The author discusses a structure of mathematical theory which would be convenient for modelling of biological systems together with their whole complexity. The main aspects are related to the multiscale properties of the system and also its integrity. Furthermore, having in mind that biological systems undergo evolution, considerable attention is devoted to the determination of the driven force for such an evolution. One distinguishes several levels of description. The first one is related to the electronic structure in which an attractor is characterized as responsible for biological self-organization. The second one is the atomic level of the description responsible for the creation of biological structures. The third level is called the functional one. It will be considered in the second part of this two-part paper and is designed for the description of selective functions of biological systems. The role of attractor in the electronic structure is accentuated. In order to characterize such an attractor, the electrons are described by means of the vacuum medium mechanics instead of the quantum mechanics. The author proposes to replace 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 the ability for the determination of the attractor in the electronic structure just by the vacuum medium mechanics. The chain state of electrons proposed here is not expressible in quantum mechanics. Having in mind that biological evolution manifests considerable persistence, one discusses the evidence for strength of the introduced attractor in order to show the ability of this concept for modelling biological evolution.