Co-operative response of chemically excitable membrane: I. Formulation: Unified theory of co-operativity

The lattice-model of Changeux, Thiery, Tung & Kittel (1966) was extended in order to examine the co-operative response of chemically excitable membrane and the exact mathematical correspondence to the Ising model was shown. In this model, two conformational states S and R with different affinities for the ligand are assumed to be accessible to each protomer, which is interacting with the nearest-neighbor protomers. The model is applicable to any kind of symmetrically interacting system consisting of oligomers and lattices and is an extension of previously proposed models of allosteric protein. It includes the model of Monod, Wyman, & Changeux (1965) and that of Koshland, Némethy & Filmer (1966) as the extreme cases of the oligomer. By assuming that a state-transition from S to R in a protomer is accompanied by a unit increase in conductance, the characteristics of dose-response curves of chemically excitable membrane are examined. The Hill's coefficient n_H of dose-response curve, the measure of the co-operativity, is shown to be proportional to the square of the mean fluctuation of the state function, the fraction of protomers in R state.     

A stochastic model of animal growth

The plasticity of growth of animals in time, due to the resilience of their response to the ways they can be fed, suggests the difficulty of describing growth by a stochastic model in the time domain. A model is presented which avoids this difficulty by describing growth as a Markov process in the food-consumed domain, assuming that, at conception, (1) the maximum mature weight as a number α of biomass units of mass μ, and (2) the probability B of production of a biomass unit per unit of food consumed, are specified. Constancy of α, μ and B, as the animal feeds, is the basis of the proposed Markov process. The mean growth from infancy to maturity in the food-consumed domain is then the old law of diminishing returns empirically formulated first by Spillman (1924) for cattle and swine, and confirmed by Titus, Jull &; Hendricks (1934) for fowl, and by Parks (1972) across species from mice to steers. The solution also leads to the possibility that the distribution of weights in a population of growing animals of the same species, is related to the distribution of mature weights among the individuals. An experiment by Lister &; McCance (1967) with well-fed and severely undernourished pigs, shows the stability of growth in the foodconsumed domain compared to the plasticity in the time domain. Other implications of the model are discussed.     

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.     

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.     

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.     

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.     

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.     

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.     

Quantitative dependence of mitochondrial oxidative phosphorylation on oxygen concentration: a mathematical model.

The model of Wilson and co-workers (2., 3., Arch. Biochem. Biophys. 182, 749–762) for the regulation of mitochondrial oxidative phosphorylation has been extended to include the dependence on oxygen tension. The derived rate expression correctly describes the observed dependence of cellular energy metabolism on oxygen tension, including the oxygen dependence at “normoxic” physiological values. Experimental evidence is presented that oxidative phosphorylation by suspensions of isolated rat liver mitochondria is also dependent on oxygen concentration up to values of at least 100 μM.     

A general theory of chromosome pairing based on the palindromic DNA model of Sobell with modifications and amplifications

A model for chromosome pairing is presented. It is based on the presence of segments of symmetric sequences of bases (palindromes) in the DNA at specific places in the chromosome. Palindromic DNA has been characterized by Wilson &; Thomas (1974), who state that these sequences are a regular feature of eukaryotic DNA. Sobell (1972) has suggested that they may be involved in synapsis and genetic recombination. Sobell's model is modified and amplified in an attempt to develop a general theory of chromosome pairing that explains congressional pairing, synapsis, non-homologous pairing, the initiation of crossing over, and interference.     

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.     

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.     

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.     

Cotranslational cleavage of immunoglobulin light chain precursors by plasmacytoma microsomes.

Murine plasmacytoma endoplasmic reticulum which has been freed of ribosomes by EDTA treatment is capable of the cotranslational proteolytic processing of representative λ₁,λ₂, and k immunoglobulin light chain precursors. Messenger RNA fractions from the MOPC-104E, MOPC-315, and MOPC-46B tumor lines were used to direct the synthesis of the light chain precursors in a cell-free system derived from Krebs II ascites cells. The precursor cleavage activity of the plasmacytoma membranes is comparable in activity and in characteristics to that of two well-defined membrane preparations: Krebs II ascites intracellular membranes (E. Szczesna and I. Boime, 1976, Proc. Nat. Acad. Sci. USA73, 1179–1183) and EDTA-treated rough endoplasmic reticulum from canine pancreas (34., 35., J. Cell Biol.67, 852–862). The efficiency of the cleavage reaction appears to be dependent upon the precursor being utilized as a substrate. An assay suitable for a preliminary characterization of the plasmacytoma membrane preparations is described.     

Warfare and hominid brain evolution.

This paper reviews literature on the evolutionary effects of warfare upon the hominid brain. Alexander &; Tinkle (1968) and Bigelow (1969) are found to be the first to propose that warfare was the principle evolutionary pressure that created the novel substance of the human brain, and that it acted at least from the early Pleistocene. These writers are distinguished from Darwin (1871), Keith (1947) and Wilson (1975) who saw warfare influencing the development of the brain only in historical or near-historical times.The warfare hypothesis of Alexander &; Tinkle is found to be an excellent explanation of the evolution of the human brain, but to be unsatisfactory from a biological viewpoint because they do not explain how warfare evolved in the first place, nor do they attempt to account for the apparent absence of warfare as a behavioral adaptation in species other than some eusocial insects.This author underpins the warfare hypothesis, arguing that it evolved as a necessary consequence of the circumstances of early hominids. Proficient tool use gave domination over predators and opened up new food resources, thereby diminishing two population controls. A population explosion resulted and, at critical densities, when starvation threatened, warfare was the genetically most successful behavioral adaptation. Alternative hypotheses are shown to be inadequate. Finally, the author asks why such an important hypothesis has been ignored for almost a decade.     

Replication of polyoma DNA in isolated nuclei. VII. Initiator RNA synthesis during nucleotide depletion.

Earlier experiments demonstrated that the Okazaki fragments synthesized during discontinuous polyoma DNA synthesis in isolated nuclei at their 5′ ends contained structural elements consisting of polyribonucleotides starting with ATP or GTP (Reichard et al., 1974). These structures could be released by digestion with pancreatic DNAase and were named initiator RNA. They consist of a large family of polyribonucleotides differing in base sequence but having a common size of about a decanucleotide. We now demonstrate that limitation of DNA synthesis by low concentrations of deoxyribonucleoside triphosphates in parallel limits the synthesis of initiator RNA. This is additional evidence for the primer function of initiator RNA. When ribonucleoside triphosphates other than ATP were deleted from the incubation medium only a small decrease of DNA and initiator RNA synthesis occurred. Under those conditions deoxyribonucleotides substituted for ribonucleotides and were incorporated internally into the primer. From this result as well as the insensitivity of initiator RNA synthesis to α-amanitin (Reichard &; Eliasson, 1979) we suggest that a mammalian counterpart to primase, the dnaG gene product of Escherichia coli(Rowen &; Kornberg, 1978a), catalyzes the synthesis of initiator RNA.     

Immortal fibroblasts?

Uncommitted fibroblasts may exist (Kirkwood &; Holliday, 1975; Holliday, Huschtscha, Tarrant &; Kirkwood, 1977). I show that, even if such cells divide significantly faster than committed ones, the uncommitted cells would be overlooked if one uses current culture techniques. Some general guidelines for testing the model are outlined. Uncommitted cells would be useful in studying the biochemical mechanisms of aging and development.     

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)).     

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.