Extant Sequence Reconstruction: The accuracy of ancestral sequence reconstructions evaluated by extant sequence cross-validation

Abstract

Ancestral sequence reconstruction (ASR) has become widely used to analyze the properties of ancient biomolecules and to elucidate the mechanisms of molecular evolution. By recapitulating the structural, mechanistic, and functional changes of proteins during their evolution, ASR has been able to address many fundamental and challenging evolutionary questions where more traditional methods have failed. Despite the tangible successes of ASR, the accuracy of its reconstructions is currently unknown, because it is generally impossible to compare resurrected proteins to the true ancient ancestors that are now extinct. Which evolutionary models are the best for ASR? How accurate are the resulting inferences? Here we answer these questions by applying cross-validation (CV) to sets of aligned extant sequences. To assess the adequacy of a chosen evolutionary model for predicting extant sequence data, our column-wise CV method iteratively cross-validates each column in an alignment. Unlike other phylogenetic model selection criteria, this method does not require bias correction and does not make restrictive assumptions commonly violated by phylogenetic data. We find that column-wise CV generally provides a more conservative criterion than the AIC by preferring less complex models. To validate ASR methods, we also apply cross-validation to each sequence in an alignment by reconstructing the extant sequences using ASR methodology, a method we term extant sequence reconstruction (ESR). We can thus quantify the accuracy of ASR methodology by comparing ESR reconstructions to the corresponding true sequences. We find that a common measure of the quality of a reconstructed sequence, the average probability of the sequence, is indeed a good estimate of the fraction of the sequence that is correct when the evolutionary model is accurate or overparameterized. However, the average probability is a poor measure for comparing reconstructions, because more accurate phylogenetic models typically result in reconstructions with lower average probabilities. In contrast, the entropy of the reconstructed distribution is a reliable indicator of the quality of a reconstruction, as the entropy provides an accurate estimate of the log-probability of the true sequence. Both column-wise CV and ESR are useful methods to validate evolutionary models used for ASR and can be applied in practice to any phylogenetic analysis of real biological sequences.

AP-LASR: Automated Protein Libraries from Ancestral Sequence Reconstruction

“…Across all protein families tested, AP-LASR achieved improved or comparable eLnP scores compared to FireProt ASR . Note that a greater (less negative) eLnP number represents greater confidence[33]. This metric was chosen for two reasons: it can compare ASR outputs from various software or models in an unbiased way and it offers assessments even in the absence of definitive ‘correct’ ancestors.…”

“…The reliability of the final reconstructed ancestry is quantified using the eLnP metric, as proposed by Sennett and Theobald (Equation 1)[33]. eLnP quantifies the overall uncertainty in the reconstructed sequence distribution and was used as our benchmark to evaluate the efficacy of AP-LASR against well-established software such as FireProt ASR .…”

The most probable ancestral sequence reconstruction yields proteins without systematic bias in thermal stability or activity

“…We have demonstrated that the number of correct residues is linearly proportional to the average sequence probability. 18 Regardless, if selecting the SMP state does indeed result in the fewest sequence errors then we should also expect that it’s physicochemical properties when resurrected is most like the true ancestral protein. However, the concern remains that systematically selecting the most probable residue at each site will impart a property bias in the SMP sequence relative to the true sequence.…”