Carcinogenesis: alterations in reciprocal interactions of normal functional structure of biologic systems.

Garri Davydyan

doi:10.1186/s13637-015-0030-9

Abstract

The evolution of biologic systems (BS) includes functional mechanisms that in some conditions may lead to the development of cancer. Using mathematical group theory and matrix analysis, previously, it was shown that normally functioning BS are steady functional structures regulated by three basis regulatory components: reciprocal links (RL), negative feedback (NFB) and positive feedback (PFB). Together, they form an integrative unit maintaining system’s autonomy and functional stability. It is proposed that phylogenetic development of different species is implemented by the splitting of “rudimentary” characters into two relatively independent functional parts that become encoded in chromosomes. The functional correlate of splitting mechanisms is RL. Inversion of phylogenetic mechanisms during ontogenetic development leads cell differentiation until cells reach mature states. Deterioration of reciprocal structure in the genome during ontogenesis gives rise of pathological conditions characterized by unsteadiness of the system. Uncontrollable cell proliferation and invasive cell growth are the leading features of the functional outcomes of malfunctioning systems. The regulatory element responsible for these changes is RL. In matrix language, pathological regulation is represented by matrices having positive values of diagonal elements (TrA > 0) and also positive values of matrix determinant (detA > 0). Regulatory structures of that kind can be obtained if the negative entry of the matrix corresponding to RL is replaced with the positive one. To describe not only normal but also pathological states of BS, a unit matrix should be added to the basis matrices representing RL, NFB and PFB. A mathematical structure corresponding to the set of these four basis functional patterns (matrices) is a split quaternion (coquaternion). The structure and specific role of basis elements comprising four-dimensional linear space of split quaternions help to understand what changes in mechanism of cell differentiation may lead to cancer development.

Highlights

The regulatory structure of normal biologic systems (BS) predisposes the development of functional states mimicking cancer growth
9 Conclusions The presented hypothetical model of mechanisms of cancer development is based on geometrical properties of the space of split quaternions where the split complex part is presented by the basis elements of Lie algebra sl(2, R)
A real part presented by ±unit matrix allows describing unsteady states of BS which can be considered as a prominent feature of a system undergoing pathological development

Summary

Introduction

The regulatory structure of normal biologic systems (BS) predisposes the development of functional states mimicking cancer growth. It makes sense, because the matrix of PFB demonstrates capabilities of the regulatory structure to manage complex systems (tissues, organs, etc.) from simpler ones (biologic cells, biochemical molecules).

Results

Conclusion