Molecular Models of Genetic and Organismic Structures

In recent studies we showed that the earlier relational theories of organismic sets (Rashevsky,1967), Metabolic-Replication (M,R)-systems (Rosen,1958)and molecular sets (Bartholomay,1968) share a joint foundation that can be studied within a unified categorical framework of functional organismic structures (Baianu,1980. This is possible because all relational theories have a biomolecular basis, that is, complex structures such as genomes, cells,organs and biological organisms are mathematically represented in terms of biomolecular properties and entities,(that are often implicit in their representation axioms. The definition of organismic sets, for example, requires that certain essential quantities be determined from experiment: these are specified by special sets of values of general observables that are derived from physicochemical measurements(Baianu,1970; Baianu,1980; Baianu et al, 2004a.)Such observables are context-dependent and lead directly to natural transformations in categories and Topoi, that are again encountered in (M,R) -systems genralized theories and their biomolecular representations, as well as in molecular set theory (as demonstrated in Baianu, 1980 and Baianu, 2004). Since the problem of uniquely decomposing such organismic structures into their functional(or active) components appears to be an unsolvable one (cf. R.Rosen, 1998, 2001), we--and more recently several other authors- have adopted the complementary procedure of building up functional biomolecular models of specific, genetic and organismic structures (Baianu,1971;1972,Baianu and Marinescu,1974; Baianu,1977,1980; Baianu, 2004; Baianu et al., 2004b. Then, we have examined their genral and specific properties in terms of their mathematical representations and of the generating formalisms (Baianu,1970; 1977;1980; Baianu et al, 2004). In this context, it is interesting that energetic considerations in categories of biological systems(Baianu,1972)considered as open systems with partial ordering of charges and protein dipoles are consistent with the metastable, multi-states postulated by us (Baianu, 1970), as well as by other authors (Frohlich et al,1998). A detailed investigation of natural transformations of biological organism structures is, therefore, essential to enable the understanding of genetic network dynamics and of cell interactomics in terms of relational theories in biology. Such studies are focused on realizability conditions, observability of molecular processes and their uniqueness of representation in categories of diagrames, functors and natural transformations of biological organismic structures.