🧬 biology

Better Protein Function Prediction by Modeling Survivorship Bias

This paper introduces Evo-PU, a positive-unlabeled learning framework that explicitly models survivorship bias through evolutionary mutation processes to significantly outperform existing methods in predicting protein functionality across various viral datasets.

Original authors: Zhongmou Chao, Poompol Buathong, Ekaterina Selivanovitch, Susan Daniel, Peter I. Frazier

Published 2026-05-11

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Zhongmou Chao, Poompol Buathong, Ekaterina Selivanovitch, Susan Daniel, Peter I. Frazier

Original paper licensed under CC BY 4.0 (http://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 ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed.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

The Big Problem: The "Survivorship" Trap

Imagine you are trying to learn how to bake the perfect cake. You go to a bakery and look at all the cakes on display. They all look delicious, and they all sold well. You might conclude, "Okay, all cakes are good."

But here is the catch: The bakery throws away every cake that burns, collapses, or tastes terrible before it ever hits the display case. You never see the failures. If you try to learn from only the cakes on display, you won't understand why some recipes fail. You only see the "survivors."

This is exactly the problem scientists face with proteins (the building blocks of life).

Nature's Filter: In the wild, proteins that don't work are eliminated by evolution. Only the ones that help an organism survive and reproduce are passed down.
The Data Gap: When scientists look at protein databases, they mostly see the "winners" (functional proteins). They rarely see the "losers" (non-functional proteins) because those were never observed in nature.

This creates a Survivorship Bias. If you train a computer to predict protein function using only the "winners," it gets confused. It doesn't know that a slightly different version of a protein might be a total failure.

The Old Solutions (and why they fell short)

Scientists have tried to fix this before, but they missed a key detail: How did the protein get there?

Standard "Positive-Unlabeled" (PU) Learning: This is like saying, "We have a list of good cakes, and a list of mystery boxes. Let's guess which mystery boxes are bad." The problem is, these methods assume every mystery box has an equal chance of being a good cake. They don't account for how the cake was made.
Protein Language Models (PLMs): These are like AI that reads millions of cookbooks to guess what a good recipe looks like. They are great at spotting general patterns, but they sometimes miss the specific, tiny details needed for a protein to do a specific job (like a specific key fitting a specific lock).
One-Class Classification: This is like a bouncer who only knows what a "good guest" looks like and turns everyone else away. It's too rigid and doesn't understand the nuance of why someone wasn't invited.

The New Solution: Evo-PU

The authors created a new tool called Evo-PU. Think of Evo-PU as a detective who doesn't just look at the cakes on the shelf; they look at the kitchen and the recipe book to understand how the cakes got there.

The Core Idea:
Evo-PU understands that proteins are built from smaller parts called nucleotides (like letters in a word).

The Analogy: Imagine you have a very common word, like "CAT."
- If you change one letter to make "BAT," it's very likely someone has already written that word down because it's easy to get from "CAT" to "BAT." If you haven't seen "BAT" in the dictionary, it's probably because "BAT" doesn't make sense (it's non-functional).
- However, if you try to change "CAT" to "XYZZY" (a random, complex string), it's highly unlikely anyone ever wrote that down just by accident. If you haven't seen "XYZZY," it's not because it's a bad word; it's just because it's so hard to stumble upon that no one has tried it yet.

How Evo-PU Works:

It tracks the "path": Evo-PU looks at the "ancestors" (the common proteins we already know) and calculates how easy it would be to mutate them into a new version.
It adjusts the odds:
- If a new protein is one step away from a common one, and we haven't seen it, Evo-PU thinks, "This is probably a failure. If it worked, we would have found it by now."
- If a new protein is many steps away from anything common, and we haven't seen it, Evo-PU thinks, "We haven't seen it just because it's rare to happen, not because it's broken."
The Result: By modeling this "path of mutation," Evo-PU can tell the difference between a protein that is missing because it's bad versus a protein that is missing because it's rare.

The Results: Did it work?

The team tested Evo-PU on viruses like Influenza, RSV, and SARS-CoV-2. They asked it to predict:

Which parts of the virus help it stick to human cells?
Which parts help it hide from our immune system?
Which new virus variants might appear in the future?

The Verdict:

In Well-Surveilled Viruses: For viruses where we have a lot of data (like the flu), Evo-PU was the clear winner. It beat all the other methods (standard PU learning, one-class classifiers, and language models). It successfully predicted which mutations would work and which would fail.
In Diverse Datasets: When they tested it on a massive, mixed dataset of many different organisms (ProteinGym), Evo-PU didn't win. The authors explain this is because their method relies on knowing exactly how many times a virus has infected a host (prevalence). In mixed datasets, that data is messy or missing, so the "detective" loses some of its clues.

Summary

The paper argues that to predict if a protein works, you can't just look at the list of "survivors." You have to understand the evolutionary journey it took to get there.

Old Way: "I see a protein. Is it good? I'll guess based on how it looks."
Evo-PU Way: "I see a protein. I know it's one mutation away from a common one. Since I haven't seen this specific mutation yet, it's likely a failure. But if it's a weird, complex mutation, I'll give it a chance because it's just hard to find."

By accounting for how likely a protein is to appear in nature, Evo-PU gives a much clearer picture of which proteins are truly functional and which are evolutionary dead ends.

Technical Summary: Better Protein Function Prediction by Modeling Survivorship Bias

Problem Statement

Protein sequence data derived from nature is inherently biased due to evolutionary and experimental selection processes. This survivorship bias results in datasets where functional sequences are systematically overrepresented, while non-functional mutations are filtered out by natural selection or experimental protocols (e.g., biopanning). Consequently, protein function prediction often faces a Positive-Unlabeled (PU) learning scenario: observed sequences are known to be functional (positive), while unobserved sequences are unlabeled—they may be functional but unobserved, or truly non-functional.

Existing PU learning methods typically assume a constant class prior (the probability that an unlabeled sequence is truly positive) across all sequences. This assumption is biologically unrealistic because the probability of a sequence being observed depends on its evolutionary accessibility. Sequences one mutation away from prevalent variants are far more likely to arise and be observed than those requiring multiple simultaneous mutations. Standard methods fail to account for this variability, limiting their predictive performance. Furthermore, while Protein Language Models (PLMs) capture evolutionary constraints, they often infer statistical patterns from observed distributions without explicitly modeling the mutational pathways and surveillance processes that determine which variants are missing.

Methodology: Evo-PU

The authors propose Evo-PU, a PU learning framework that explicitly models survivorship bias through an evolution-informed, sequence-dependent class prior. The core insight is that functional nucleotide sequences closer to those prevalent in nature are more likely to be observed because they can arise through feasible mutational pathways.

1. Probabilistic Data-Generating Process

Evo-PU formalizes the observation process through three stages:

Emergence ( $E$ ): A nucleotide sequence $y$ emerges via mutation from an ancestor.
Functionality ( $A$ ): The sequence encodes a functional protein.
Observation ( $O$ ): The sequence is detected by a surveillance process with probability $p_o$ .

The likelihood of observing an amino acid sequence $x$ is derived as:
$P(O_X(x) = 1) = p_a(x; \theta) \left[ 1 - \prod_{y \in Y(x)} (1 - p_o p_e(y; \alpha)) \right]$
Where:

$p_a(x; \theta)$ is the classifier estimating the probability of functionality.
The term in brackets represents the sequence-dependent class prior, capturing the probability that a functional sequence $x$ is observed.
$p_e(y; \alpha)$ is the probability that a nucleotide sequence $y$ emerges from observed ancestors via mutation.

2. Nucleotide Emergence Model

To estimate $p_e(y; \alpha)$ , the model assumes observed nucleotide sequences ( $D_Y$ ) serve as ancestors. The emergence probability for an unobserved sequence $y$ is calculated based on:

Mutational Distance: The probability of mutation from an ancestor $y'$ to $y$ , distinguishing between transitions (more common) and transversions (less common).
Prevalence: The frequency of the ancestor $y'$ in the observed data, denoted as $c(y')$ .
Scaling: A hyperparameter $\alpha$ scales the effective emergence rate to account for factors like reproductive failure.

The emergence probability is approximated as:
$p_e(y; \alpha) \approx 1 - \exp\left( -\sum_{y' \in D_Y} P(y' \to y) \alpha c(y') \right)$

3. Efficient Likelihood Approximation

Exact computation of the likelihood is intractable for long sequences due to the exponential size of the unobserved sequence space. Evo-PU employs an efficient approximation:

It restricts the set of unobserved sequences ( $\hat{D}'_X$ ) to those generated by single-nucleotide mutations from observed data that have a high probability of emergence ( $p_e > \epsilon$ ).
It restricts the set of encoding nucleotides $Y(x)$ for any amino acid sequence to the intersection of observed and likely emergent nucleotides.
This allows for tractable optimization of the log-likelihood function using standard gradient-based methods.

4. Implementation Details

Classifier: The framework is agnostic to the classifier architecture but utilizes Logistic Regression (LR) and a Wide & Deep (WD) neural network in experiments.
Representation: Sequences are encoded using physicochemical properties of amino acids (CHEM) to enable continuous optimization.
Training: The model jointly estimates classifier parameters $\theta$ , surveillance efficiency $p_o$ , and the emergence scaling factor $\alpha$ by maximizing the approximated log-likelihood with $L_2$ regularization.

Key Contributions

Novel Framework: Introduction of Evo-PU, the first PU learning framework that incorporates a scientific understanding of nucleotide mutation to model survivorship bias via a sequence-dependent class prior.
Biological Grounding: Unlike standard PU methods that assume a constant class prior, Evo-PU explicitly models how mutational accessibility and prevalence jointly determine observation probabilities.
Scalable Approximation: Development of an efficient approximation method that focuses on biologically plausible, nucleotide-derived variants, making the likelihood computation tractable for large sequence spaces.
Comprehensive Evaluation: Rigorous testing across single-organism viral datasets (Influenza, RSV, SARS-CoV-2) and multi-organism benchmarks (ProteinGym).

Experimental Results

The authors evaluated Evo-PU on three single-organism tasks (predicting functional motifs in Influenza, RSV, and SARS-CoV-2) and two multi-organism ProteinGym benchmarks.

Single-Organism Tasks: Evo-PU consistently outperformed standard PU learning methods (Protein-PU, 2Step), One-Class Classification (OCC) methods (OC-SVM, iForest), and Protein Language Models (PLMs like EVE, ESM-1v, kNN-ESM2).
- Notable improvements were seen in predicting Influenza fusion and binding motifs, RSV HRC motifs, and future SARS-CoV-2 variant emergence.
- In the SARS-CoV-2 emergence task, Evo-PU achieved the highest Spearman correlation ( $\rho$ ) between predicted functional probability and observed variant frequencies.
Multi-Organism Tasks (ProteinGym): On heterogeneous datasets (PSAE and A0), PLM-based methods achieved the strongest performance. The authors attribute Evo-PU's reduced performance in this regime to its design for well-surveilled single-organism data and the assumption of equal prevalence across sequences, which limits its ability to model heterogeneous surveillance rates.

Significance and Claims

The paper claims that Evo-PU provides a principled approach to modeling survivorship bias in protein databases, advancing the scientific understanding of biochemistry and biology. By explicitly embedding nucleotide-level mutation and natural selection into the observation model, the method yields a biologically grounded likelihood for amino acid sequences.

The authors state that this work has potential positive impacts in:

Drug Discovery: Accelerating the identification of therapeutic targets and the design of effective biologics.
Biomaterials: Guiding the engineering of proteins with desired properties.
Basic Research: Providing a framework to better understand the relationship between protein sequence and function in the presence of selection bias.

The paper modestly acknowledges limitations, noting that the current model does not account for insertions or deletions and that extending the framework to handle heterogeneous observability and datasets lacking prevalence information remains a direction for future work. It also emphasizes the need for responsible use to prevent the design of dangerous protein sequences.