🧬 biology

Empirical substitution models of SARS-CoV-2 protein evolution for phylogenetic inference

This study develops and validates novel empirical substitution models specifically for SARS-CoV-2 proteins, demonstrating that they yield more accurate phylogenetic inferences and biologically realistic evolutionary predictions compared to existing generalist models.

Original authors: David Ferreiro, Luis Daniel González-Vázquez, Miguel Arenas

Published 2026-07-21

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CC BY 4.0

Original authors: David Ferreiro, Luis Daniel González-Vázquez, Miguel Arenas

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are trying to trace the family history of a very famous, very busy celebrity. To do this, you need a rulebook that tells you how likely it is for one family member to change into another over time. In the world of biology, this rulebook is called a "substitution model." Scientists use these models to build family trees (called phylogenies) for viruses, animals, and plants. The goal is to figure out who is related to whom and how they changed over time. However, most rulebooks out there are "generalist" guides—they work okay for many different types of proteins, kind of like a generic "how to cook" book that tries to cover everything from baking a cake to grilling a steak. The problem is that different proteins have very specific jobs and rules. A protein that acts as a virus's engine (a protease) has different rules than a protein that acts as the virus's key to unlock a cell (the spike protein). If you use a generic rulebook for a specific job, your family tree might end up looking a bit wobbly and inaccurate. This is especially true for SARS-CoV-2, the virus that causes COVID-19, which has been evolving rapidly and changing the world. Until now, scientists didn't have a custom rulebook specifically for this virus's proteins, which meant they were trying to fit a square peg into a round hole.

In this study, the researchers decided to write their own, custom rulebooks specifically for SARS-CoV-2. They looked at thousands of real virus sequences to see exactly how the amino acids (the building blocks of proteins) swapped places in the virus's main protease, its papain-like protease, its spike protein, and the whole virus package. Think of it like watching a massive, real-time dance floor of the virus to see which dancers actually switch partners and which ones stay put. They found that the virus has its own unique dance moves that generic rulebooks simply missed. For instance, they discovered that in the virus's proteases (the enzymes that cut up other proteins), certain swaps happen very rarely because the structure is so tight and fragile, while the spike protein is much more flexible and allows for wilder changes, especially those that help the virus hide from our immune system.

The team then tested their new, custom rulebooks against the old, generic ones. They did this in two ways. First, they checked which rulebook could best explain the real data they collected, like a detective checking which theory fits the clues best. Their custom models won almost every time, showing that they are much better at describing how this specific virus evolves. Second, they ran computer simulations where they let the virus evolve forward in time using their new rules versus the old rules. They checked the "folding stability" of the resulting proteins—imagine checking if a paper crane made from the new rules still holds its shape, while the one made from the old rules falls apart or becomes too stiff. The proteins evolved using the new SARS-CoV-2-specific models held their shape much more realistically, looking just like the real virus proteins found in nature.

The researchers conclude that using these new, virus-specific models gives a much clearer and more accurate picture of how SARS-CoV-2 is changing. They suggest that for the best results, scientists should stop using the "one-size-fits-all" rulebooks and switch to these custom guides. While the study shows these models work better in simulations and fit the data more tightly, the authors note that this is a significant step toward understanding the virus's past and predicting its future moves, helping us stay one step ahead in the ongoing battle against the virus.

Technical Summary: Empirical Substitution Models of SARS-CoV-2 Protein Evolution

Problem Statement
Probabilistic phylogenetic inference relies on substitution models of molecular evolution to generate accurate predictions. While empirical substitution models are well-established for protein evolution, the available repertoire remains limited relative to the diversity of protein families. Crucially, no empirical substitution models had been developed specifically for SARS-CoV-2 proteins prior to this study. The authors note that evolutionary patterns vary among proteins, and the use of generalist models for specific viral proteins can lead to unrealistic modeling, potentially compromising the accuracy of phylogenetic trees, ancestral sequence reconstructions, and evolutionary trajectory predictions.

Methodology
The study employed a maximum likelihood (ML) approach to estimate new empirical substitution models for SARS-CoV-2.

Data Curation: Sequences were retrieved from GISAID and NCBI. A filtering process excluded sequences with ambiguities, indels of 10+ amino acids relative to the reference (NCBI Protein ID: YP_009724389.1), and those sharing less than 75% amino acid identity with the reference.
Dataset Construction:
- Method Datasets: For the Spike, Main Protease (Mpro/nsp5), and Papain-like Protease (PLpro/nsp3), datasets of 100,000 randomly sampled sequences were constructed. For the complete proteome, a dataset of 20,000 sequences was used.
- Test Datasets: 10 independent test datasets were generated for each protein (1,000 sequences each) and for the proteome (100 sequences each), excluding sequences used in the method datasets.
Model Estimation: Using the QMaker method implemented in IQ-TREE2, the authors estimated general time-reversible 20×20 exchangeability matrices ( $Q$ ) and equilibrium amino acid frequencies ( $\pi$ ) for each target. Phylogenetic trees required for estimation were reconstructed using the best-fitting existing model selected via ModelFinder.
Validation:
- Phylogenetic Likelihood: The fit of the new models (SC2-Mpro, SC2-PLpro, SC2-Spike, SC2-Proteome) was compared against existing empirical models using Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) on test datasets.
- Protein Folding Stability: Forward-in-time evolutionary simulations were conducted for Mpro and PLpro under the new models, the best-fitting traditional model, and a structurally constrained substitution (SCS) model. The resulting simulated sequences were evaluated for folding stability ( $\Delta G$ ) using DeltaGREM, comparing them to real sequences.
- Similarity Analysis: Principal Component Analysis (PCA) was performed on normalized rate matrices to assess the distance between SARS-CoV-2 models and other empirical models (e.g., JTT, HIVw, FLU).

Key Contributions
The authors present a set of four new empirical substitution models:

SC2-Mpro: Specific to the main protease.
SC2-PLpro: Specific to the papain-like protease.
SC2-Spike: Specific to the spike protein.
SC2-Proteome: A general model for the entire SARS-CoV-2 proteome.

These models have been made publicly available via the eModelDB database.

Results

Substitution Patterns: The models revealed distinct evolutionary patterns. The protease models (SC2-Mpro, SC2-PLpro) showed more restrictive substitution rates compared to the Spike and Proteome models.
- Physicochemical Trends: High rates were observed for substitutions conserving size and hydrophobicity (e.g., Ala-Val, Val-Ile). The models also captured specific charge-conserving substitutions (e.g., Lys-Arg in Mpro; Arg-Lys in Spike) and diversification events (e.g., Pro-His, Pro-Ser).
- Stationary Frequencies: Distinct amino acid frequencies were noted, such as elevated Proline in Mpro, Leucine/Isoleucine in PLpro, Phenylalanine/Valine in Spike, and Lysine in the Proteome.
Phylogenetic Fit: The SARS-CoV-2-specific models generally outperformed existing empirical models, yielding lower BIC and AIC scores across test datasets.
- Frequency Handling: For Mpro and PLpro, models using estimated equilibrium frequencies performed better than those using observed test frequencies. Conversely, for Spike and the Proteome, incorporating observed amino acid frequencies from the test data further enhanced model performance.
- PCA Analysis: The SARS-CoV-2-specific models clustered separately from generalist models (e.g., JTT, VT) and lineage-specific models (e.g., HIVw, FLU). Notably, the Alanine-Valine (A-V) substitution rate was significantly higher in SARS-CoV-2 models compared to standard models, while Threonine-Serine (T-S) rates were lower.
Folding Stability: In forward-time simulations, sequences evolved under the SC2-Mpro and SC2-PLpro models exhibited folding stabilities closer to real viral proteins than those generated by traditional empirical models or the SCS model. Specifically, the SC2-PLpro model produced stability profiles more realistic than the SCS model, which tended to generate overly stable proteins.

Significance and Claims
The authors conclude that evolutionary inferences based on protein-specific substitution models are generally more accurate and biologically realistic than those based on generalist models. The study demonstrates that SARS-CoV-2 proteins evolve under distinct constraints that are not captured by existing models.

Accuracy: The new models improve the fit to SARS-CoV-2 data, suggesting they better capture the specific selective pressures acting on the virus.
Biological Realism: The ability of these models to generate protein variants with realistic folding stabilities indicates they implicitly capture evolutionary constraints related to protein structure and function.
Recommendation: The authors recommend the use of these specific models for evolutionary predictions of SARS-CoV-2 proteins to enhance the reliability of phylogenetic inferences and trajectory projections. They also call for phylogenetic frameworks to expand their implemented model sets to include such protein-specific options.

Technical Summary: Empirical Substitution Models of SARS-CoV-2 Protein Evolution

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