Our studies identify four f-divergence functions, namely cross-entropy, Kullback-Leibler (KL), reverse KL, and Jensen-Shannon, that can be effectively integrated with the generative adversarial imputation network to generate imputed values without any assumptions, and mathematically prove that the distribution of imputed data using sc-fGAIN algorithm is same as the distribution of original data. Real scRNA-seq data analysis has shown that, compared to many traditional methods, the imputed values generated by sc-fGAIN algorithm have a smaller root-mean-square error, and it is robust to varying missing rates, moreover, it can reduce imputation variability. The flexibility offered by the f-divergence allows the sc-fGAIN method to accommodate various types of data, making it a more universal approach for imputing missing values of scRNA-seq data.Comprehensive analysis of single-cell RNA sequencing (scRNA-seq) data can enhance our understanding of cellular diversity and aid in the development of personalized therapies for individuals. The abundance of missing values, known as dropouts, makes the analysis of scRNA-seq data a challenging task. Most traditional methods made assumptions about specific distributions for missing values, which limit their capability to capture the intricacy of high-dimensional scRNA-seq data. Moreover, the imputation performance of traditional methods decreases with higher missing rates. We propose a novel  The genomics and transcriptomics studies have been revolutionized by the swift advancements in single-cell RNA sequencing (scRNA-seq) technology, which enable researchers to simultaneously profile the transcriptomes of thousands of individual cells , 2, provThe missing values, which account for more than 50% and sometimes over 90% of the scRNA-seq data , 15, areNumerous computational techniques –25 have f-divergence in the GAN’s architecture.The outstanding performance of deep learning methods have attracted lot of research attention in the field of computational biology . Deep gefGAIN, standing for f-divergence based generative adversarial imputation network, for the scRNA-seq data analysis. Our work has two major novelties compared with vanilla GAIN and other existing methods. For the first time, our studies identify four f-divergence functions, namely cross-entropy, Kullback-Leibler (KL), reverse KL, and Jensen-Shannon, that can be integrated with GAIN to generate imputed values without any assumptions, and mathematically prove that the distribution of imputed data using sc-fGAIN algorithm is same as the distribution of original data. Finally, we evaluated the effectiveness and potential limitations of sc-fGAIN method by training it on real scRNA-seq data and comparing it to other imputation methods.In this work, we are motivated to develop a novel imputation approach that does not rely on distribution assumptions, called sc-x ∼ p(x)) d. If the f-divergence based objective function is defined by thethen, given a fixed generator G, there always exists one optimal discriminator D* if f = CE, FKL, RKL, JS, PC.Proof. The f-divergence based objective function G, the optimal Discriminator D* is obtained by solving the equation f-divergence’s output activation functions and conjugate functions given in Sϕ(x), we identified five f-divergences, including CE, FKL, RKL, JS, and PC, that always have an optimal discriminator D* given a fixed G, for i ∈ {0, 1}d,After inserting the D* derived in Theorem 1 into the objective function G as follows:If we substitute the optimal discriminator Theorem 2. The f-divergence based loss functionhas a global minimum if and only if the density p satisfies:for each i ∈ {1, …, d}, x ∈ Xandsuch that p(h|mi = t) > 0. And this theorem is true only if f = CE, FKL, RKL, JS.et al’s work  using the min-max normalization formula. Our simulation studies revealed that running the sc-ation as , while eation as  also shoe Github .fGAIN’s imputation algorithm based on different f-divergence functions and compare with other imputation methods. In the first type of experiment, we intentionally introduced missing values into a portion of the data with varying rates of missingness to assess the effectiveness of sc-fGAIN in imputing missing values.Next, we designed different experiments and used real scRNA-seq data with known ground truth values to evaluate the accuracy of sc-fGAIN algorithm and other imputation methods, we computed the root-mean-square error (RMSE) between the true values and the imputed values in the scRNA-seq data, which has been used in many studies [Yi and To validate the imputation accuracy of sc- studies , 43. TheMost traditional imputation methods do not perform well when the cells are difficult to differentiate from one another. In order to achieve a high level of imputation accuracy for comparison purposes, we select a small subset of genes showing significant differential expression (DE) for the imputation process. Many methods –46 have fGAIN method outperformed most traditional imputation methods, with the CE and JS based sc-fGAIN method achieving the smallest RMSE score. Notably, our sc-fGAIN method exhibits remarkable robustness and minimal sensitivity to missing data rates, surpassing traditional imputation methods even under high missing data scenarios. The exceptional performance can be attributed to a fundamental advantage of our sc-fGAIN algorithm: it does not impose any assumptions about the underlying data distribution. This characteristic enhances the versatility of our approach, making it resilient against varying missing rates. Moreover, our method’s reliability is further underscored by rigorous theoretical analysis, confirming that the distribution of imputed data using the sc-fGAIN algorithm closely mirrors that of the original data. In comparsion, MAGIC only performed well when the missing rate was relatively low, but its performance deteriorated with higher dropout rates, moreover, PBLR and scImpute showed poor performance across all missing rates, and as the missing rate increases, all traditional methods’ imputation accuracy declines.fGAIN algorithm is influenced by the selection of f-divergence functions. One major reason for the poor performance of traditional methods is the assumption that the missing values follow some specific distributions, which could not accurately capture the intricacy of the high-dimensional scRNA-seq data, and they rely on additional information about adjacent genes for constructing k-nearest neighbor graphs and clustering before imputation. Given that single-cell RNA sequencing data often exhibits a high dropout rate, our sc-fGAIN method outperforms many traditional methods and proves to be superior in handling scRNA-seq data. fGAIN method outperforms all the traditional methods when the missing rate is very high.Furthermore, the results presented in fGAIN algorithm, we divided the entire dataset across genes into three equally sized parts and conducted imputation experiments on each split dataset. We also calculated the RMSE metric between the observed dataset and the combined imputed split data, which allows us to compare the results with those presented in Tables fGAIN method is not very sensitive when the missing rate is low, but its performance will improve when the rate is high. Moreover, we observed that the sc-fGAIN method takes shorter running times to impute smaller split datasets. This observation presents an opportunity to leverage parallel computing and reduce imputation time by partitioning large datasets into smaller subsets across genes.To investigate the impact of data size on the performance of the sc-fGAIN (FKL) and MAGIC methods achieves the lowest RMSE scores across all missing rates, and the other two sc-fGAIN methods based on CE and JS divergences remain competitive compared with the PBLR and scImpute, particularly when dealing with the data with high dropout rates. Both MAGIC and SAVER methods performed well when the missing rate was relatively low, but their performance deteriorated with higher dropout rates. MAGIC and sc-fGAIN are two competitive methods, their performance difference is small, this difference could be partially due to different normalization and rescaling approaches employed by MAGIC and sc-fGAIN, which can have an impact on how imputed values align with the original data. Our studies also found that, the sc-fGAIN method’s performance is influenced by the choice of loss function which is described by the f-divergence, as evident from the results in Tables fGAIN offers a more comprehensive and versatile approach compared to the original GAIN model. To further explore the capabilities of sc-fGAIN, we have developed a convenient Huggingface tool. This tool, accessible at [f-divergence function for imputing a given dataset, leading to the lowest RMSE score. The corresponding code is hosted on GitHub at [In another experiment, we included a larger dataset consisting of 2000 highly differentially expressed genes as input. These genes were selected using a similar approach as the work , 43. Thesible at , provideitHub at .fGAIN method is a generative model that does not rely on any predefined data distribution assumptions. As a result, it is theoretically expected to mitigate the imputation bias compared to some traditional methods.Single-cell RNA sequencing data frequently encounters high dropout events, some traditional imputation methods make assumptions about the data distribution when filling in missing values. However, these assumptions can introduce bias and potentially lead to incorrect estimates of gene expression levels, thereby affecting downstream analysis. In contrast, the proposed sc-To assess the effectiveness of the imputation methods in reducing prediction variability, the gene-specific standard deviation (SD) across cells can be compared before and after imputation in the scRNA-seq data analysis. This standard deviation measures the inherent variability in gene expression for each gene across the single cells. A reduction in the standard deviation after imputation suggests that the imputation method has reduced prediction variability for the given gene, which also indicate that the imputed values have brought the data closer to a more stable or less noisy state. If the imputation method is not well-suited to the data or if it makes incorrect assumptions about the data distribution, there will be an increase in standard deviation after imputation.fGAIN methods, by leveraging generative adversarial networks and utilizing different f-divergences , overcome the limitations imposed by the assumptions made in traditional imputation methods. When using the sc-fGAIN methods, the resulting standard deviation values are consistently lower compared to traditional imputation methods. All the median values are lower than 0.1 with small variations, which indicates a significant decrease in the variability of the imputed values compared to the initial missing values. Among the traditional methods, only MAGIC demonstrates comparable performance to our sc-fGAIN method. However, it is important to note that our sc-fGAIN method offers flexibility in choosing different f-divergences, allowing for better adaptation to diverse data patterns. This finding suggests that imputation using sc-fGAIN reduce the imputation variability compared to traditional methods. Consequently, sc-fGAIN enables accurate imputation of missing expression values without significantly altering the overall variability of the data, thereby facilitating improved downstream analyses of single-cell RNA sequencing data.In contrast, our sc-f-divergence based generative adversarial imputation network method, called sc-fGAIN, to impute missing values in single-cell RNA sequencing data. Unlike some traditional imputation methods, sc-fGAIN employs a generative model to generate synthetic values without making any distribution assumptions, the missing values are imputed by training two neural networks whose objective functions are described by f-divergence. Our theoretical studies, for the first time, identified only four f-divergences, namely cross-entropy, forward Kullback-Leibler (KL), reverse KL, and Jensen-Shannon, that can be effectively used as loss functions to train the sc-fGAIN algorithm to generate imputed values without any assumptions, and mathematically proved that the distribution of imputed data using sc-fGAIN algorithm is same as the distribution of original data.In this work, we have developed a novel fGAIN method has many advantages compared with some traditional imputation methods and vanilla GAIN. Specifically, the imputed values generated by sc-fGAIN have a smaller root-mean-square error compared to many traditional methods. Importantly, the performance of sc-fGAIN is robust to varying missing rates of scRNA-seq data, whereas most traditional methods’ performance will deteriorate with higher missing rates. The studies also indicate that the performance of sc-fGAIN is sensitive to the choice of f-divergence used in the loss function. So, the proposed sc-fGAIN algorithm is more comprehensive and versatile compared to the naive GAIN model. Our tool can also help to identify a suitable f-divergence function to optimize the performance of the sc-fGAIN algorithm. Moreover, our investigation also revealed that the sc-fGAIN method can reduce imputation variability by producing smaller standard deviations of gene expression values compared to most traditional methods. This indicates that sc-fGAIN is capable of accurately imputing missing values without altering the overall variability of the data. Such an ability can help improve downstream analyses that rely on accurate estimation of gene expression levels.Our experiments with public scRNA-seq data have shown that the proposed sc-fGAIN has some limitations that should be acknowledged. One such limitation is its training speed, particularly when working with large datasets. For instance, analyzing the scRNAseq dataset GSE118767 using sc-fGAIN can take approximately 3 hours on a Tesla V100-SXM2 16GB GPU. However, there are several approaches that can be implemented to mitigate this issue, including reducing the batch size, minimizing the number of iterations, and partitioning the dataset into smaller subsets for separate imputations. Our investigations have revealed that employing these strategies does not significantly compromise the accuracy of the results, making them feasible solutions for addressing the training speed limitation. Another limitation we acknowledge is our inability to distinguish between biological zeros (genes that were genuinely not expressed during sequencing) and technical zeros (genes that were expressed during sequencing but not accurately measured), which has been investigated using a low-rank matrix approximation method [fGAIN in enhancing the quality of single-cell RNA sequencing data and facilitating more precise and reliable downstream analyses.Despite its promising potential, sc-n method  recentlyS1 AppendixfGAIN Algorithm.Detailed proof of the Theorem 1-2 in the Section: Theoretical analysis of sc-(PDF)Click here for additional data file.


Personalised cancer screening before therapy paves the way toward improving diagnostic accuracy and treatment outcomes. Most approaches are limited to a single data type and do not consider interactions between features, leaving aside the complementary insights that multimodality and systems biology can provide. In this project, we demonstrate the use of graph theory for data integration via individual networks where nodes and edges are individual-specific. We showcase the consequences of early, intermediate, and late graph-based fusion of RNA-Seq data and histopathology whole-slide images for predicting cancer subtypes and severity. The methodology developed is as follows: (1) we create individual networks; (2) we compute the similarity between individuals from these graphs; (3) we train our model on the similarity matrices; (4) we evaluate the performance using the macro F1 score. Pros and cons of elements of the pipeline are evaluated on publicly available real-life datasets. We find that graph-based methods can increase performance over methods that do not study interactions. Additionally, merging multiple data sources often improves classification compared to models based on single data, especially through intermediate fusion. The proposed workflow can easily be adapted to other disease contexts to accelerate and enhance personalized healthcare. Many methods for disease subtyping analyses rely on a single data modality only. However, one modality is unlikely to be informative enough to capture the whole complexity of complex diseases. In addition, a large panel of data is available, making multi-modality integration realistic. More and more studies investigate combining multiple data sources36 to overcome the oversimplification of approaches based on a unique data type. For instance, multiple studies investigate the benefits of combining images, and genomic data44.Disease subtyping refers to the identification of homogeneous groups of patients. It can be used to detect a disease’s severity or target treatments with the highest probability of success. Disease subtyping is essential in cancer research48 performs data fusion and dimensionality reduction at the same time. This method uses a Gaussian latent variable model with lasso-type penalty terms to induce sparsity in the coefficient matrices toward feature selection. One drawback of this approach is its high computational complexity. An alternative is Affinity Aggregation for Spectral Clustering23. The main idea is to compute a matrix of similarity between samples for each data source . Then, these multiple affinity networks are clustered via Spectral Clustering using linear combination with weights optimised using multiple kernel learning. In the same vein, Similarity Network Fusion (SNF) (53) was implemented to combine multiple similarity matrices into a single one by iteratively updating the matrices to make them more and more similar until the algorithm converges. This final matrix becomes the new input to the classification algorithm. Later, regularised unsupervised multiple kernel learning49 was introduced. It extends multiple kernel learning for dimensionality reduction approaches with a regularisation term to avoid overfitting during the optimisation procedure and using several kernels per data type.Often, late integration is performed. In such studies, the data sources are investigated independently before classification results are merged. Nevertheless, independent analyses may lead to inconsistent outcomes that are complex to aggregate. The main disadvantages of this method are that it does not take advantage of the possible complementarity of the modalities. Another standard integration procedure is early fusion, which considers the concatenation of the data sources before applying a machine-learning model. Whereas this solution is simple to implement, concatenation may decrease the signal-to-noise ratio in each data modality if not processed appropriately, as it increases the input space’s dimensionality, and potentially introduces irrelevant information that can decrease the model’s performance. In the last decade, several developments have been proposed to combine data between the start and end steps to solve these issues. For example, iCluster16. Exploiting individual-specific interactions rather than population-level systems will help capture the heterogeneity between individuals and enhance the identification of new biomarkers for precision medicine. This observation paves the way for developing individual networks (INs). INs are networks where nodes and/or edges are individual-specific. For each individual, nodes are variables , and edges show the link between these variables for that individual. Since INs represent individual relations between variables, we can readily use them for precision medicine. Individual networks can be inferred via multiple approaches. For example, individual’s variables values  can be superimposed to a reference network obtained from external knowledge 39, but then only node values will differ between individuals and not the graph topology. Another option is Linear Interpolation to Obtain Network Estimates for Single Samples (LIONESS)32. LIONESS computes edge weights from the difference in edge weights for a network constructed using all the samples and a network reconstructed using all but the sample of interest. Single sample networks based on the Pearson correlation (ssPCC) algorithm37 are also built from the perturbation of an individual against a group of given samples. These individual networks are derived from the perturbation of the Pearson correlation caused by the addition of this individual from a different population. Alternatively, an edge weight can be computed without a reference panel by adding Z-scores of log-transformed values of the two associated nodes29 or by using repeated measurements per variable per individual. Recent work11 explores individual networks for clustering tasks, which fall under unsupervised learning. In contrast, this work focuses on the supervised scenario, where we harness the power of INs for supervised tasks. The performance of supervised data integration methods in association with INs remains to be investigated. In this project, we explore three main questions. We study to what extent it can predict disease subtypes and severity from the patient data. We examine which modality yields the best prediction. We leverage the consequences of using individual networks to combine two modalities at various steps, keeping the rest of the pipeline unchanged.Most of the graph analyses for complex diseases aggregate information across a whole cohort, failing to detect individual characteristicsWe developed a multi-step workflow see Fig.  to predi54 (https://www.cancer.gov/tcga). We focused on three use cases: prostate cancer severity using the Gleason score, Brain low-grade gliomas (lgg) versus Glioblastoma multiforme (gbm) differentiation, and lung adenocarcinoma (luad) versus lung squamous cell carcinoma (lusc) differentiation. An overview of the data structure is presented in Table 57.Results on the impact of using individual graphs or not are based upon publicly available real-life data generated by the TCGA Research Network14, and prostate cancer stages are commonly described according to the Gleason Score, which helps evaluate the prognosis55. This score is derived from the appearance of cancerous cells that can correspond to 5 patterns . Grade 1 cells do not differ from normal prostate tissue; grade 5 corresponds to tumour cells. Thus, cancers with a higher Gleason score are more severe. Physicians determine the Gleason score by looking at biopsy samples and assigning one grade to the predominant pattern (primary Gleason score). Usually, a second Gleason grade is given to the second most predominant pattern, and the two grades are added to set the secondary Gleason score. This project focuses on the primary Gleason score and specifically on patterns 3 and 4. Indeed, the differentiation between Gleason score 3 and Gleason score 4 may play a pivotal role in understanding the inherent prognosis associated with these distinct biological behaviour patterns, and aid in guiding the translation of findings from molecular and histological levels into more precise treatment selection33 (details in supplementary). In this work, we examine if our workflow can highlight the differences between these two patterns. The database contains 297 individuals in the training set  and 71 in the testing set .Prostate cancer is the most common cancer in men28. Here, we study if INs and combining RNA-Seq and histopathology data can help identify these two brain tumours. The training set contains 344 individuals , and the testing set 156 individuals .Brain low-grade gliomas (lgg) are cancerous brain tumours. They arise from the support cells in the brain. Glioblastoma multiforme (gbm) is an aggressive cancer in the brain or spinal cord. Studies have already identified variations between these two tumours, such as gender-specific molecular differences7. The training data contains 603 patients , and the testing data has 140 patients .Lung adenocarcinoma (luad) and lung squamous cell carcinoma (lusc) are among the most common lung cancer subtypes and are both considered non-small cell lung cancer (NSCLC). They have different biological signatures, but these variations in their biological mechanisms remain to be disentangled even though recent studies have made progress19 and attention MIL24, trained for 100 epochs on all TCGA slides, sampling 128 random tiles per slide every epoch. The 512 features contained in layer N-1 are selected as new variables. Each feature is a vector of length the number of individuals and contains discriminative information for cancer type. We assumed that the difference in cancer types would provide relevant information for differentiating the groups in our 3 use cases.Feature extraction is performed on the histopathology Whole Slide Images (WSI). We considered the full TCGA dataset with 30 cancer types (See supplementary Table 1), including the types to classify in the 3 use cases described above , but excluding the individuals in the testing sets. A pretrained neural network model is applied to differentiate between the cancer types. In particular, we use Resnet18node level approaches. This approach can be considered not relying on individual network structures as the interactions between features are not used in the model. Three ways of obtaining a Person-to-Person network We created baselines where only the node weights of the individual networks are used, i.e., only the raw feature values. We will refer to them as affinityMatrix in package SNFtools52. This function takes three arguments: a distance matrix (obtained with the euclidean distance), a parameter K, and K is the number of neighbours, where affinities outside of the neighbourhood are set to zero, and affinities inside are normalised. The first option was to use the euclidean distance between each pair of individuals’ features and to compute the affinity matrix that represents the neighbourhood graph of the individuals using the function gausskernel from the package KLRS13. Given two vectors x and y, the Gaussian kernel is defined as A variation was to apply the Gaussian kernel via the function rcorr from package Hmisc18.The third option was to compute the Spearman correlation between each pair of patients using the function A second type of Person-to-Person network Because individual networks can be very large when the number of variables per data source increases, we performed feature selection at the node and edge levels. This strategy allowed us to focus on relevant signals and to decrease the computing time. Since a change in the node and edge selection can produce different final results, our pipeline integrates the optimization of the feature selection process, ensuring an efficient network sparsification. The feature selection process unfolded as follows. First, we selected data features  with the highest standard deviation. The aim was to evaluate the inclusion of the first 100, 200, ..., to 1400 genes. Then we performed the edge-level feature selection. We created condition-specific networks for each subgroup to predict. We calculated the difference between these condition-specific network adjacency matrices and selected edges with the largest absolute differences. Namely, we evaluated the edge weights percentile thresholds 0.25, 0.5, and 0.75. To select the optimal thresholds, we performed a stratified 5-fold cross-validation within the training set and chose the parameters giving rise to the higher macro F1 score on average.Node Product, we applied a minimum-maximum normalisation algorithm across all variable values to scale them between 0 and 1: i and x, the weight of the edge between nodes i and j is LIONESS algorithm30. The general idea is to study the difference between a network constructed from all individuals and a network derived from all but one individual. If a difference appears, it must be due to the individual being left out. The LIONESS equation is the following: i and j in a network modeled on all N samples and x. For each individual, we derived edge weights using the lionessR function31. Notably, these edge weights are specific to the reference panel. We reduced the INs obtained to the previously identified selection of edges. Finally, we applied the minimum-maximum scaling algorithm on INs so that the edge weights range between 0 and 1. In particular, we considered the minimum and maximum weights across all INs in the scaling so that the ordering of the weights remained the same between individuals. We used the similarities to individuals in the training sets as new variables for prediction.We derived individual edge weights based on two approaches. In the first one, which we called Using as the predictor variable, how similar individuals are from a reference panel requires defining a measure of distance between individuals. Many methods have been developed to compare graphs. The specificities of our context limited the choice of distance. Indeed, the measure should be computed in a reasonable amount of time, even on large graphs, and should handle undirected and weighted networks. Since the same variables  are used for all the individuals, there is a node correspondence between the different INs (multiplex). Only the edge weights differed from one person to another. That implies that without additional filters, all the graph distances based on structural differences will not allow us to identify if some graphs are more similar than others. For example, the euclidean, Jaccard, edge difference, or DeltaCon distances suited our context. We used the edge difference distance in this project because of its good computational properties. This distance takes two adjacency matrices and computes the Frobenius norm of their differences. We applied this distance to each pair of individual networks to obtain a matrix of similarity between individuals.There is no reason to assume that both individual node and edge information could not be complementary. Thus, we also investigated the combination of Person-to-Person networks built from individual nodes and individual edges. We built the Person-to-Person networks independently for the two approaches, and we averaged their corresponding adjacency matrices to merge them.One option to integrate multiple database information was concatenating the original data (early fusion) and applying the pipeline as in the single data procedure. When using individual edges, or edges and nodes, we included the additional step: for each data source, the top variables are selected as described in Sect. “53. SNF has proven efficient in combining multiple data such as mRNA expression, DNA methylation and microRNA expression data for cancer data. In this project, we tested both the average and the Similarity Network Fusion algorithms. Then, an SVM model was applied as described in Sect. “Fusion can also be performed at the PPN level (intermediate fusion). PPNs are obtained for each data source separately and merged to benefit from their potential complementary. Simple methods can be applied for this task, such as computing the average of the different PPNs. More advanced approaches include the Similarity Network Fusion (SNF)The last alternative considered was late fusion, where data are merged after an independent investigation of each data source (a and b). With continuous outcomes, it can be computed by summation or averaging. Since we are performing classification, we used the majority vote approach. In most of our application settings, we considered two data modalities only, so a majority vote would not provide additional knowledge. Hence, we applied late fusion only on results obtained from Person-to-Person Networks derived from the combination of individual nodes and edges, where we consider prediction from four outcomes: kernlab package25. Instead of working with the original sample representation in the original dimensional space, SVM classification methods operate directly on similarity matrices. We tested multiple options of C . This function fits a linear model for each gene-pair and returns a MArrayLM object, denoted as fit, containing the results of these fits. Subsequently, we applied the contrasts.fit function on fit to compute estimated coefficients and standard errors for each linear model. Next, the eBayes function was applied to the output of the contrasts.fit function to compute moderated t-statistics, moderated F-statistics, and log-odds of differential expression using empirical Bayes moderation to adjust standard errors towards a common value. Finally, we used the toptable function to extract a matrix containing the top-ranked gene-pairs based on the linear model fit. We focused on identifying the top 50 most differentially co-expressed gene pairs and colored the edges in the network based on their values within the classes to predict. This approach highlighted edges with significantly distinct weights between different groups, thus enhancing our comprehension of the underlying data. In parallel, we also conducted a LIMMA analysis to assess significant differences in gene expression levels between groups. Hence, nodes in the network were colored based on the t-statistics resulting from the LIMMA analysis.First, we applied the 17. We focused on the largest connected components. Since all the genes in that module are connected, they can indicate a broader biological mechanism responsible for the group difference. For the pathway analysis, we performed the LIMMA analysis on the features selected as described in Sect. “fgsea package45 to perform gene set enrichment analysis with a minimum gene size of 10 and 5000 permutations. Two inputs were required: a ranked gene list and a list of gene sets to test for enrichment. For the former, we used the gene t-values of the genes in the largest component from the LIMMA analysis. It represents the gene statistical difference between the two groups compared. For the latter, we downloaded all ontology and curated Molecular Signature Database (MSigDB version 7) gene sets50. We applied FDR cut-off of 0.05 for significant assessment.We investigated networks obtained with LIMMA with a gene set enrichment analysisWe compared our graph-based approach to multiple classification methods applied to the raw features. Namely, we used a penalized logistic regression, a classification tree, a random forest, AdaBoost, a naive Bayes method, and a neural network approach. The algorithms were applied on each data type separately (RNA-Seq and histopathology features) and on the combined dataset (RNA-Seq and histopathology features concatenated). For each algorithm, we computed the associated macro We compared the prediction performance obtained using different levels of information in the individual graphs. To create INs, feature selection is performed as described in Sect. “node level. It motivated the choice of the Spearman correlation for the combination of node level and edge level information.The first two columns of each heatmap Fig.  show thenode level information achieved higher prediction with histopathology data for the prostate (max F1=0.82) and brain classifications (max F1=0.94).We observed that using more than node information increased the macro F1 score for the prostate (max F1=0.71) and brain  use cases with RNA-Seq data, and for the lung use case (max F1=0.94) with histopathology data. Using individual edges or individual nodes led to an equal performance in the context of lung cancer (max F1=0.94) from RNA-Seq data. Pipelines based on Node Product performed better than the LIONESS algorithm in all situations except the prediction of prostate cancer severity using RNA-Seq data. However, when combining individual nodes and edges, the LIONESS method yielded higher results in half of the situations. In general, on single data, classification based on individual edge weights, with or without combination with individual node weights, was better or equal to predictions from individual nodes only  in two-thirds of the scenarios.Among the two approaches to build similarity matrices via individual edges, the Moreover, we compared graph-based models to multiple classification algorithms applied to the raw features, separately for each data type: a penalized logistic regression, a classification tree, a random forest, AdaBoost, a naive Bayes method, and a neural network approach. The data were pre-processed following the same approach as in the graph method, specifically selecting the same variables. Results are detailed in Table This analysis’s first goal was to study whether it is possible to predict disease subtypes and severity from the patient data using graphs. The results showed that in brain cancer, the workflow achieved perfect predictions. We also obtained high performances in the lung cancer use case . Our analysis with the graph-based approach revealed an average difference of 3.3% between the F1 scores of the different cancer subtypes (e.g. lgg/gbm), with two analyses showing equal F1 scores for both classes. The largest discrepancy (11%) was observed in prostate cancer classification based on RNA-Seq data. These results indicate that there is no substantial disparity between the F1 scores achieved in the two groups, and suggests that the approach adeptly handles data imbalance. Furthermore, we observed no discernible patterns associated with genes or histopathology features among the misclassified samples. In some cases, the characteristics of different cancer subtypes might overlap, making it challenging to differentiate between them. In our study, this phenomenon becomes particularly relevant in the context of prostate cancer, where Gleason scores are derived manually by doctors. This can result in ambiguous cases that are prone to misclassification.The dataset’s size may also play a role in misclassifications. We are training our model on relatively small datasets (maximum 603 patients), so the model may struggle to capture the full spectrum of variation, leading to errors. Data noise in RNA-Seq or histopathology data can also misguide the algorithm, potentially arising from data collection, preprocessing, or annotation errors. Incomplete information in the dataset, missing important features influencing cancer subtype, can contribute to misclassifications as well. Therefore, including additional data modalities could reduce the number of misclassified patients. Finally, the algorithm’s complexity might not be perfectly-suited to the dataset. Overly complex models can overfit the data and lead to misclassifications. For instance, in the case of prostate cancer, while node information from histopathology data provides valuable insights for disease subtyping (macro F1 score of 0.82), the edge information lacks meaningful contributions and even hinders predictions (maximum macro F1 score of 0.70).The predictive capabilities of data modalities in cancer classification is influenced by their inherent informativeness, and their capacity to complement each other. In the case of prostate cancer, the high performance of histopathology images was expected since primary Gleason scores are typically assessed through biopsy samples. This data modality inherently captures valuable information essential for subtype classification. Still, when the Person-to-Person networks generated from both the individual edge weights and individual node weights  were considered, the fusion of RNA-Seq and histopathology data yielded improved predictions for prostate cancer (F1=0.79) compared to single-modality predictions (0.65 and 0.63). This suggests that the two modality types contain complementary information that, when combined, can enhance predictive power. For brain cancers, the two modalities already exhibited strong predictive capabilities individually, indicating that both the gene expression and the histopathology data can help differentiate the brain low-grade gliomas and glioblastoma multiforme. However, the highest performance was achieved by integrating both modalities. Table We evaluated the benefits of using nodes, edges, or nodes and edges in the workflow. In the context of brain and lung cancers, the highest macro F1 scores were achieved when considering nodes, either alone or in combination with edges. This suggests that the superior performance of the latter configuration primarily arises from the contribution of individual nodes. However, we observed more heterogeneous performance outcomes when exclusively focusing on nodes or edges, compared to the results when incorporating both nodes and edges. For instance, with lung cancers, the utilization of node-based information (Spearman) yielded an average macro F1 score of 87.5 across all possible data type combinations, including RNA-Seq only, histopathology only, early, intermediate, or late integration. When both nodes and edges were incorporated, the average macro F1 score increased to 95.1. We observed similar results with brain cancers. These findings underscore the significance of including both nodes and edges information, as it reduces the risk of achieving very low performance results and enhances the overall predictive stability.We compared the two types of intermediate fusion: SNF versus the average approach. The Similarity Network Fusion approach offers the advantage of capturing complex relationships between data sources, which can be especially valuable when dealing with multiple modalities. It can model dependencies that might be overlooked by simple averaging. However, in our specific analysis, we only considered two data modalities, which might explain why the average method outperformed SNF in most cases. The average approach, while simpler, can still deliver strong results when dealing with a limited number of modalities. It might be less suitable when complex interactions exist between numerous data sources. One drawback of averaging is that it assumes equal importance for all data sources, which may not always hold true. This could account for the reduced performance of the average approach in the context of prostate cancer, given that the predominant predictive strength originates from histopathology images. On the other hand, SNF can be computationally demanding, particularly with large datasets or when dealing with numerous data sources. It also requires defining parameter values, such as determining the number of nearest neighbors. This parameter selection process can introduce complexity and affect the results. Hence, we recommend considering SNF in the presence of intricate relationships between multiple data sources. However, for scenarios with a limited number of modalities, average fusion remains a simpler, computationally efficient option that can still yield higher performance.We applied a LIMMA analysis and a gene set enrichment analysis to the RNA-Seq data to illustrate the potential of individual networks to understand biological mechanisms.t-statistic from the LIMMA analysis , the top 50 most differentially co-expressed edges were selected and coloured  using networks of similarities between patients. First, we evaluated the benefits of transforming the input data into individual graphs on single data. We showed that considering the features as a connected system could improve the prediction performance. Second, we demonstrated that combining individual networks and multi-modality integration can yield better performance. Finally, as we illustrated with cancer data, one strength of graph-based approaches is the ability to visualise and provide insights into the causal factors accounting for the differences between the disease subtypes. Although we focus here on RNA-Seq and histopathology data, our framework applies to any multiplex data. In clinical studies, it offers opportunities to integrate various measurements such as demographic, microbiome, and metabolomics data.As any machine learning algorithm, the performance of the graph-based models on other datasets that might lack uniform processing can be influenced by several factors, such as sequencing depth, batch variation, and unknown combinations of technical and biological noise. To mitigate the impact of these challenges, our approach incorporates various strategies.We employ a dataset-specific feature selection step at both the node and edge levels of the individual networks within our workflow. This process optimizes feature selection, promoting an efficient individual network sparsification. By focusing on the most informative features, which are less susceptible to noise, we aim to enhance model performance. Also, our pipeline incorporates cross-validation techniques, particularly when applying the Support Vector Machine on the Person-to-Person network. Cross-validation assesses the model’s performance across multiple data subsets, thereby helping identify potential overfitting to a single dataset.25. It essentially determines the balance between two objectives: the minimization of training error and the minimization of model complexity10. Specifically, opting for a higher value of C results in a more flexible model, characterized by a narrower margin, and fewer misclassification. Conversely, a lower C value allows for a wider margin, potentially leading to more misclassifications within the training dataset. We selected C giving rise to the best performance. Feature selection and hyperparameter tuning are performed on the training set, presenting a potential risk of overfitting in the intermediate results. Also, selecting an algorithm based solely on its performance evaluation on a test set, after training on a training set, could introduce potential overfitting concerns. We acknowledge that opting for a separate validation set, instead of the training set, during hyperparameter tuning would enhance the model’s capacity to generalize to new data. Nonetheless, we assess the model’s performance using a distinct test set , can enhance overall model performance and limit the impact of unknown combinations of technical and biological noise. Alternatively, users may consider adopting the construction of Person-to-Person networks, leveraging both individual network nodes and edges in conjunction with an intermediate fusion (average) approach. This strategy demonstrated high performance in multiple scenarios.38 visualizations for different sets of options or parameter configurations, users can compare the effects of these options on data transformation. We employed UMAP to visualize PPNs and color-coded data points according to their prediction labels. Specifically, we applied the umap function from the R package umap with default settings. This approach enabled us to assess how well the algorithm’s predictions align with the patterns in UMAP representations, shedding light on when the network approach added value. The association between a discernible group pattern in UMAP visualizations and enhanced prediction performance using SVM is noteworthy. In UMAP plots generated for the prostate use case, most visualizations lack a clear separation between groups, which reflects the challenges in distinguishing cancer severity (supplementary figure 3). Conversely, in the brain cancer plot, options that yield the best prediction performance, such as the combination of nodes and edges information of the IN (the two last rows), exhibit a more distinct division between groups (supplementary figure 4). The same trend can be observed in the lung analysis. For example, the utilization of nodes and edges information from the INs, particularly when based on RNAseq only, early integration, and average intermediate integration, produces discernible patterns (supplementary figure 5). These options, in turn, are associated with more favorable prediction outcomes. UMAP, therefore, can serve as a visual guide for users, facilitating their comprehension of how the algorithm transforms raw data into input for SVM. They can experiment with different options and observe the impact of these alterations on UMAP visualizations for their specific dataset and problem. In particular, when UMAP visualizations unveil well-defined clusters or meaningful patterns within the labels, we recommend considering the utilization of the associated options.Furthermore, by creating UMAPFurthermore, we encourage users to implement appropriate preprocessing steps, such as batch effect correction and noise reduction techniques. These steps can substantially enhance the model’s adaptability to diverse datasets and improve overall performance.In this study, one data type in the cancer use cases was histopathology Whole Slide Images. This data was transformed beforehand to convert images to image features with continuous values. To achieve this transformation, we considered a dataset that included but was not restricted to the individuals of our use cases, and we applied a neural network model to predict the cancer type. From this model, we derived features that discriminate between cancer types. Even though it may seem more straightforward to apply a neural network for each use case and train on the label of interest , we observed that differentiating among cancer types yielded better results (data not shown). One possible explanation is that the image model trained purely on the groups to identify resulted in a not general enough embedding. Indeed, a more general model on cancer types contains more individuals, which may lead to a better embedding that recognizes essential features.Node Product approach. However, with the LIONESS algorithm, the INs of the reference panel change when we consider a new individual. Also, the derivation of the IN for a new individual depends on this panel. Hence, to create INs for new individuals, we used all individuals from the training set and one new individual at a time. If we directly add all the new individuals to the ones from the train set, we could considerably modify the relations between the INs of the training set. Adding only one individual at a time to the training set minimises the impact on the similarities between individuals from the train. To summarise, with the LIONESS algorithm, for each individual x from the test set, we created a new database containing the reference panel and x, and we constructed the INs for all the patients in this temporary database. From these new INs, we computed the similarity between x and each individual in the training set. Hence, the complexity of creating individual networks for individuals in the test set with the LIONESS algorithm motivates starting investigations using the Node Product approach.Computing how similar a new individual is to each individual in the training set is straightforward with the LIONESS offers a significant advantage over the Node Product method by leveraging interaction information rather than simply combining node values. However, the LIONESS method does come with a higher computational demand compared to the Node Product approach. As a result, for the feature selection, we opted for the Node Product approach. Therefore, the improved results observed with the Node Product method could, at least in part, be attributed to this choice. Nevertheless, the LIONESS approach can still yield superior results in certain scenarios. For instance, in the Prostate use case, the intermediate fusion (average) outperformed using LIONESS. Additionally, in the Lung use case, when considering histopathology data exclusively, the combination of nodes and edges with LIONESS proved more effective than the Node Product method. Hence, both approaches have their distinct advantages and disadvantages, and their suitability depends on the specific context and requirements of the analysis.In theory, Future enhancements include a data integration strategy that takes advantage of graph specificities. In this work, we studied the impact of combining individual graphs and data integration, but we did not use the network characteristics in the integration itself. Data were integrated before the computation of individual graphs (early integration) or after the derivation of similarity matrices (intermediate and late integration). An alternative would be to combine the data within the process of creating individual networks. In Fig. Whereas research on disease subtyping has received significant attention recently, individual treatment decisions remain a cumbersome issue. Taking advantage of the complementarity of multiple data sources could help provide more precise subtypes. Ongoing research on multi-modality integration mainly considers one variable at a time, ignoring their interactions. Fusion based on individual graphs accounting for these interactions can bring additional information. In this study, we showcased the potential of graph theory. In particular, we underlined the advantages and limits of this approach in the context of prostate, brain, and lung cancers subtyping and severity assessment.We observed that individual graphs could be beneficial even on single data sources, and we highlighted that intermediate integration was often among the best performers. Graph-based methods achieved competitive performance while bringing additional explainability properties. We identified biologically relevant genes, gene interactions, and pathways for different use cases. The presented workflow is flexible and can readily be applied to other data modalities. The results motivate more research on methodological developments of individual networks for precision medicine.Supplementary Information.


However, comprehensive chemical screens in diverse biological models are impractical. To address this challenge, we developed ChemProbe, a model that predicts cellular sensitivity to hundreds of molecular probes and drugs by learning to combine transcriptomes and chemical structures. Using ChemProbe, we inferred the chemical sensitivity of cancer cell lines and tumor samples and analyzed how the model makes predictions. We retrospectively evaluated drug response predictions for precision breast cancer treatment and prospectively validated chemical sensitivity predictions in new cellular models, including a genetically modified cell line. Our model interpretation analysis identified transcriptome features reflecting compound targets and protein network modules, identifying genes that drive ferroptosis. ChemProbe is an interpretable  These tools are crucial for understanding the role of specific proteins in biological processes and diseases, and have been instrumental in investigating a range of functions such as those related to the cell cytoskeleton, immunosuppression, mTOR signaling, protein kinase dynamics, and have often served as the starting point for drug development3. In addition to their primary use as therapeutic agents, drugs can serve as chemical probes in complex diseases like cancer. Addressing cancer heterogeneity necessitates precision clinical treatment strategies and research into the mechanisms that control disease resistance and sensitivity5. By improving our understanding of gene expression patterns contributing to variance in drug response, we can develop better solutions for cancer patients exploiting specific tumor vulnerabilities.Chemical probes are highly potent small molecules that selectively target known mechanism-of-action proteins6. Early approaches often relied on a single cellular feature set, such as mutation status or gene expression profile7. However, significant improvements have been achieved by incorporating multimodal information, such as chemical structure and pharmacological features9. These advancements have demonstrated the value of integrating diverse types of data to enhance drug response prediction.Ideally, we could test large libraries of chemicals on disease models, engineered cell lines, and patient samples to probe disease mechanisms. However, screening biological samples against a large library of chemical probes is resource-prohibitive. To overcome this problem, a variety of traditional machine learning methods have been applied to predict drug response, including support vector machines (SVMs), random forests (RFs), and multi-layer perceptrons (MLPs)11. In one example, variational auto-encoders (VAEs) can also leverage pretraining for transfer learning15. More broadly, neural networks are adaptable to novel inputs, such as graph representations for chemical structures18 and their composability provides exciting opportunities for feature integration such as cross-attention19.Deep learning has become a way to effectively represent and integrate diverse feature sets. These methods commonly employ separate feature encoders that learn rich representations prior to integration22. Gradient-based attribution methods can also help identify features driving a particular prediction15. On the other hand, integrating biological priors into neural networks effectively reduces the feature space and incorporates interpretable features, such as gene ontologies and pathway annotations25. By imposing constraints through priors, learning operates in the context of existing biological knowledge. However, this approach can limit a model’s capacity to learn novel gene combinations and systems mechanisms that are not well understood.Interpreting the computational structure of predictive models themselves can inform on the underlying biology of compound response. On one hand, ensemble models offer confidence scores, and direct interpretation of model coefficients  reveals feature relationshipsin silico chemical screening of biological models and mechanistic interpretation of learned gene dependencies.We developed a deep learning model that predicts the sensitivity of new cellular samples to a panel of chemicals along with a framework for understanding the gene features implicated in the response. ChemProbe learns to combine cellular transcriptomes and chemical structures to predict sensitivity. The model can be applied to new biological samples and leverages interpretable learned gene features relevant to known compound mechanisms. ChemProbe accurately models chemical response without biological priors, enabling 26. These compounds span cell circuitry targets, offering a nuanced view of cellular response to pathway perturbations across a broad range of cellular components. The Cancer Cell Line Encyclopedia (CCLE) provides basal transcriptomic characterizations of all 842 CTRP cell lines27. We combined compound structures and concentrations from the CTRP with protein-coding gene transcriptomes from the CCLE to create a dataset of compound-cell line pairs consisting of approximately 5.8 million labeled examples , where y is cellular viability, x is a matrix of standardized RNA abundance values, n is a matrix of chemical features, and f is parameterized by a neural network (2). Accounting for comparable model sizes, we trained, validated, and hyperparameter-optimized different model architectures across five data folds stratified by cell line . We compared three methods of learned feature conditioning against a baseline feature concatenation approach28. All conditioning approaches outperformed feature concatenation by a notable margin (γ) parameters grouped compounds by identity (β) parameters  of models in subsequent experiments 32. I-SPY2 assigned patients to treatment arms based on biomarkers such as hormone receptor status, human epidermal growth factor receptor-2 expression, and MammaPrint status. Absence of invasive cancer in the breast and regional lymph nodes at the time of surgery defined the endpoint of pathological complete response (pCR) .We next asked whether learned transcriptional patterns would generalize to an 33. Neural networks often fail on “out of distribution” samples whose features  come from different assays than their training data. To determine the extent to which the I-SPY2 data was outside ChemProbe’s training distribution, we compared dataset expression profiles across the top two principal components. A subset of the I-SPY2 data fell outside the training data distribution, consistent with the expectation that assay types introduce systematic measurement effects  and non-responders (−) (ChemProbe+/−). Since the model determines cellular viability by drug concentration, we established a decision threshold for detecting responders . ChemPro37. We compared the gene expression profiles of the two cell lines to their CCLE counterparts by analyzing the top two gene-expression principal components. Our analysis showed significant disparities in the gene expression patterns of the two cell lines compared to the training data, highlighting the challenges of maintaining consistency across cellular models , fit log-logistic models, and determined 50% inhibitory concentration (IC50) values from each se curve . ChemProse curve . We focuse curve ,d. In viferences . We compferences . Additioferences . These rferences ,c. ChemP41. Using integrated gradients saliency mapping,42 we determined IC50 values for each compound-cell line pair with ChemProbe and computed its gene attribution vectors. However, we acknowledge that integrated gradient attribution vectors may correlate with input feature magnitudes, potentially undermining their usefulness in quantifying feature importances.43 We used principal component analysis to determine the first two principal components of attribution vectors by cell line to check this. We found that attribution and transcriptome vectors correlated  and cell line-effect corrected (adjusted) attribution vectors. The raw attribution vectors were highly correlated with transcriptome profiles, random-model, and permuted-model attribution vectors, failing the tests of independence from learned parameters and the training data. However, the adjusted attribution vectors were not correlated with those derived from the control models, indicating that adjusted attribution vectors do not simply reflect data or parameter artifacts  based on nominal target classes, each with at least two compounds successfully predicted in all seven cell lines. We applied K-means clustering to the CCS attribution vectors and computed the adjusted mutual information (AMI) between clusters and target class labels to determine whether transcriptomic attribution vector similarity corresponded to known compound mechanisms of action (MOA) . We alsoThe attribution vector clusters AMI was significantly greater than that of structural clusters, a randomly initialized model, and a model trained on permuted labels , Methods45 to interrogate biological relevance. We clustered attribution vectors, gathered target annotations within each cluster, and queried STRING for the respective target interactome  or overexpression can inform on mechanisms of gene-dependent protection or resistance. Accordingly, we assessed ChemProbe’s utility for screening gene-dependent ferroptosis resistance nd CIL56 .We noticed several correlations between cellular response and the expression of highly attributed genes for compounds that induce ferroptosis ,c. We woUsing a conditional deep learning approach, ChemProbe evaluates cellular transcriptomic signatures against bioactive molecular structures to predict cellular responses to chemical perturbations. In experiments on cellular models and clinical tumor samples, this tool accurately predicts cellular viabilities prospectively. ChemProbe complements more clinically-oriented approaches with its ability to directly screen engineered cell lines and interrogate potential molecular mechanisms. Engineered cell lines, which possess specific genetic modifications or alterations, physically model disease conditions or the results of targeting pathways of interest. By leveraging ChemProbe, researchers can evaluate the sensitivity of known and newly engineered lines to a panel of chemical probes to assess how specific genetic modifications or alterations influence compound response.Intriguingly, deep learning model interpretation reflects compound mechanisms of action . The dif50. The ability to expedite treatment at earlier disease stages and target cellular vulnerabilities would be particularly impactful for tumors whose resistance mechanisms rapidly evolve.Extending to clinical samples, ChemProbe becomes a tool for targeted therapy and precision medicine. We found that it predicts drug sensitivity in breast cancer patients across heterogeneous clinical tumor samples . Likewis52.Nonetheless, several caveats merit mention. The experiments were constrained to a limited set of cell lines and compounds, and model interpretation reflects a limited set of biological factors. Without further study, gene features achieving high model attribution may reflect useful but obtuse patterns in the datasets rather than biological causality. Similarly, without a more diverse training set of chemical structures, the model may not be leveraging generalizable structural features. As always, deep learning model attribution methods are a moving target, so the potential compound mechanisms of action they reveal ultimately necessitate prospective biological testing54. Similarly, integrating ChemProbe with pretrained cellular transcriptomic or small-molecule structure foundation models may be a means to expand into broader biological and chemical space.ChemProbe screens cell lines against half a thousand chemical probes and drug-like compounds. However, expanding its predictions to a larger subset of chemical space would require collecting biological screening training data at a commensurate scale, which is currently impractical. Deep learning models like AlphaFold and ESM have leveraged self-supervised learning to extract emergent properties from extensive unlabeled protein sequence dataWhen used to screen disease models, engineered cell lines, and clinical samples, ChemProbe is a powerful tool to assess how cells respond to various compounds. It supports exploring new therapeutic targets, suggests disease mechanisms, and can help researchers develop more precise and effective treatments. In this study, ChemProbe predicted drug sensitivities in multiple contexts, from cancer cells and tumor samples to data on breast cancer patient responses. Looking forward, we hope that ChemProbe’s availability as an open-source tool will contribute to a range of research efforts in precision medicine and beyond.Drug sensitivity data was obtained from the Cancer Therapeutic Response Portal v1 and v2 (CTRP v1/2). These datasets comprise 864 cell line responses to 481 individual compounds and 64 compound pairs across a range of concentrations. Response phenotypes were quantified by cellular viability, a normalized measure characterizing complete cell killing to cell stasis (0–1) and cell growth (>1). We utilized predicted cellular viability derived from fitted dose-response curves of each experimental set, in which replicate cell line-compound experiments were fit with a log-logistic function and predicted cellular viability was derived at the original experimental concentrations (Seashore-Ludlow). Compound structure was represented as 512-bit Morgan fingerprints (radius = 2) converted by RDKit from SMILES provided by the CTRP. Experimental micromolar compound concentrations were concatenated with Morgan fingerprints, resulting in 513-length compound feature vectors. We matched CTRP cell lines with the Cancer Cell Line Encyclopedia (CCLE) molecular characterizations and extracted protein-coding gene expression measurements, resulting in 19144-length cell line feature vectors. In total, 545 total compounds or compound pairs and 860 cell lines comprised 366,710 unique pairs and 5,849,340 total individual examples of compound response at various concentrations.The study focused on predicting drug sensitivity in the context of pharmacological intervention by integrating cell state features with compound features. To achieve this, we formulated a conditional model where cellular viability is predicted based on a vector of standardized protein-coding RNA abundance values and a vector of chemical features, including structure and concentration. We explored two methods of integrating gene expression and small molecule feature representations: simple concatenation and hierarchical integration using feature-wise linear modulation (FiLM).c and an inputs encoder that embeds gene expression features into a vector of length g. We used a FiLM generator to predict γ and β parameters of length g based on compound embeddings. The FiLM layer then applies an affine transformation of gene expression embeddings by γ and β parameters. This process repeats across n FiLM layers, and the modulated gene expression embeddings pass through a linear block consisting of a linear layer, ReLU activation, batch normalization, and dropout. The final linear block compresses feature maps to a vector of length 1, and the mean-squared error is calculated between predicted cellular viability and true cellular viability.ChemProbe includes a conditional encoder that embeds compound features into a vector of length To evaluate the performance of our model, we used cross-validation and split cell line-compound pairs into five groups of approximately equal size by cell line to avoid data leakage and performance inflation. We trained five individual models in a leave-one-out cross-validation scenario and applied 20 rounds of hyperparameter optimization to all five individually trained models. We implemented the ChemProbe model in PyTorch and applied hyperparameter optimization with Optuna.β=0) and learned only the scale parameters (γ), whereas the “shift” model held scale parameters constant (γ=1) and learned only the shift parameters (β). We assessed ChemProbe’s dependence on compound concentration by creating a “permuted” model that used random binary fingerprints for each compound, ablating structural information. We trained and evaluated all models using 5-fold cross-validation on the originally defined dataset splits for three rounds of hyperparameter optimization.We compared different models that modify gene expression features by compound structure and concentration using various transformations. Our baseline model, “concatenation” architecture, simply combined gene expression and compound features into a single vector, which was fed into a multi-layer perceptron. We independently evaluated the isolated effects of learning transformation types using the “scale” and “shift” variants of the ChemProbe model. The “scale” model held shift parameters constant  as an indicator of relative potency, calculating it with the EDcomp function. Significant differences in compound effects between cell lines were assessed using t-values and p-values obtained from EDcomp.We obtained I-SPY2 clinical trial metadata and microarray characterizations of 988 patient transcriptomes from the Gene Expression Omnibus (GEO) (GSE194040). We matched 90% of the recorded genes to our training dataset, mean-imputed the remaining 10% of genes, and standardized the data using Z-score transformation. We then evaluated the alignment of I-SPY2 patient data with CCLE cell line training data across the first two principal components. Next, we predicted drug sensitivity for each patient across 32 concentrations (1E-3 uM – 300 uM) in response to all 545 compounds and compound pairs in the CTRP. We generated patient-drug response predictions using independent models and computed the area under the curve (AUC) of each predicted dose-response assay. We scaled the AUC of each patient-drug prediction between 0–1 based on the drug’s minimum and maximum predicted AUC across all I-SPY2 patients.Participants in the I-SPY2 trial were placed in treatment arms based on analyses of clinical and molecular information analyses, including clinical characteristics, gene expression patterns measured via microarray, and protein abundance as measured by reverse phase protein array (RPPA). The trial assessed the efficacy of various combination therapies relative to paclitaxel treatment, the clinical standard of care. We identified drugs matched between I-SPY2 treatment arms and the CTRP, including paclitaxel, neratinib, MK2206, veliparib, and carboplatin. In the I-SPY2 experimental arms, patients were treated with a combination of paclitaxel and an additional drug(s) to assess response relative to paclitaxel treatment only. As the predictive ability of ChemProbe was only evaluated with respect to the available compounds and compound pairs in the CTRP, the ChemProbe predictions for I-SPY2 patients reflected predicted patient response to a single compound rather than a combination therapy.in vitro testing. We based selection criteria on the completeness of dose-response curves in each cell line, including adequate Emax and Emin boundaries within the predicted concentration range.To identify differentially potent compounds between HCC1806-Par and MDA-MB-231-Par cell lines, we computed the difference in predicted IC50 values for compounds that passed dose-response modeling. We visually examined dose-response curves of the top 50 differentially sensitive compounds and selected candidates for We conducted a preliminary dose-response experiment to determine appropriate concentration points for the subsequent dose-response experiments across a broader range of concentrations than our predictions  ,c. We nan feature vectors between a designated baseline and the query feature vector. We used zero-vector baselines for compound and gene expression features and set n = 50 as the step size. At each interpolated feature vector step, gradients of the inputs are calculated with respect to the corresponding prediction. Finally, the integral of each feature along the path of feature gradients between the baseline vector and the query vector is computed. The python package captum was used to compute integrated gradients.We employed integrated gradients, a path-based model attribution technique, to determine the extent to which feature gradients changed compared to a baseline feature vector. The method involves linearly interpolating To account for potential differences in cellular responses, we used the predicted compound IC50 for each cell line-compound pair to calculate integrated gradients and obtain an attribution vector at the predicted IC50. We then extracted the cell line feature attribution vector for each pair to investigate the influence of conditional compound information on gradient changes in the input gene expression features. To address cell line-specific effects, we standardized the transcriptome attribution vectors of each cell line separately using a Z-score transformation, resulting in adjusted attribution vectors ,c.To evaluate the sensitivity of the attribution method to learned parameters and data features, we conducted soundness checks. First, we assessed model-dependent attribution method invariance by comparing the attribution vectors of randomly initialized parameters of architecturally identical models with those of the trained models. We applied integrated gradients to the trained and randomly initialized models and compared the attribution vectors. Second, we evaluated data-dependent attribution method invariance by permuting the data labels, training architecturally identical models, and applying integrated gradients to compare the true-model and permuted-model attribution vectors . We usedWe investigated the relationship between compound MOAs and learned gene expression feature dependence by examining attribution vector similarity. First, we filtered attribution vectors by considering compound MOA classes with at least two compounds successfully attributed in all seven cell lines to obtain MOA classes with sufficient samples for analysis (control compound set). This resulted in 28 MOA classes, which served as a true label baseline. We then compared these true labels to unsupervised labels generated by K-means clustering of attribution vectors from a trained model, a randomly initialized model, compound fingerprints, and a label-permutation baseline . We applWe analyzed gene target attributions to further investigate the model dependence on individual nominal targets within each MOA class. Specifically, we applied a two-sided Wilcoxon-rank sum test to group attributions for each nominal target in the MOA class of interest and adjusted for false discovery rate (FDR) using the Benjamini-Hochberg (BH) procedure. We visualized the nominal target with the largest average attribution difference between groups for each MOA class .We extended our analysis to include all attribution vectors generated from the 7-cell line test set. We randomly selected a single nominal target from each compound MOA class to avoid bias towards closely associated targets. This is because the nominal targets of a single compound likely fall in close network proximity, and downstream network analysis of target sets would reflect artificial over-connectivity. For example, the MOA class of neratinib includes nominal targets EGFR and HER2, which are involved in the same pathway. Therefore, we randomly chose one target from this set.We applied Leiden clustering unsupervised discovery of attribution clusters. As described above, we defined attribution cluster MOA classes by random target selection from each compound MOA class. We filtered the STRING database to consider only high-confidence protein-protein associations (combined score > 0.7). We queried STRING for attribution cluster nominal targets and computed the connectivity of the resulting subgraph. To account for random subgraph connectivity due to target biases in STRING, we randomly sampled from available targets, queried the filtered STRING database, and computed connectivity. We repeated this procedure with randomly sampled protein-coding genes to account for random protein associations . We usedTo test for protein interaction enrichment, we defined attribution cluster nominal targets by random target selection from each compound MOA class, as described above. Next, we queried the STRING API for protein-protein interaction enrichment in the network of high-confidence protein-protein associations (combined score > 0.7). We computed statistical enrichment using the hypergeometric test, which tests if a query set of proteins has more interactions than expected relative to the background proteome-wide interaction distribution. We also applied the hypergeometric test for functional enrichment of GO terms, KEGG pathways, and Reactome pathways. We used the stringdb python package to access the STRING API. To infer potential modules of action for compounds, we selected the unique set of all nominal targets associated with an attribution cluster.55. Using RNA that was rRNA-depleted with Ribo-Zero Gold (Illumina), libraries were prepared with SciptSeq-v2 (Illumina) and sequenced on an Illumina HiSeq4000 at UCSF Center for Advanced Technologies. Transcript abundances were quantified using Salmon, and tximport was utilized to summarize transcript-level measurements. We employed DESeq2 to identify differentially expressed genes.RNA sequencing was conducted on seven test cell lines, namely HCC1806-Par, HCC1806-LMb/c, MDA-MB-231-Par, MDA-MB-231-LM2, SW480, and SW480-LvM2To assess model dependence on individual genes within attribution clusters, we conducted an unbiased analysis. We applied a two-sided Wilcoxon-rank sum test to each gene to analyze gene attributions within a cluster relative to all remaining samples. We adjusted for FDR using BH to account for multiple testing. We utilized scanpy to apply tests across genes in each cluster relative to all other samples. Attributions were standard scaled and each cluster’s top 10 most significant genes were plotted. Leiden groups were hierarchically clustered (complete linkage) by Pearson correlation. Scanpy was used for computation and visualization. We obtained gene expression—sensitivity Pearson correlation z-scores and corresponding visualizations from the Cancer Therapeutics Response Portal v2 feature correlation analysis ,c.MDA-MB-231-Par and HCC1806-Par cells were seeded at 1,000 cells per well in quadruplicate per condition in a white opaque 96-well plate . Twenty-four hours later, cells were treated with serial dilutions between 2.05pM and 100uM of the following compounds: neratinib , CAY10618, 1S,3R-RSL-3 , AZD7762 , ceranib-2 , and ML162 , and DMSO control. Cells were treated for 72 hours with media replaced every 24 hours. Cell viability was measured with the CellTiter-Glo 2.0 Assay  with 1,000 ms integration time.All cells were cultured at 37 °C in a humidified incubator with 5% CO2. MDA-MB-231 (ATCC HTB-26) cells were grown in DMEM supplemented with 10% FCS, penicillin (100 U ml−1), streptomycin (100 μg ml−1) and amphotericin (1 μg ml−1). HCC1806 (ATCC CRL-2335) cells were grown in Roswell Park Memorial Institute-1640 medium supplemented with 10% FCS, L-glutamine (2 mM), sodium pyruvate (1 mM), penicillin (100 U ml−1), streptomycin (100 μg ml−1) and amphotericin (1 μg ml−1).https://github.com/keiserlab/chemprobe.Our code to download, preprocess data, reproduce model training, load pretrained weights, and run model inference is available as open source at Relative potency of each compound at the median effective dose (ED50) between cell lines.


Virgin coconut oil (VCO) is a functional food with important health benefits. Its economic interest encourages fraudsters to deliberately adulterate VCO with cheap and low-quality vegetable oils for financial gain, causing health and safety problems for consumers. In this context, there is an urgent need for rapid, accurate, and precise analytical techniques to detect VCO adulteration. In this study, the use of Fourier transform infrared (FTIR) spectroscopy combined with multivariate curve resolution–alternating least squares (MCR-ALS) methodology was evaluated to verify the purity or adulteration of VCO with reference to low-cost commercial oils such as sunflower (SO), maize (MO) and peanut (PO) oils. A two-step analytical procedure was developed, where an initial control chart approach was designed to assess the purity of oil samples using the MCR-ALS score values calculated on a data set of pure and adulterated oils. The pre-treatment of the spectral data by derivatization with the Savitzky–Golay algorithm allowed to obtain the classification limits able to distinguish the pure samples with 100% of correct classifications in the external validation. In the next step, three calibration models were developed using MCR-ALS with correlation constraints for analysis of adulterated coconut oil samples in order to assess the blend composition. Different data pre-treatment strategies were tested to best extract the information contained in the sample fingerprints. The best results were achieved by derivative and standard normal variate procedures obtaining RMSEP and RE% values in the ranges of 1.79–2.66 and 6.48–8.35%, respectively. The models were optimized using a genetic algorithm (GA) to select the most important variables and the final models in the external validations gave satisfactory results in quantifying adulterants, with absolute errors and RMSEP of less than 4.6% and 1.470, respectively. Cocos nucifera L. is a palm belonging to the Arecaceae family, native to the Eastern tropical regions, mainly cultivated in Asia, Central and South America, and Africa ) were assembled, each containing the calibration subset and the subset of the samples to be used in the model external validations. Each calD matrix consisted of 70 samples of blended coconut oil with adulterant concentration between 5 and 50% and 5 samples of pure coconut and adulterant oils, while the pD matrix contained 22 samples of both adulterated and pure VCO.Three different calibration models by the MCR-ALS algorithm were built for the determination of the amount of maize, peanut, and sunflower oils added to the VCO, respectively. For this purpose, three augmented matrices  is a popular variable selection approach that uses an evolutionary selection of individuals from a larger population . In the v/v with an increase of 5%, replicated three times. All oil mixtures were stored in borosilicate flasks at 4 °C, in the absence of light. Before the spectral analysis, each sample was returned to room temperature and vortexed for 1 min at 5000 rpm. Finally, 90 VCO blended samples were produced for each adulterant oil, with a total of 270 samples, as reported in VCO of three Italian brands  and three different types of adulterant oils, maize (MO), peanut (PO), and sunflower (SO) from the same brand were purchased from the local market at Rende, Italy. Five samples from each VCO brand and adulterant oils were collected for the analysis of pure sample oils . The ble−1. All spectra were acquired at a resolution of 4 cm−1 and 32 scans. After cleaning and drying the ATR element, the room air spectrum was selected as the background. The ATR plate was cleaned prior to each analysis with dry paper and wiped with hexane and ethanol, making it possible to dry the surface of the ATR. Cleanliness was verified by comparing the background spectrum with the previous ones to check the instrumental conditions and laboratory interferences from H2O and CO2. The spectral data were converted into .csv files suitable for direct import into statistical tools. The computing environment MATLAB®  and The Unscrambler X from CAMO  were used for the handling of ATR-FTIR spectral data.FTIR spectra were acquired on a Fourier transform infrared spectrometer  equipped with a diamond crystal cell attenuated total reflection accessory . Oil samples were placed on the ATR surface and infrared spectra were recorded between 4000 and 450 cm−1 and 2500–1900 cm−1 were not considered due to a lack of information [−1 and 1900–450 cm−1 with a data vector consisting of 2052 wave variables. According to the sample preparation and FTIR spectra acquisition, the experimental data were arranged in four data matrices, one matrix dedicated to pure oil samples with dimensions 30 × 2025 and three matrices for blended samples (70 × 2025 for each adulterant). All the matrices were divided into their respective subsets dedicated to the calibration and validation of the models, as described in the previous section. Prior to the multivariate analysis, a pre-treatment of the data was applied converting the spectral signal from reflectance to absorbance unit and the baseline correction to allow the exploitation of Beer’s law and adjust the spectral offset adjusting the data to the minimum values.The spectral windows 4000–3100 cmormation , so eachThe vibrational spectra of food samples and their adulterants are in many cases very similar, and this is certainly the case for edible vegetable oils. Therefore, chemometric tools for instrumental data handling and spectral identification and quantification are fundamental for the development of quality control strategies. Multivariate curve resolution methodologies are characterized by their ability to process the recorded spectral data and distinguish the spectral contribution of the individual components that make up complex chemical samples, which may consist of two single substances up to highly complex natural mixtures such as food samples.n,m), where the sample spectra (n) are arranged with the corresponding wavenumbers (m). The MCR modeling produces two smaller matrices containing information about the pure components in terms of their respective concentrations (matrix C) and spectra (matrix S); these matrices can be used for classification or quantification purposes, while the spectral profile of the components present in the complex mixtures is useful for their identification. Finally, as shown in Equation (1), where the decomposition is described mathematically, matrix E includes information not explained by the model.The MCR-ALS approach is based on the extraction of relevant information about the single components in a complex chemical system by means of a bilinear decomposition procedure from the experimental data matrix D  algorithm, which involves the generation of a sequence of approximate solutions that change with the execution of several cycles. The ALS procedure is often unable to provide unique solutions due to intensity and/or rotational ambiguity in the elaborations, however, a series of constraints can be applied to reduce the number of responses and fit the optimized result with a chemical significance. The non-negativity constraint can only guarantee positive values for matrix C and S when applied and the correlation constraint is usually dedicated to the MCR-ALS calibration and mixture determination, even in the presence of unknown interferences. The correlation constraint is implemented in the ALS iteration, where the relationship between the reference concentrations and calibration samples is used to predict the concentration of unknown samples. Multivariate resolution was achieved by using the MCR-ALS 2.0 toolbox for Matlab® .In order to evaluate the prediction performance of the MCR-ALS models, external validation was made by using new samples . The following figures of merit were calculated to describe the validation results:RMSEP)Root mean squares error of prediction (RE%)Error in predicted concentrations in% (® available on website: https://michem.unimib.it/ (accessed on 1 October 2022) [Data pre-treatment procedures and variable selection were elaborated by using a regression toolbox for Matlaber 2022) .Many of the analytical methods developed so far to quantify the adulteration of oils often require extensive use of solvents, are time-consuming, and cause the destruction of the samples. The use of FTIR spectroscopy combined with MCR-ALS analysis has proven to be a fast, clean, and non-destructive method. An analytical strategy based on two-step data processing was built, which first used the control chart method to distinguish samples of pure coconut oil from adulterated samples. The collection of the data into augmented matrices, the pre-treatment of the data, variable selection, and the use of correlation constraint, subsequently allowed the quantification of the adulterated samples using MCR calibration models ensuring that the values predicted in the concentration matrices match the effective concentration. Derivative and SNV pre-treatment approaches were very useful to improve the extraction of information from FTIR data and allowed the detection of VCO adulteration when the multivariate spectral analysis was performed. The MCR calibration models were optimized by applying a Genetic Algorithm (GA), which selected the most important variables that showed satisfactory predictive ability in assessing the addition of adulterants with errors below 4.58%. This work confirmed that ATR-FTIR spectroscopy has great potential in the control of food matrices, such as the detection of virgin coconut oil adulteration, and was particularly effective when combined with chemometric tools capable of resolving and understanding spectral signals even from complex food samples.