1. The ancestral sequence reconstruction (ASR) is a molecular evolution technique that provides applications to a variety of fields such as biotechnology and biomedicine. To infer ancestral sequences with realistic biological properties, the accuracy of ASR methods is crucial. We previously developed an ASR framework for proteins, called ProtASR, which is based on our site‐specific stability‐constrained substitution (SCS) model with selection on protein folding stability against both unfolding and misfolding. This model improved the empirical substitution models traditionally applied in ASR without increasing the computational complexity. However, it adopted a global exchangeability matrix, an approximation that we overcome here by considering site‐specific exchangeability matrices based on the Halpern–Bruno approach.
2. Here we present ProtASR2, a new version of our ASR framework that implements novel SCS models of protein evolution, namely mean‐field (MF) and wild‐type (WT).
3. ProtASR2 under MF and WT SCS models outperforms empirical models and previous SCS models in terms of goodness of fit and site‐specific distributions of amino acids. Importantly, the framework infers ancestral sequences with more realistic predicted folding stability with respect to simulated sequences, while empirical, CAT and other SCS models tend to overestimate the folding stability. We applied ProtASR2 to explore the evolution of two protein families present in diverse Prokaryota and found fluctuations of protein stability over time in both families. ProtASR2 is available from https://github.com/miguelarenas/protasr and the new SCS models are also available from https://github.com/ugobas/protevol.
4. Use of ProtASR2 will allow more realistic inferences of ancestral proteins in terms of folding stability with respect to those based on traditional empirical and CAT substitution models of protein evolution.

中文翻译：

---

ProtASR2：蛋白质序列的祖先重建，说明折叠稳定性

1. 祖先序列重建（ASR）是一种分子进化技术，可将其应用于各种领域，例如生物技术和生物医学。为了推断具有现实生物学特性的祖先序列，ASR方法的准确性至关重要。我们以前开发了一种蛋白质的ASR框架，称为ProtASR，这是基于我们的特定于位点的稳定性受限置换（SCS）模型，并选择了针对折叠和错误折叠的蛋白质折叠稳定性。该模型改进了传统上用于ASR的经验替换模型，而没有增加计算复杂性。但是，它采用了全局可交换性矩阵，在此基础上，我们通过考虑基于Halpern-Bruno方法的特定于站点的可交换性矩阵来克服了这种近似。
2. 在这里，我们介绍ProtASR2，这是我们ASR框架的新版本，可实现蛋白质进化的新型SCS模型，即均值场（MF）和野生型（WT）。
3. MF和WT SCS模型下的ProtASR2在拟合优度和氨基酸的位点特异性分布方面优于经验模型和先前的SCS模型。重要的是，框架相对于模拟序列推断祖先序列具有更现实的预测折叠稳定性，而经验，CAT和其他SCS模型往往会高估折叠稳定性。我们应用ProtASR2探索了在不同原核生物中存在的两个蛋白质家族的进化，并发现了两个家族中蛋白质稳定性随时间的波动。ProtASR2可从https://github.com/miguelarenas/protasr获得，新的SCS模型也可从https://github.com/ugobas/protevol获得。
4. 与基于蛋白质进化的传统经验和CAT替代模型的折叠稳定性相比，ProtASR2的使用将使祖先蛋白质在折叠稳定性方面更具现实意义。