Engineering Protein Expression Noise via Synonymous Codon Sequence Design: A Predictive Computational Approach using a Simplified Model

Gene expression is an inherently stochastic process, resulting in cell-to-cell variability (noise) in mRNA and protein levels. While controlling the mean expression level is a cornerstone of synthetic biology, the ability to independently modulate expression noise offers an additional layer of control with profound functional implications. Synonymous codon usage bias is known to affect translation efficiency and speed, thereby influencing mean protein production levels. Here, we computationally investigate the hypothesis that strategic synonymous codon choices can also serve as an engineering tool to quantitatively modulate protein expression noise. We utilize a computationally efficient two-stage stochastic model (transcription-translation), where the impact of different codon usage strategies (e.g., optimized, deoptimized) is captured through distinct effective translation rates (k_tl_variant). Our simulations demonstrate that varying k_tl_variant affects both the mean protein level () and the noise metrics (Coefficient of Variation, CV; Fano Factor, FF). Example results for a variant with rapid translation (k_tl=60 min⁻¹) show low relative noise (CV ≈ 0.07) but significantly bursty protein production (FF ≈ 39), highlighting the complexity of stochastic dynamics even in simplified models. Although this model does not explicitly capture ribosome traffic effects (like congestion potentially leading to Mean-Noise decoupling), it validates the basic principle that codon sequence, by modulating the average translation rate, influences expression statistics. We discuss how detailed ribosome traffic mechanisms (TASEP hypothesis) might enable finer noise control and present a detailed experimental plan to investigate these effects in vivo. This work provides an initial computational guide and framework for the rational design of genes with customized stochastic profiles.