Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?

Martin, R. R.; Montero, S.; Silva, E.; Bizzarri, Mariano; Cocho, G.; Mansilla, Ricardo; Nieto-Villar, J.M.

doi:10.1016/j.physa.2017.06.001

Cited by 19 publications

(21 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…46 In a previous work 47 we have shown that the rate of entropy production is a Lyapunov function, in fact we extended this formalism to the development of cancer. 41,42,[48][49][50] Thus we have the entropy production per unit time meets the necessary and sufficient conditions for Lyapunov function, 51 see formula (8); where Ω is the vector of control parameters. In this case, we take the age of the subjects as the control parameter (Ω ≡ chronological age).…”

Section: Figurementioning

confidence: 99%

On the relationship between aging & cancer

Ja¹,

Mansilla²,

Cocho³

et al. 2018

MOJGG

View full text Add to dashboard Cite

Section: Figurementioning

confidence: 99%

On the relationship between aging & cancer

Ja¹,

Mansilla²,

Cocho³

et al. 2018

MOJGG

View full text Add to dashboard Cite

“…Additionally, very detailed models for cancer glycolysis have been developed to investigate the basic cellular physiology such as enzymatic and transport properties (Marín-Hernández et al, 2011;Khazaei et al, 2012;and Marín-Hernández et al, 2014); however, no glycolytic oscillations have been investigated in these models. A kinetic model was proposed recently to reproduce glycolytic oscillations of HeLa cells qualitatively (Martin et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Modeling studies of heterogeneities in glycolytic oscillations in HeLa cervical cancer cells

Amemiya

Shibata

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Previous experiments demonstrated that a population of HeLa cells starved of glucose or both glucose and serum exhibited a strong heterogeneity in the glycolytic oscillations in terms of the number of oscillatory cells, periods of oscillations, and duration of oscillations. Here, we report numerical simulations of this heterogeneous oscillatory behavior in HeLa cells by using a newly developed mathematical model. It is simple enough that we can apply a mathematical analysis, but capture the core of the glycolytic pathway and the activity of the glucose transporter (GLUT). Lognormal distributions of the values of the four rate constants in the model were obtained from the experimental distributions in the periods of oscillations. Thus, the heterogeneity in the periods of oscillations can be attributed to the di erence in the rate constants of the enzymatic reactions. The activity of GLUT is found to determine whether the HeLa cells were oscillatory or non-oscillatory under the same experimental conditions. Simulation with the log-normal distribution of the maximum uptake velocity of glucose and the four randomized rate constants based on the log-normal distributions successfully reproduced the time-dependent number of oscillatory cells (oscillatory ratios) under the two starving conditions. The di erence in the initial values of the metabolites has little e ect on the simulated results.

show abstract

“…In a previous work [31] we have shown that the rate of entropy production is a Lyapunov function, in fact we extended this formalism to the development of cancer [32,33,34,35,36,37]. Thus, we have the entropy production per unit time meets the necessary and sufficient conditions for Lyapunov function [30], such that , that allows us to affirm that the rate of entropy production is a Lyapunov function.…”

Section: Thermodynamics Frameworkmentioning

confidence: 87%

Deciphering the longevity of the mole-rats

Triana¹,

Cocho²,

Mansilla³

et al. 2018

IJOAR

View full text Add to dashboard Cite

A theoretical model of a nonlinear network that outlines the general aspects of mole-rat resistance to age-related diseases, such as cancer and the action of ROS was elaborated. According to our conjecture, it was shown that the protection is established because hyaluronic acid of high molecular mass forms a non-linear network of interactions. That network leads to self-organization away from the thermodynamical equilibrium, which appears through a "first order" phase transition as a supercritical bifurcation of Andronov-Hopf type. Finally, it is shown how the rate of entropy production is a Lyapunov function of the dynamics of the process. Keywords:mole-rat

show abstract

Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?

Cited by 19 publications

References 44 publications

On the relationship between aging & cancer

On the relationship between aging & cancer

Modeling studies of heterogeneities in glycolytic oscillations in HeLa cervical cancer cells

Deciphering the longevity of the mole-rats

Contact Info

Product

Resources

About