Molecular sequences are shaped by selection, where the strength of selection relative to drift is determined by effective population size (N_e). Populations with high N_e are expected to undergo stronger purifying selection, and consequently to show a lower substitution rate for selected mutations relative to the substitution rate for neutral mutations (ω=dN/dS). However, computational models based on biophysics of protein stability have suggested that ω can also be independent of N_e, a result proven under general conditions. Together, the response of ω to changes in N_e depends on the specific mapping from sequence to fitness. Importantly, an increase in protein expression level has been found empirically to result in decrease of ω, an observation predicted by theoretical models assuming selection for protein stability. Here, we derive a theoretical approximation for the response of ω to changes in N_e and expression level, under an explicit genotype-phenotype-fitness map. The method is generally valid for additive traits and log-concave fitness functions. We applied these results to protein undergoing selection for their conformational stability and corroborate out findings with simulations under more complex models. We predict a weak response of ω to changes in either N_e or expression level, which are interchangeable. Based on empirical data, we propose that fitness based on the conformational stability may not be a sufficient mechanism to explain the empirically observed variation in ω across species. Other aspects of protein biophysics might be explored, such as protein-protein interactions, which can lead to a stronger response of ω to changes in N_e.

中文翻译：

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一种量化有效群体大小和表达水平变化对编码序列进化速率影响的理论方法

分子序列通过选择形成，其中相对于漂移的选择强度由有效种群大小（N _e）确定。预计具有高N _e的种群会经历更强的纯化选择，因此相对于中性突变的替代率（ω= dN / dS），对选定突变的替代率更低。但是，基于蛋白质稳定性的生物物理学的计算模型表明，ω也可以独立于N _e，这一结果在一般条件下得到了证明。在一起，ω对N _e变化的响应取决于从序列到适合度的特定映射。重要的是，已凭经验发现蛋白质表达水平的提高可导致ω的降低，这是通过理论模型预测得出的，假设选择了蛋白质稳定性。在这里，我们在一个明确的基因型-表型适应度图下得出ω对N _e和表达水平变化的响应的理论近似值。该方法通常对加性和对数适应度函数有效。我们将这些结果应用于蛋白质的构象稳定性选择中，并通过更复杂的模型进行模拟来证实结果。我们预测ω对任一N _e变化的弱响应或表达级别，可以互换。基于经验数据，我们提出基于构象稳定性的适应度可能不足以解释经验观察到的物种间ω的变化。可以探索蛋白质生物物理学的其他方面，例如蛋白质-蛋白质相互作用，这可以导致ω对N _e变化的更强响应。