Limits...
A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems.

Wong MK, Krycer JR, Burchfield JG, James DE, Kuncic Z - FEBS Open Bio (2015)

Bottom Line: The dQSSA was found to be easily adaptable for reversible enzyme kinetic systems with complex topologies and to predict behaviour consistent with mass action kinetics in silico.Whilst the dQSSA does not account for the physical and thermodynamic interactions of all intermediate enzyme-substrate complex states, it is proposed to be suitable for modelling complex enzyme mediated biochemical systems.This is due to its simpler application, reduced parameter dimensionality and improved accuracy.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, University of Sydney, Sydney, NSW 2006, Australia ; Charles Perkins Centre, University of Sydney, Sydney, NSW 2006, Australia ; Diabetes and Metabolism Program, Garvan Institute of Medical Research, Darlinghurst, NSW 2010, Australia.

ABSTRACT
Quasi steady-state enzyme kinetic models are increasingly used in systems modelling. The Michaelis Menten model is popular due to its reduced parameter dimensionality, but its low-enzyme and irreversibility assumption may not always be valid in the in vivo context. Whilst the total quasi-steady state assumption (tQSSA) model eliminates the reactant stationary assumptions, its mathematical complexity is increased. Here, we propose the differential quasi-steady state approximation (dQSSA) kinetic model, which expresses the differential equations as a linear algebraic equation. It eliminates the reactant stationary assumptions of the Michaelis Menten model without increasing model dimensionality. The dQSSA was found to be easily adaptable for reversible enzyme kinetic systems with complex topologies and to predict behaviour consistent with mass action kinetics in silico. Additionally, the dQSSA was able to predict coenzyme inhibition in the reversible lactate dehydrogenase enzyme, which the Michaelis Menten model failed to do. Whilst the dQSSA does not account for the physical and thermodynamic interactions of all intermediate enzyme-substrate complex states, it is proposed to be suitable for modelling complex enzyme mediated biochemical systems. This is due to its simpler application, reduced parameter dimensionality and improved accuracy.

No MeSH data available.


Related in: MedlinePlus

In the hypothetical network, the dQSSA is consistent with mass action kinetics whilst the Michaeli–Menten model is not. Time courses of the network simulation were predicted by the mass action model (crosses), Michaelis–Menten model (pluses) and dQSSA model (crosses). The total (i.e. free and in complex) concentration of each species are shown to enable a fair comparison between models (a–c). I is only added at t = 10 s (d).
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4383669&req=5

f0015: In the hypothetical network, the dQSSA is consistent with mass action kinetics whilst the Michaeli–Menten model is not. Time courses of the network simulation were predicted by the mass action model (crosses), Michaelis–Menten model (pluses) and dQSSA model (crosses). The total (i.e. free and in complex) concentration of each species are shown to enable a fair comparison between models (a–c). I is only added at t = 10 s (d).

Mentions: As seen in the theoretical analysis, this is most likely due to a violation of the low enzyme assumption of Eq. (26). Therefore, we further investigated whether this inconsistency requires the low enzyme assumption to be violated throughout the whole network, or whether a single instance is sufficient to cause inaccuracies in the whole network. To investigate this, we tested parameters such that the low enzyme assumption in all reactions except the forward direction of reaction 9. As such, the Michaelis–Menten model should be consistent with the other two models during the I-off phase but inconsistent in the I-on phase. The parameters used are given in Table 1. We found that all three models were consistent during the I-off phase (Fig. 3). However, in the I-on phase, the dQSSA and mass action model remained consistent with each other whilst the Michaelis–Menten model became inconsistent and varied between 7% and 45% consistency at equilibrium. The A and pA states had a difference of approximately 20% even though these are not directly related to the species involved with the high enzyme concentration reaction. Hence, this result demonstrates that violation of the low enzyme assumption even in just one reaction can lead to non-trivial discrepancies in the Michaelis–Menten model’s predictions.


A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems.

Wong MK, Krycer JR, Burchfield JG, James DE, Kuncic Z - FEBS Open Bio (2015)

In the hypothetical network, the dQSSA is consistent with mass action kinetics whilst the Michaeli–Menten model is not. Time courses of the network simulation were predicted by the mass action model (crosses), Michaelis–Menten model (pluses) and dQSSA model (crosses). The total (i.e. free and in complex) concentration of each species are shown to enable a fair comparison between models (a–c). I is only added at t = 10 s (d).
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4383669&req=5

f0015: In the hypothetical network, the dQSSA is consistent with mass action kinetics whilst the Michaeli–Menten model is not. Time courses of the network simulation were predicted by the mass action model (crosses), Michaelis–Menten model (pluses) and dQSSA model (crosses). The total (i.e. free and in complex) concentration of each species are shown to enable a fair comparison between models (a–c). I is only added at t = 10 s (d).
Mentions: As seen in the theoretical analysis, this is most likely due to a violation of the low enzyme assumption of Eq. (26). Therefore, we further investigated whether this inconsistency requires the low enzyme assumption to be violated throughout the whole network, or whether a single instance is sufficient to cause inaccuracies in the whole network. To investigate this, we tested parameters such that the low enzyme assumption in all reactions except the forward direction of reaction 9. As such, the Michaelis–Menten model should be consistent with the other two models during the I-off phase but inconsistent in the I-on phase. The parameters used are given in Table 1. We found that all three models were consistent during the I-off phase (Fig. 3). However, in the I-on phase, the dQSSA and mass action model remained consistent with each other whilst the Michaelis–Menten model became inconsistent and varied between 7% and 45% consistency at equilibrium. The A and pA states had a difference of approximately 20% even though these are not directly related to the species involved with the high enzyme concentration reaction. Hence, this result demonstrates that violation of the low enzyme assumption even in just one reaction can lead to non-trivial discrepancies in the Michaelis–Menten model’s predictions.

Bottom Line: The dQSSA was found to be easily adaptable for reversible enzyme kinetic systems with complex topologies and to predict behaviour consistent with mass action kinetics in silico.Whilst the dQSSA does not account for the physical and thermodynamic interactions of all intermediate enzyme-substrate complex states, it is proposed to be suitable for modelling complex enzyme mediated biochemical systems.This is due to its simpler application, reduced parameter dimensionality and improved accuracy.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, University of Sydney, Sydney, NSW 2006, Australia ; Charles Perkins Centre, University of Sydney, Sydney, NSW 2006, Australia ; Diabetes and Metabolism Program, Garvan Institute of Medical Research, Darlinghurst, NSW 2010, Australia.

ABSTRACT
Quasi steady-state enzyme kinetic models are increasingly used in systems modelling. The Michaelis Menten model is popular due to its reduced parameter dimensionality, but its low-enzyme and irreversibility assumption may not always be valid in the in vivo context. Whilst the total quasi-steady state assumption (tQSSA) model eliminates the reactant stationary assumptions, its mathematical complexity is increased. Here, we propose the differential quasi-steady state approximation (dQSSA) kinetic model, which expresses the differential equations as a linear algebraic equation. It eliminates the reactant stationary assumptions of the Michaelis Menten model without increasing model dimensionality. The dQSSA was found to be easily adaptable for reversible enzyme kinetic systems with complex topologies and to predict behaviour consistent with mass action kinetics in silico. Additionally, the dQSSA was able to predict coenzyme inhibition in the reversible lactate dehydrogenase enzyme, which the Michaelis Menten model failed to do. Whilst the dQSSA does not account for the physical and thermodynamic interactions of all intermediate enzyme-substrate complex states, it is proposed to be suitable for modelling complex enzyme mediated biochemical systems. This is due to its simpler application, reduced parameter dimensionality and improved accuracy.

No MeSH data available.


Related in: MedlinePlus