Unbounded solutions of models for glycolysis

Brechmann, Pia; Rendall, Alan D.

doi:10.1007/s00285-021-01560-y

Cited by 13 publications

(6 citation statements)

References 17 publications

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“…A significant number of papers have been devoted to the theoretical and experimental study of oscillations in glycolysis [ 26 , 27 , 28 , 29 , 30 ]. However, the possibility of oscillations in human erythrocyte glycolysis, caused by the modulation of the GAPDH reaction rate by [NAD], has not been reported so far to our knowledge.…”

Section: Resultsmentioning

confidence: 99%

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Prediction of Oscillations in Glycolysis in Ethanol-Consuming Erythrocyte-Bioreactors

Protasov

Martinov

Sinauridze

et al. 2023

IJMS

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A mathematical model of energy metabolism in erythrocyte-bioreactors loaded with alcohol dehydrogenase and acetaldehyde dehydrogenase was constructed and analyzed. Such erythrocytes can convert ethanol to acetate using intracellular NAD and can therefore be used to treat alcohol intoxication. Analysis of the model revealed that the rate of ethanol consumption by the erythrocyte-bioreactors increases proportionally to the activity of incorporated ethanol-consuming enzymes until their activity reaches a specific threshold level. When the ethanol-consuming enzyme activity exceeds this threshold, the steady state in the model becomes unstable and the model switches to an oscillation mode caused by the competition between glyceraldehyde phosphate dehydrogenase and ethanol-consuming enzymes for NAD. The amplitude and period of metabolite oscillations first increase with the increase in the activity of the encapsulated enzymes. A further increase in these activities leads to a loss of the glycolysis steady state, and a permanent accumulation of glycolytic intermediates. The oscillation mode and the loss of the steady state can lead to the osmotic destruction of erythrocyte-bioreactors due to an accumulation of intracellular metabolites. Our results demonstrate that the interaction of enzymes encapsulated in erythrocyte-bioreactors with erythrocyte metabolism should be taken into account in order to achieve the optimal efficacy of these bioreactors.

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Section: Resultsmentioning

confidence: 99%

“…a DPGM = 3892 mM/h, K 1 DPGM = 0.04 mM, K 2 DPGM = 0.013 mM Diphosphoglycerate phosphatase [22] V Na + /K + -ATPase [22] V NaKATP = a NaKATP Na + [ATP] a NaKATP = 0.045 mM/h, Na + = 10 mM [30] All other ATPases are presented by the following equation [22] V ATP = a ATP…”

Section: Mathematical Modelmentioning

confidence: 99%

Prediction of Oscillations in Glycolysis in Ethanol-Consuming Erythrocyte-Bioreactors

Protasov

Martinov

Sinauridze

et al. 2023

IJMS

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“…Again, h denotes the interval length. In Table 4, we give the errors produced by the use of Taylor method and in We have shown that the Extended Picard reinforced with segmentary integration gives an excellent approximation to solutions of a strongly non-linear ordinary system such as (33). Same can be said for the Mathieu equation as an inspection of Table 2.…”

Section: Quintic Duffing Equationmentioning

confidence: 98%

An Extended Picard Method to solve non-linear systems of ODE. Some applications to chemical reactions

Gadella,

Lara

2024

Preprint

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We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This method is a mixture between an iterative process, a la Picard, plus a segmentary integration, which gives explicit approximate solutions in terms of trigonometric functions and polynomials. The segmentary part is particularly important if the integration interval is large. This procedure provide a new tool so as to obtain approximate solutions of systems of interest in the analysis of chemical reactions. We test the method on some classical equations like Mathieu, Duffing quintic equation or Bratu’s equation and have applied it on some models of chemical reactions.

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“…We remark again that even though this procedure is computationally costly, it pays off by offering a control strategy that is robust to a number of possible (and highly likely) scenarios, by taking into account the uncertainty on parameter estimates [ 29 ].…”

Section: Optimised Mobility Values Based On Uncertaintymentioning

confidence: 99%

Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic

et al. 2021

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A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France.

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Unbounded solutions of models for glycolysis

Cited by 13 publications

References 17 publications

Prediction of Oscillations in Glycolysis in Ethanol-Consuming Erythrocyte-Bioreactors

Prediction of Oscillations in Glycolysis in Ethanol-Consuming Erythrocyte-Bioreactors

An Extended Picard Method to solve non-linear systems of ODE. Some applications to chemical reactions

Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic

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