Tag Archives: Krebs cycle

Instability and invariant measure in the mathematical model for oxidative phosphorylation and ATP synthesis in the cell

V. I. Grytsay

Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv;
e-mail: vigrytsay@gmail.com

Received: 13 October 2023; Revised: 28 November 2023;
Accepted: 01 December 2023; Available on-line: 18 December 2023

The aim of this work was to analyze the process of oxidative phosphorylation and ATP synthesis in a cell using a mathematical model. The scenario of occurrence of the autoperiodic and chaotic modes depending on the ATP dissipation values was determined. The invariant measure of the strange attractor was calculated, and histograms of its projections on the phase plane were plotted. Some recommendations were made on how to eliminate biochemically the chaotic mode and restore the stability of the self-organization of the cell biosystem.

The Nobel laureates’ contributions to the study of carbohydrate metabolism and its regulation. A. Harden, H. Euler-Chelpin, C. F. Cori, G. T. Cori, E. Sutherland, L. F. Leloir, H. Krebs, F. Lipmann, P. Mitchell

R. P. Vynogradova, V. M. Danilova, S. V. Komisarenko

Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, Kiyv;
e-mail: valdan@biochem.kiev.ua

Received: 13 November 2019; Accepted: 29 November 2019

Carbohydrate metabolism is a complex and multi-stage process. Many scientists (biochemists, physiologists, chemists) worked on deciphering this process, but only some of them were awarded the Nobel Prize. Thus, in the early XXth century, the work of A. Garden and H. Euler-Chelpin with yeast cells revealed that the conversion of carbohydrates (sugars) into end products occurs in living cells in several steps with the involvement of enzymes and that this conversion requires the presence of phosphoric acid residue. These studies were the beginning of exploring the chemical reactions (the reactions of intermediate metabolism) that are fundamentals for the vital functions of cells. In 1932, Hans Krebs discovered the ornithine cycle, a sequence of chemical reactions, in which the end product of nitrogen metabolism, urea, is formed in the liver of animals. The apogee of his research was the discovery of tri- and dicarboxylic acid cycle, which combines the oxidation of almost all organic compounds in living organisms. Fritz Lipmann, who in 1945 discovered coenzyme A and identified its role in the activation of organic compounds, furthered the works of H. Krebs. At the time, it became clear how inactive acetic acid and other organic acids are activated in living organisms to be oxidized in the tricarboxylic acid cycle. The great work was done by the spouses Gerty and Carl Cori,  and Bernardo Houssay, as well as their students and followers, in particular, Luis Leloir to clarify the mechanism of conversion (synthesis and breakdown) of glycogen in the liver and muscles. The peak of studying the carbohydrate metabolism was the research of Earl Sutherland who in 1958 revealed the regulation of the activity of enzymes involved in the conversion of chemical compounds (the example – phosphorylase), with the participation of the adenylate cyclase enzyme and c-AMP. The discovery of c-AMR established one of the fundamental principles of almost all vital processes. And the culmination of research on carbohydrate metabolism was the unrivaled works of Peter Mitchell, who studied the course of biochemical reactions in cells relative to certain intracellular “landmarks” and who formulated the chemiosmotic theory of oxidative phosphorylation that underlies bioenergetics.

Self-organization and fractality in a metabolic processes of the Krebs cycle

V. I. Grytsay1, I. V. Musatenko2

1Bogolyubov Institute for Theoretical Physics,
National Academy of Sciences of Ukraine, Kyiv;
e-mail: vgrytsay@bitp.kiev.ua;
2Taras Shevchenko National University of Kyiv, Ukraine;
e-mail: ivmusatenko@gmail.com

The metabolic processes of the Krebs cycle is studied with the help of a mathematical model. The autocatalytic processes resulting in both the formation of the self-organization in the Krebs cycle and the appearance of a cyclicity of its dynamics are determined. Some structural-functional connections creating the synchronism of an autoperiodic functioning at the transport in the respiratory chain and the oxidative phosphorylation are investigated. The conditions for breaking the synchronization of processes, increasing the multiplicity of cyclicity, and for the appearance of chaotic modes are analyzed. The phase-parametric diagram of a cascade of bifurcations showing the transition to a chaotic mode by the Feigenbaum scenario is obtained. The fractal nature of the revealed cascade of bifurcations is demonstrated. The strange attractors formed as a result of the folding are obtained. The results obtained give the idea of structural-functional connections, due to which the self-organization appears in the metabolism running in a cell. The constructed mathematical model can be applied to the study of the toxic and allergic effects of drugs and various substances on cell metabolism.