Complexity-stability relationship of two-prey-one-predator species system model: Local and global stability

Parrish & Saila (1970), motivated by the experiments of Paine (1966), constructed a simple mathematical model for a two-prey-one-predator system. They were unable to find, in their model, a set of parametric values with which the three-species system can be stable, whereas a twoprey species system without a predator is unstable. Cramer & May (1972) showed that, in fact, such parametric values exist, and gave the necessary mathematical condition. I have investigated the complete conditions for the stability of the system around the equilibrium point, and show that the conditions must be more stringent than given by Cramer & May (1972). Also, it is shown that the present model can have a globally stable limit cycle in three species even when the equilibrium point is locally unstable.     

An approach to a physico-chemical model of olfactory stimulation in vertebrates by single compounds

During recent years, numerous attempts have been made to correlate both quantitative (Davies &; Taylor, 1959; Engen, 1962; Beck, 1964; Engen, Cain &; Rovee, 1968; Cain, 1969; Dravnieks &; Laffoit, 1970; Laffort, 1969a,b) and qualitative (Davies, 1965; Amoore &; Venstrom, 1965; Döving, 1966a,b; Wright &; Michels, 1964; Leveteau &; MacLeod, 1969) odorous properties of single compounds to their molecular properties. These attempts have been only partially successful.In the present paper we will try to explain the several odorous properties of single compounds on the basis of the non-specific properties of odorants involved in solubility.This model is a first approach, and although it gives statistically highly significant relations, it is not as accurate as those advanced with respect to the physical and sensory dimensions of stimuli in the fields of vision and audition.We will first give the present definitions of the most suitable physicochemical parameters, and then advance quantitative and qualitative models for single compounds. Quantitative odorous properties are: odour threshold, rate of change of odour intensity with odorant concentration in the suprathreshold region, and the somewhat controversial upper odour intensity. Qualitative properties refer to odour character.     

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.     

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)).     

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).     

Co-operative response of chemically excitable membrane III. Three-state model

The general three-state model is formulated first, which is the direct extension of the unified two-state model previously formulated (Kijima & Kijima, 1978). In this model, each protomer in a symmetrically interacting system (oligomers or lattices) can take three states, S, R and Q, where S and R states are the same as in the two-state model and Q state is another state either corresponding to a different open-state of ionophore from R open-state or corresponding to another closed state of ionophore. The model has no restriction on the value of Hill coefficient at the midpoint of the dose-response curves in contrast to two-state models. It is applied on GABA sensitive inhibitory synapse of crayfish muscle to account for anomalous behaviour of the membrane in I^? solution.The simplified versions of the above general three-state model are also formulated (simplified three-state model), in which it is assumed that R and Q state are equivalent in regard to the nearest neighbor interaction. By this assumption, R and Q state are collectively treated as state A and mathematical formula obtained on Ising model are applicable on this model. This model is applied on the insect sugar receptor which was shown to be incompatible with the two-state models (Kijima & Kijima, 1980). Further simplification of the above simplified model results in two convenient models: three-state KNF model and three-state MWC model, which have minimum parameters but sufficient to account for most experiments. They give plausible physico-chemical base on the “classical model” in which the existence of both inactive and active ligand-receptor complex is assumed.     

Xylidine isomers. VII. Structure-hepatotoxic activity relationships of some xylidines

Hepatotoxic studies of xylidines differ with regard to the animal species and type of isomer. The aim of the present paper is to correlate electronic structure data and physical-chemical properties, studied by the authors during a few previous papers (Sahini & Weinberg, 1973; Sahini, Weinberg & Vasilescu 1976, Weinberg & Sahini, to be published; Weinberg & Sahini, 1980), with the hepatotoxic activity of xylidines. Two possible biochemical mechanisms are advanced by help of correlation equations.     

The fine structure of Ameson pulvis (Microspora,Microsporida) and its implications regarding classification and chromosome cycle

Nosema pulvisPerez, 1905, Ameson pulvis (Perez) Sprague, 1977, in muscles of the crabs Carcinus maenas and C. mediterraneus from the coast of France, was observed with the electron microscope. It was found to be structurally similar to the type species A. michaelis (Sprague, 1970). Sprague, 1977, having moniliform sporogonial plasmodia, unikaryotic sporoblasts, and hirsute sporulation stages. It is treated as distinct from A. michaelis because it has slightly smaller spores (by comparison with syntype material of A. michaelis) and appears to have fewer coils in the polar filament. The results require the removal of the genus Ameson from the family Nosematidae Labbé, 1899, where Sprague (1977) had placed it under the erroneous supposition that its sporoblasts are diplokaryotic. Ameson is transferred to family Unikaryonidae Sprague, 1977. Ameson is distinguished from PereziaLéger and Duboscq, 1909, shown by Ormieres et al. to have a similar developmental pattern, by presence of appendages on its sporulation stage. A. nelsoni (Sprague, 1950), the third, and only other species of Ameson, lacks the appendages and is transferred to genus Perezia.     

Pattern regulation in tergite of Drosophila: a model

Roseland & Schneiderman's (1979) observations on the presence of the intersegmental region anterior to the posterior duplications in the tergite of Drosophila, led them to postulate intercalary regeneration by shortest route to account for pattern duplications. Our observations on the absence of the intersegmental region in these posterior duplications, on the other hand, suggest that pattern duplication in Drosophila abdomen could be explained on the basis of a diffusion morphogen model. Based on the interpretations of the results of grafting experiments in Calliphora (Pearson, 1977) and cauterization studies in Drosophila (Roseland & Schneiderman, 1979), we suggest that the larval epidermal cells located between the dorsal histoblast nests could be the source of this morphogen. During normal development, this morphogen appears to be responsible for the posterior orientation of the cuticular outgrowths in the posterior half of the tergite and the differentiation of the macrochaetae, pigment band and posterior hairy region. Thus, the posteriorizing effects of the morphogen resemble those of the zone of polarizing activity (ZPA) of the developing appendages of the vertebrate embryos.     

The role of migration in the genetic structure of populations in temporally and spatially varying environments II. Island Models

The Island Model introduced by Sewall Wright (1951) has proven to be a useful construction for studying the interaction of genetic drift, population subdivision, and mutation. Interest in the model has recently increased because of its relevance to certain questions involving the rate of differentiation of sub-populations under the neutral allele hypothesis (e.g., Smith, 1970; Latter, 1973). It is perhaps the only realistic population structure in which the test for neutrality proposed by Lewontin and Krakauer (1973) is valid (Lewontin and Krakauer, 1975). If data from natural populations is to be compared to the predictions of the Island Model, it is desirable to have an alternative model with the same migration pattern but with natural selection operating. In this paper one such model will be introduced where the stochastic element comes from random fluctuations in the environment rather than from genetic drift. The model is a direct extension of the one in the previous paper in this series (Gillespie, 1975) which dealt with a population which is subdivided into two patches with restricted migration between them.     

Does a functional relationship exist between the polymerization and catalytic activity of beef liver glutamate dehydrogenase?

The recent work of Cohen &; Benedek (1976) and Cohen et al. (1975, 1976) on the apparent interdependence of beef liver glutamate dohydrogenase catalytic activity and degree of polymerization is examined in the light of previously published equilibrium and kinetic results. It is shown that some of the hypotheses central to the Cohen &; Benedek (1976) model are in contradiction with existent data. Consideration of all available information leads to the conclusion that effector-induced depolymerization may simply be an incidental side reaction in the events leading to inhibition.     

Banding patterns of the chromosomes of the Rhesus monkey (Macaca mulatta)

The Rhesus monkey (Macaca mulatta) has 21 pairs of chromosomes, many of which can easily be confused with one another by the traditional staining methods. By using the method of banding with trypsin (Seabright, 1971) we have been able to characterize the various pairs of homologous chromosomes and we have classified them by following the criteria adopted by Rothfels & Siminovich (1958). The evolutionary meaning of the results are discussed.     

Force-velocity relationship in single muscle fibres

In recent papers, it has been shown experimentally that the force-velocity relationship in single muscle fibres presents deviations from hyperbolicity at high values of the load (Edman, Mulieri & Scubon-Mulieri, 1976; Edman & Hwang,1977). It has been shown independently and on theoretical bases, that the parameter “b” in Hill's characteristic equation also presents deviations from its normal value at low values of the speed of shortening, i.e. at high values of the load (Morel, Pinset-Härström & Gingold, 1976). In the present paper, it is shown that both the experimental and the theoretical results are in excellent agreement and a theoretical force-velocity relationship is proposed.     

The Plasmodium vaughani--Complex

Plasmodium vaughaniNovy and MacNeal, 1904, Plasmodium tenueLaveran and Marullaz, 1914, and Plasmodium merulaeCorradetti and Scanga, 1972 are shown to differ. It is suggested that P. tenue and P. merulae should be considered as subspecies belonging to Plasmodium vaughani-complex.More investigations are needed for a sufficient knowledge of the complex, particularly because at least 36 species of birds harbor P. vaughani-like parasites and cover an immense geographical area in all the parts of the world.     

Box-Jenkins forecasting in ecology: An answer to poole

This answering of Poole, 1978, Poole, 1976 aims at rounding off our exchange of views, without losing the readership from an excess of toing and froing between the four contributions. So my final rejoinder only attempts at treating the general points raised by Poole (1978), rather than taking issue with all the minutiae, which would require too many quotes of quotes and counterquotes. The main nub of contention remains as to whether or not statistical fits can be meaningfully interpreted biologically.     

The myosin filament: VII. Changes in internal structure along the length of the filament

Improved fixation procedures have enabled substructure to be observed by electron microscopy in transverse sections of vertebrate skeletal muscle thick filaments as thin as 140 nm. Optical diffraction combined with digital autocorrelation analysis, focal series and tilting experiments have confirmed the presence of a regular substructure having a repeat near 4 nm and shown that it is highly unlikely to be an artifact associated with the electron microscope imaging system. The results obtained strongly suggest that the thick filament is constructed from a bundle of rod-like subfilaments arranged parallel to the thick filament axis to within less than a degree. This cannot easily be reconciled with the general theory of thick filament structure proposed by Squire (1973), but it is consistent with the model proposed by Pepe, 1966, Pepe, 1967. Optical diffraction of 140 nm thick serial transverse sections has also suggested a structural change along the length of the filament that is manifest by a variation in the proportion of filaments showing strong diffraction maxima in one, two or three directions.     

An autoradiographic analysis of the time of appearance of neurons in the developing chick neural retina

The pattern of incorporation of [³H]thymidine into the chick neural retina has been used to establish the time and order in which different classes of neuroepithelial cells withdraw from the cell cycle and initiate migration and differentiation.The posterior pole of the retina is the first to form during development. In this region most neuroepithelial cells complete mitotic activity between the third and sixth day of incubation. Presumptive ganglion cells initiate the withdrawal process, and they are soon followed by the neuroepithelial precursors of amacrine, horizontal, and receptor cells. Bipolar cell precursors are the last to begin and the last to complete cell cycle activity. It is worthy of note, however, that, in any given region of the retina, neuroepithelial cells of all types cease mitosis in close, overlapping succession.These results are in reasonable agreement with those previously published on the chick retina by Fujita and Horii (1963), and other investigators on the mouse (Mus), killifish (Fundulus), and toad (Xenopus). The present data are also consistent with those proposals of Angevine (1970), Jacobson, 1968a, Jacobson, 1968b, Jacobson, 1970, and others that relate the cessation of mitotic activity of neuroepithelial cells to the determination of neuronal size, axon length, and the specification of neuronal connections.     

Proteolysis in eucaryotic cells: Aminopeptidases and dipeptidyl aminopeptidases of yeast revisited

Using nine different l-aminoacyl-4-nitroanilides and four different dipeptidyl-4-nitroanilides, aminopeptidases and dipeptidyl aminopeptidases active at pH 7.5 and (or) pH 5.5 in logarithmically growing and stationary-phase cells of Saccharomyces cerevisiae were searched for. Ion-exchange chromatography was used to separate the proteins of the soluble cell extract. Besides the three already-characterized aminopeptidases—aminopeptidase I (P. Matile, A. Wiemken, and W. Guyer (1971) Planta (Berlin)96, 43–53; J. Frey and K. H. Röhm (1978) Biochim. Biophys. Acta527, 31–41), aminopeptidase II (J. Frey and K. H. Röhm (1978) Biochim. Biophys. Acta527, 31–41; J. Knüver (1982) Thesis, Fachbereich Chemie, Marburg, FRG), and aminopeptidase Co (T. Achstetter, C. Ehmann, and D. H. Wolf (1982) Biochem. Biophys. Res. Commun.109, 341–347)—12 additional aminopeptidase activities are found in soluble cell extracts eluting from the ion-exchange column. These activities differ from the characterized aminopeptidases in one or more of the parameters such as charge, size, substrate specificity, inhibition pattern, pH optimum for activity and regulation. Also, a particulate aminopeptidase, called aminopeptidase P, is found in the nonsoluble fraction of disintegrated cells. Besides the described particulate X-prolyl-dipeptidyl aminopeptidase (M. P. Suarez Rendueles, J. Schwencke, N. Garcia-Alvarez and S. Gascon (1981) FEBS Lett.131, 296–300), three additional dipeptidyl aminopeptidase activities of different substrate specificities are found in the soluble extract.