Tag Archives: mathematical model
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.
Mathematical modeling of calcium homeostasis in smooth muscle cells while activity of plasma membrane calcium pump is modulated
S. O. Karakhim, V. F. Gorchev, P. F. Zhuk, S. O. Kosterin
Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, Kyiv;
e-mail: laserlab@biochem.kiev.ua; kinet@biochem.kiev.ua
A mathematical model of intracellular calcium homeostasis in smooth muscle cells has been investigated by computer modelling method. The results of calculations showed that for the plasma membrane calcium pump (PMCA) the limiting rate (VmPM) increasing or the Michaelis constant (KmPM) decreasing result in a lowering of the Ca2+ concentration in cytosol and sarcoplasmic reticulum (SR); the slight VmPM decreasing or KmPM increasing result in fluent cytosolic Ca2+ strengthening due to slow basal influx (SBI) since a massive release of Ca2+ from SR does not occur. The further VmPM decreasing or KmPM increasing stimulate the Ca2+-induced Ca2+ release from SR and the system passes into oscillation mode; when the certain low VmPM or high KmPM level is reached the oscillations of Ca2+ concentration in cytosol are stopped, there is only first oscillation after which a new level of cytosolic Ca2+ concentration is formed fluently: this level is higher than in the initial basal condition (IBC). Sensitivity of myocytes with the lowering of VmPM or increasing KmPM to agonist action is rising but sensitivity of myocytes with increasing VmPM or decreasing KmPM to agonist action is reducing. If the PMCA parameters (VmPM or KmPM) are changed then passive influx of Ca2+ in cytosol from extracellular space remains virtually invariable and it is equal to SBI value during the whole process. Initial rate of PMCA in a new equilibrium condition (NEC) is equal virtually to initial rate in IBC: it allows to calculate a new value VmPM or KmPM from cytosolic Ca2+ concentration in NEC.