Sufficient Conditions for Coordination of a Forced Biochemical System With the Interplay of Activation and Inhibition

Liu, Junli

doi:10.1142/s0218339000000201

Cited by 4 publications

(1 citation statement)

References 17 publications

(66 reference statements)

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“…The reaction scheme employed in this work is derived from glycolysis and only includes one positive feedback. Previous studies (Liu 1999b(Liu , 2000 have showed that more complicated reaction schemes such as the interplay of positive and negative regulation have similar dynamical features to those in figure 1-namely, finite stable states may collapse. It is expected that the conclusions drawn in this work can be applied to other more complicated systems.…”

Section: Discussionmentioning

confidence: 69%

Collapse of single stable states via a fractal attraction basin: analysis of a representative metabolic network

Liu¹,

Crawford

Leontiou

2005

Proc. R. Soc. A.

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The impact of external forcing on an enzymatic reaction system with a single finite stable state is investigated. External forcing impacts on the system in two distinct ways: firstly, the reaction system undergoes a series of discontinuous changes in dynamical state. Secondly, a critical level of forcing exists, beyond which all finite states become unstable. It is shown that the results stem from the conditions for global stability of the system. Competition between the attractor for stable states and the unbounded states leads to a loss of integrity and the fractal fragmentation of the attraction basin for the finite state. The consequences of a fractal basin in this context are profound. Initial states which are infinitesimally close diverge to a finite and an unbounded state where only the finite state is consistent with biological functionality. Furthermore, above a critical forcing amplitude, the system does not converge to a finite state from any initial state, implying that there is no configuration of metabolite concentrations that is consistent with sustained evolution of the system. These results point to opportunities for constraining uncertainty in cell networks where nonlinear saturating kinetics form an important component.

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Section: Discussionmentioning

confidence: 69%

Collapse of single stable states via a fractal attraction basin: analysis of a representative metabolic network

Liu¹,

Crawford

Leontiou

2005

Proc. R. Soc. A.

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Enhancement and Restriction of System Coordination by Interaction of Pathways

Liu¹

2001

J. Biol. Syst.

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System coordination for a system with interaction of two pathways is investigated. Sufficient conditions for guaranteeing system coordination subject to any type, amplitude or period of external forcing are analytically derived. Effects of a pathway operating in the opposite direction on system coordination are examined in detail, and it is revealed that the pathway may enhance or restrict system coordination, depending on the values of kinetic parameters. It is concluded that increasing the complexity of enzymatic network by introducing interaction of pathways does not necessarily enhance system coordination. Numerical results using rectangular and sinusoidal forcing support the analytical results, and they quantitatively show how the system with interaction of two pathways maintain its coordination. When the sufficient conditions are satisfied, the system always develops to a finite stable (time-dependent) state under the forcing of any type, amplitude or period. When not, system coordination depends quantitatively on parameter values and the type, amplitude or period of external forcing. When two parameters are forced simultaneously, an additional factor, namely phase shifts between two forced parameters, also affects system coordination. It is shown that, unless the sufficient coordination conditions are maintained, external forcing may induce 'loss of coordination', resulting in the system having no biological functioning. The implications of the results for understanding biochemical coordination and for assessing possible consequences of modulating biochemical systems are discussed.

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Sufficient Conditions for Coordination of Coupled Nonlinear Biochemical Systems: Analysis of a Simple, Representative Example

Liu¹,

Marshall²

2003

J. Biol. Syst.

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Under conditions of stress and environmental fluctuations, how do coupled biochemical systems maintain the balance of metabolic fluxes? Using a model derived from a representative glycolysis example, this work derives sufficient coordination conditions for guaranteeing the balance of metabolic fluxes in the coupled systems subjected to any fluctuations. For diffusion-like coupling, it is explicitly shown that the sufficient conditions are the linear summation of individual uncoupled systems. For this case, coupling strength is not a key factor affecting the balance of metabolic fluxes, although it may affect the emergence of certain dynamic patterns. When the sufficient coordination conditions are satisfied, coupled systems always settle onto stable finite states, independently of the nature (type, period or amplitude) of external signals. When they are not, external signals may force the stable states of coupled systems to lose their coordination, resulting in the coupled systems having no stable finite states which is inconsistent with most normal biological functions. Numerical simulations support the analytical results. The generalization of this result for other coupled nonlinear biochemical systems is discussed. Finally, the maintenance of such biological coordination is discussed in the context of genetic engineering and environmental fluctuations.

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Sufficient Conditions for Coordination of a Forced Biochemical System With the Interplay of Activation and Inhibition

Cited by 4 publications

References 17 publications

Collapse of single stable states via a fractal attraction basin: analysis of a representative metabolic network

Collapse of single stable states via a fractal attraction basin: analysis of a representative metabolic network

Enhancement and Restriction of System Coordination by Interaction of Pathways

Sufficient Conditions for Coordination of Coupled Nonlinear Biochemical Systems: Analysis of a Simple, Representative Example

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