<p>The model considered here represents a cubic nonlinear reaction–diffusion process where an alosteric enzyme is being activated by its reaction product and inhibited by the influence of the substrate reactant. This model relies on the earlier seminal approach established to mimic some oscillations in mitosis and the glycolytic oscillations of adenosine triphosphate substrate (inhibitor) and adenosine diphosphate product (activator). Our aim was to examine whether the inclusion of product and substrate diffusion can cause the symmetry breaking instability under the influence of small perturbations. The perturbations are supposed to be spatially harmonic and temporally exponentially growing. The careful analysis clearly demonstrates that necessary and sufficient condition for the appearance of symmetry breaking instability and possible morphogenesis could be achieved if the value of diffusion coefficient of substrate reactant is remarkably greater than the corresponding value of product. We expect that under suitable technological conditions where the diffusion of reactants can be controllably tuned, the reaction of this type can lead to morphogenesis (inhomogeneous spatial distribution of reactants). We have proved that in the case of glycolysis under normal physiological conditions the symmetry breaking instability is not possible, which is important since the spatial distribution of pertaining activators and inhibitors should be uniform. Otherwise, their nonuniform distribution is inherent in cancer cells.</p>