Transitions and new dynamical states induced by noise in a multiply regulated biochemical system

ENHANCEMENT AND RESTRICTION OF SYSTEM COORDINATION BY INTERACTION OF PATHWAYS

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.

DEPENDENCE OF FLUX DISTRIBUTION AND SYSTEM COORDINATION ON DYNAMICAL STATES FOR BIOCHEMICAL SYSTEMS WITH MULTIPLE COEXISTING STATES

Flux distribution and system coordination in branched biochemical systems with a source producing multiple coexisting states have been studied both theoretically and numerically. For such systems, flux distribution depends sensitively on the dynamical states and the parameter values of enzymatic kinetics at branching point. Various dynamical states including noise-induced new states can be located by superimposing noisy fluctuations on a branched biochemical system with multiple coexisting states. Once noise induces transitions or new dynamical states, the flux through a specific branch may increase, maintain or decrease, depending on parameter values of enzymatic kinetics at branching point. Furthermore, system coordination can be destroyed by noise-induced dynamical changes. When at least one state cannot be coordinated in the absence of noise, noise-induced transitions may destroy system coordination. When all coexisting states are coordinated in the absence of noise, noise-induced new states may be still able to destroy system coordination. It is revealed that destruction of system coordination is due to the interaction of enzyme saturation and noise-induced dynamical changes. Finally, control of flux distribution and maintenance of system coordination for biochemical systems with multiple coexisting states are discussed.

State selection in coupled identical biochemical systems with coexisting stable states

This work examines state selection for coupled biochemical systems with coexisting stable states. For biochemically identical biochemical systems, different coupled systems are examined for the coexistence of (a) one steady state and one oscillatory state or (b) two oscillatory states. For case (a), it is revealed that state selection is always governed by two key factors: the values of kinetic parameters and the coupling strength. When the coupling strength is small, the coupled systems remain in the basin of attraction of their original states. When it is sufficiently large, all coupled systems are always entrained, independently of their original states. Furthermore, for the entrainment, which of the two coexisting states is selected depends sensitively on the activity of recycling enzyme (one of kinetic parameters). It is shown that this is because changing the activity of recycling enzyme alters the size of basin of attraction of each state. When both systems in the same oscillatory state are coupled, an additional factor, namely phase shift between two oscillations, may also affect state selection, and coupling may cause the systems to select either the original oscillatory state or the coexisting steady state. In addition to the features of case (a), case (b) also supports quasiperiodic oscillations and synchronisation of two periodic oscillations. Implications of the results for understanding state selection during the evolution of coupled biochemical systems with coexisting stable states are discussed.