ALBERT

Notes: Abstract The entropy budget of a white-tailed deer (50kg) on a maintenance diet and a full-feed diet in a standing posture in an open field under clear nocturnal skies with an air temperature of −20°C is investigated based on the energetics given by Moen. Entropy inflow into a white-tailed deer due to infra-red radiation and entropy outflows from a deer due to infra-red radiation, convection, evaporation of water and conduction to ingested food are calculated. Also the entropy production due to metabolic heat production is estimated. Net entropy flow into a deer from its environment becomes negative. On the assumption that a white-tailed deer is in a steady state in entropy, the total entropy production in a deer on a maintenance diet becomes +0.46 J/sec/K. Positiveness of the entropy production shows that the Second Law of Thermodynamics certainly holds in a white-tailed deer. The entropy production per effective radiating surface area of a deer on a maintenance diet is 0.32×10−4 J/cm2/sec/K. On the other hand, the entropy production in a deer on a full-feed diet is 0.59 J/sec/K and that per effective surface area is 0.41×10−4 J/cm2/sec/K. Uptake of 1 g of food produces 22 J/K of entropy within the body of a white-tailed deer. Comparison is made with the results for entropy production in a lizard and in plant leaves.

Notes: Abstract Biological adaptability has been proved to be analysable by means of the Maximum Entropy Formalism (MAXENT) in some cases of non-interacting systems. This formalism is extended to the biomass statistical structures of populations exhibiting internal interactions (i.e. predatorprey effects).

Notes: Abstract The temporal behaviours of the nonlinear substructure of a self-organized compartmental model of calcium metabolism were investigated. The order-two autocatalytic process included in this simple two-dimensional model is compared to some secondary nucleation mechanisms which should take place at the extracellular fluid-bone interface. The model gives rise to complex dynamic behaviours, and multistability properties, involving up to two stable periodic regimes (birhythmicity), were established in different topological configurations. The bifurcations occurring on the boundaries between regions of different qualitative behaviour have been determined. These properties are discussed in relation to the dynamical behaviour of other two-variable models, especially those including the same nonlinearity.

Notes: Abstract A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math. XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by Gurney, Blythe and Nisbet (1980,Nature, Lond. 287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation result for difference equations and applied it to several equations taken from the biological literature.

Notes: Abstract A theoretical approach to the explanation of the structural design of metabolic pathway is presented. It is based on the hypothesis that due to natural selection during evolution the cellular metabolism of present-day organisms may be characterized by optimal properties. Two cardinal terms enter the theory: (i) the efficiency of a metabolic pathway and (ii) the evolutionary effort for the change of the kinetic parameters of enzymes by mutations of the corresponding genes. For both quantities simple mathematical expressions are proposed. While the efficiency is related to the reaction rates of the enzymes constituting the metabolic pathway, the evolutionary effort is considered to be a monotonically increasing function of the parameter values. By maximizing the efficiency under the constraint of a fixed evolutionary effort the theory allows the calculation of the optimal parameter distribution as the outcome of evolution processes. The methods developed are applied to the following systems: (a) linear reaction sequences with very low affinities of the enzymes towards substrates, (b) linear sequences consisting of saturable enzymatic reactions, (c) branched metabolic pathways consisting of segments of linear chains and (d) glycolysis of erythrocytes. The conclusion is derived that the optimal distribution of kinetic constants depends strongly on the equilibrium constants of the reactions as well as on the total osmolarity of the metabolic intermediates. Without osmotic constraints the evolutionary effort is mainly spent on the enzymes at the beginning of the chain. Using Michaelis-Menten equations the optimal state is characterized by a decrease of the maximal activities of the enzymes towards the end of the chain. These results are modified if osmotic constraints are taken into account. At the investigation of branched pathways the following results were obtained: firstly, if a certain end product may be synthesized along different pathways those which are thermodynamically more unfavourable (e.g. characterized by a small change of free energy) are eliminated in the course of evolution; secondly, if a branched pathway leads to several important end products those reaction segments which are thermodynamically unfavourable are characterized by a higher evolutionary effort. The application of the theory to a realistic model of glycolysis of erythrocytes leads to a correct description of various functionally important properties of the system, such as the ratio between fluxes through different branches and the ATP/ADP ratio, whereas the theory cannot predict the strong separation of time constants observed in the real glycolytic system. It is concluded that the improvement of the predictive power of the theory necessitates the use of more complex functionals for the efficiency which take into account not only the fluxes but also other system properties such as the stability of the pathway or homoeostatic effects.