Narrow Results

Control theory is concerned mainly with the treatment of signals. This article takes into account that living beings not only treat information, but they are open systems traversed by flows of energy and mass. A new block diagram of the regulation process is proposed, taking into account this fundamental difference between engineered and living systems. This new diagram possesses both didactic and heuristic advantages.

Developmental processes may impose limitations and directionality in the mode of development of a particular structure. The main problem is to determine the nature and the respective effects of physical and biological constraints in the development of organisms. The Aboav-Weaire law is a semi-empirical law developed to explain the topological structure of physical materials. In the present paper, we make a formal analysis of the quantitative relationships between physical and biological constraints in biological structures by using the inflorescence of the Araceae as a case study. The Aboav-Weaire law permits to obtain a quantitative estimate of the biological constraint acting on the inflorescences of this family. In the case of the Araceae, the empirical curve presents a constant deviation with respect to the Aboav-Weaire law. This deviation is due to the presence of a biological constraint as opposed to a physical constraint. The biological constraint tends to decrease the variance of the number of sides while it is the inverse situation for the physical constraint. The results obtained using the Araceae model can be used to study the interrelationships between biological and physical constraints in any organism or biological structure.

Current model for circadian rhythms is wrong both theoretically and practically. A new model, called yin yang model, is proposed to explain the mechanism of circadian rhythms. The yin yang model separate circadian activities in a circadian system into yin (night activities) and yang (day activities) and a circadian clock into a day clock and a night clock. The day clock is the product of night activities, but it promotes day activities; the night clock is the product of day activities, but it promotes night activities. The clock maintains redox or energy homeostasis of the internal environment and allows temporal separations between biological processes with opposite impacts on the internal environment of a circadian system.

The paper deals with a statistical method to analyze irregular phyllotactic patterns. To characterize the degree of order in phyllotactic systems, we determine the variation of the angle of divergence of a given leaf with regard to the preceding one. By knowing the range of uncertainty of the angle of divergence, it is possible to determine from which leaves rank a system becomes completely disorganized. We show that there is a quantitative link between the degree of uncertainty of the angle of divergence, and the number of regularly and randomly distributed leaves. To quantify this relationship, we deduced a formula from numerical simulations involving different ranges of uncertainty that can be observed in the angle of divergence in three different phyllotactic patterns: distichous (two orthostichies), opposite-decussate (four orthostichies) and spiral (137°). A χ² statistical test allows us to determine the threshold of transition between ordered and disordered phyllotactic patterns with a fixed level of confidence. By using the sho mutants described by Itoh et al.¹ as a case study, we show that this formula is useful mainly for analyzing the degree of order in phyllotactic mutants from two complementary points of view: the number of regularly distributed leaves and the degree of uncertainty of the divergence angle.

Fluoride-contaminated drinking water is a serious public health hazard in some parts of India. Field surveys have been conducted in fluoride-affected areas of the Birbhum district, West Bengal, India. From these surveys, it is found that in certain locations the drinking water contains less fluoride (within the permissible limit¹) than in adjoining areas. We have isolated a strain of Streptococcus species from these wells that has the ability to remove the fluoride ion from the water. We have grown the bacteria in different concentrations of fluoride and monitored the decline in the free fluoride ion concentration. A simplified model of fluoride and bacterial dynamics is proposed. The model is handled both analytically and numerically. For numerical solution mainly our own laboratory data are used. Calibration and validation are performed with different sets of experimental data. Analytical solutions show that the bacterial consumption and growth rates are the most important parameters in the system. Analysis shows asymptotic stability of the system.

Extremal principles or ecological orientors or goal functions are the most modern approach in theoretical ecology. There are many such principles proposed by different theoretical ecologists. In this paper, the most important extremal principles are discussed based on their theoretical backgrounds. Two widely accepted goal functions, i.e. exergy and ascendency are optimized and treated in a quantitative manner in an aquatic ecosystem model of planktonic and fish systems for their appropriateness. In the model varied body sizes of phytoplankton and zooplankton are considered. Parameter values varied according to the allometric principle with the body sizes. For self-organization of the model system two goal functions predict different results, however both are realistic.

In previous experiments, a synergistic lethal effect on the honeybee has been demonstrated with two toxic agents: deltamethrin and prochloraz. The toxic agents were applied simultaneously or sequentially. Deltamethrin is metabolized by esterase and by cytochrome P-450-dependent monooxygenase. Prochloraz is a potent competitive inhibitor of cytochrome P-450. An attractive hypothesis explaining this synergic toxicity is that the persistence of deltamethrin is due to inhibition of the oxidative metabolism of deltamethrin by prochloraz. We tested this hypothesis using a mathematical model. A compartmental model in continuous time was constructed to represent this synergy by analyzing the degradation of toxic agents. This pharmacokinetic model was based on differential equations, using numerical resolution and Runge-Kutta’s integration method. When applied to a mixture of toxic agents, this model implies that the cumulative mortality of both compounds might be delayed compared to the mortality from treatment with toxic agents used separately. The hypothesis of metabolic synergy is compatible with experimental data only if the half-life of deltamethrin is short. The data from the model and the experimental data, diverged when deltamethrin was administered before prochloraz, which suggests that the phenomenon is more complex than expected.

The inflorescence of Symplocarpus foetidus constitutes good material to analyse the biological processes and physical constraints involved in the development of plants. During the development of the inflorescence, two morphogenetic periods can be distinguished (i) before and (ii) during and after the development of floral parts. In the first period, when the floral primordia appear, the phyllotactic system could be explained by global processes at the inflorescence level. In the second period, the development of floral parts produces patterns which can be explained by local processes at the floral level. In this analysis the author defines the concepts of open system and closed system in phyllotaxis. In a closed system (e.g. spadix) the elements are arranged on a continuous and closed surface. In an open system (e.g. shoot apex) the elements appear on a surface periodically renewed and are removed from each other by the intercalary growth.

We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies^12–14 have shown that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. The development of the spatial pattern occurs on a timescale comparable to jaw growth. Based on biological data we develop a dynamic patterning mechanism, which crucially includes domain growth. The mechanism can reproduce the spatial pattern development of the first seven teeth primordia in the lower jaw of A. mississippiensis. The results for the precise spatio-temporal sequence compare well with experiment.

Coexpressed genes are tentatively translated into proteins that are involved in similar biological functions. Here, we constructed gene coexpression networks from collected microarray data of the organisms Arabidopsis thaliana, Saccharomyces cerevisiae, and Escherichia coli. Their degree distributions show the common property of an overrepresentation of highly connected nodes followed by a sudden truncation. In order to analyze this behavior, we present an evolutionary model simulating the genetic evolution. This model assumes that new genes emerge by duplication from a small initial set of primordial genes. Our model does not include the removal of unused genes but selective pressure is indirectly taken into account by preferentially duplicating the old genes. Thus, gene duplication represents the emergence of a new gene and its successful establishment. After a duplication event, all genes are slightly but iteratively mutated, thus altering their expression patterns. Our model is capable of reproducing global properties of the investigated coexpression networks. We show that our model reflects the mean inter-node distances and especially the characteristic humps in the degree distribution that, in the biological examples, result from functionally related genes.

This chapter gives an overview of various ventricular assist devices with a particular focus on axial flow pumps. Using the Hemopump as an example, we developed a model of a canine circulatory system assisted by an axial flow pump, and used computer simulation to predict the effects of the assist device under various hemodynamic conditions. In general, the results from the simulation are in good agreement with that observed in clinical and animal experiments. The same model is further used to explore the techniques and strategy for optimum control of the assist device by introducing an objective function, and choosing suitable membership functions with associated weighting factors, the model offers great flexibility in choosing the targeted hemodynamic variables, in specifying the particular way that each of these variables is to be optimized, and in assigning the relative importance of each targeted variable. The methods used and the results obtained in this study can be incorporated into the design of an advanced physiological controller for a long-term operation of the axial flow pump-based assist device as well as other types of continuous-flow LVAD.