Biological growth and spread modeled by systems of recursions. II. Biological theory

The mathematical theory developed in Part I is applied to a selection-migration model in population genetics with sex-linked locus and to the host-vector or venereal disease epidemic model. In both models, a constant c*(xi) is found for each unit vector xi. The mathematical results imply that under certain initial conditions, the frequency of the advantageous gene in the male and female gametic outputs or the epidemic will spread at a speed c*(xi) in the direction xi as time goes to infinity. Time is measured in discrete nonoverlapping generations. In most cases, we can find a formula for c*(xi).     

Biological properties of selenobiotin.

Selenobiotin is an excellent growth factor, as efficient as biotin in supporting the growth of biotin requiring microorganisms. It is incorporated in carboxylases leading to active “selenocarboxylases”. With E. Coli, the activity of the selenoacetyl CoA carboxylase is very similar to that of the normal enzyme.     

Biological low-dose radiation effects.

It is theorized that biological responses to ionizing radiation in the low dose range are determined according to a doubly dichotomous pattern. Energy depositions fall into 2 categories: events at thermal energy levels where they may be experienced by cells as rates even at background exposure conditions, and events at energy levels of the order of 10-100 eV where damage to DNA may be caused. Variations in background exposure intensity may or may not lead preemptively to changes in the cell's capacity for response to radiation damage. High-level energy depositions lead post hoc to an initial stabilizing reaction largely leading to the fixation of the initial DNA damage, and to a subsequent restorative or palliative repair process. This model entails reinterpretation of some experimental results. The model has implications for the relationship between scientific analysis of low-dose effects and the regulatory needs for simplicity and homogeneity in risk evaluation. This represents a new challenge for the acceptability of radiation protection norms.     

Biological complexes of poly-beta-hydroxybutyrate.

Short-chain complexed poly-beta-hydroxybutyrate, 130-170 monomer units, is a ubiquitous constituent of cells, wherein it is usually associated with other macromolecules by multiple coordinate bonds, or by hydrogen bonding and hydrophobic interactions. This conserved PHB has been isolated from the plasma membranes of bacteria, from a variety of plant tissues, and from the plasma membranes, mitochondria, and microsomes of animal cells. In bacterial membranes, PHB has been found complexed to the calcium salts of inorganic polyphosphates, and to single-stranded DNAs. The ability of PHB to solvate salts, consisting of cations having high solvation energies and large delocalized anions, is in accordance with its molecular characteristics, that of a flexible linear molecule possessing a large number of electron-donating ester oxygens suitably spaced to replace the hydration shell of cations. In turn, PHB may be rendered soluble in aqueous media by complexation to water-soluble proteins, such as serum lipoproteins and albumin. Such solvates are highly resistant to hydrolytic enzymes. These findings suggest that the physiological roles of this unique biopolymer may include the solvation of salts of polymeric anions to facilitate their movement through hydrophobic barriers, and the protection of cellular polymers from enzymatic degradation.     

Biological activity of agarose-immobilized catecholamines.

Catecholamines substituted to agarose were synthesized in various ways. Norepinephrine and isoproterenol were linked to p-aminobenzamidohexyl agarose by an azo linkage to the catechol ring. Norepinephrine was also couple to hexyl agaros via the amino group, forming an amino, guanidino or amido bond. Biological activity of the immobilized catecholamines was determined by assessing their abilities to interact with adenylate cyclase in several membrane preparations and intact preparations of erythrocytes. In dog heart membranes, stimulation of adenylate cyclase by the catecholamine-gels could be accounted for by leached hormone which had been released from the gels. In frog erythrocyte membranes, leaching was minimal and no significant stimulation of adenylate cyclase was observed. Agarose-immobilized catecholamines, however, competitively inhibited isoproterenol stimulation of adenylate cyclase in these erythrocyte membranes indicating that catecholamines which are bound to agarose interact with the beta-adrenergic receptors as antagonists rather than agonists. When tested on intact frog erythrocytes, agarose immobilzed catecholamines did not increase the intracellular levels of cyclic AMP, although isoproterenol caused as 8-10 fold rise in these levels. Similarly, when tested for antagonist activity in the intact cells the agarose-catecholamines failed to inhibit the stimulation of cyclic AMP caused by isoproterenol. The difference observed in the beta-adrenergic antagonist activity of the agarose-bound catecholamines in membrane preparations and intact cells can be attributed to steric factors which could have prevented the access of the bead-bound ligands with the surface of the cell or to the possibility that receptors might be buried in the membrane matrix.     

Biological adaptabilities and quantum entropies.

The entropy-based theory of adaptability set forth by Michael Conrad in the early 1970s continued to appear in his work for over two decades, and was the subject of the only book he published in his lifetime. He applied this theory to a host of subjects ranging from enzyme dynamics to sociology. This paper reviews the formalism of adaptability theory, clarifying some of its mathematical and interpretive difficulties. The theory frames the computational tradeoff principle, a thesis that was the most frequently recurring claim in his work. The formulation of adaptability theory presented here allows the introduction of quantum entropy functions into the theory, revealing an interesting relationship between adaptability and another one of Conrad's deep preoccupations, the role of quantum processes in life.     

Axiomatization of genetics. 1. Biological meaning

Axiomatization is a trend in science to settle and reduce fundamental assertions, from which all the others are deducible. Classical genetics has been extensively axiomatized and formalized by Woodger (1952), who resorted to 53 axioms and 12 theorems. The molecular settlement of modern genetics provides the basis for a different axiomatic theory. In this paper 3 axioms and 14 theorems are informally expressed. They cover a few elementary laws of "chromosome genetics" in Eukaryotes. The biological problems connected with the further development of this first attempt are discussed.