The coupling between spatial and temporal order in systems of chemically reacting and diffusing components has an important role in some spatially periodic phenomena including the pattern formation. The model considered here represents a nonlinear reaction-diffusion process where an allosteric enzyme is activated by its reaction product and the reaction is inhibited by depletion of substrate component. The special emphasis here is on the possible role of diffusion of reactants in the initiation of symmetry-breaking instabilities under small spatio-temporal perturbation. We analyzed the necessary and sufficient conditions for possible technological scenario for this kind of autocatalysis where the substrate reactant diffuses faster enough than the product activator, thus enabling the possible symmetry-breaking instability yielding the pattern formation.