111 Towards the manifold representations of biological object

Abstract

Most entities of biological world somebody considered a biological object are conditionally discrete, locally isolated, and partly closed systems with capacity of development. Concentrating on the last characteristics, we describe the individual development of object by means of expression O = (G,F,Ph), which is a kinematic description of locally isolated object developing in accord with its internal laws. Mesoscopic organisms are well-known examples of such systems where , , and stand for signs and sets of genotype, phenotype, and for map, respectively, thus indicating that g entails ph causally. However, such superposition of genotype and phenotype can be broken during the individual development in different ways, e.g. because some phenotype signs can be received from mother in their complete form before fertilization (before appearing the new individual with new genotype). The individual development per se starts with a division of zygote. That division and some follow-up ones giving globe embryos in the vessel plants or multicellular blastocyst in mammals can be described as f 0(g 0) → 2g 0. This description is valid for meristem (in plants) and stem cells due to their status of low level of differentiation. Diverging from zygote as a central position in the imaginary diagram representation, the trajectories of divisions describe the history of development whereas the real embryo includes only the cells of current state of division and differentiation. The cell differentiations g 0 → g d and dedifferentiations g d → g 0 assemble the main body of events of development in their relation to genotype. Besides, in the time intervals between divisions, the maps of f(g) → ph type occur. Resulting from these maps the stable sets of phenotype signs correspond to ontogeny stages. In the general case, the iterations of {g 0 ↔ g d, g d → ph d} block can form a time series in space of states. As a transition from one element of time series to another one is directed by the partial order set on the antecedent, it turned out that the backbone of series is represented by succession of genotype states whereas there are no direct connections between phenotype states. During development, biological object becomes more and more open system. Thus, butterfly consumes nectar, transfers the blossom dust or becomes a pray of predator. In such representations, the biological object can be defined as an operator transforming one external object in the other external one: : , , . It means that due to the neogenic phenotypic part, an object receives an interaction potential which was absent in the former locally isolated entity considered as a partly closed system. This potential can be realized in many ways. So, the dynamics of biological object consists in the transitions of stable genotype state in the other stable states, whereas the latter transit into (final) states of phenotype. That demands to describe the individual development as a process in the complex space that changes with every small step of ontogeny depending on the current states of its genotypic and phenotypic constituents and on their interaction. Such dynamics of object and its related space provides the biological object with multifold representations on the wide spectrum of thermodynamic descriptions.