Conception of Biologic System: Basis Functional Elements and Metric Properties

A notion of biologic system or just a system implies a functional wholeness of comprising system components. Positive and negative feedback are the examples of how the idea to unite anatomical elements in the whole functional structure was successfully used in practice to explain regulatory mechanisms in biology and medicine. There are numerous examples of functional and metabolic pathways which are not regulated by feedback loops and have a structure of reciprocal relationships. Expressed in the matrix form positive feedback, negative feedback, and reciprocal links represent three basis elements of a Lie algebra of a special linear group . It is proposed that the mathematical group structure can be realized through the three regulatory elements playing a role of a functional basis of biologic systems. The structure of the basis elements endows the space of biological variables with indefinite metric. Metric structure resembles Minkowski's space-time (+, ？, ？) making the carrier spaces of biologic variables and the space of transformations inhomogeneous. It endows biologic systems with a rich functional structure, giving the regulatory elements special differentiating features to form steady autonomous subsystems reducible to one-dimensional components. 1. Introduction The concept “system,” introduced in the middle of the last century, was proposed to describe self-organizing properties of biologic matter. The essence of it is the ability of biologic objects to maintain their own anatomical and functional structure [1–3]. Until now positive and negative feedback are used to describe the regulatory mechanisms of biologic system. Existing data show that positive and negative feedback do not explain some of the physiological and medical data. It was an attractive idea to find out whether some regulatory components can form a functional basis of the system. In challenging the existing hypotheses it was found that reciprocal links have the same importance as positive and negative feedback in functional regulation of biological systems. In fact, positive and negative feedback and reciprocal links can form a functional basis of biological systems. Regulatory functions of the system comprise numerous metabolic pathways and biochemical reactions, which, in fact, realize only a number of core mechanisms. Until now a great deal of effort has been undertaken to find these functional invariants. Positive and negative feedback are the only known functional structures with universal properties [4–8]. Widely presented as common regulatory mechanisms in general biology