A Minimal Model of Functional Redundancy as a Route to Enzyme Specialisation

Functional overlap among enzymes could permit individual proteins to specialise while maintaining organismal reaction performance. We examine this possibility in a minimal origin--fixation model in which weak generalists jointly supply 120 reactions and fitness depends on aggregate catalytic capacity. Pleiotropic mutations act on loop-local activity profiles subject to a tunable structural incompatibility constraint. No gene duplication occurs during evolution. A factorial sweep combines five initial redundancies, two mutation kernels, and four incompatibility values, with five replicates per combination and 250 fixed substitutions per simulation. Across all 40 parameter combinations, effective protein breadth decreases and the strongest function accounts for a larger share of activity. Mean breadth reductions range from 1.59 to 3.97 under the loss-biased kernel and from 6.32 to 8.16 under the symmetric kernel. Specialisation therefore does not require a mutational bias towards biochemical loss. Higher redundancy generally buffers weakest-reaction performance under loss-biased mutation, while structural incompatibility has a non-monotonic effect on specialisation. Total activity increases, but is not conserved by the model and does not measure a conservation-based efficiency gain. These results establish that duplication is not a logical prerequisite for specialisation in this class of model: distributed catalytic contributions can reorganise while aggregate reaction performance remains comparatively buffered.