Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade.

Prompted by the recent growing evidence of oscillatory behavior involving MAPK cascades we present a systematic approach of analyzing models and elucidating the nature of biochemical oscillations based on reaction network theory. In particular, we formulate a minimal biochemically consistent mass action subnetwork of the Huang-Ferrell model of the MAPK signalling that provides an oscillatory response when a parameter controlling the activation of the top-tier kinase is varied. Such dynamics are either intertwined with or separated from the earlier found bistable/hysteretic behavior in this model. Using the theory of stability of stoichiometric networks, we reduce the original MAPK model, convert kinetic to convex parameters and examine those properties of the minimal subnetwork that underlie the oscillatory dynamics. We also use the methods of classification of chemical oscillatory networks to explain the rhythmic behavior in physicochemical terms, i.e., we identify of the role of individual biochemical species in positive and negative feedback loops and describe their coordinated action leading to oscillations. Our approach provides an insight into dynamics without the necessity of knowing rate coefficients and thus is useful prior the statistical evaluation of parameters.

Oscillations and patterns in a model of simultaneous CO and C2H2 oxidation and NO(x) reduction in a cross-flow reactor.

A model describing simultaneous catalytic oxidation of CO and C2H2 and reduction of NOx in a cross-flow tubular reactor is explored with the aim of relating spatiotemporal patterns to specific pathways in the mechanism. For that purpose, a detailed mechanism proposed for three-way catalytic converters is split into two subsystems, (i) simultaneous oxidation of CO and C2H2, and (ii) oxidation of CO combined with NOx reduction. The ability of these two subsystems to display mechanism-specific dynamical effects is studied initially by neglecting transport phenomena and applying stoichiometric network and bifurcation analyses. We obtain inlet temperature - inlet oxygen concentration bifurcation diagrams, where each region possessing specific dynamics - oscillatory, bistable and excitable - is associated with a dominant reaction pathway. Next, the spatiotemporal behaviour due to reaction kinetics combined with transport processes is studied. The observed spatiotemporal patterns include phase waves, travelling fronts, pulse waves and spatiotemporal chaos. Although these types of pattern occur generally when the kinetic scheme possesses autocatalysis, we find that some of their properties depend on the underlying dominant reaction pathway. The relation of patterns to specific reaction pathways is discussed.

Stoichiometric network analysis of the photochemical processes in the mesopause region.

The mechanism of photochemistry in the mesopause region entails a chemical oscillator forced by solar short-wave radiation. A model with periodic forcing between day and night conditions produces nonlinear dynamics including period-doubling bifurcations and chaos. The photochemical mechanism represents a network involving positive and negative feedbacks that can be examined by methods of stoichiometric network analysis. We use these methods to decompose the network into irreducible subnetworks and then apply linear stability analysis to find all possible sources of oscillatory instabilities in the mesopause chemistry. These oscillators are classified according to topological features in their reaction networks and phase shifts of oscillating species. We subsequently compare phase shifts indicated by the network analysis with those from direct simulations to identify a specific subnetwork in the mechanism underlying the complex oscillatory dynamics observed in earlier simulations.

Oscillations, period doublings, and chaos in CO oxidation and catalytic mufflers.

Early experimental observations of chaotic behavior arising via the period-doubling route for the CO catalytic oxidation both on Pt(110) and Ptgamma-Al(2)O(3) porous catalyst were reported more than 15 years ago. Recently, a detailed kinetic reaction scheme including over 20 reaction steps was proposed for the catalytic CO oxidation, NO(x) reduction, and hydrocarbon oxidation taking place in a three-way catalyst (TWC) converter, the most common reactor for detoxification of automobile exhaust gases. This reactor is typically operated with periodic variation of inlet oxygen concentration. For an unforced lumped model, we report results of the stoichiometric network analysis of a CO reaction subnetwork determining feedback loops, which cause the oscillations within certain regions of parameters in bifurcation diagrams constructed by numerical continuation techniques. For a forced system, numerical simulations of the CO oxidation reveal the existence of a period-doubling route to chaos. The dependence of the rotation number on the amplitude and period of forcing shows a typical bifurcation structure of Arnold tongues ordered according to Farey sequences, and positive Lyapunov exponents for sufficiently large forcing amplitudes indicate the presence of chaotic dynamics. Multiple periodic and aperiodic time courses of outlet concentrations were also found in simulations using the lumped model with the full TWC kinetics. Numerical solutions of the distributed model in two geometric coordinates with the CO oxidation subnetwork consisting of several tens of nonlinear partial differential equations show oscillations of the outlet reactor concentrations and, in the presence of forcing, multiple periodic and aperiodic oscillations. Spatiotemporal concentration patterns illustrate the complexity of processes within the reactor.