Moments and order statistics of extinction times in multitype branching processes and their relation to random selection models

We investigate the circumstances under which the moments of the order statistics of the extinction times of a set of independent branching processes exist. This extends a result of Schuster and Sigmund,Bull. math. Biol. 46, 11–17, 1984, which was found in a special random selection model. Furthermore we discussed existence of the expectation of extinction times of multitype branching processes and extend well known results for irreducible processes to the reducible case.     

Winter energy deficits and the importance of fruit versus insects in a tropical island bird population

The sedentary population of 200 to 500 silver-eyes on Heron Island, Australian Great Barrier Reef, experiences high mortality during the winter non-breeding season. The omnivorous silvereyes feed mainly on small insects gleaned from foliage, and on fruits, especially the fig Ficus opposita. Estimates of the energy content of food items reveal that small insects (2–5 mm long) provide little assimilable energy (9 J), whereas large insects (>8 mm) and bites of fig provide most assimilable energy (217 J and 181 J respectively). An analysis of the average daily intakes and expenditures (estimated by the time-budget method) for three sampling occasions showed that the rates of insect consumption (10,15 and 11 kJ day^-1) were significantly less than the energy requirements (37, 38 and 37 kJ day^-1). While many individuals may have been able to balance their energy budgets by eating figs, the calculated fruit intake rates (38, 9 and 0.5 kJ day^-1 respectively), together with high inter-individual variation in fig consumption, suggest that figs were often in short supply. The birds visited fig trees most frequently during the first 2 h after sunrise, and the feeding success rate in fig trees (approximately 20% of visits successful) during this time was significantly greater than that during the rest of the day (approximately 10% of visits successful). Alternative hypotheses for these patterns, based on protein requirements, on diurnal rhythms imposed by insect availability, or on satiation, are considered and rejected. These results indicate that the pre-breeding population size is limited by winter energy shortage, the extent of which is dependent on the size and phenology of the fig crop. Natural selection should favour individual strategies for maximization of net energy intake.     

Inhibition of S-adenosyl-L-methionine sterol-C-24-methyltransferase by analogues of a carbocationic ion high-energy intermediate. Structure activity relationships for C-25 heteroatoms (N, As, S) substituted triterpenoid derivatives

Microsomes from maize seedlings are capable of catalyzing the C-24 alkylation of 4,4,14 alpha-trimethyl-9 beta,19-cyclo-5 alpha-cholest-24-en-3 beta-ol (cycloartenol) by (S)-adenosyl-L-methionine (AdoMet) leading to 24-methylene cycloartanol. Derivatives of cycloartenol bearing a nitrogen atom at C-25 have been previously shown to be potent inhibitors of the AdoMet-cycloartenol-C-24-methyltransferase (Narula, A. S., Rahier, A., Benveniste, P., and Schuber, F. (1981) J. Am. Chem. Soc. 103, 2408-2409). In order to determine the molecular parameters of the inhibition and to gain information about its mechanism, various azasteroids and analogues have been synthesized and assayed. The following results have been obtained. i) The presence of a positive charge at position 25 was found to be the major cause of the inhibition since electrostatically neutral isosteric compounds possessing a carbon in place of the nitrogen atom were not inhibitory. The positive charge leading to inhibition may be conferred by a protonated amine, a quaternary ammonium group, as well as by a sulfonium or an arsonium group. ii) A steroid-like structure of the inhibitor was also important. And iii) the presence of a free 3 beta-hydroxy group and the bent conformation of cycloartenol, which are essential molecular features of the substrate for the methylation reaction, were no longer required to observe inhibition. The data obtained strongly support the idea that C-25 heteroatoms (N, As, and S), substituted triterpenoid derivatives possessing a positive charge at position 25, are analogues of a carbocationic high-energy intermediate involved during the reaction catalyzed by the AdoMet-cycloartenol-C-24-methyltransferase.     

The branch point effect. Ultrasensitivity and subsensitivity to metabolic control

The interdependence of the activities of branch point enzymes which compete for a common substrate can yield ultrasensitivity or subsensitivity to control, even if the competing enzymes follow Michaelis-Menten kinetics. The nature of this "branch point effect" for a particular system depends on the kinetic parameters of the competing enzymes, the rate of substrate production leading into the branch point and the type of regulatory mechanism involved. With physiologically reasonable parameter values, the branch point effect can give ultrasensitivity equivalent to an allosteric enzyme with a Hill coefficient of 8 or higher. An experimental example of this ultrasensitivity was provided by the branch point between isocitrate lyase (of the glyoxylate bypass) and isocitrate dehydrogenase in Escherichia coli. The glyoxylate bypass is very active during growth on acetate but its flux decreases by a factor of approximately 150 upon addition of glucose. This inhibition is brought about by two relatively modest events: a 4-fold increase in the maximum velocity of isocitrate dehydrogenase and a factor of 5.5 decrease in the rate of isocitrate production. The mechanism which underlies this sensitivity amplification is discussed.     

Effect of dissolved oxygen on nitrogen fixation by A. vinelandii. I. Free cell cultures

As part of an investigation into the use of biological nitrogen fixation for fertilizer ammonia production, continuous culture studies of respiration and nitrogen fixation in the aerobic bacteria Azotobacter vinelandii under oxygen-limited conditions were conducted. Respiration and growth rates followed Monod forms with respect to dissolved oxygen concentration. However, specific nitrogen fixation rate and nitrogenase activity exhibited maximum values at dissolved oxygen concentrations of ca. 0.02 mM (10% of air saturation). These results suggest careful control of oxygen in the environment is necessary to optimize fixed nitrogen production by this organism.     

Changes in erythrocyte and thrombocyte aggregation after ultraviolet irradiation

Lipid peroxidation which occurs in blood serum under ultraviolet irradiation was studied. The products of these reaction suppress ADP-induced aggregation of native platelets. The rouleaux-forming capacity increased after UV-irradiation of plasma and serum albumin. Under UV-irradiation the aggregates of albumin molecules are supposed to form the aggregates of albumin molecules which bind the erythrocytes in rouleaux.     

Two-stage clinical trial stopping rules

Two-stage stopping rules for clinical trials are considered. The nominal significance level needed for the second-stage test, for any choice of first-stage significance level, is derived for rules with overall significance levels of .01 and .05 and for studies with either half or two-thirds of the patients analyzed in the first stage. A graphical demonstration is given of the inherent tradeoff between power and expected sample size (or probability of early termination). A specific rule, intermediate to those advocated by Pocock (1977, Biometrika 64, 191-199) and O'Brien and Fleming (1979, Biometrics 5, 549-556), is recommended.