Parameter Evolvability in Gene Expression Models Drives Phenotypic Adaptation

Gene expression transforms information encoded in DNA into functional protein activity. Although these systems are often assumed to be static-thus enabling the programming of genetic circuits to meet predefined specifications-they are, in fact, dynamic and subject to evolutionary change. As sequences accumulate subtle mutations, their phenotypic responses may shift, potentially undermining initial design goals. Here, we investigate the evolutionary distance between gene expression models and their future (mutated) versions over time, while tracing their phenotypic adaptation. We use four-parameter gene expression models as individuals and apply a genetic algorithm to evolve them towards both fixed and oscillatory protein targets. To quantify divergence in expression rates, we introduce a parameter distance metric that captures differences within and between individuals. When evolving towards a fixed phenotype, individuals often follow consistent patterns in distance-to-protein space ("V-shaped" trajectories), suggesting that certain parameter deviations enable faster adaptation. Furthermore, groups with identical phenotypic outputs but differing parameter distances follow distinct evolutionary paths to reach the same target. In fluctuating environments, large mutational steps across all parameters allow populations to closely track a moving protein target, while small steps result in the population being unable to keep pace with the target, leading to a delayed, repeated pattern in the protein response. These findings highlight that both the underlying parameter architecture-directly translatable into DNA sequences-and the scale of mutation critically shape adaptive dynamics. We advocate accounting for this effect to incorporate evolution as a design element in the engineering of biocomputations.