A simple model of the Calvin cycle has only one physiologically feasible steady state under the same external conditions

Zhu, Xin-Guang; Alba, Rafael Dall; Sturler, Eric de

doi:10.1016/j.nonrwa.2008.01.021

Cited by 18 publications

(58 citation statements)

References 35 publications

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“…The difference between our reduced photosynthetic carbon metabolic network (Fig. 2) and that of [6] is that our reduced network includes the photorespiration pathway (i.e. RuBP → PGCA → GCA → GCEA → PGA).…”

Section: A Effect Of Photorespirationmentioning

confidence: 97%

“…We take the values of the parameters (K M ,V max , AT P) used [10], [4], [6] as nominal values in our work (see Table I). For such nominal values (K M0 ,V max0 , AT P 0 ), the corresponding roots of the polynomial (23) are: [17].…”

Section: B Steady State With Parameter Variationsmentioning

confidence: 99%

“…Let 22,4,5,6, V max j ≤ V max j ≤ V max j , j = 2, 4, 5, 6, AT P ≤ AT P ≤ AT P}, where K Mi ≤ K Mi0 and K Mi ≥ K Mi0 , i = 21, 22, 4, 5, 6, V max j ≤ V max j0 and V max j ≥ V max j0 , j = 2, 4, 5, 6, AT P ≤ AT P 0 and AT P ≥ AT P 0 are some positive numbers. In other words, Ω x is a domain of the parameter (K M ,V max , AT P) around the nominal value (K M0 ,V max0 , AT P 0 ).…”

Section: B Steady State With Parameter Variationsmentioning

confidence: 99%

“…Poolman et al [5] showed that the Calvin cycle has two different steady states in plant leaves at different ages. Zhu et al [6] proposed a simple model of the Calvin cycle which has two key ingredients of the Calvin cycle: the autocatalytic cycle and the utilization of photosynthate. For a group of fixed parameters, Zhu et al found that the model has multiple steady states from numerical computation, but only one is physiologically feasible.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, an important question was posed out: how many steady states can photosynthesis reside in under the same external conditions? Since there is no currently biological experiment available to answer this question [9], [6], one has to resort to a mathematical modeling approach to gain insight on this question.…”

Section: Introductionmentioning

confidence: 99%

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Analysis on steady states of photosynthetic carbon metabolic system

Lei

Wang

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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In this paper, we propose a reduced molecular network of the photosynthetic carbon metabolism, which includes the nine major metabolites with 48 parameters. The reduced molecular network can represent the key ingredients of photosynthetic carbon metabolism, i.e. the autocatalytic cycle, the utilization of photosynthate, and the effect of photorespiration. Based on the model, we theoretically study steady states or stable equilibria of photosynthetic carbon metabolism, and prove that such a system actually has at most one feasible steady state in the domain of a parameter set defined around nominal values for that parameter set. Specifically, we first equivalently transform the original system into an independent 2-dimensional subsystem which contains just 10 parameters, and then show that steady states of the original system can be determined by the 2-dimensional subsystem uniquely. Finally, we show that when the 10 parameters for the 2-dimensional subsystem all stay in an appropriate domain around the nominal value of each parameter, the reduced model has at most one physiologically feasible steady state no matter how the other 38 parameters in the original model are taken. In addition, we also derive parameter domain to ensure such an asymptotical behavior.

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Section: A Effect Of Photorespirationmentioning

confidence: 97%

Section: B Steady State With Parameter Variationsmentioning

confidence: 99%

Section: B Steady State With Parameter Variationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis on steady states of photosynthetic carbon metabolic system

Lei

Wang

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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A parameter condition for ruling out multiple equilibria of the photosynthetic carbon metabolism

Lei

Wang

et al. 2011

Asian Journal of Control

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In this paper, we propose a reduced molecular network for the photosynthetic carbon metabolism, which can describe the following key characteristics: Calvin cycle, utilization of photosynthate, and photorespiration. Taking the concentrations of the nine major metabolites as variables, we represent the reduced network by deriving a nonlinear differential‐algebraic system with 48 parameters, and theoretically study the multi‐equilibrium property in the photosynthetic carbon metabolism. Specifically, we equivalently transform the original 9‐dimensional system into an independent 2‐dimensional subsystem with ten parameters, and show that the original system has no more than one physiologically feasible equilibrium when the ten parameters of the subsystem stay in a certain field around the nominal value of each parameter, no matter what values the other 38 parameters in the original model are taken. Such a theoretical result not only provides profound insights for qualitatively understanding of the dynamic features of the photosynthetic carbon metabolism, but also can be used to make an accurate judgement on a correct strategy for improving the photosynthesis in plants. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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Multi‐equilibrium property of metabolic networks: MMN module

Guo

Zhang

Zhao

2012

Intl J Robust & Nonlinear

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SUMMARYThis paper studies the multi‐equilibrium property of the multiple substrates and multiple products with no inhibition (MMN) module. On the basis of the topological structure, a model for such module is established in the form of a set of nonlinear ordinary differential equations. It is shown that the injectivity of the MMN module is equivalent to the nonsingularity of Jacobian matrix of its rate function, and a necessary and sufficient condition for the injectivity is obtained by using the Hadamard product. For non‐injective MMN module, a sufficient condition for existence of multiple positive equilibria is provided by introducing the concept of input‐matrix. For a type of commonly encountered MMN module— scriptA‐MMN module—a structure‐oriented criterion for judging its injectivity is given. For scriptA‐MMN modules with some special structure, it is shown that there does not exist multiply equilibria and the equilibrium (if exists) is asymptotically stable. Examples and simulations are given to illustrate the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.

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A simple model of the Calvin cycle has only one physiologically feasible steady state under the same external conditions

Cited by 18 publications

References 35 publications

Analysis on steady states of photosynthetic carbon metabolic system

Analysis on steady states of photosynthetic carbon metabolic system

A parameter condition for ruling out multiple equilibria of the photosynthetic carbon metabolism

Multi‐equilibrium property of metabolic networks: MMN module

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