The consequences of interactive noise for understanding the dynamics of complex biochemical systems

Abstract

The dynamical consequence of interactive noise in a model for complex 5&-heiiikczl sjisieiiis is exaiiifiied Giiiijjhii ,.jjSti7.biilt.d ij sGp,7';,;,lpJt.d iiri ;jie concentrations of metabolites in enzymatic reactions, and the effect of the noise amplitude on the dj~namical behaviour is studied in a range of dynamical regimes, For a steady stare far from a Hopf bifurcation, noise does not result in a qualitative change in the dynamical behaviour. For a steadv state on one side o f a Hopf bifurcation, and for the small amplitude oscillation which occurs just beyond the bifurcation point, noise may result in a qualitative change in dynamical behaviour: large amplitude bursting may be observed. W e r e two attractors coexist, noise may cause switching from one attractor to the other and renders the attractors indistinguishable. Complex oscillations which do not coexist with small amplitude oscillations are relatively insensitive to noise. The implications of these results for the understanding of complex biochemical systems are discussed.

Dynamic modeling of the central carbon metabolism of Escherichia coli

“…In context with the envisaged application of the model for tasks of metabolic design it is also important to emphasize that enzymes with negligible¯ux control coecients may strongly in¯uence the stability of a steady state exposed to noise perturbation (Liu et al, 1996(Liu et al, , 1997. As these noises are common in industrial practice, careful analysis of the stability of redesigned``in silico'' strains should be mandatory (Mauch et al, 2001).…”

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

“…The model system was previously developed for studying the interaction of PFK and PFP in the glycolysis of higher plant cells [15,16]. The model (Fig.…”

“…The conversion of S into P 2 is catalysed by another enzyme, E 3 , which is inhibited by P 1 . The model system can be described by the following differential equations: [15,16]. The system comprises three species, five enzymes and the interplay of two positive and one negative regulations.…”

“…This paper examines the coordination of a model system previously developed [15,16] for PFK-PFP interaction in the glycolysis of higher plant cells. The system comprises five enzymes and the interplay of two positive and one negative regulations.…”

“…This paper analytically determines the sufficient conditions for system coordination, and employs three types of external signals, namely rectangular, sinusoidal and noisy signals, to numerically support the theoretical analysis. Figure 1 [15,16] is employed as a model system to study the coordination of biochemical systems with the interplay of positive and negative feedbacks.…”