrophoretic properties were observed for both the native and dissociated diploid and tetraploid ryegrass proteins, including native and subunit molecular weights and the isoelectric points of the native proteins and the large and small subunit component polypeptides. The quantity of carboxylase protein or total soluble leaf protein did not differ significantly between the diploid and tetraploid cultivars. Contrary to a previous report (M. K. Garrett, 1978, Nature (London)274, 913–915), these results indicate that increased ploidy level (i.e., nuclear gene dosage) has had essentially no effect on the quantity or enzymic and physicochemical properties of ribulosebisphosphate carboxylase/ oxygenase in perennial ryegrass.     

Unified theory of 1f and conductance noise in nerve membrane

A theory of $\text{1}\text{f}$ and conductance noise is given for ionic channels in nerve membrane. The theory is based on the assumption that the channels are in constant, stochastically independent, rotational motion within a fluid bilayer membrane. The resulting expression for the current noise power density S contains a conduction noise term consistent withStevens (1972) and Hill & Chen (1972) and a $\text{1}\text{f}$ noise term consistent with Lundstrom & McQueen (1974) and Clay & Shlesinger (1976). The expression for S also contains a third term which is the spectrum of the product of the single channel conduction noise and $\text{1}\text{f}$ noise correlation functions. This term is independent of the number of channels in the membrane, R. Consequently, the expression for S effectively reduces to a sum of $\text{1}\text{f}$ and conduction noise for R 10–100 which is in agreement with noise measurements on squid axon. The theory is applied in detail to potassium squid noise measurements of Conti, DeFelice & Wanke (1975) using the stochastic analysis of single file ion motion developed in our previous paper (Clay & Shlesinger (1976)).     

Cell surface glycosyltransferase activities during normal and mutant (TT) mesenchyme migration

Migrating cells possess surface glycosyltransferase activity toward extracellular substrates, and the appearance of enzyme activity coincides with the onset of cellular migration (Shur, 1977a, Shur, 1977b, Develop. Biol.58, 23–39, 40–55; E. A. Turley and S. Roth, 1979, Cell17, 109–115). In this paper, surface glycosyltransferases were examined during normal and $\text{T}\text{T}$ mutant mesenchyme migration. Of six glycosyltransferases that were assayed, only galactosyltransferase was present at significant levels on the cell surface, despite the presence of a variety of intracellular glycosyltransferases. All controls have been performed to show clearly the enzyme activity was cell surface localized. In both normal and $\text{T}\text{T}$ embryos, surface galactosyltransferase activity was localized, by autoradiography, primarily to migrating mesenchymal cells, and to a lesser degree, to presumptive neural epithelium. During primitive streak formation, putative $\text{T}\text{T}$ embryos were devoid of surface galactosyltransferase activity. However, as development progressed, the $\text{T}\text{T}$ level of activity eventually exceeded wild-type levels by two- to sixfold and was evident in $\text{T}\text{T}$ tissues prior to the onset of microscopic pathology. Other surface enzymes assayed did not show any $\text{T}\text{T}\text{-}\text{dependent}$ increase in activity. The extracellular galactosyl acceptors were not chloroform:methanol soluble, and glycopeptides prepared by exhaustive Pronase digestion were excluded from Sephadex G-50. This large galactosylated glycoconjugate was readily digestable with endo-β-galactosidase, and, therefore, is similar to the poly-N-acetyllactosamine chains previously identified on early embryonic tissues (A. Kapadia, T. Feizi, and M. J. Evans, 1981, Exp. Cell. Res.131, 185–195; T. Muramatsu, G. Gachelin, M. Damonneville, C. Delarbre, and F. Jacob, 1979, Cell18, 183–191; A. Heifetz, W. J. Lennarz, B. Libbus, and Y. -C. Hsu, 1980, Develop. Biol.80, 398–408). These results support an involvement of surface galactosyltransferases in mesenchyme formation and during migration on poly-N-acetyllactosamine substrates.     

Localization at the ultrastructural level of maternality derived enzyme and determination of the time of paternal gene expression for acid phosphatase-1 in Drosophila melanogaster.

Ultrastructural histochemistry instead of acrylamide gel electrophoresis (see R. Yasbin, J. Sawicki, and R. J. MacIntyre, 1978, Develop. Biol. 63, 00-00) is used to determine the time of paternal gene expression for the enzyme acid phosphatase-1 of Drosophila melanogaster in $\text{Acph-1}{}^{\mathrm{n}}\text{Acph-1}{}^{\mathrm{B}}$ embryos in which the null allele is derived from the female parent. Timed embryos were histochemically stained for acid phosphatase activity according to the lead phosphate method of Gomori and were examined at the ultrastructural level. Enzyme activity, resulting from activation of the paternal Acph-1 gene, is detected as early as 5 hr after fertilization. Maternally derived enzyme in $\text{Acph-1}{}^{\mathrm{B}}\text{Acph-1}{}^{\mathrm{B}}$ embryos is found principally in the yolk regions and around invaginations. This suggests that acid phosphatase-1 functions in yolk digestion and in cell movements during early embryogenesis.     

Trehalose-6-phosphate synthetase activity in extracts of Dictyostelium discoideum.

Trehalose-6-phosphate (T-6-P) synthetase activity in extracts of Dictyostelium discoideum has been reexamined in an effort to resolve discrepancies between the results of previous studies (R. Roth and M. Sussman (1966). Biochim. Biophys. Acta, 122, 225; K. A. Killick and B. E. Wright (1972). J. Biol. Chem., 247, 2967). We find that T-6-P synthetase is not cold sensitive as reported by Killick and Wright (1972), is not present in bacterial-grown vegetative cells (though subject to some modulation by other nutritional conditions), and is not in our hands unmasked or activated by ammonium sulfate fractionation. We conclude that the pattern of T-6-P synthetase accumulation and disappearance during fruiting body construction in D. discoideum is as originally described by R. Roth and M. Sussman (1968). J. Biol. Chem., 243, 5081) and confirmed elsewhere (P. C. Newell et al. (1972). J. Mol. Biol., 63, 373; R. W. Brackenbury et al. (1974). J. Mol. Biol., 90, 529; B. D. Hames and J. M. Ashworth (1974). Biochem. J., 142, 301).     

A model for propagation of action potentials in smooth muscle

A modified Hodgkin & Huxley (1952) model for axons was used to simulate smooth muscle action potentials. The modifications were such as to match our own experimental results and published data on the passive and active behavior of smooth muscle.A brief account of the modifications introduced to the HH model is as follows. The resting ionic conductances were obtained from the data of Casteels (1969). Chloride conductance was replaced by an ad hoc leakage conductance ($\text{g}\text{?}{}_{\mathrm{L}}$) in order to obtain a resting membrane resistance of about 11 kΩcm². The ionic equilibrium potentials were according to Kao & Nishiyama (1969). The rate constants m, n and h have similar form to those in axons, but their different numerical values produce action potentials that match the duration of the smooth muscle action potential (about 16 ms) at half its maximum amplitude. The effective membrane capacitance was taken as 2.5 μF/cm².The results obtained by implementing those smooth muscle parameters in the HH formulation include: (a) a membrane potential that matches the main characteristics of experimentally recorded action potentials in uterine smooth muscle and guinea-pig taenia-coli, and (b) a propagated action potential which, on a cable diameter of 5 μm (similar to the diameter of a single smooth muscle cell), has a speed of propagation within the range of the values experimentally recorded in smooth muscle. This observed velocity of propagation is not compatible with a large cable and it is concluded that “functional units” are not required to sustain propagation of action potentials in smooth muscle.     

Refinement of the coomassie blue method of protein quantitation. A simple and linear spectrophotometric assay for less than or equal to 0.5 to 50 microgram of protein

The Coomassie brilliant blue G assay for proteins described by Bradford (1976) (Anal. Biochem.72, 248) was reexamined. It was found that the extinction coefficient of the dye-protein complex solution remained constant over the protein concentration range of 0.8 to 10 μg/ml of solution. This unchanging extinction coefficient, $\text{A}{}_{595}\text{=}\text{0.60 ± 0.01}\text{10}\text{μ}\text{g}$ of protein/ml of solution, enhances both the sensitivity and versatility of the assay. Selection of a volume of dye-reagent (0.5 to 5.0 ml) which dilutes the protein sample to a final concentration of 0.8 to 10 μg/ml permits the application of Beer's Law for accurate determinations of ≤0.5 to 50 μg of protein. A combination of Bradford's study and the present one indicates that most common laboratory reagents and chemicals exert little or no influence on the A₅₉₅ of the dye-reagent.     

Quantitation of intracellular membrane-bound enzymes and receptors in digitonin-permeabilized cells

The distribution of membrane-bound receptors and enzymes between the cell surface and the cell interior can be determined without solubilization or gross disruption of cell organelles in the presence of the nonionic detergent digitonin. This steroid glycoside permeabilizes cells, releases cytoplasmic proteins with subunit molecular weights up to 200,000, and allows exogenous molecules to gain access to intracellular receptors. All cell types examined were affected similarly by digitonin. Permeabilization was complete within 2 min at 0°C and did not require the continued presence of digitonin. A characteristic amount of protein (～50%) was lost between 0.02 and 0.08% ($\text{w}\text{v}$) digitonin. Three independent systems were examined: the insulin receptor in 3T3 fibroblasts and the asialoglycoprotein receptor and the $\text{Na}{}^{\mathrm{+}}\text{K}{}^{\mathrm{+}}\text{-ATPase}$ in rat hepatocytes. In each case an increase in the specific activity of enzyme/receptor occurred over a range of detergent concentration in which the retention of cell protein was constant and virtually no solubilization of membrane-bound activity occurred. The binding of ¹²⁵I-asialo-orosomucoid to rat hepatocytes at 0°C in the presence of digitonin was linear with cell number and kinetically indistinguishable from binding to intact cells. Receptors exposed by digitonin were shown to be intracellular by light microscopic examination of permeabilized cells first treated with antiserum to the receptor and then with a second antibody horseradish peroxidase conjugate. The use of digitonin has many advantages over procedures which require total cell disruption or solubilization to assess intracellular receptors. The technique has already been valuable in studies on recycling and endocytosis mediated by the asialoglycoprotein receptor (P. H. Weigel and J. A. Oka (1983)J. Biol. Chem.258, 5095–5102) and should also be useful in studies with other membrane-bound receptors and enzymes in other cell types.     

Modification of the aggregation state of the multifunctional enzyme complex catalyzing the first steps in pyrimidine biosynthesis in the course of development of Drosophila melanogaster

Mutations at the bithoraxoid (bxd) and postbithorax (pbx) loci cause a transformation of posterior haltere to posterior wing. It has previously been shown that pbx and $\text{pbx}\text{Ubx}{}^{101}$ cause this transformation by affecting the maintenance (or cell heredity function) of determination so that the transformed cells are indistinguishable from normal wing cells, and have no “memory” of having been part of a haltere disk (Adler, 1978a). I report here that Tp(3) $\text{bxd}{}^{100}\text{Ubx}{}^{101}$ and bxd¹, pbx, e^w both cause the transformation of posterior haltere to posterior wing in the same way as pbx. On the other hand, bxd¹, $\text{bxd}{}^1\text{Ubx}{}^{101}$, bxd^51j, $\text{bxd}{}^{\mathrm{<mtext>51</mtext><mtext>j</mtext>}}\text{Ubx}{}^{101}$, and $\text{bxd}{}^{\mathrm{<mtext>51</mtext><mtext>j</mtext>}}\text{red pbx}$ cause this same transformation of posterior haltere to posterior wing by interfering with the expression of the determined state so that the developmental information of posterior haltere is “misread” as posterior wing. The transformed cells in these disks retain the memory of having been part of a haltere disk; that is, these posterior cells that would secrete wing cuticle during metamorphosis regenerate anterior haltere structures. Thus it appears clear that it is possible to uncouple the expression and cell heredity functions of determination in the haltere disk of Drosophila.     

Equilibrium and kinetic measurements of carbon monoxide binding to hemoglobin kansas in the presence of inositol hexaphosphate

Previous proton nuclear magnetic resonance (nmr) studies have indicated that inositol hexaphosphate (IHP) can stabilize hemoglobin (Hb) Kansas in a deoxy-like quaternary structure even when fully liganded with carbon monoxide (CO) (S. Ogawa, A. Mayer, and R. G. Shulman, 1972, Biochem. Biophys. Res. Commun., 49, 1485–1491). In the present report we have investigated both CO binding at equilibrium and the CO binding and release kinetics to determine if Hb Kansas + IHP is devoid of cooperativity, as would be suggested by the nmr studies just quoted. The equilibrium measurements show that Hb Kansas + IHP has a very low affinity for CO ($\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.2}\text{mm}$ Hg and K_eq = 5.4 × 10⁵M^?1) and almost no cooperativity (n = 1.1) at pH 7, 25 °C. The CO “on” and “off” kinetics also show no evidence for cooperativity. In addition, the equilibrium constant estimated from the kinetic rate constants (K_eq = 5.2 × 10⁵M^?1 with k_on = 1.03 × 10⁵M^?1 · S^? and k_off = 0.198 S^?1) is in excellent agreement with the equilibrium constant determined directly. Thus, both kinetic and equilibrium measurements allow us to conclude that CO binding to Hb Kansas + IHP occurs without significant cooperativity.     

A note on the sampling theory for infinite alleles and infinite sites models

This note considers sampling theory for a selectively neutral locus where it is supposed that the data provide nucleotide sequences for the genes sampled. It thus anticipates that technical advances will soon provide data of this form in volume approaching that currently obtained from electrophoresis. The assumption made on the nature of the data will require us to use, in the terminology ofKimura (Theor. Pop. Biol.2, 174–208 (1971)), the “infinite sites” model of Karlin and McGregor (Proc. Fifth Berkeley Symp. Math. Statist. Prob.4, 415–438 (1967)) rather that the “infinite alleles” model of Kimura and Crow (Genetics49, 174–738 (1964)). We emphasize that these two models refer not to two different real-world circumstances, but rather to two different assumptions concerning our capacity to investigate the real world. We compare our results where appropriate with corresponding sampling theory of Ewens (Theor. Pop. Biol.3, 87–112 (1972)) for the “infinite alleles” model. Note finally that some of our results depend on an assumption of independence of behavior at individual sites; a parallel paper byWatterson (submitted for publication (1974)) assumes no recombination between sites. Real-world behavior will lie between these two assumptions, closer to the situation assumed by Watterson than in this note. Our analysis provides upper bounds for increased efficiency in using complete nucleotide sequences.     

Kinship and covariance

Price's (1970) covariance theorem can be used to derive an expression for gene frequency change in kin selection models in which the fitness effect of an act is independent of the genotype of the recipient. This expression defines a coefficient of relatedness which subsumes r(Wright, 1922), b(Hamilton, 1972), ρ (Orlove &; Wood, 1978), and R(Michod &; Hamilton, 1980). The new coefficient extends the domain of Hamilton's rule to models in which the average gene frequency of actors differs from that of recipients.     

Large scale isolation and storage of Neurospora plasma membranes.

Functionally inverted plasma membrane vesieles isolated from the eukaryotic microorganism Neurospora crassa generate and maintain a transmembrane electrical potential via ATP hydrolysis catalyzed by a plasma membrane ATPase (G. A. Scarborough, 1976, Proc. Nat. Acad. Sci. USA73, 1485–1488). In order to facilitate investigation of the molecular mechanism of the electrogenic ATPase, and other transport systems, we have developed a method for the large scale isolation and storage of Neurospora plasma membranes in a stable form. Large quantities of open plasma membrane sheets (ghosts) are isolated by a scaled-up modification of the original method (G. A. Scarborough, 1975, J. Biol. Chem.250, 1106–1111) and stored at ?26°C in 60% glycerol ($\text{v}\text{v}$). As needed, the ghosts are washed free of glycerol and then converted to closed vesicles by a modification of the original method. With this technique, plasma membrane vesicles with normal electrogenic pump activity can be prepared daily in approximately 2.5 h.