SoluProtMut: Siamese Deep Learning for Predicting Solubility Effects of Protein Mutations with Experimental Validation

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Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results SoluProtMut: Siamese Deep Learning for Predicting Solubility Effects of Protein Mutations with Experimental Validation Jan Velecký , View ORCID Profile Hana Faldynová , View ORCID Profile Pedro Hermosilla , Nela Sendlerová , View ORCID Profile Mark Doerr , View ORCID Profile Sára Egersdorfová , View ORCID Profile Uwe Bornscheuer , View ORCID Profile Jiří Damborský , View ORCID Profile Zbyněk Prokop , View ORCID Profile Stanislav Mazurenko doi: https://doi.org/10.1101/2025.09.26.676459 Jan Velecký 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic 2 International Clinical Research Centre, St. Anne’s University Hospital Brno , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site Hana Faldynová 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic 2 International Clinical Research Centre, St. Anne’s University Hospital Brno , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Hana Faldynová Pedro Hermosilla 3 TU Wien , Vienna, Austria Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Pedro Hermosilla Nela Sendlerová 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic 2 International Clinical Research Centre, St. Anne’s University Hospital Brno , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site Mark Doerr 4 Department of Biotechnology & Enzyme Catalysis, Institute of Biochemistry, University of Greifswald , Greifswald, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Mark Doerr Sára Egersdorfová 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Sára Egersdorfová Uwe Bornscheuer 4 Department of Biotechnology & Enzyme Catalysis, Institute of Biochemistry, University of Greifswald , Greifswald, Germany Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Uwe Bornscheuer Jiří Damborský 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic 2 International Clinical Research Centre, St. Anne’s University Hospital Brno , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jiří Damborský Zbyněk Prokop 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic 2 International Clinical Research Centre, St. Anne’s University Hospital Brno , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Zbyněk Prokop For correspondence: zbynek{at}chemi.muni.cz mazurenko{at}mail.muni.cz Stanislav Mazurenko 1 Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University , Brno, Czech Republic 2 International Clinical Research Centre, St. Anne’s University Hospital Brno , Brno, Czech Republic Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Stanislav Mazurenko For correspondence: zbynek{at}chemi.muni.cz mazurenko{at}mail.muni.cz Abstract Full Text Info/History Metrics Preview PDF Abstract Protein solubility is an attractive engineering target because it is a critical property influencing the scalability of protein production and the success of therapeutic proteins in biomedical applications. However, predicting solubility changes upon mutation in silico is challenging due to data heterogeneity and protein bias. Here, we explore how different sources of solubility data can be used for machine learning and present SoluProtMut, a Siamese deep geometric neural network trained to predict the impact of mutations on protein solubility. Our final model was trained exclusively on deep mutational scanning data. We compare our model with five established solubility prediction methods. The model achieves state-of-the-art performance on an independent dataset of various proteins, especially in predicting the effects of multipoint mutations (informedness of 26.5 %). Our findings also reaffirm that the scarcity of solubility data continues to hamper progress in this field. To address this limitation, we experimentally quantified solubility changes for hundreds of single-point and multipoint mutants of haloalkane dehalogenase. Complemented with recent deep-mutational-scanning data on myoglobin, we employed both these data for external validation. Although the generalization to unseen proteins remains limited, our findings demonstrate the potential of integrating high-throughput assays with deep learning to improve the accuracy and scope of solubility prediction. Highlights - We present a novel anti-symmetric Siamese architecture for mutational prediction on structures built on graph-based convolutional neural networks ensuring SE(3) invariance. - We demonstrate that a model trained only on single-point mutants of a single protein derived from high-throughput experiments generalizes to multipoint mutants of unseen proteins, achieving the state-of-the-art binary prediction informedness of 26.5 %. - We address the key limitation in the domain by extending the available data with 277 single-point and multipoint mutants of haloalkane dehalogenase labelled in-house and a selection of recently published 1037 single-point mutants of myoglobin. - We systematically study how different data subsets affect the performance of the trained models, revealing that including yeast-derived high-throughput data in training hampers generalization to low-throughput assays but recovers the performance on the yeast-derived myoglobin dataset. 1. Introduction Protein solubility is a fundamental property of globular proteins with broad implications in both biotechnology and medicine. It is a maximum concentration at which a protein remains freely dissolved in solution under given conditions ( Kramer et al ., 2012 ). Low solubility often limits the yield of recombinant protein production, impacting the economy of industrial applications. It may also complicate the administration of protein biopharmaceuticals in sufficient dosing ( Shire et al ., 2004 ; Rosace et al ., 2023 ). As such, solubility has become an important target in protein design. Traditionally, solubility of mutant designs is assessed using classical biochemical assays, such as Native-PAGE or SDS-PAGE. More recently, high-throughput approaches emerged, particularly those involving deep mutational scanning (DMS), which allows a rapid and systematic screening of thousands of protein variants. These approaches often employ green fluorescent protein (GFP) with fluorescence signal as a proxy for solubility. One of these approaches utilizes the complementation of GFP fragments ( Cabantous, Terwilliger, et al ., 2005 ; Cabantous, Pédelacq, et al ., 2005 ), where a small non-fluorescent GFP fragment is fused to the protein of interest, and only upon expression and correct folding, the fluorescence is detected. Despite these advances, experimental approaches remain labour-intensive or costly, motivating the development of accurate in silico predictors. Early efforts to predict protein solubility began with the Wilkinson–Harrison model, which used a logistic regression to estimate the likelihood of soluble expression in E. coli ( Wilkinson and Harrison, 1991 ). Later, this model was revised to consider only turn-forming and charged residues ( Davis et al ., 1999 ). Afterwards, the development of solubility prediction methods split into two branches: (a) absolute predictors, which classify the protein as soluble or insoluble, and (b) mutational predictors, which assess the impact of specific mutations. Several absolute predictors are widely used today, such as SolPro ( Magnan et al ., 2009 ), PROSO II ( Smialowski et al ., 2012 ) or SoluProt ( Hon et al ., 2021 ), to name a few. These methods are typically validated for expression in E. coli , offering a strategy to assess the viability of heterologous expression. In contrast, mutational predictors are less common. Notable examples include OptSolMut ( Tian et al ., 2010 ), the first computational model and the first dataset for this task; and PON-Sol2 ( Yang et al ., 2021 ), which significantly expanded the training data by incorporating the available DMS data. A middle ground between absolute and mutational predictors is CamSol ( Sormanni et al ., 2015 ), which provides solubility profiles to guide site-specific design. Nevertheless, the state-of-the-art methods report a correct prediction ratio of around 70 % on test data, highlighting substantial room for improvement ( Yang et al ., 2021 ; Wee et al ., 2024 ). One of the major challenges is the training data heterogeneity, as annotations for protein solubility come from a wide selection of experimental assays – from low-throughput experiments for many proteins, often with precise quantifications, to high-throughput enrichment ratios collected for only a few proteins ( Velecký et al ., 2022 ). Here, we introduce SoluProtMut, a model for predicting the impact of mutations on protein solubility. With SoluProtMut, we delved into different solubility datasets to explore their machine learning potential. Our final model was trained exclusively on the DMS-derived data. SoluProtMut builds upon the IEConv architecture, originally developed for protein representation learning ( Hermosilla et al ., 2020 ). To adapt the model for mutational prediction, we employed a Siamese architecture ( Chicco, 2021 ), a strategy previously used in a neighbouring field of mutational stability prediction ( Zhou et al ., 2023 ; Zhang et al ., 2025 ). Our Siamese design enforces anti-symmetry ( Sanavia et al ., 2020 ) through a differential connection, diverging from the prior works that rely on regularization terms in the loss function. Our model outperformed the previous state of the art and displayed higher precision in identifying desolubilizing mutations, which is critical for avoiding detrimental designs in protein engineering. In addition, we assembled two new datasets for independent validation: myoglobin, from the previously published DMS data ( Küng et al ., 2025 ), and LinB haloalkane dehalogenase, new split-GFP-based data collected in-house. Our study revealed an evaluation dependence on a particular protein, highlighting the need for broader mutational solubility data covering unrepresented proteins. 2. Materials & methods Primary data source The mutational solubility data used in this study comprises protein sequences, specific mutations and their experimentally observed effects on solubility. Each datapoint thus represents a pair of protein variants (original and mutant) measured under equivalent experimental conditions, and importantly, within a single study. We acquired such data from SoluProtMut DB ( Velecký et al ., 2022 ), a curated mutational solubility database. The exported data (dump date: May 27, 2024) contains 32 992 datapoints across 103 proteins, 72 of which have a structure assigned from the Protein Data Bank. Each datapoint is labelled with one of the discrete solubility effect classes: highly desolubilizing (−−), desolubilizing (−), neutral (N), solubilizing (+) and highly solubilizing (++). It is worth noting that the database is class-imbalanced, with the desolubilizing cases substantially overrepresented over the solubilizing ones in a ratio of 7:2 (Table S1). Additionally, the class distribution among the variants of a protein is typically highly skewed towards one direction. For instance, only desolubilizing and only solubilizing mutations are reported for 6 and 13 proteins, respectively. Over 97 % of the data (32 081 datapoints) originates from deep mutational scanning (DMS) experiments, which combine generation of large mutational libraries, high-throughput population filtering, and deep sequencing to explore the mutational landscape. Three proteins were subjects of DMS campaigns ( Klesmith et al ., 2017 ; Wrenbeck et al ., 2019 ): levoglucosan kinase (LGK) from Lipomyces starkeyi , pyrrolidine ketide synthase (PKS) from Atropa belladonna and beta-lactamase (TEM) from E. coli . Each protein was assessed in two distinct assays, resulting in duplicated variants. It is important to note that high-throughput assay scores serve only as proxies for actual solubility. For instance, they may as well correlate highly with thermodynamic stability ( Klesmith et al., 2017 ). Training and test data We divided the SoluProtMut DB data into DMS and non-DMS sets, based on whether DMS was used in the experimental assay. The DMS data are well-suited for deep learning thanks to their abundance and relatively unbiased coverage of the mutational landscape. This should mitigate overfitting to the biases often observed in low-throughput methods: specific protein outcomes (e.g. highly soluble or insoluble proteins), particular amino-acid substitutions (e.g. data from alanine scanning), or specific positions in sequence (e.g. data from site-directed mutagenesis). In contrast, the non-DMS data are characterized by greater protein diversity, providing a more representative benchmark for assessing the generalization of a model across unseen proteins. Thus, the DMS data were used primarily for the main training, while the non-DMS data were intended for either fine-tuning or final model evaluation. The data splits and the overall study design are illustrated in Figure 1E . Download figure Open in new tab Figure 1. Design of this study. A: High-level architecture Siamese network. Our change predictor consists of two identical base networks (GCNN) with shared weights, one fed with a wild-type and the other with a mutant. The classification is based on the difference between the predicted solubility scores. B: Low-level architecture . The base network (GCNN) consists of an encoding layer, three rounds of convolution and pooling layers, and a double-layer perceptron that implements the final classification layer and produces a solubility score. Each convolution layer is doubled and utilizes a bottleneck connection. The green nodes are learnable. C: Convolution formula for the convolution step over the vertices closer than r Å (B r ) from the vertex . Kernels are learnable and parametrized by both sequential and Euclidean distances between the vertices. D: Protein representation . The structures inside the network are represented as linear point clouds, allowing on-the-fly creation of a multigraph for each convolution step. On-the-fly edges (dashed) connect close vertices in Euclidean space. E: Data processing . We conducted the study in three phases: training, evaluation and independent validation. We drew data from SoluProtMut DB after filtering and binarizing the classes. We divided these data into deep mutational scanning data (DMS) and non-DMS data. The DMS data come from three proteins (PKS, LGK and TEM) and two different assays (YSD and GFP), resulting in four experimental setups. We used these data to create several data splits and train multiple models in 5-fold cross-validation, each resulting in a 5-ensemble predictor. We created only one test set for LGK, comprising variants with a consistent effect on solubility in both assays. We weight-balanced each data split to counteract a higher abundance of the desolubilizing examples. The non-DMS data were used either to fine-tune the models or for evaluation. Finally, we collected solubility data for 277 haloalkane dehalogenase variants in a wet lab, using a split-GFP medium-throughput assay, to independently validate the resulting models. DMS data preprocessing To ensure the quality and consistency of the training data, we excluded datapoints originating from the Tat-export assay, following the authors’ observation about a high false detection rate of solubilizing variants ( Klesmith et al ., 2017 ). This only marginally reduced the number of available variants due to the overlap in the coverage by a second assay for each protein. After this exclusion, LGK was the only protein with duplicated variants labelled by two different assays – GFP and yeast surface display (YSD). The overview of the used DMS data is in Table 1 . View this table: View inline View popup Download powerpoint Table 1: Overview of deep mutational scanning experiments. These four DMS experiments provide training data of three proteins for the SoluProtMut predictor. The data comes from two different high-throughput assays (and also, host organisms), with LGK screened in both. The number of mutations roughly corresponds to the size of a respective protein with coverage from 66 % (PKS) up to 83 % (TEM). PKS stands out from the other two proteins with a high occurrence of rather solubilizing mutations. Next, we binarized the effects into two classes: negative (desolubilizing) and positive (non-desolubilizing), using a threshold of −10%, which was established as a threshold between desolubilizing and neutral mutations in previous works ( Klesmith et al ., 2017 ; Velecký et al ., 2022 ). This helped alleviate the imbalance between the amount of solubilizing and desolubilizing mutations. We created stratified splits for training and test subsets, with 12 % of the data reserved for testing, for three assays: PKS, TEM and LGK-GFP. Furthermore, we created a curated LGK dataset by sampling the datapoints with consistent solubility effects in both assays (YSD and GFP). The remaining datapoints were used for training. Additionally, we created a split for the entire DMS dataset by combining the respective splits of each DMS protein. Since PKS has no experimentally determined structure, we employed a homology model generated using I-TASSER with default parameters ( Yang et al ., 2015 ). To counteract the class imbalance, we applied class weighting to the created subsets, as training on unweighted data often resulted in the model predicting the majority class. In the case of the combined DMS set, we further rebalanced the weights protein-wise to ensure equal contribution of each protein to the training. Non-DMS data preprocessing As our chosen network architecture learns on structures, we first filtered out all examples without assigned structures or those whose structures had other than wild-type amino acids at the mutated positions. This resulted in 563 datapoints of 44 proteins in the dataset. We then split the data into training and test subsets as follows. Proteins observing mixed effects (both solubilizing and desolubilizing) for different mutations were kept for fine-tuning. Consequently, the holdout test set comprised remaining proteins with consistent or neutral effects, thus also including all single-datapoint proteins. The split was designed to prevent the model from learning protein-specific biases. To simplify the learning task, we binned non-DMS data into the positive (N, +, ++) and negative (−−, −) classes. Unlike the DMS data, no class- or protein-wise weighting was applied here due to the highly varying number of recorded examples per protein (from one to dozens) and many proteins featuring only one direction of effect for all their variants. Network design SoluProtMut is a deep learning model designed to predict qualitative change between two (wild-type and mutant) protein variants. We adopted Siamese architecture, which consists of a pair of identical base-model instances that share weights ( Figure 1A ). Each instance processes one of the two input structures and produces a score S ∈ [0,1]. The difference between the two scores is a basis for a binary prediction. Mutations with Δ S below and above 0.5 are classified as desolubilizing and solubilizing, respectively. To improve robustness, the final predictor is implemented as an ensemble of five base model pairs, with the final prediction determined by simple average voting. The underlying regressor of SoluProtMut is a geometric neural network tailored for learning from protein structures. It is a graph-based convolutional neural network (GCNN) that leverages insights from the 3D organization of proteins and is based on the IEConv architecture ( Hermosilla et al ., 2020 ), initially developed for structural classification tasks such as EC number or fold classification. The network operates in three logical stages ( Figure 1B ): (1) processing and encoding of the input protein structure, (2) hierarchical convolution and (3) final regression. First, a structure representation is derived from the backbone coordinates provided in the input PDB file ( Figure 1D ). The coordinates are normalized so that the bounding box of the point cloud is centred at the origin of the coordinate system. The model uses wild-type backbones (C-α atoms) along with the mutant sequences as inputs. This approach eliminates the need for mutant structures and makes the trained model robust to side-chain conformational changes or optimizations. The model input can be understood either as a linear vertex-weighted 3D graph or, equivalently, as a linear (ordered) point cloud. In both, each vertex or point corresponds initially to an amino acid, embedded in 3D space through its C-α atom. The vertex weights carry the information about the residue types, while the edges reflect peptide bonds between the residues. Each residue-type information is encoded using an 8-dimensional VHSE physicochemical descriptor ( Mei et al ., 2005 ). Thanks to the provided chemically meaningful features, the need to learn basic amino-acid properties from scratch is eliminated – a key distinction from the original IEConv design. Second, the structure representation undergoes rounds of convolution and pooling. Each round consists of two convolutional layers followed by a pooling layer. A special convolution operation (described further) is performed in the 3D neighbourhood of each vertex, which initially represents an amino acid and later becomes a meta-residue after pooling. Pooling halves the number of vertices using average feature pooling, with new coordinates computed as midpoints between paired vertices. The neighbourhood expands progressively at each stage, enabling the network to capture both local and global structural patterns. The last average pooling operates over all vertices while creating a global feature vector. Each representation in convolution is treated as an edge-weighted multigraph, generated on-the-fly from the point cloud representation ( Figure 1D ). The edges are generated between all vertices within Euclidean distance of r, progressively increasing from 8 to 16 Å with every convolution round. Importantly, the convolution kernel is trainable and parameterized by the linear distance (i.e. sequential) and the Euclidean distance between vertices ( Figure 1C ). This allows the network to distinguish between spatially close residues adjacent or distant in the primary sequence. The convolution layers are organized into residual bottleneck blocks surrounding the actual convolution operation, inspired by ResNet ( He et al ., 2016 ). This enables efficient propagation of local features to subsequent layers ( Figure 1B ). Since the convolution operates on these graphs, it is also rotationally and translationally invariant to the input structure. As the last step, the final score is produced by a double-layer perceptron (DLP) that operates on global features. This resulting regression value implicitly represents a solubility of the input structure, emerging from the differential training objective. To improve generalization and training stability, batch normalization layers are applied after each linear layer. The entire network has 2.6 million trainable parameters. A summary of key modifications implemented over the original IEConv study is provided in Table S2. Training procedure The initial training of the models was conducted in a five-fold cross-validation (CV5) setup, resulting in five independently trained models. The models were trained using a fixed learning rate scheduler with three learning rate stages. We used minibatch stochastic gradient descent with binary cross-entropy as the loss function, comparing the predicted solubility effect against the true class. For each fold, the model with the highest validation accuracy was retained for evaluation. To regularize training, we applied weight decay (5e-4). We augmented the training data by perturbing the C-α coordinates of each input pair with Gaussian noise: 𝒩(0, 0.05 2 ). Crucially, identical perturbations were applied to both the wild-type and mutant structures to preserve the relative geometry. We conducted fine-tuning experiments in two ways. In the full-model retraining, we started from a model trained on any two of the three DMS proteins and fine-tuned the entire network on the third, previously unseen protein. In the partial-model fine-tuning with only the non-DMS training subset, all the layers were frozen apart from the final regression module. Independent data collection We used haloalkane dehalogenase LinB (UniProt: D4Z2G1) as a target to collect data on mutational effects on solubility using the split-GFP assay ( Waldo et al ., 1999 ). In this assay, adjusted for solubility, GFP is divided into two non-fluorescent fragments: GFP 1-10 (detector) and GFP 11 (fusion tag). The tag is expressed in a fusion with a protein of interest, while the detector is produced and purified separately. The fluorescence is measured upon co-cultivation. A LinB substitution library with a GFP 11 linker was constructed via error-prone PCR ( Copp et al ., 2014 ). All plasmids were expressed in the Escherichia coli BL21(DE3) strain (New England Biolabs). For overnight growth and protein production in the 96-well microtiter plates, Luria-Bertani (LB) media (Sigma Aldrich) supplemented with a selective antibiotic was used. The expression was induced by IPTG (isopropyl β-d-1-thiogalactopyranoside, Duchefa Biochemie). Chemical cell lysis was performed using SoluLyse® protein extraction reagent (Genlantis), followed by centrifugation. The soluble supernatant was collected and mixed with the GFP 1-10 fragment in access. The GFP 1-10 fragment was produced and purified separately from the inclusion bodies, following the protocol by Cabantous and Waldo (2006) with minor modifications. After 5 hours of GFP fragments co-cultivation and protein maturation, the fluorescence was measured using a plate reader CLARIOstar® Plus (BMG LABTECH) with excitation/emission settings of 485 and 510 nm, respectively. The individual mutations were determined via Sanger sequencing (PlateSeq, Eurofins Genomics, Germany). A significant part of the LinB dataset was collected using a semi-automated robotic screening platform for enzyme libraries ( Dörr et al ., 2016 ). The system integrates robotic liquid handling, cell cultivation and downstream analysis in microtiter plates, including a fluorescence readout of the split-GFP assay. This allowed us to apply the same assay principles under more standardized and reproducible conditions, while increasing throughput compared to manual handling. Data for external validation We utilized recently published DMS data for human myoglobin (UniProt: P02144, PDB: 3RGK), obtained via the established YSD assay ( Küng et al ., 2025 ) and measured in duplication. We created three subsets of the 2351 single-point mutants reported to filter out variants with an ambiguous effect. Based on the mean and standard deviation (SD) of fitness, we kept approximately a third of the datapoints satisfying the following conditions: | mean | − SD > 0.05 (1037 datapoints), | mean | − 3 SD > 0 (966 datapoints) and | mean | > 0.01 ∧ SD < 0.01 (801 datapoints). Evaluation protocol To assess the performance of models, we employed informedness ( Powers, 2011 ) as the primary metric, as it is robust to class imbalance and provides an intuitive scale: 100 % indicates a fully informed predictor, 0 corresponds to a random or naïve predictor, and −100 % denotes a predictor that is always wrong. Informedness can be understood as balanced accuracy (BA) adjusted to the range [−100 %, 100 %]. For binary classification, informedness is given by I 2 = sensitivity + specificity − 1 = 2 BA − 1 = TP / P + TN / N − 1, where TP and TN are true positives and negatives, P and N are the total positive and negative cases, respectively. In subsets where some class was not represented, and thus informedness was undefined, we used the correct prediction ratio (CPR) as an alternative: CPR = # ( correct predictions ) / # ( all predictions ) CPR generalizes accuracy for multiclass classification ( Yang et al ., 2021 ). We applied bootstrap resampling to each prediction set with 1000 iterations to estimate prediction uncertainty. The resulting 95 % confidence intervals were derived using percentile-based estimation. 3. Results Cross-evaluation of the models Our DMS training data consists of three proteins: TEM, LGK and PKS. We trained models on every combination of these proteins. We also included a model trained solely on the LGK-GFP assay, bringing the total to eight trained models (Table S1). Each model was evaluated on all the DMS test subsets ( Figure 2 ). Download figure Open in new tab Figure 2. Cross-evaluation of models trained on different training subsets of deep mutational scanning (DMS) data. The first group of the models is trained on a single protein, the second group is trained on two proteins and the last model is trained on all three proteins. No strong generalization was observed across the DMS proteins – when a protein was excluded from the training, the model could not predict its solubility. The performance metric used is informedness (−100 % to 100 %), with a performance higher and lower than 0 (better and worse than that of a random predictor) highlighted in cyan or red, respectively. The lighter cyan signifies 95%-confidence intervals. As can be expected, every model performed best on the protein(s) it was trained on. The single-assay models achieved the following informedness scores on their respective test sets: 26.8 % for PKS, 33.2 % for TEM and 39.6 % for LGK-GFP. Interestingly, the TEM model performed better than the PKS model, despite having 15 % smaller data size. The DMS model, trained on all three proteins, clearly outperforms the others, achieving informedness scores ranging from 29.5 % for PKS to 61.0 % for LGK test subsets. We investigated whether the models could generalize to DMS proteins not included in their training. In most cases, no significant generalization was observed. However, two models, trained on TEM and TEM+PKS, both showed weak generalization to LGK, with informedness of 16.9 % and 19.0 %, respectively. The former also weakly generalized to PKS (9.7 %). While limited in practical significance, these results are statistically significant. Notably, in the case of LGK, generalization was only observed on the curated LGK test set and not on the LGK-GFP data alone. We also conducted experiments focused on optimizing training parameters and how stricter data splits by mutation position (bypos) affect the performance of our models. Detailed results are provided in the Supplement. Synergic effect of additional training data To better understand the patterns observed in Figure 2 , we further looked into how the inclusion of additional proteins or assays improves prediction accuracy on the original target protein ( Figure 3 ). The synergic improvement was observed for all three target proteins, as training on a combination of our three proteins always outperforms that on a single protein alone. In the most extreme case of predicting LGK mutants, the model performance increased from 39.6 % (LGK-GFP) to 61.0 % (DMS). Download figure Open in new tab Figure 3. Synergistic effect of additional data inclusion into the training on model performance. The chart shows how the prediction performance of base models, trained for a single protein target, changes when additional protein data are included in the training. Each column represents a specific base model and its corresponding test protein, e.g. the LGK model evaluated on the LGK data. All base models benefited from adding both remaining proteins. When only one was added, the performance of the model on the TEM dataset deteriorated. In the case of the LGK model, adding LGK data refers to incorporating the data from the YSD assay, complementing the GFP data. In the case of TEM, synergy was observed only when both other proteins were included in the training. Importantly, the synergic effect was not limited to combining different proteins, but it also appears when combining different assays for the same protein, as the case of LGK shows. Despite inconsistencies between the YSD and GFP assays, a model trained on both assays improves performance from 39.6 % to 49.4 %. Independent validation To assess the generalization capability of our models to proteins unseen in training, we performed a validation on independent data ( Figure 4 ). We used the non-DMS test subset, i.e. low-throughput data comprising a diverse set of proteins. This evaluation also included four fine-tuned models: three models fully fine-tuned on individual DMS proteins and one DMS model partially fine-tuned on the non-DMS training data. Only half demonstrated moderate generalization (lower confidence bound greater than 5 %) to the non-DMS proteins. None of them included the TEM data in the final training, and the two worst performers were the models trained for TEM. On the other hand, the best-performing model was the one trained on LGK, with an informedness of 45.6 %. Partial fine-tuning on the non-DMS data was unsuccessful, as the resulting model underperformed even compared to the DMS model from which it was derived. Download figure Open in new tab Figure 4. Validation of the trained models. The table shows the prediction performance of the various trained models on unseen proteins from the test non-DMS data. Some models do demonstrate significant generalization on these never-seen proteins. Interestingly, the models trained with the TEM protein data fail to generalize. The test set in each row corresponds to the results of the respective model on its designated test set, i.e. on the combination of the test subsets of each dataset included in the training, e.g. the TEM test data for the TEM model. Note that the non-DMS fine-tuning data does not overlap with non-DMS proteins from the test set. The performance metric used is informedness (−100 % to 100 %) – the value of zero corresponds to the random predictor and the performance higher or lower than that is highlighted in cyan or red, respectively. The lighter color signifies 95%-confidence intervals. Comparison against the state of the art We compared our models against a selection of existing solubility predictors using unseen data ( Table 2 ). We chose two of our models for this evaluation: (a) the LGK-GFP model, the best-performing single-assay model, and (b) the LGK model, the best-performing DMS-based model ( Figure 2 ). We included three existing previously published predictors validated for mutational prediction: structure-based OptSolMut ( Tian et al ., 2010 ) and sequence-based CamSol ( Sormanni et al ., 2015 ) and PON-Sol2 ( Yang et al ., 2021 ). The remaining mutational tools, namely PON-Sol ( Yang et al ., 2016 ), TopLapGBT ( Wee et al ., 2024 ) and DeepMutSol ( Wang et al ., 2024 ), were considered but excluded due to unavailability or technical constraints. For completeness, we also included two general-purpose solubility scoring methods: the revised Wilkinson-Harris method (rWH, Davis et al ., 1999 ), an early model for solubility prediction, and SoluProt as a popular representative of absolute solubility predictors. To enable comparison, we derived mutational classifications for rWH and SoluProt ( Hon et al ., 2021 ) based on the difference in predicted scores between original and mutant sequences. A complete list of all the tools we considered is provided in Table S4. View this table: View inline View popup Download powerpoint Table 2: Results of predictors for protein solubility on different subsets of the non-DMS data. The used metrics were informedness (I, ternary, from −100 to 100 %) and precision for the solubilizing/desolubilizing class (P+/P−, 0–100 %). For objective comparison with the OptSolMut and PON-Sol2 predictors, we used subsets that excluded the datapoints seen in the training by the respective tool. When a subset containing such data was used, both tools performed substantially better (as seen in the grey cells). Excluding these, our LGK predictor was leading in overall prediction performance as measured by informedness and precision for the desolubilizing class. Our model showed a considerably stronger performance in the case of multipoint mutants. We used the non-DMS dataset for the comparison, in which datapoints were binned into three classes: desolubilizing, neutral and solubilizing (−, N, +, respectively). To ensure a fair and objective comparison between predictors, we constructed two evaluation subsets excluding datapoints from either the OptSolMut or the PON-Sol2 datasets. We also created the third subset, which consisted of all the multipoint mutants only. The entire non-DMS dataset was also used for evaluation, as neither of our chosen SoluProtMut models had been trained on these data. Using these four overlapping subsets allowed us to avoid an otherwise excessive reduction of datapoints available for analysis. The performance results for each model across these subsets are in Table 2 . Our LGK model outperformed existing solubility predictors in terms of informedness. It exceeded the performance of OptSolMut by 6.8 pp, PON-Sol2 by 4.5 pp, SoluProt by 3.4 % and CamSol by 3.3 %. Notably, both mutational predictors in the test showed a significant drop in performance when evaluated on unseen proteins, scoring informedness of only 6.8 % and 6.3 %. Surprisingly, SoluProt, a predictor not explicitly designed for mutational analysis, outperformed both, highlighting the limitations of current mutational predictors. Our LGK model, PON-Sol2, SoluProt or CamSol each scored best at least in one of the evaluation categories (highlighted in Table 2 ). The least performing model is almost consistently rWH, often yielding negative informedness. Nonetheless, this is an expected outcome as its simplistic design considers only eight amino-acid types. As a result, it misclassifies 161 impactful mutations, treating substitutions among the remaining twelve amino-acid types as neutral. Furthermore, SoluProtMut demonstrated a clear advantage in identifying desolubilizing mutations (precision of 65.5 %), whereas SoluProt was more effective at detecting solubilizing mutations (precision of 34.4 %). More importantly, our model was significantly ahead of the competing models in predicting the effects of multipoint mutations, achieving informedness of 26.5 %, 8.8 pp above the next best model, CamSol. Validation on external data We collected data on the solubility effect for a couple of hundred mutant variants of LinB. In addition, we used 1037 mutants from the recently published data on the myoglobin protein. These datasets were not considered in the development, making them ideal for independent validation ( Figure 5 ). We also included PON-Sol2 and CamSol in this validation. Download figure Open in new tab Figure 5. Validation on the external data (informedness), which comprise mutants of LinB haloalkane dehalogenase and myoglobin. Data for both were collected after the training phase of SoluProtMut. For myoglobin, we show results on the full dataset as well as on a reduced dataset by quality-control filtering. While some of the models showed promising results on the protein-diverse non-DMS data, they struggled to correctly predict mutational effects on these two proteins. In the case of LinB, the highest informedness achieved was 13.8 % (the TEM model), followed by 12.6 % (the DMS model) and 12.3 % (the fine-tuned DMS model). The remaining models scored below 10 %. In the case of the reduced myoglobin dataset (1037 datapoints), the highest informedness was 23.7 % for PON-Sol2, followed by 17.8 % for the TEM model with the more stringent data split strategy by position (see the Supplement). Some of the remaining models showed negative informedness, such as the DMS model (−27.3 %) or CamSol (−22.3 %). All but one model showed higher informedness on the reduced dataset than on the full dataset. These conclusions hold for the two alternative reductions as well (Figure S2). Per-protein accuracy variation Considering the results on external data, we investigated how the prediction accuracy varies across the 44 proteins of the non-DMS dataset ( Figure 6 ). We focused on the LGK model here, as it demonstrated the best performance on the independent test data. After excluding single-example proteins, the model achieved a 100 % success rate on five proteins, and only two proteins showed a 0 % success rate. Our model outperformed random guessing for the absolute majority of the considered non-DMS proteins (23 out of 34). The hardest proteins to predict were those primarily containing mutations classified as neutral, which our binary predictor cannot classify correctly. Both solubilizing and desolubilizing effects were predicted among proteins with multiple mutants. Interestingly, this contrasts with the PON-Sol2 predictions, which generally are unvaried per protein (Figure S3). Download figure Open in new tab Figure 6. Per-protein performance of our LGK model on unseen proteins. The evaluation on 34 previously unseen non-DMS proteins (n = 553) shows that the predictor performance varies per protein. The left part of the chart shows the per-protein counts of the correctly (saturated colors) and incorrectly (light colors) predicted de/solubilizing (blue/orange) or neutral (gray) effects of mutations. The proteins are sorted by the correct prediction ratio (CPR, the right part) of the model on the given protein. We chose CPR as a number of proteins contain only a single type of effect. The overall CPR is 44.5 % and our predictor outperforms random guessing for most proteins. For comparison, the CPR corresponding to that of a random predictor (⅓) is drawn by the black line. Note that the proteins with only one example in the dataset were excluded from the chart. 4. Discussion In this work, we leveraged the anti-symmetric design, a property found crucial for the reliability of mutational predictors for stability ( Sanavia et al ., 2020 ), and recent progress in structure-based deep learning to tackle the problem of protein solubility prediction. Our results demonstrate that SoluProtMut surpassed existing predictors on the non-DMS data in all tested scenarios ( Table 2 ). The lead of our model is most pronounced in the case of multipoint-mutant effect prediction, where it reached informedness of 26.5 %, despite being trained exclusively on single-point mutations. We substantially extended the available data for the problem of mutational solubility prediction by collecting 277 new datapoints for haloalkane dehalogenase LinB in-house, which we will deposit in SoluProtMut DB ( Velecký et al ., 2022 ). We used these, along with myoglobin DMS data ( Küng et al ., 2025 ), for external validation. Additional filtering was needed for the myoglobin data to reduce noise in the validation scores. We tried three criteria, all yielding comparable results (Figure S2). Although our models did not generalize well to these data ( Figure 5 ), this limitation appears protein-specific rather than systemic, as we observed variation in prediction performance across different proteins ( Figure 6 ). Furthermore, LinB is known to be a challenging protein target due to its high aggregation propensity and poor solubility, particularly at higher protein concentrations ( Havlásek et al ., 2025 ), posing as an ideal validation target. Importantly, SoluProtMut does not exhibit a per-protein prediction bias, which we noticed with PON-Sol2, that tends to predict a single class per protein (Figure S3). This suggests that PON-Sol2 may tend to predict whether a mutated protein is a difficult target for solubility design, rather than the effect of the mutation, although this hypothesis will need further investigation on a larger dataset. Among the simple models, trained on a single protein, the PKS model showed unexpectedly low test performance, 7 pp lower than the TEM model, which has 20 % less training data. This may be attributed to two key differences in the data: lower coverage of the PKS mutational landscape (66 %) compared to TEM (75 %, Table 1 ) and reliance on a homology model rather than an experimentally determined structure. While experimenting with different combinations of the DMS data, we observed that incorporating data from different proteins or even assays not only broadened the scope of a model but also synergically enhanced model performance ( Figure 3 ). A particularly illustrative case is the LGK model, where supplementing the GFP assay data with the additional data from the YSD assay led to notable improvements: +9.8 pp on the test data and +14.2 pp on the independent data. We hypothesize that this is due to an implicit regularization effect introduced by mixing assay data, which introduced datapoints with inconsistent effects, leading to improved generalization. Strong performance on DMS test subsets does not always translate to generalization. All TEM-based models failed to generalize to non-DMS data ( Figure 4 ). This may stem from the TEM data being derived from the YSD assay, possibly overfitting a model to yeast-specific features. The non-DMS data then predominantly originate from E. coli . This explanation is further supported by the validation results on myoglobin data, from another YSD assay, where PON-Sol2 and the TEM (bypos) model significantly outperformed other models ( Figure 5 ). Note that a significant part of the PON-Sol2 training dataset is yeast-derived solubility. No similar observation was made with the LGK data, which also contains the yeast measurements. Our study also highlights the limitations imposed by data scarcity and imbalance. Even though SoluProtMut showed top-ranking performance in the benchmark experiments, the overall accuracy of the tool is moderate, and there is room for improvement, e.g. by increasing the training dataset size ( Figure 3 ). Moreover, drawing statistically significant conclusions is difficult due to the wide confidence intervals, sometimes as wide as 38.5 pp for non-DMS data or 30 pp for LinB. The issue of insufficient data on mutational solubility was already raised in prior studies on predicting solubility ( Sormanni et al ., 2015 ; Yang et al ., 2021 ; Wang et al ., 2024 ). Solubility is a context-dependent phenotype, making it inherently difficult to model across heterogeneous data. Solubility measurements are condition-dependent and influenced by pH, temperature, buffer composition or an expression system ( Baranowski et al ., 2025 ). Similar to previous predictors, our model abstracts away these factors, assuming that identical mutations yield similar effects across conditions. Thanks to it, we could avoid overfitting our model to experimental conditions (rarely annotated) or excessive data pruning. On the other hand, it constitutes a significant limitation of the state of the art, which is probably why there is currently no predictor performing best in all use cases. For instance, PON-Sol2 or our TEM (bypos) model seems to be a better choice for predicting solubility in yeast over CamSol or our LGK model, which performed best overall. Moreover, even synonymous mutations can affect expression due to codon usage, as manifested by intra-variant score deviations in DMS studies ( Klesmith et al ., 2017 ; Küng et al ., 2025 ), therefore, adding this information to predictors might be another promising strategy to explore. Finally, transfer learning offers another promising path forward. Our network could be pre-trained on related tasks, such as mutational stability prediction, where extensive data are readily available in databases like FireProt DB ( Stourac et al ., 2021 ) or ProThermDB ( Nikam et al ., 2021 ). In contrast to solubility data, these databases span hundreds of proteins and provide continuous and high-quality labels, possibly enabling models to learn generalizable protein features through regression, such as protein folding principles, that also determine solubility. These labels are well-defined quantities of kinetic and thermodynamic stability ( Musil et al ., 2019 ), providing more homogeneous data. Interestingly, pre-training suits the modular nature of Siamese architecture as it does not require differential data. The base network, therefore, can also be trained independently on absolute solubility or stability values, leveraging datasets beyond mutation-paired examples. 5. Conclusions This study addresses the challenge of predicting solubility changes upon a mutation. We introduce SoluProtMut, a model based on a novel differential Siamese architecture with implicit anti-symmetry, designed to predict the impact of mutations on solubility using structural data. The underlying convolutional network is capable of learning from 3D protein structures. SoluProtMut is the first model in this domain trained solely on data from DMS assays, yet it outperforms the state-of-the-art methods, trained at least partially on the scarce low-throughput data. Thus, our study has proven that high-throughput data are auspicious in tackling the lack of protein mutational data. We believe the new experimental data on the solubility of a couple of hundred LinB mutants collected within this study will also help address this problem. However, more comprehensive and less imbalanced solubility data are needed to unlock the full potential of deep learning and to enable more statistically robust conclusions. Looking ahead, promising directions include transfer learning from related domains such as protein stability prediction, where abundant data are available. Another interesting direction is the incorporation of experimental conditions into models, as they strongly influence solubility, yet are rarely annotated. Lastly, we encourage future machine learning developers to report confidence intervals in the validation of their models, as they are essential for interpreting the predictor reliability. Availability and implementation We implemented SoluProtMut in Python using PyTorch ( Paszke et al ., 2019 ), PyTorch Geometric ( Fey and Lenssen, 2019 ) and Biopython ( Cock et al ., 2009 ). The model will be made publicly available through a web interface upon submission at huggingface.co/spaces/vvelda/SoluProtMut. Training of the ensemble of 5 base-network instances takes 1.5 days for the largest data split of all DMS proteins (15 741 training datapoints) using a single CUDA-enabled GPU (Nvidia 1080 Ti). Nonetheless, inference takes only seconds per mutation on a CPU, i.e. no specific or performant hardware is required. The provided statistics and analyses were created using pandas ( McKinney, 2010 ) and the R reactable, boot and ggplot2 ( Wickham, 2011 ) libraries. Acknowledgments The authors would like to express their thanks to the Czech Ministry of Education, Youth and Sports (TEAMING CZ - CZ.02.01.01/00/23_029/0008437-, EXCELES Onco - LX22NPO5102, ESFRI RECETOX - LM2023069) and the Czech Science Foundation (GX25-17329X). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 857560 TEAMING, and by the European Union Centre of Excellence CLARA (101136607). The article reflects the author’s view, and the Agency is not responsible for any use that may be made of the information it contains. Computational resources were provided by the e-INFRA CZ and ELIXIR-CZ projects (LM2023055 and LM2018140), supported by the Ministry of Education, Youth and Sports of the Czech Republic. We are grateful to the Deutsche Forschungsgemeinschaft (DFG, INST 292/118-1 FUGG) and the federal state Mecklenburg-Vorpommern for financing the LARA robotic platform. Funder Information Declared Czech Ministry of Education, Youth and Sports , CZ.02.01.01/00/23_029/0008437 , LM2023069 , LM2023055 , LM2018140 , LX22NPO5102 the Czech Science Foundation , GX25-17329X European Union’s Horizon 2020 research and innovation programme , 857560 European Union Centre of Excellence CLARA , 101136607 Deutsche Forschungsgemeinschaft , DFG, INST 292/118-1 FUGG the federal state Mecklenburg-Vorpommern Footnotes ↵ # joint first authors References ↵ Baranowski , C. et al. ( 2025 ) Can protein expression be ‘solved’? Trends in Biotechnology . ↵ Cabantous , S. , Terwilliger , T.C. , et al. ( 2005 ) Protein tagging and detection with engineered self-assembling fragments of green fluorescent protein . Nat Biotechnol , 23 , 102 – 107 . 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Share SoluProtMut: Siamese Deep Learning for Predicting Solubility Effects of Protein Mutations with Experimental Validation Jan Velecký , Hana Faldynová , Pedro Hermosilla , Nela Sendlerová , Mark Doerr , Sára Egersdorfová , Uwe Bornscheuer , Jiří Damborský , Zbyněk Prokop , Stanislav Mazurenko bioRxiv 2025.09.26.676459; doi: https://doi.org/10.1101/2025.09.26.676459 Share This Article: Copy Citation Tools SoluProtMut: Siamese Deep Learning for Predicting Solubility Effects of Protein Mutations with Experimental Validation Jan Velecký , Hana Faldynová , Pedro Hermosilla , Nela Sendlerová , Mark Doerr , Sára Egersdorfová , Uwe Bornscheuer , Jiří Damborský , Zbyněk Prokop , Stanislav Mazurenko bioRxiv 2025.09.26.676459; doi: https://doi.org/10.1101/2025.09.26.676459 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Bioinformatics Subject Areas All Articles Animal Behavior and Cognition (7618) Biochemistry (17635) Bioengineering (13859) Bioinformatics (41846) Biophysics (21401) Cancer Biology (18534) Cell Biology (25422) Clinical Trials (138) Developmental Biology (13352) Ecology (19860) Epidemiology (2067) Evolutionary Biology (24285) Genetics (15582) Genomics (22463) Immunology (17700) Microbiology (40298) Molecular Biology (17141) Neuroscience (88424) Paleontology (666) Pathology (2825) Pharmacology and Toxicology (4813) Physiology (7633) Plant Biology (15107) Scientific Communication and Education (2042) Synthetic Biology (4284) Systems Biology (9808) Zoology (2267)