Algorithm

Engineering

Biology

Theoretical computer science

Substitution (logic)

Stability (learning theory)

Folding (DSP implementation)

Selection (genetic algorithm)

Biochemistry

Protein folding

Computer science

Computational biology

Genetics

Sequence (biology)

Artificial intelligence

Programming language

Biological system

Machine learning

Electrical engineering

Methods in Ecology and Evolution

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. 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). 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 . 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.

ProtASR2: Ancestral reconstruction of protein sequences accounting for folding stability