In this paper considered as the first one of the two-part paper one discusses a structure of mathematical theory which would be convenient for modelling of biological systems together with their whole complexity. Main aspects which are accentuated are related to multiscale properties of the system and also integrity of it. Furthermore, having in mind that biological systems undergo evolution considerable attention is devoted to determination of driven force for such an evolution. One discriminates several levels of description. The first one is related to electronic structure in which an attractor is characterized as responsible for biological selforganization. The second one is atomic level of description responsible for creation of biological structures. The third level is called functional one. It will be considered in the second part of the two-part paper and is designed to description of selective functions of biological systems. Role of attractor in electronic structure is accentuated. In order to characterize such an attractor electrons are described by means of the vacuum medium mechanics instead of the quantum mechanics. Thereby one proposes replacing of the quantum mechanics as well as the quantum chemistry by atomic and molecular physics and also theoretical chemistry based on vacuum medium mechanics. The main reason for such a replacement is related to ability for determination of the attractor in electronic structure just by the vacuum medium mechanics. Proposed here chain state of electrons is not expressible in quantum mechanics. Having in mind that biological evolution manifests considerable persistence one discusses evidence for strength of introduced attractor in order to show ability of this concept for modelling of biological evolution. Thereby, for the first time we have at our disposal proposition for attractor governing evolutionary processes in biological systems and considered at the most elementary physical level.

structure of theory for modelling of biological processes, mechanisms of biological evolution.