Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations

Garri Davydyan

doi:10.20944/preprints202205.0148.v2

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preprints.org > medicine and pharmacology > complementary and alternative medicine > doi: 10.20944/preprints202205.0148.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations

Garri Davydyan

Version 1 : Received: 10 May 2022 / Approved: 11 May 2022 / Online: 11 May 2022 (07:47:21 CEST)
Version 2 : Received: 20 October 2022 / Approved: 21 October 2022 / Online: 21 October 2022 (03:58:52 CEST)

How to cite: Davydyan, G. Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations. Preprints 2022, 2022050148. https://doi.org/10.20944/preprints202205.0148.v2 Davydyan, G. Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations. Preprints 2022, 2022050148. https://doi.org/10.20944/preprints202205.0148.v2

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MDPI and ACS Style

Davydyan, G. Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations. Preprints 2022, 2022050148. https://doi.org/10.20944/preprints202205.0148.v2

APA Style

Davydyan, G. (2022). Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations. Preprints. https://doi.org/10.20944/preprints202205.0148.v2

Chicago/Turabian Style

Davydyan, G. 2022 "Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations" Preprints. https://doi.org/10.20944/preprints202205.0148.v2

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 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

Medicine and Pharmacology, Complementary and Alternative Medicine

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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Comments (2)

Comment 1

Received: 21 October 2022
Commenter: Garri Davydyan
Commenter's Conflict of Interests: Author

Comment: Changes have been made throughout the whole text and figures. Introduction, Section 5.1, Results have been rewritten, four referenced added. Figure 9 was replaced on the Table1. General idea of the manuscript remains the same. Changes have been made to clarify some approaches and the obtained results.

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Comment 2

Received: 20 November 2022
Commenter: Alvin Gentry
The commenter has declared there is no conflict of interests.

Comment: Not bad..needs a few tweaks.

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