The queen in relation to wax secretion and comb building in honeybees

Summary The role of the queen in relation to wax secretion and comb building in honeybees was analyzed with respect to queen status (mated, virgin and dead queens and queenlessness), and pheromones of the head and abdominal tergite of queens. Worker variables considered were colony size, percentage of bees bearing wax scales, wax scale weight, and weight of constructed combs.The amount of wax recovered from festoon bees and the percentage of festoon bees bearing wax were independent of queen status, the pheromones of queens and access to the queen. Colonies with full access to freely moving mated queens always constructed significantly more comb than those headed by virgin or dead queens as well as all permutations of caged and division board queens whose mandibular glands and/or abdominal tergite glands were operative or not.Despite pheromonal similarity of virgin queens to mated ones, colonies headed by virgin queens constructed as little comb as did queenless colonies. The bouquets of the mandibular glands did not differ significantly among queens nor was the amount of comb constructed correlated with pheromonal bouquet. Comb building is greatest among colonies having full access to freely moving queens but the stimulus for such building is not attributable to the 90DA, 9HDA and 10HDA components of the queen's mandibular gland secretions.     

Population dynamics in a spin-glass model of chemical evolution

Summary We introduce a simple model describing the evolution of a population of information-carrying macromolecules. We discuss the asymptotic dependence of the variability of the population on different parameters, representing the severity or the fluctuations of the environment. We show the existence of a transition separating a neutralist evolutionary regime from a trapped one. We investigate the dependence of the evolutionary behavior of the population on the correlation properties of the fitness landscape.     

First and second moments and the mean hamming distance in a stochastic replication-mutation model for biological macromolecules

In this work first and second moments for a many species Moran model are calculated. The model describes by means of a time-continuous birth- and death process the evolution of an ensemble of N macromolecules out of n possible species. The molecules may replicate (correct or erroneous, in the latter case producing mutants) and may undergo elimination. Replication and elimination will be coupled in order to keep population size constant. In the case of arbitrary replication rates an expansion of the moments in powers of 1/N is found. For equal replication rates exact calculation of the moments is possible. In the case of a v-cube model (binary macromolecules) the second moments may be used to find a simple expression for the mean Hamming distance in the system. This quantity provides a measure for the localization of the ensemble.Supported by Stiftung Volkswagenwerk     

A one-dimensional model of trail propagation by army ants

We develop and analyze a model for the swarming behaviour observed in army ants. The model assumes that the ants coordinate their movements by using chemical pheromones as trail markers. The markers continuously evaporate, and are reinforced by new markers laid down by the ants as they move. The motion of the swarm is modelled by a system of partial differential equations (PDEs). The equations are derived from the motions of the individuals, but represent the collective motion of the group, and the formation and decay of the trail network. The PDEs have travelling wave solutions which correspond to the propagation of the leading edge of the swarm. We describe these solutions qualitatively, and use them to determine how both the shape and the speed of the swarm depend on the parameters describing the motion of the individual ants.     

Mathematical model of self-cycling fermentation

This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation. (c) 1995 John Wiley & Sons, Inc.     

Mathematical model of children mortality

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.     

Mathematical model of immune processes

In the model the time lags of the antibody production and immune memory formation are taken into account explicitly. The antibody-antigen reaction is supposed to be very fast. The cases of a reproducing antigen as well as that of a non-reproducting antigen are considered. The conditions of the infinite increase of the antigen quantity and of the antigen elimination are obtained. For the rapidly reproducing antigen the latter condition includes the requirement for the time lag of the immune response to be not too short or not too long. In the case of the poorly catabolized non-reproducing antigen the cyclic appearance of the antibody producing cells due to the immune memory is described in the frame-work of the model.The mathematical structure of the model is similar to that of the Volterra-Lotka jequations. The only difference is the presence of the time lags in the non-linear terms. The time lags lead to the instability of the stationary state. In the prolonged reaction the antigen quantity may perform several oscillations before the elimination of the antigen.     

Mathematical model of visual perception

A mathematical model of visual perception is presented with the intention of throwing some light on the problem of perceptual invariance. Two types of differential manifolds (receptive and effector) are associated with the repertoire which is the fundamental concept in the model. The elements of the repertoire carry weights which control the input-output relation in the repertoire and which can be modified by a learning process. It is shown that, under reasonable conditions, these repertoires possess good stability properties and can adjust to the various environments to which they may be subjected. In particular cases, it is shown that the stochastic learning process can be considered as deterministic to a first approximation.     

Mathematical model of autoimmunity]

A mathematical model of autoimmunity is developed. This model is a system of two nonlinear differential equations, which describe the concentration dynamics of tissue cells and agressive lymphocytes. An analysis of the solutions shows that this model reproduces general behaviour of autoimmune diseases.     

Epigenetic landscape of interacting cells: A model simulation for developmental process

We propose a physical model for developmental process at cellular level to discuss the mechanism of epigenetic landscape. In our simplified model, a minimal model, the network of the interaction among cells generates the landscape epigenetically and the differentiation in developmental process is understood as a self-organization. The effect of the regulation by gene expression which is a key ingredient in development is renormalized into the interaction and the environment. At earlier stage of the development the energy landscape of the model is rugged with small amplitude. The state of cells in such a landscape is susceptible to fluctuations and not uniquely determined. These cells are regarded as stem cells. At later stage of the development the landscape has a funnel-like structure corresponding to the canalization in differentiation. The rewinding or stability of the differentiation is also demonstrated by substituting test cells into the time sequence of the model development.     

Random sampling of evolution time space and Fourier transform processing

Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and ¹⁵N-edited NOESY-HSQC spectra of ¹³C ¹⁵N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time.     

Mathematical model of polar auxin transport

Polar auxin transport can be simulated by a model which achieves polarity through the preferential secretion of more auxin from the lower end than from the upper end of each cell. Solution of the model using a computer provides a possible explanation of the differences between the polarity expressed by different tissues and the differences between pieces of different lengths, on the basis of small differences in the polarity of auxin secretion from individual cells. A method of estimating the polarity of individual cells is described.     

Mathematical model of retinal mosaic formation

The retina is one of the best examples of modular organisation in neural circuitry. This modular structure enables it to perform parallel processing. A mathematical model of the retina has been set up, focusing on mechanical features of retinal neurons and on the interaction and dendritic overlapping among retinal cells. The model focuses on the actions of local mechanical forces on the neuron's cytoskeleton. The cytoskeleton is regarded as a structure in which elastic and rigid elements are combined according to the tensegrity concept. We have assumed that dendritic overlap takes place in such a way as to favour uniform retinal neurons' distribution and that dendritic overlap is the only cause of neuron's motion on the retinal surface. This overlap depends on the growth of the dendrites due to the cytoskeletic deformation. The results obtained are in agreement with experimental results that support the notion that local mechanical interaction and dendritic overlapping are capable to transform random cell distributions into regular mosaics.     

Mathematical model of red cell sickling

A mathematical model of red cell sickling without crisis was established in vitro as a function of the parameters on which it depends: the oxygen partial pressure, the abnormal hemoglobin S concentration, the temperature and the pH. This model was verified both for the homozygotic sickling SS and heterozygotic sickling SC. Such a model allows systematic investigation of patients. Moreover, it opens up the way for rational comparison in the testing of drugs which are effective in the treatment of red cell sickling.