Title: Predicting a Protein's Stability under a Million Mutations
Venue: NeurIPS 2023
Accepted: yes
Keywords: stability

proteins

biology

physical
Abstract: Stabilizing proteins is a foundational step in protein engineering. However, the evolutionary pressure of all extant proteins makes identifying the scarce number of mutations that will improve thermodynamic stability challenging. 
Deep learning has recently emerged as a powerful tool for identifying promising mutations.
Existing approaches, however, are computationally expensive, as the number of model inferences scales with the number of mutations queried. 
Our main contribution is a simple, parallel decoding algorithm.
Mutate Everything is capable of predicting the effect of all single and double mutations in one forward pass. 
It is even versatile enough to predict higher-order mutations with minimal computational overhead.
We build Mutate Everything on top of ESM2 and AlphaFold, neither of which were trained to predict thermodynamic stability.
We trained on the Mega-Scale cDNA proteolysis dataset and achieved state-of-the-art performance on single and higher-order mutations on S669, ProTherm, and ProteinGym datasets.
Our code is available at https://github.com/jozhang97/MutateEverything.

Predicting a Protein's Stability under a Million Mutations

Abstract

Stabilizing proteins is a foundational step in protein engineering. However, the evolutionary pressure of all extant proteins makes identifying the scarce number of mutations that will improve thermodynamic stability challenging. Deep learning has recently emerged as a powerful tool for identifying promising mutations. Existing approaches, however, are computationally expensive, as the number of model inferences scales with the number of mutations queried. Our main contribution is a simple, parallel decoding algorithm. Our Mutate Everything is capable of predicting the effect of all single and double mutations in one forward pass. It is even versatile enough to predict higher-order mutations with minimal computational overhead. We build our Mutate Everything on top of ESM2 and AlphaFold, neither of which were trained to predict thermodynamic stability. We trained on the MegaScale cDNA proteolysis dataset and achieved state-of-the-art performance on single and higher-order mutations on S669, ProTherm, and ProteinGym datasets. Our code is available at https://github.com/jozhang97/MutateEverything .

1 Introduction

Protein engineering is the discipline of mutating a natural protein sequence to improve properties for industrial [5, 78] and pharmaceutical applications [2, 25, 41]. However, evolution simultaneously optimizes several properties of a protein within its native environment, resulting in proteins with marginal thermodynamic stability ( ∼ 5-15 kcal/mol) [39] which become non-functional in an industrial setting. Therefore, repurposing a natural protein for biotechnological applications usually begins with identifying non-deleterious mutations that stabilize the structure. With a stabilized structure, downstream engineering goals, which often require exploring destabilizing mutations, become tractable. Historically, this process has been bottlenecked by the requirements of extensive laboratory characterization of rational designs [33, 79] or directed evolution libraries [4, 12, 21, 22]. The recent explosion in biological data [9, 29, 72, 73] has enabled deep learning frameworks to accelerate the identification of stabilizing mutations. A successfully stabilized protein often requires several mutations. However, current frameworks do not take into account epistatic interactions between multiple mutations. Thus, to significantly accelerate protein engineering, it is critical to efficiently navigate the epistatic landscape of higher-order mutations [10, 69]. However, due to its combinatorial nature, thorough exploration quickly becomes computationally prohibitive.

In this paper, we introduce Mutate Everything to directly predict changes in thermodynamic stability ( ∆∆ G ) for all single and higher-order mutations jointly. Mutate Everything is a parallel decoding algorithm that works in conjunction with a sequence model for predicting thermodynamic stability.

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Prior models for predicting thermodynamic stability work by producing an embedding or representation of the input sequence. Our decoder takes this representation and uses a linear network to create further representations, one for every possible single mutation. These mutation-level representations are then further aggregated to form representations for higher-order mutations. We feed these higher-order representations into a lightweight multi-layer perception (MLP) head to output predicted ∆∆ G measurements. Since the mutation-level representations are computed only once, we are able to scale to millions of (higher-order) mutations, as the aggregation and MLP-head computations are inexpensive. As such, given a fixed computational budget, our model evaluates millions more potential mutations than prior methods.

Mutate Everything estimates the effects of all single and double mutations for a single protein in seconds on one GPU. This can efficiently compute the stability of all single and double mutants across all ∼ 20,000 proteins in the human proteome within a short time frame. To the best of our knowledge, Mutate Everything is the first tool that renders the computational analysis of double mutants across the entire proteome tractable. Mutate Everything can be used in conjunction with any model that generates representations for protein sequences. In this paper, we use AlphaFold [31] as a backbone architecture and fine-tune it on a dataset labeled by experimentally derived ∆∆ G measurements. This results in the first accurate model of stability prediction based on AlphaFold.

We evaluate the performance of our Mutate Everything on well-established benchmarks for predicting experimentally-validated ∆∆ G measurements of mutations: ProTherm [48], S669 [54], and ProteinGym [49]. On ProTherm high-order mutations (PTMul), our model achieves a Spearman of 0.53, compared to 0.50 in the next best method. On S669 single mutations, our model achieves a Spearman of 0.56, outperforming the state-of-the-art at 0.53. On ProteinGym, the Mutate Everything outperforms state-of-the-art methods from 0.48 to 0.49. Our model makes finding the most stabilizing double mutations computationally tractable. We show on the double mutant subset of the cDNA-proteolysis dataset (cDNA2) [72], where only 3% of known mutations are stabilizing, that Mutate Everything effectively ranks stabilizing mutations ahead of destabilizing ones.

2 Related Works

2.1 Protein Engineering

Protein engineering is the process of mutating a natural protein to improve particular phenotypes, such as thermodynamic stability and function. The field has historically relied on rational design and stochastic methods, such as error-prone PCR [1], DNA shuffling [71], and directed evolution (DE) [4, 27], to identify gain-of-function mutations. Rational design is limited to proteins with solved structures and requires an extensive understanding of biochemistry and specific knowledge of the particular protein to select mutations highly likely to improve the target phenotypes [33, 79]. Directed evolution requires little to no knowledge of the protein and instead generates a library of protein variants that are then screened for the target phenotypes (e.g. fluorescence brightness, antibiotic

resistance, stability, activity) [4, 27]. The library can be generated via site-saturated mutagenesis of a handful of positions in the sequence [12] or DNA shuffling, in which the gene is digested into random fragments and reassembled into full-length sequences [71]. After screening the library, the most "fit" variant is then selected as the initial sequence for the next round of directed evolution. This iterative process repeats until it obtains a protein variant with the desired phenotypes.

Machine learning has demonstrated its ability to augment rational design and accelerate the stabilization of a variety of proteins [20, 28, 40, 52, 68]. Separately, machine learning-guided directed evolution (MLDE)[75] has been shown to improve the likelihood of obtaining the global fitness maximum by 81-fold compared to traditional DE [76]. MLDE has accelerated the engineering of several proteins, such as the enantioselectivity of enzymes for kinetic resolution of epoxides [23] and the activity and expression of a glutathione transferase [46]. Mutate Everything empowers the experimentalist to accelerate the stabilization of a protein for both rational design and MLDE.

2.2 Machine Learning for Protein Structure Prediction

Recent advances in machine learning have led to remarkable progress in protein structure prediction. AlphaFold [31] has demonstrated that deep learning is highly effective at predicting protein structures from a sequence by using evolutionary history via a multiple sequence alignment (MSA). AlphaFold passes the MSA and a pairwise representation of the sequence into Evoformer to capture the coevolutionary patterns between residues. The Evoformer output is then processed by the Structure Module, which predicts the protein's structure. We challenge prior works postulating that AlphaFold cannot be used for stability prediction and show that fine-tuning these rich co-evolutionary and structural features yield highly performant stability predictors [53].

Evolutionary Scale Modeling (ESM) [38, 62] has shown that protein structure prediction can be performed without MSAs and specialized architectures by leveraging large transformers pre-trained on masked token prediction. Other works extended this masked pre-training framework, including MSA-Transformer [60] which incorporates a sequence's MSA as input, and Tranception [49], which develops a hybrid convolution and attention based autoregressive architecture. We show that finetuning these evolutionary representations excels at protein stability assessment without MSAs.

2.3 Protein Stability Assessment

Traditional approaches to protein stability assessment relied on a combination of physics-based methods, statistical analysis, and traditional machine learning techniques. Physics-based tools, such as FoldX, Rosetta, and SDM, utilize energy functions and statistical patterns to assess how mutations affect a protein's stability [32, 67, 77]. DDGun [44] directly inferred ∆∆ G from heuristics, including Blosum substitution scores, differences in interaction energy with neighboring residues, and changes in hydrophobicity. Many traditional machine learning approaches used support vector machines and decision trees with physics-based feature engineering [11, 14, 15, 17, 37, 66]. Others ensemble existing machine learning methods [35, 56, 59, 63, 64].

Recently, deep learning-based approaches have recently begun to outperform existing physics and traditional machine learning approaches [13, 19, 34]. ACDC-NN [6] trains an asymmetric convolutional neural network for predicting forward and reverse mutation effects. Thermonet [36] voxelizes and feeds both the wild-type and mutant protein structures into a 3D-CNN to regress a ∆∆ G value. PROSTATA feeds the wild-type and mutant protein sequence into a pre-trained ESM2 model and then regresses a ∆∆ G value [74]. Stability Oracle takes the native and mutant amino acid type along with the local structure as input and regresses ∆∆ G [18]. Several deep learning frameworks [64, 80, 81] model multiple mutations in addition to single mutations. In this paper, we develop a framework that models the protein to enable efficient enumeration of all mutation candidates.

3 Preliminary

Problem Setup. A protein w = ( w 1 , ..., w L ) is a sequence of amino acids w l ∈ AA , where AA = { A,C,..., Y } are the 20 different amino acid types encoded by genetic information. Let µ = ( p, t ) denote a mutation substituting the amino acid w p at position p ∈ [1 , ..., L ] to amino acid type t ∈ AA . Our goal is to determine the change in thermodynamic stability ∆∆ G ∈ R for a protein w under a large number of mutation sets ( M 1 , ..., M N ) where a mutation set M i = { µ k } K i k =1 .

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The mutation sets include higher-order mutations ( K > 1 ), which is beyond the scope of state-of-theart single mutation predictors ( K = 1 ) [18, 36, 74]. These higher-order mutations are strictly more challenging than single mutations. The model must understand the effect of each single mutation and also the epistatic interactions that arise between individual mutations. We introduce a method that captures these interactions for any mutation set and decodes a corresponding ∆∆ G .

Furthermore, existing paradigms cannot efficiently scale to a large number of mutations. Higher-order mutation models [16, 35, 44, 64] take a protein and its mutant as input and predict the change in stability. These methods would need to enumerate and sort over a million model evaluations to find the most stabilizing mutations for a small protein of 75 amino acids. Our model runs a fine-tuned backbone only once and a lightweight decoder once for each mutation in parallel.

Feature Extraction. We fine-tune AlphaFold and other pre-trained models to alleviate the scarcity of labeled data. AlphaFold's Evoformer learns co-evolutionary patterns, such as residue interactions, and the Structure Module learns structural information, such as solvent accessibility or residue-residue distance. We demonstrate this is connected to a protein's stability and how mutations affect stability.

Each element of the protein sequence is tokenized by its amino acid type w l and positionally encoded. This produces a set of high-dimensional tokens for the transformer to take as input. The tokens are fed into a pre-trained model, which extracts per-position features ( x l ) L l =1 where x l ∈ R d . The transformer feature extractor is finetuned with our training objective. This is illustrated in Figure 2a.

4 Methodology

Our model uses per-position features ( x l ) L l =1 to determine the stability of a mutation set M . We distinguish between single point mutations K = | M | = 1 , and higher-order mutations K > 1 .

Both single and higher-order mutations share the same backbone architecture and encoding scheme, see Figure 2b. For each mutation µ = ( p, t ) at position p to amino acid t , we compute a latent mutation representation z ( µ ) ∈ R d , which captures the effect of the mutation on the protein. We decompose the mutation representation z ( µ ) = f t ( x p ) + h t , where sequence-dependent features f t ∈ { f A , ..., f Y } project the per-position feature according to the mutated amino acid type, and sequence-independent features h t ∈ { h A , ...h Y } are embeddings unique to the amino acid types A,C,..., Y . Intuitively, f t captures a contextualized feature at the position, and h t captures information about the mutated amino acid type. This mutation representation builds up a feature representing the amino acid substitution.

Decoding single mutations. Figure 2b illustrates single mutation decoding. The change in thermodynamic stability ∆∆ G for a single mutation µ is read out from its mutation representation z ( µ ) . A lightweight linear head g 1 : R d → R decodes this representation into the change in thermodynamic stability: ∆∆ G pr = g ( z ( µ )) .

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Decoding higher-order mutations. Figure 2c illustrates higher-order mutation decoding. The ∆∆ G for a higher-order mutation M = { µ k } K k =1 is read out from its K corresponding single point mutation representations { z ( µ k ) } K k =1 . Mutate Everything aggregates the representations for each single point mutation within a higher-order mutation. By aggregating the single mutations in the latent space, the model learns to account for the interactions between them. We aggregate with summation for its simplicity. A lightweight head g : R d → R then decodes the higher-order mutation ∆∆ G pr = g ( ∑ k z ( µ k )) . This formulation allows us to seamlessly parameterize any higher-order mutation. For higher-order mutations (e.g. K > 1 ), we empirically find that it is beneficial to predict the residual to the sum of single mutation ∆∆ G s from our single mutation decoder (see Table 5d).

Decoding a million mutations in one forward pass. This decoding scheme efficiently compute ∆∆ G for millions of mutations, whether single or higher-order (see Figure 3). Our insight is to precompute all mutation features and reuse them for all predictions. First, we compute all L × 20 mutation representations Z = { z (( p, t )) : p ∈ [1 , ..., L ] , t ∈ AA } . This expands each token x l to 20 representations that each capture the effect of mutating to one specific amino acid (including the wild-type amino acid). The backbone and this expansion are executed once for a protein sequence.

A lightweight head decodes ∆∆ G for any higher-order mutation (a mutation set). For each mutation set, we index and add the relevant mutation representations in Z . Index and sum operations are parallelized with outer-summation for K = 2 and the 'gather' operation for K > 2 . Finally, the lightweight decoder g computes the ∆∆ G for each mutation set in parallel.

Training. Our model is fine-tuned using supervised learning. We optimize the Huber loss.

where w is a protein sequence and ( M i , ∆∆ G exp i ) N i =1 are the mutation sets for this protein with experimentally validated ∆∆ G . This approach efficiently backpropagates the loss through all labeled mutations for a given protein in a single pass, unlike prior work which backpropagates through only one mutation in a single pass. We train on single and double mutants with on average 2000 mutations for each protein. When training on double mutants, we learn the residual to the sum of the experimental (ground truth) ∆∆ G for the constituent single mutations. Note that we use the experimental ∆∆ G of the single mutants to train double mutants but during testing, we use the model's predicted ∆∆ G of the single mutants to infer double mutant ∆∆ G . Thus, we do not need experimental data for single effects to predict combined effects.

Only 3% of the double mutants in our training set are stabilizing ( ∆∆ G < -0.5 kcal/mol [8]). To improve our performance on stabilizing mutations, we subsample the number of destabilizing double mutations to at most 8 times the number of stabilizing double mutations.

5 Results

5.1 Implementation Details

Our primary feature extractor is AlphaFold, implemented in OpenFold [3, 31]. The multiple sequence alignment (MSA) is computed using Colabfold [43]. Sequence features from the Evoformer and Structure Module are aggregated as input to the decoder. An adapter maps the backbone hidden dimension to D = 128 . Our amino acid projections and single mutation decoders are implemented with a linear layer. The higher-order mutation decoder transforms the previous embedding with a 2-layer MLP. These representations are aggregated and fed into a 3-layer MLP to predict ∆∆ G .

We train on the cDNA display proteolysis dataset [72], which leverages a high throughput proteolysis screen enabled by next generation sequencing (NGS) to extract noisy ∆∆ G values for 100 miniproteins totaling over 100,000 single and double mutations. To evaluate generalization on unseen proteins, we remove proteins from our training set that have high sequence similarity using MMSeqs2 [70] to any protein in our evaluation benchmarks. The short protein lengths ( < 100 amino acids) keep the memory requirement small for the higher-order decoder. See Section A.1 for more information about cDNA and other datasets.

We fine-tune a pre-trained backbone on single mutations for 20 epochs. Then, we finetune the model on both single and double mutations for 100 epochs using a cosine learning rate schedule with 10 warmup epochs. We use a batch size of 3 proteins due to the high memory requirements of AlphaFold. We use a learning rate of 3 × 10 -4 and weight decay of 0 . 5 . Training takes 6 hours on 3 A100 GPUs.

5.2 Finding Stabilizing Double Mutations

We evaluate our model's ability to find the stabilizing mutations on cDNA2. cDNA2 is our validation split of the cDNA double mutations dataset, consisting of 18 mini-proteins totaling 22,000 double mutations. The proteins in the validation set have at most 36% homology with those in the cDNA training set. Of these mutations, only 198 or 0.8% are stabilizing with ∆∆ G< -0 . 5 kcal/mol [8]. Like protein engineering, this scenario closely resembles the challenge of identifying a small number of stabilizing mutations amidst a much larger pool of destabilizing or neutral mutations.

We evaluate different methods on stabilizing mutations in Table 1. Stabilizing r s is the Spearman coefficient on the experimentally stabilizing subset introduced in [65]. Normalized discounted cumulative gain (nDCG) [30] measures the quality of the ranked mutation list by taking into account its experimentally validated ∆∆ G and position in the list [59]. Detection Precision (DetPr) is the proportion of experimentally validated stabilizing mutations among the top K = 30 predictions. We adapt previous state-of-the-art single mutation predictors by naively adding both single mutation predictions. A detailed description of the metrics is found in Section A.2.

Our model demonstrates exceptional performance in prioritizing stabilizing double mutations over destabilizing ones, achieving a significantly higher normalized discounted cumulative gain of 0.43 compared to 0.25, as well as a superior detection precision of 0.16 compared to 0.10. Our model additionally improves classification metrics Matthews Correlation Coefficient (MCC) and Area under Precision-Recall Curve (AUC) by 0.02 and 0.03, respectively.

To the best of our knowledge, Mutate Everything is the first work that models all double mutations in a computationally tractable manner. Figure 4 shows the runtime of several methods on a protein of 317 amino acids on an A100 GPU. The dashed line indicates the transition from evaluating single mutants to double mutants. Mutate Everything predicts ∆∆ G for all single and double mutations in one pass of the model. It runs in 0.6 seconds using an ESM2 backbone, and 12.1 seconds on an AlphaFold backbone. PROSTATA [74] also uses the ESM2 backbone but takes a protein sequence and its mutated sequence as input and outputs the change in stability. PROSTATA takes 306 hours to evaluate all double mutations with a batch size of 768. On an 8 GPU node, this will take 1.5 days.

5.3 Higher-order Mutation Results

We evaluate our model for predicting changes in thermodynamic stability for higher-order mutations in ProTherm. ProTherm is a database of thermodynamic ( ∆∆ G ) and thermostability ( ∆ T m ) experimental characterization of protein mutations curated from the literature. We consider a subset of this database that contains ∆∆ G values for higher-order mutations, named ProTherm Multiple ( PTMul ). PTMul contains 858 mutations [44]. We keep 846 experimentally validated ∆∆ G for higher-order mutants, including 536 doubles and 183 triples, after removing 4 duplicate and 8 ambiguous mutations. PTMul proteins have at most 35% homology to the proteins used in training.

Table 2 shows our results on PTMul. A description of baselines is provided in Section A.3. Our additive baselines naively add the sum of single mutation ∆∆ G s. This baseline rigorously evaluates our model's ability to learn epistasis, or the non-additive interactions when combining two mutations. Mean always predicts the global test dataset mean statistic. ESM and MSA perform poorly when comparing mutations across proteins. On ProTherm, Mutate Everything achieves the state-of-the-art performance of 0.53 Spearman correlation r s , compared to 0.50 of our additive baseline. A breakdown of PTMul performance on double mutations and more ( > 2 ) mutations is found in Table 6.

While other methods also handle multiple mutations, they usually adopt a mutation- or protein-level train and test split. This results in data leakage since the same protein or a homolog will have mutations in both the training and testing sets, leading to inflated reported metrics [16, 18, 35, 64]. In our study, we use sequence similarity-based splitting where our training proteins have at most 35% homology to those in PTMul. To fairly evaluate generalization to new proteins, we exclude these inflated comparisons from our study.

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5.4 Single Mutation Results

We additionally validate our model's ability to predict changes in thermodynamic stability under single mutations. We compare Mutate Everything to prior works on the newly introduced S669 dataset, which was established to address the data leakage issue and enable fair comparisons between existing methods [54]. We also evaluate the commonly studied reverse dataset setting, in which the model takes the mutant sequence as input and predicts ∆∆ G for mutating back to the wild-type sequence. The experimental value is obtained by negating the original ∆∆ G value going from the wild-type sequence to the mutant sequence. S669 is well curated and extensive, containing 94 proteins totaling 669 mutations [54]. S669 proteins have at most 30% sequence similarity with those in our training set to ensure separation between the training and validation sets.

Table 3 shows our comparisons with prior works. Mutate Everything is state-of-the-art on S669, achieving a Spearman correlation of 0.56, where the prior art obtained 0.53. Mutate Everything outperforms the existing sequence model by a large margin, with a 6-point gain on Spearman correlation and a 3-point improvement on AUC. Our method is even as powerful as the latest structure-based methods which have access to atom coordinates.

Mutate Everything is competitive on the reverse dataset evaluation, in which the original and mutated sequences are flipped and ∆∆ G negated. Our performance drops on reverse mutations because reverse mutations are out of distribution for our model. We did not perform data augmentation to train on reversed mutations as commonly done in the literature [18, 36, 74]. We found that it was beneficial to bias our reverse predictions using ∆∆ G to the amino acid found in the original sequence. We found the performance to be similar across 5 runs ( < 0 . 01 standard error).

5.5 Generalization to other Phenotypes

We show that stability predictors generalize to other phenotypes as well. ProteinGym substitutions is a dataset of 87 proteins with 1.6 million mutation sets labeled with a generic fitness score, such as activity, growth, or expression. The mutation sets have up to 20 substitutions and 14 proteins contain higher-order mutations. The ProteinGym-Stability split contains 7 proteins and 26,000 mutations with fitness labels that are known to correlate with thermodynamic stability (thermostability, abundance, expression). ProteinGym proteins have at most 45% sequence similarity with those in our training set. Due to memory constraints, we truncate proteins to at most 2000 amino acids.

Table 4 compares our work with previous works. Our MSA baseline uses the empirical amino acid distribution in the MSA at a given position to compute a likelihood ratio. The MSA retrieval prior weights the scores using the per-position first-order statistics in a multiple sequence alignment. On ProteinGym-Stability, Mutate Everything obtains a Spearman correlation of 0.52, compared to 0.50 of the next best method, TranceptEVE. On the one protein with labeled stability, Mutate Everything obtains 0.51 vs 0.33 of Tranception with MSA retrieval [51]. On the full ProteinGym benchmark, we outperform the strongest methods by ensembling our predictions with Tranception [49]. Ensembling our method with evolutionary models by averaging scores gains 0.11 points on ProteinGym and 0.01 points on ProteinGym-Stability, suggesting that our model learns complementary information to the evolutionary models. For comparison, TransEVE ensembles an evolutionary model (Tranception) and a family-based model (EVE) for a 0.03 point gain [50]. We found the performance to be similar across 5 runs ( < 0 . 01 standard error). An in-depth study on how protein stability related to function can be found in [26].

5.6 Ablation Studies

We ablate several architectural design choices in Table 5. Core architectural designs are evaluated on S669. Architectural designs for only multiple mutations are evaluated on cDNA2.

Backbone . We analyze the effect of different feature extractors on single mutation stability assessment in Table 5a. ESM2 [38] takes only sequence as input whereas MSA-Transformer [60] and AlphaFold [31] take the sequence and its MSA as input. Both ESM2 and MSA-Transformer are trained on masking residue modeling while AlphaFold is also trained on structure prediction. MSA input improves the stability prediction performance and AlphaFold's architecture and training further improve stability prediction.

(a) Backbone on S669. MSA inputs improve performance. A pre-trained AlphaFold model performs the strongest.

(c) Backbone Optimization on S669 . Finetuning the AlphaFold backbone improves performance.

(d) Higher-order Modeling on cDNA2. We model the ∆∆ G of the double mutation as a residual combined with the ∆∆ G of its single mutation.

Table 5: Mutate Everything ablation experiments. Default Settings are marked in grey.

Backbone Optimization Wetry fine-tuning and freezing the AlphaFold backbone during stability finetuning in Table 5c. We find that fine-tuning the backbone improves stability prediction performance.

Aggregation The technique to aggregate mutation representations for higher-order mutations is ablated in Table 5b. To control for feature dimension size, we reduce the head dimension when aggregating with outer product and flattening. Aggregating with product and summation performs similarly on double mutations. We add the features for a natural extension to more mutations.

Higher Order Modeling In the direct prediction model, the multi-mutant head directly predicts ∆∆ G . In the multiply and add models, the multi-mutant head learns how interactions among single mutations affect the higher-order mutation's ∆∆ G . In these models, the multi-mutant head output learns an additive bias or multiplicative scaling to the sum of single mutation ∆∆ G s. In Table 5d, we show that learning a bias performs the strongest among these three options.

6 Limitations

First, our training dataset contains biases that may affect model performance. The training set contains only small proteins, which may limit performance on larger ones. Our model may exhibit biases towards certain types of mutations due to the data imbalance in our training set. Second, the limited availability of experimental stability data poses a challenge for in-silico evaluation. Evaluation on larger and more diverse datasets is necessary to fully assess the generalizability of our model. In the future, we hope that high-throughput experimental assays will enable more rigorous evaluation and further improvements in protein stability prediction.

7 Conclusion

We present a method that efficiently scales thermodynamic stability prediction from single mutations to higher-order mutations. Our key insight is that the effects of mutations on the same protein are correlated. Thus, for a target protein, it suffices to run a deep backbone once and decode the effect of all mutations simultaneously using a shallow decoder. With the AlphaFold model as our backbone, our method outperforms existing methods on a variety of single and multiple mutation benchmarks. Our method scales to millions of mutations with minimal computational overhead and runs in a fraction of the time it would take prior works.

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A Experimental Setting

We elaborate on our experimental protocol, including the datasets used for training and testing, the evaluation metrics, and the baselines that calibrate our models.

A.1 Datasets

A fundamental principle in machine learning is to partition data so that the model is not evaluated on the same data it was trained on. This is essential to assess the model's ability to generalize beyond its training data (in our case, to new proteins). Protein sequences are regarded as the same protein when they have large sequence similarity (e.g. > 50% ), even when they are not exactly the same string. The impact of training on protein sequences similar to those in the test set has received considerable attention [18, 45, 54]. We list the datasets we use below and report the maximum sequence similarity of our training set with each test set. This ensures a clear separation between our training and test sets.

cDNA proteolysis [72] is a large scale dataset containing mutant proteins with ∆∆ G measurements. The dataset is generated by cDNA display proteolysis, a massively parallel technique that measures thermodynamic folding stability for millions of protein variants [72]. The cDNA proteins average 56.1 amino acids in length with a maximum length of 72 and a minimum length of 30 amino acids. The mean MSA depth is 7797 with a standard deviation of 6282. The maximum depth is 23525 and the minimum depth is 5. The mutations contain either one or two substitutions on a small protein. We follow the train-val split introduced in [18] and additionally filter out proteins in our training set that are similar to those in our evaluation datasets. Specifically, we train on 116 proteins with 213,000 total mutations, of which 97,000 are double mutants and 117,000 are single mutants. We hold out cDNA2, a validation set of 18 mini-proteins with 22,000 total double mutations. The proteins in our training set have at most 36% sequence similarity to those in cDNA2. A comprehensive analysis of the dataset, experimental assay, and filtering criteria are found in their paper [1].

ProTherm [48] contains experimentally measured thermodynamic data ∆∆ G for protein mutants. We use PTMul, a split containing only higher-order mutations curated by DDGun [44]. There are 88 proteins with 846 total mutations in PTMul. The proteins in our training set have at most 35% sequence similarity to those in PTMul.

S669 [54] is a manually curated dataset of mutant proteins and their ∆∆ G measurements. S669 contains mutations with one substitution. There are 94 proteins with 669 total single mutations in S669. The proteins in our training set have at most 30% sequence similarity to those in S669.

ProteinGym [49] is a curated set of proteins in which mutations are assessed for some fitness phenotype. These fitness phenotypes vary drastically, from cell growth to expression to fluorescence. The fitness values are always normalized so a higher value indicates stronger fitness. For classification metrics, the fitness values are binarized by some threshold either defined manually or arbitrarily at the median value. We also consider a subset of the proteins in ProteinGym in which fitness correlates highly with thermodynamic stability. These phenotypes include thermostability, expression, etc. There are 87 proteins totaling over 1.6 million (potentially higher-order) mutations. The proteins in our training set have at most 45% sequence similarity to those in ProteinGym.

T2837 [18] is an aggregate dataset with mutant proteins and their ∆∆ G measurements. T2837 contains mutations with one substitution. There are 129 proteins with 2837 total single mutations in T2837. The proteins in our training set have at most 34% sequence similarity to those in T2837.

A.2 Metrics

Weevaluate our model's ability to assess mutations in ProTherm, S669, and ProteinGym. Additionally, we evaluate our model's ability to detect stabilizing mutations in cDNA2.

A.2.1 Mutation Assessment

The model predicts the ∆∆ G measurement under all mutations with experimental data. The models are evaluated by the following regression and classification metrics. The classification metrics are

useful in applications where it is unnecessary to provide exact ∆∆ G and a binary stabilizing or de-stabilizing label (or third label, neutral) is sufficient.

Following the literature, we additionally evaluate reverse mutations (in contrast to the standard 'forward' mutations) where the 'to' and 'from' amino acids are flipped (e.g. P1K to K1P). The model takes the mutant sequence as input and is expected to output the negation of the original ∆∆ G value when mutating to the original native amino acid.

Spearman correlation coefficient (r s ) evaluates the model's ability to rank the mutations by their ∆∆ G values. This metric considers only the relative ordering between mutations and disregards the predicted values. Spearman has its limitations because our datasets contain predominantly destabilizing mutations ( ∆∆ G > 0). Spearman applied on these datasets overwhelmingly measures the model's ability to rank destabilizing mutations which does not directly translate to identifying the most stabilizing mutations [8, 58].

Root Mean Square Error (RMSE) provides a measure of how closely the predicted measurements align with the true measurements.

Area Under the receiver operating characteristic Curve (AUC) is a popular classification metric that focuses on positives. The receiver operating characteristic curve is created by plotting precision against recall at various classification thresholds. Precision is calculated as the ratio of true positives to the sum of true positives and false positives. Recall is calculated as the ratio of true positives to the sum of true positives and false negatives.

Matthew correlation coefficient (MCC) evaluates a model's classification performance under imbalanced datasets. It takes into account true positive, true negative, false positive, and false negative predictions to measure the overall performance of a model.

A.2.2 Mutation Detection

The regression metrics for mutation assessment are not directly suitable for protein engineering where the goal is to find stabilizing mutations. In addition to the classification metrics, we evaluate our models using per-protein metrics which evaluate the model's ability to detect a few stabilizing mutations from a large number of possible mutations. These metrics are applied to heavily annotated proteins ( ∼ 1000 ∆∆ G measurements) with randomly sampled mutations.

Stabilizing Spearman correlation coefficient r s is the Spearman coefficient calculated on the subset of experimentally stabilizing mutations. This mimics the case in protein engineering where there are too many stabilizing mutations to test in vitro and the goal is to prioritize the most stabilizing ones. This metric is used in [18, 65].

Normalized Discounted Cumulative Gain (nDCG) [30] quantifies the quality of a ranking among mutations by considering both the experimental ∆∆ G and predicted rank of each mutation. Specifically, nDCG computes the sum of experimentally stabilizing ∆∆ G s weighted inversely by their ranks. This metric rewards a model that ranks the best mutations first. We truncate the ranking at K = 30 mutations to approximate the number of in-vitro experiments that can typically be run in parallel. This metric is found in [59].

Detection Precision (DetPr) measures the fraction of experimentally stabilizing mutations among the top K = 30 predicted mutations by the model. This simulates the success rate a protein engineer might expect when deploying this model. K is set to approximate the number of in-vitro experiments that can typically be run in parallel.

A.3 Baselines

Several baselines calibrate performance across datasets. A subset of the critical baselines is introduced briefly (see [54] for more).

Mean is a simple baseline in which the mean measurement is predicted for all mutations. This baseline is not conditioned on the protein or mutation and instead uses only the dataset statistic.

Multiple Sequence Alignment (MSA) leverages the statistics from a set of similar protein sequences to rank mutations. Similar protein sequences are fetched, aligned, and indexed at a mutation position.

This yields an amino acid frequency count normalized into a probability distribution. The score is defined as the likelihood ratio between the mutated and native amino acid types. While calibrated for a given position and protein, it may not be well-calibrated across proteins.

ESM [38] also computes the likelihood ratio between a mutated and native amino acid type [42]. Unlike MSA, the probability distribution is decoded from ESM2 [38], a model pre-trained on masked amino acid prediction. Like MSA, ESM may not be well-calibrated across proteins.

DDGun [44] uses a linear combination of scores derived from evolutionary and structural features to compute ∆∆ G .

FoldX [67] leverages an empirical force field to estimate the change in stability. It models the Van Der Waals interactions, solvation and hydrogen bonding interactions, changes in entropy, and other physical values.

PROSTATA [74] is a sequence model for stability prediction built on the ESM2 model. It takes native and mutant protein sequences as input and produces a ∆∆ G value.

Stability Oracle [18] is a structure-based graph-transformer model for stability prediction.

Tranception [49] is a specialized autoregressive transformer that uses grouped attention to encourage specialization across heads.

B Additional Results

B.1 Higher-order Mutation Results on PTMul Breakdown

ProTherm Multiple (PTMul) contains 846 mutations, of which 536 are double mutations and 310 mutations with more than two mutations. We breakdown the performance on PTMul into double mutations and higher-order mutations (greater than 2) in Table 6. While our model performs similarly against the additive baseline on double mutations, Mutate Everything outperforms the additive baseline on higher-order mutations.

Table 6: Results on PTMul splits containing double mutations and more than 2 mutations. Mutate Everything outperforms existing methods, especially when there are multiple mutations.

B.2 Single Mutation Results on T2837

We include our results on the newly proposed T2837 dataset in Table 7 [18]. Mutate Everything achieves a Spearman correlation of 0.65 compared to 0.62 of Stability Oracle, outperforming existing methods on the forward dataset. PROSTATA-IFML [18] fine-tunes PROSTATA [74] on the cDNA proteolysis dataset for more direct comparison. Mutate Everything performs competitively with other sequence models on the reverse dataset even without training on reverse mutations. We show our performance on additional metrics for T2837 in Table 8.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a new method, Mutate Everything Method, to model a protein's thermodynamic stability based on mutations in a protein's sequence. A key distinguishing feature of the method is the ability to perform large amount of parallel evaluations, which significantly speed up computational efficiency. The authors first introduce the general challenge in designing stable protein though mutations, describe thermal stability as a physical metric and introduce the general outline of their method. Next, the authors describe related work in protein engineering, protein structure prediction and protein stability modeling followed by a more precise, mathematical description of the problem setup for the proposed method. Essentially, the Mutate Everything Method relies on taking protein sequence embeddings from pretrained models (AlphaFold, ESM) and then predicting thermal stability of the mutations with lightweight MLP heads with one head corresponding to each mutation. In the case of multiple mutations, the authors aggregate the outputs from each individual mutation head. In their experiments, the authors study their method on a variety of sequence mutation datasets, including both single and higher-order mutations with the general results indicating better modeling and compute performance of the Mutate Everything Method. The order also perform an ablation of representations from different embedding encoders, including AlphaFold, ESM2 and MSA-Transformer.\n\nSTRENGTHS:\nThe paper has the following strengths:\n* Originality: The paper proposes a new, pragmatic method for a relevant problem in modeling how mutations affect a protein thermodynamic stability.\n* Quality: The paper performs detailed evaluations of the method on multiple types of tasks, including multiple datasets, and compares to various other methods along both modeling performance and compute efficiency.\n* Clarity: The purpose, goals and details of the method and results are generally well presented.\n* Significance: The paper tackles a relevant problem and show notable performance improvements in multiple settings.\n\nWEAKNESSES:\nThe paper could be improved by:\n* Providing more clarity into the parallel evaluation pipeline. Figure 3 is not very clear in how exactly multiple mutation evaluations are processed and aggregated. I suggest adding labels that show how a mutation changes a particular part in the sequence similar to Figure 2. [Clarity]\n* The analysis on homology in Section 5.3 is interesting and adds an important dimension on how to properly design data splits for these kinds of tasks. It would be nice to see a deeper discussion on this; potentially in the appendix due to space constraints. [Quality, Significance]\n\nQUESTIONS:\n* Can you provide more detail on how you ensure the mapping of the mutation in the embedding space is aligned with the mapping of the mutation in the original sequence space?\n* Can you describe in more detail how your parallel evaluation ensure proper mapping of mutations to the correct protein sequence? I am trying to get a better sense of whether the parallel evaluation are essentially operating by creating a larger \"meta-sequence\" or if there is any type of multi-processing happening.\n* It seems like the method requires a frozen embedding encoder as it is implemented right now. How robust would the method be to finetuning the encoder?\n\nLIMITATIONS:\nThe authors include a section on limitations mainly focused on modeling shortcomings.", "TITLE": "Official Review", "RECOMMENDATION": 8, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2023-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present the \"Mutate Everything Method\", a simple method that builds on top of protein representations obtained through existing models to predict the effect of single and higher-order mutations. They apply the method to representations from ESM2 and AlphaFold, and show the performance on several downstream tasks.\n\nSTRENGTHS:\nThe proposed method is based on a very simple but effective idea, and the paper is written in a clear and mostly comprehensive manner. This seems like a relatively low-resource and fast method to get more use out of existing representations. Additionally, a substantial amount of results is presented over a wide range of benchmarks and metrics.\n\nWEAKNESSES:\nEven though I enjoyed reading this paper and I appreciate the idea that a simple method can make a difference for real downstream tasks, I am not entirely convinced that this method, which esentially consists of training a lot of MLPs on top of existing representations, fits the NeurIPS venue well. It doesn't seem like a substantial contribution to the field of machine learning, and this paper might therefore be better suited for a different venue where it would have more impact. Moreover, the reported spearman correlations to experimental results are very low in some places, and around 0.5 at most, signifying a very weak correlation at best. This begs the question whether this is an unfortunate metric or if there's a deeper issue causing the correlation to experimental results to be weak.\n\nQUESTIONS:\n1. The way the method is presented, it seems like the authors claim that it will be possible to reliably predict the effect of single mutations as well as high-order effects. Even though some evidence is presented, it is not conclusive, especially not for the higher-order case. I understand that this depends on e.g. the availability of data sets, but perhaps the presentation can be a bit more nuanced.\n2. Even though the method is presented as being simple, there seem to be a lot of MLPs to train! Can you give more details about these MLPs (i.e. how many layers, size of the layers) and the overall memory requirements?\n3. The paper goes straight from results to \"Limitations\", without any conclusions or discussion. As a reader, this section is clearly missing.\n4. Table 4, 5, and 6 show no standard deviations. Is there a good reason for that? Otherwise, it would be great if those could be added.\n5. The part where you predict the residual between single mutation $\\Delta\\Delta G$s and teh combined effect is a bit vague to me. Why was this beneficial? \n6. Related to the previous point, when you say in line 174-175 that you learn the residual to the sum of experimental $\\Delta\\Delta G$s for the constituent single mutations, what does this mean? Are you giving the model the experimental values of single mutations? Does this mean you always need to have experimental data for single effects if you want to predict combined effects? Or am I misunderstanding the sentence? The wording is a bit confusing.\n7. For clarity, it would be great if you could incorporate $x$, $\\mu$, and $z$ (and perhaps $f$ and $h$) in Figure 2.\n8. What is the dimensionality of $d$?\n9. Some of the baselines only show up in tables without really being explained in the main text or the appendix.\n10. There seem to be some references missing in the first part of the introduction (line 25-30), about the use of machine learning for finding stabilizing mutations. And perhaps more citations can be added to section 2.3 (line 104-111) as well.\n\nLIMITATIONS:\nThe authors describe the limitations of their work briefly but accurately. The only thing missing could be a discussion about the low spearman correlation values (in general).", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors are concerned with the task of predicting the effects of single- and double-residue mutations on the thermodynamic stability of a protein. They propose a simple method that involves passing combinations of embeddings from a pretrained model (AlphaFold2 or ESM) to MLPs. Compared to existing approaches, theirs is computationally efficient and conceptually simple. It also achieves good results on various benchmarks.\n\nSTRENGTHS:\nThe method is original, efficient, simple to understand, and works well. It addresses an important question in structural biology that is currently far from a solution. It has several favorable properties; for example, one can hot-swap in better embeddings as new models become available.\n\nWEAKNESSES:\nSome of the evaluations lack some important details, and a few claims seem questionable to me. See the \"questions\" section below. Overall, I think the evaluation for high-order mutations is a little light. In particular, while the model is evaluated on a mixture of double- and triple-residue mutations, individual results for each group are not provided. Given that the model wasn't trained on triple-residue mutations, and a purported strength of this method its ability to cleanly generalize to high-order mutations, this seems like an important omission.\n\nQUESTIONS:\n-     \"We compute z(μ) = ft(xp) + ht...\" \n\nIf h^t depends solely on t, why separate f^t and h^t?\n\n-     “Sequence features from the Evoformer and Structure Module are aggregated as input to the decoder.”\n\nWhich sequence features exactly? How are they aggregated?\n\n-     “To evaluate generalization on unseen proteins, we train on cDNA proteins with low similarity to those in all evaluation benchmarks.”\n\nHow exactly?\n\n-     “We train on the cDNA display proteolysis dataset [61], which leverages a high throughput selection assay to extract noisy ∆∆G values for 100 mini-proteins totaling over 100,000 single and double mutations.”\n\nWould be good to see some stats in the main paper. Protein length, MSA depth, etc.\n\n-     “Our model demonstrates exceptional performance in prioritizing stabilizing double mutations over destabilizing ones, achieving a significantly higher normalized discounted cumulative gain of 0.43 compared to 0.25, as well as a superior detection precision of 0.16 compared to 0.10. Our model additionally improves classification metrics MCC and AUC by 0.02 and 0.03 respectively.”\n\nIf I understand this correctly, the baseline referenced here is just a version of your model where the heads at the end are replaced with simple addition? Why is that a meaningful comparison?\n\n-     “While other methods also handle multiple mutations, they adopt a train and test split where unique mutations in the test set are not included in the training process. This inadvertently leads to training and testing on the same set of proteins [12, 28, 55]. PTMul proteins have at most 35% homology to the proteins used in these methods’ training. To fairly evaluate generalization to new proteins, we exclude these inflated comparisons from our study.”\n\nIs this widely known? If not, this’ll require more specific justification, either in the main paper or the supplement.\n\n- You finetune AlphaFold2 for the task. I'm kind of curious how well the method works if you simply train the MLPs with the embedding model frozen.\n\n- Could you elaborate more on how AlphaFold2 was finetuned? There are some nontrivial implementation details here; e.g. how cropping is handled.\n\nLIMITATIONS:\nAuthors include a brief discussion of limitations. They do not address potential negative societal impacts of their work (not that I think that would be warranted in this case).", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work predicts changes in thermodynamic stability for single or higher-order mutations on top of AlphaFold2 modules. The proposed model leverages linear aggregation of mutational scores on all possible sites in the latent space to decode $\\Delta\\Delta G$ value for deep mutations in parallel.\n\nSTRENGTHS:\n- The workflow is easy to understand, which proposes a lightweight solution for an important direction of research. \n- Compared to most existing work, the proposed method 'runs a strong backbone only once and a lightweight decoder N times in parallel'.\n\nWEAKNESSES:\n- The innovation is incremental. The main algorithm relies heavily on the existing AlphaFold2 model. \n- While the authors claim the main contribution is that they designed 'a simple, parallel decoding algorithm', this is not the first method that tries to decode all possible mutational scores from a large latent representation (a $L\\times 20$ matrix in this paper). See, for instance, https://arxiv.org/pdf/2304.08299.pdf. \n- Notations are poorly explained. For instance, the meaning of p, t, and superscription A, Y are undefined on page 4. \n- References are missed in many places (for instance, ESM2 in Table 3). Also please define abbreviations properly when they first appear (even when they are used widely). For example, AUC and MCC are on page 6.\n- A conclusion section is missed at the end.\n\nQUESTIONS:\n- How is the ratio '3%' observed in line 176?\n- Similarly, why $\\Delta\\Delta G<-0.5$ are considered stabilizing? Any reference here?\n- Since the authors use ProteinGym, is the proposed method applicable to amino acid addition and deletion?\n\nLIMITATIONS:\nAlthough the authors discussed limitations of the research in Section 6, they focused mainly on the technical limitations. No negative society impact was mentioned.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-06"}