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.