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Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations
Version 1
: Received: 29 December 2022 / Approved: 29 December 2022 / Online: 29 December 2022 (09:10:32 CET)
A peer-reviewed article of this Preprint also exists.
Davydyan, G. Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations. AppliedMath 2023, 3, 60-87. Davydyan, G. Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations. AppliedMath 2023, 3, 60-87.
Abstract
Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra sl(2,R) and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R42: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.
Keywords
biologic system; feedback; malignant transformations; Lie algebra; coquaternion; indefinite metric; quadratic form; hierarchy; entropy; anabolism; catabolism
Subject
Biology and Life Sciences, Biochemistry and Molecular Biology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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