On the solution of mathematical models of herd immunity in human helminth infections

The general solution of the mathematical model of herd immunity to human helminth infections recently proposed by Anderson and May [3] is obtained. The numerical solution of a more accurate biological model is indistinguishable from the corresponding exact solution of a more tractable mathematical model. Computer simulations of some particular cases of this model support the notion that both ecological and immunological factors determine the observed convex patterns of age-prevalence and age-intensity curves of human helminth infections.This work was made thanks to the advise and support of Dr. Robert M. May while the author was Postdoctoral Fellow at Princeton University     

Effect of Zeitgeber Intensity Reduction on a Simulated Dual-Oscillator Human Circadian System: Classical and Dynamic Analysis

The two-oscillator model of human circadian rhythmicity was analyzed when a zeitgeber relative intensity of 1, 0.5, or 0.1 was introduced into the equations. Fourier analysis was compared with dynamic analysis such as attractor reconstruction or Liapunov exponent calculation. After a 50 or 90% reduction in zeitgeber intensity, the dynamics of the system became equivalent and differed significantly from those of a system with maximal zeitgeber intensity. When 10% aleatory noise was added to the data, the analysis was still applicable, and the results obtained were essentially the same as in the absence of noise. Dynamic analysis could thus provide a distinct classification for periodic data, based on the type of analysis.     

Regional environmental simulation of African cattle herding societies

Regional analyses of the interaction between human populations and natural resources must integrate landscape scale environmental problems. An approach that considers human culture, environmental processes, and resource needs offers an appropriate methodology. With this methodology, we analyze problems of food availability in African cattle-keeping societies. The analysis interrelates cattle biomass, forage availability, milk and blood production, crop yields, gathering, food subsidies, population, and variable precipitation. While an excess of cattle leads to overgrazing, cattle also serve as valuable food storage mechanisms during low rainfall periods. Food subsidies support higher population levels but do not alter drought-induced population fluctuations. Variable precipitation patterns require solutions that stabilize year-to-year food production and also address problems of overpopulation.     

Ion-specific diffusion rates through transmembrane protein channels. A molecular dynamics study

The migration of different alkali metal cations through a transmembrane model channel is simulated by means of the molecular dynamics technique. The parameters of the model are chosen in close relation to the gramicidin A channel. Coulomb- and van der Waals-type potentials between the ions and flexible carbonyl groups of the pore-forming molecule are used to describe the ion channel interaction. The diffusion properties of the ions are obtained from three-dimensional trajectory calculations. The diffusion rates for the different ions Li+, Na+, K+ and Rb+ are affected not only by the mass of the particles but also very strongly by their size. The latter effect is more pronounced for rigid channels, i.e., for binding vibrational frequencies of the CO groups with v greater than 400 cm-1. In this range the selectivity sequence for the diffusion rates is the inverse of that expected from normal rate theory but agrees with that found in experiments for gramicidin A.     

A note on sequence-dependence of DNA structure

A circular dichroism study was conducted on the solution structure of several different oligonucleotides, whose X-ray structures have been solved. It is suggested that in aqueous solution the oligonucleotides can form structures that maintain geometrical elements which are typical of B-DNA, A-DNA, and their intermediate forms. It is shown that 5'GGATGGGAG:5'CTCCCATCC, which forms an A-DNA helix in the crystal state (McCall et al. 1986), in aqueous solution maintains an A-DNA like structure at temperatures below 10 degrees C. At temperatures between 10 degrees C and 25 degrees C it shows a tendency to form an intermediate structure between A-DNA and B-DNA. Also, it is shown that TFE does not cause a transition from B-DNA to A-DNA helix in short DNA fragments, but instead disrupts the helix.     

Blurry artifacts: a retraction

Abstract. This note is to apologize for an error in the computer program used to evaluate the random data used in Fuzzy Set Ordination according to Zhang & Oxley. After correction of this error no artifacts could be detected any longer. However, the basic conclusion of the earlier critical note still stands: if one selects environmental variables after analyzing the results of a multivariate gradient analysis, and then uses these variables as input into a multiple univariate gradient analysis, the results are expected to be comparable.     

Comparative studies on the dynamics of crosslinked insulin

Molecular dynamics simulations were carried out on an insulin crosslinked between the N-terminal A chain and the C-terminal B chain to form a so-called mini-proinsulin: N -^A1-N -^B29-diaminosuberoyl insulin (DASI). To investigate the influence of crosslinking on the dynamics of the insulin moiety, the bridge was removed from a transient DASI structure and simulation was carried on independently with the then unlinked (ULKI) as well as with the crosslinked species. The effects of crystal packing and quaternary interactions were checked by simulating both types of monomers and dimers known from the hexamer structure. All simulations were compared to previous ones of native insulin. DASI shows general similarity to the native simulations in most parts of the structure. Deviations are visible in the segments to which the bridge is directly connected, i.e. their flexibility is reduced. Upon removal of the bridge the ULKI simulations reapproach those of native insulin. The influence of the bridge spreads over the whole molecule, but all of its main structural features remain intact. The simulations suggest that the displacement of the C-terminal B chain of native insulin, considered important for receptor interaction, is prevented by the bridge, which also partially shields some binding residues. This is in accordance with the poor biological potency of A1-B29-crosslinked insulins.Abbreviations DASI-insulin(DASI) bovineN -^A1-N -^B29-di-aminosuberoyl insulin - ULK-insulin (ULKI) Native beef insulin with the bridge of DASI removed     

On some formulas in a partnership model from the perspective of a semi-Markov process

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways,for extensions to the age-dependent case.This research was partially supported by NATO Grant D.890350     

Species composition of dabbling duck assemblages: ecomorphological patterns compared with null models

Ecomorphological patterns of breeding dabbling duck (Anas spp.) assemblages were studied in six regions in northern Europe. Observed spacings among species in terms of bill lamellar density and body length were compared with expected spacings based on null models incorporating different levels of constraints (regional species pools, species relative abundances, lake size and habitat requirements of species). Deviations of observed spacings from expected ones were compared with prey abundance and prey size diversity in the lakes. Observed spacings in terms of body length, but not in terms of bill lamellar density, were greater than expected on the basis of null models. The most abundant species were generally relatively more different than less abundant species in terms of body length but not in terms of bill lamellar density. Deviations between observed and expected spacings in terms of body length were more like those predicted by the competition hypothesis in lakes with low food abundance than in lakes with high food abundance. Patterns in bill lamellar spacings were not related to food abundance nor to food size diversity. In general, patterns in body length spacings were consistent with the competition hypothesis whether the null model used in comparisons was constrained or not.