The name MANTRA stands for Multi-view ANalysis with Tensor and matRix Alignment, and the framework was developed by Kevin De Azevedo, Yusuf Berk Oruc, and Florian Buettner, who contributed to the German Cancer Consortium and the Frankfurt Cancer Institute. Conceptually, MANTRA can be understood as a generalization of group factor analysis to tensor-valued data, or conversely, as an extension of classical tensor decomposition into the multi-view setting. It takes as input a collection of datasets, some three-dimensional and some two-dimensional, and decomposes them jointly into shared low-dimensional latent factors. Each mode of the data, whether patients, drugs, cytokines, cell types, or genes, receives its own embedding matrix, and products of these matrices yield interpretable loadings that expose interactions between the different dimensions.

What makes MANTRA technically distinctive is its Bayesian formulation with structured sparsity priors. The model places horseshoe priors on feature embeddings, a multi-scale shrinkage approach well suited to variational inference. Within this scheme, an Automatic Relevance Determination prior allows individual factors to be active in only a subset of data views, while local regularization encourages sparsity within each factor itself. This design has two practical consequences. First, unneeded factors are automatically driven toward zero, making the model remarkably robust when the true rank of the data is unknown, a common and frustrating problem in real applications. Second, the sparse factors highlight only the most relevant features, making the results biologically interpretable rather than opaque. Missing values, a perennial headache in clinical studies where not every omics layer can be profiled for every patient, are handled natively and in a principled manner.

The team validated MANTRA extensively on synthetic data before turning to real biology. In systematic benchmarks against PARAFAC, a state-of-the-art tensor decomposition implementation from the TensorLy package, MANTRA performed comparably in the high signal-to-noise regime and substantially better in the noisy, sparse, low-sample conditions that mimic real-world datasets. When the models were deliberately fitted with more factors than the true rank, MANTRA’s sparsity priors switched off the excess factors, whereas PARAFAC degraded. Scalability analyses on GPU hardware showed favorable scaling across sample counts, feature dimensions, and ranks, and sensitivity analyses confirmed that the choice of prior hyperparameters for the noise model leaves reconstruction accuracy stable across a broad range of data conditions.

The first real-world application focused on Chronic Lymphocytic Leukemia, a disease in which inter-patient heterogeneity strongly influences treatment outcomes. The researchers analyzed a published dataset of 192 primary CLL samples in which cell viability had been measured in response to 12 drugs under 17 different microenvironmental stimuli, complemented by bulk RNA sequencing of the same patients. This produced exactly the kind of mixed-order collection MANTRA was designed for: a third-order drug viability tensor of patients, drugs, and cytokines, alongside a second-order RNA-seq matrix of patients and genes. When trained on the drug tensor alone, MANTRA’s patient embeddings showed only a partial association with IGHV mutation status, one of the most important prognostic markers in CLL, distinguishing patients with typically aggressive unmutated disease from those with more indolent mutated disease.

The picture changed dramatically when the transcriptomic view was added. In the joint multi-view model, the patient embeddings separated sharply by IGHV status, and the drug loadings recovered known biological relationships, with drugs targeting the B-cell receptor, MAPK, and DNA damage response pathways clustering together. Quantitatively, the researchers used Leiden clustering of the learned latent space and measured alignment with clinical labels using adjusted Rand index and normalized mutual information, following standard practice from the single-cell integration literature. MANTRA outperformed MOFA+ and MOFA-FLEX, two leading matrix-based multi-omics tools, which had to flatten the three-dimensional drug tensor into stacks of two-dimensional matrices. MANTRA also separated patients by Trisomy 12, an intermediate-risk cytogenetic abnormality present in roughly ten to twenty percent of CLL patients, more accurately than the baselines, demonstrating that the model captures clinically meaningful axes of variation relevant to stratification and treatment response.

The second application pushed MANTRA into the single-cell arena, where the stakes were even higher. The team analyzed a multi-omics dataset from 18 pediatric patients with KMT2A-rearranged Acute Lymphoblastic Leukemia and 5 healthy donors, constructing two third-order tensors of patients, cell types, and features: one for single-cell RNA sequencing and one for single-cell ATAC sequencing. Because MANTRA tolerates missing values, it could use all 18 patients, whereas the specialized tool scITD, which requires every cell type to be observed in every donor, had to discard 7 of them. Both methods separated healthy donors from leukemia patients, but only MANTRA went further, splitting the patients into two distinct subgroups driven by a factor that was predominantly active in plasmacytoid dendritic cells, a rare immune cell population that turned out to be the surprising driver of disease heterogeneity.

Pathway analysis revealed what this plasmacytoid dendritic cell factor meant biologically. Genes loading strongly on the factor were enriched for interferon signaling and other immune-active pathways as well as endoplasmic reticulum stress programs, while lymphoid transcription factors such as ETV6 showed low loadings and genes typically implicated in T-cell lineage leukemia, including BCL2, MYC, and LYL1, showed high loadings. One patient subgroup carried a high-immune-activity, low-ER-stress program in their plasmacytoid dendritic cells, while the other occupied the opposite end of the spectrum. Critically, neither MOFA+, MOFA-FLEX, nor scITD detected this cell-type-specific stratification; all of their factors were dominated by blast cells. The finding was validated in an independent cohort of 7 pediatric B-ALL patients and 4 healthy donors, and when MANTRA was run on pediatric T-ALL data as a negative control, no such factor appeared, confirming that the plasmacytoid dendritic cell program is specific to B-cell acute lymphoblastic leukemia.

The linear structure of MANTRA is both its strength and its acknowledged limitation. Linear factor models are inherently interpretable, allowing biologists to trace each factor back to specific cell types, drugs, and pathways through the generalized loadings matrix. But capturing non-linear relationships would require kernel methods or deep architectures that would sacrifice precisely this transparency. The authors also note that in datasets where structural dependencies between dimensions are negligible, or where extreme sparsity and noise prevail, simpler matrix factorizations may remain equally effective or more stable. Identifiability and rotational invariance, perennial issues for all latent variable models, also apply here. Still, the researchers point toward supervised extensions of the framework as a promising future direction, albeit one that brings new overfitting challenges.

The implications reach well beyond leukemia. Drug screens that measure patient-derived cells across drugs and microenvironmental conditions, single-cell atlases that profile multiple tissues per donor, and multi-modal studies combining expression with chromatin accessibility all generate data with exactly the mixed-order tensor structure that MANTRA handles natively. By refusing to flatten higher-order structure into matrices, and by handling missing data through principled Bayesian inference rather than ad hoc imputation, the tool opens a window onto biological variation that existing methods systematically miss. The code is publicly available on GitHub, implemented in Python using the probabilistic programming library Pyro, and the discovery that a rare immune cell type defines clinically relevant leukemia subgroups offers a vivid demonstration of what becomes visible when algorithms finally learn to see data in all of its dimensions.

Subject of Research: Interpretable Bayesian integration of mixed-order multi-omics tensors for leukemia patient stratification

Article Title: Interpretable multi-omics integration across mixed-order tensors with MANTRA

Article References: De Azevedo, K., Oruc, Y. B., & Buettner, F. (2026). Interpretable multi-omics integration across mixed-order tensors with MANTRA. Molecular Systems Biology, 22(9), 1415-1429. https://doi.org/10.1038/s44320-026-00223-8

Image Credits: AI Generated

DOI: 10.1038/s44320-026-00223-8

Keywords: MANTRA, tensor decomposition, multi-omics, Bayesian inference, chronic lymphocytic leukemia, acute lymphoblastic leukemia, drug response, single-cell RNA-seq, single-cell ATAC-seq, plasmacytoid dendritic cells, structured sparsity, patient stratification

The work, led by Mitali U. Sheth, Wen-Lyong Qiu, Xiang Ru Ma and colleagues, addresses a gap that has widened as single-cell genomics has exploded in scale. Technologies such as single-cell RNA sequencing can now measure gene expression in hundreds of thousands of individual cells simultaneously, and single-cell ATAC-seq can profile chromatin accessibility, revealing which regulatory regions are open and potentially active in each cell. But these measurements, taken separately, do not by themselves reveal regulatory wiring. An enhancer may be accessible in a neuron, yet without evidence linking its activity to a target gene’s expression, its functional role remains speculative. Traditional approaches to establishing enhancer–gene links, such as CRISPR-based enhancer deletion or perturbation screens, are powerful but labor-intensive and difficult to scale across the enormous diversity of cell types in complex tissues.

The framework developed by the team leverages a key statistical insight: regulatory interactions leave fingerprints in the natural variation of gene expression and chromatin state across cells. If an enhancer genuinely controls a gene, then across the thousands of cells captured in a single-cell dataset, variation in that enhancer’s activity should be correlated with variation in the target gene’s expression, with effects that appear at the expected genomic distance and that are shaped by transcription factor binding motifs embedded in the enhancer sequence. By aggregating these weak signals across large cell populations and modeling them jointly, the method can distinguish true regulatory links from the many spurious correlations that arise from shared cellular states, cell cycle effects, or batch artifacts — confounders that have historically plagued correlation-based enhancer–gene inference.

A critical component of the approach is its handling of confounding at the level of cell identity. Because all genes in a given cell type tend to rise and fall together, naive correlation analysis assigns enhancers promiscuously to nearby genes, inflating the apparent regulatory network. The new method explicitly models and removes this shared component of variation, isolating the residual, enhancer-specific signal that reflects direct regulation. It also incorporates prior biological knowledge, including enhancer–promoter distance constraints, chromatin contact frequency data from technologies such as Hi-C and promoter capture assays, and sequence features that indicate which transcription factors bind a given enhancer. The result is a ranked set of candidate enhancer–gene pairs for each cell type, each accompanied by a quantitative confidence score that researchers can use to prioritize downstream experimental validation.

To benchmark the framework, the authors compared its predictions against gold-standard perturbation data — instances in which individual enhancers had been experimentally deleted or repressed and the resulting change in target gene expression measured directly. Across the validation sets, the computational predictions recovered a substantial fraction of experimentally confirmed enhancer–gene pairs while maintaining specificity, meaning they did not drown the true positives in a sea of false links. Notably, the method correctly identified many cases in which the nearest gene is not the actual target, a phenomenon that single-cell perturbation screens have increasingly shown to be common. Enhancers frequently skip over adjacent genes to contact promoters further away, and distance-based or nearest-gene assumptions systematically miss these long-range relationships.

One of the most striking demonstrations of the framework’s power comes from its application to disease genetics. When the researchers overlaid genome-wide association study summary statistics for a range of traits and diseases onto their enhancer–gene maps, they were able to trace risk variants to plausible target genes in a cell-type-specific manner. This step is where the method’s value becomes tangible for translational research. A noncoding variant associated with, say, an autoimmune disorder may lie within an enhancer active only in a specific subset of immune cells; by linking that enhancer to its gene targets computationally, researchers gain immediate hypotheses about the molecular mechanism of disease risk and the cellular context in which it operates. The maps effectively convert a list of statistically associated genomic coordinates into a functional annotation, complete with directionality and tissue relevance.

The study also illustrates how the same regulatory architecture can produce different outcomes in different cell types. The authors found that a substantial proportion of enhancers exhibit cell-type-specific target preferences: a given regulatory element may drive expression of one gene in a cortical neuron and an entirely different gene in an astrocyte, even when both cell types share the same underlying genome. This context dependence has major implications for interpreting both normal development and disease. It means that a single variant in a pleiotropic enhancer can contribute to multiple phenotypes through distinct target genes depending on where it is active, and it underscores why bulk-tissue studies, which average signals across mixed cell populations, often fail to resolve the relevant biology.

Technically, the framework operates on paired or unpaired single-cell multi-ome data, in which gene expression and chromatin accessibility are profiled either in the same individual cells or in parallel samples from the same biological condition. The method constructs a graph-based representation of cell-to-cell similarity, smooths sparse single-cell measurements over this graph to recover signal lost to dropout and shallow sequencing depth, and then evaluates enhancer–gene relationships using a regularized regression model that jointly considers all candidate enhancers within a defined genomic window around each gene. Regularization is essential: with tens of thousands of candidate enhancers competing to explain each gene’s expression, the model must penalize complexity to avoid overfitting noise. The learned weights, combined with the motif and chromatin contact priors, yield the final interaction scores. The authors have made the pipeline available to the community, and its computational design allows it to scale to the atlas-sized datasets — millions of cells spanning dozens of tissues — that are now being generated by consortia worldwide.

The implications extend well beyond human genetics. Enhancer–gene maps of this kind provide a substrate for studying gene regulatory network evolution, allowing comparative analyses of how regulatory wiring differs between species or between healthy and diseased states. In cancer genomics, where structural variants frequently rewire enhancer–promoter contacts to activate oncogenes, cell-type-resolved regulatory maps could help identify which tumors depend on which enhancer hijacking events. In developmental biology, the framework offers a way to trace how transcriptional programs are controlled as cells progress through differentiation, capturing transient regulatory relationships that exist only in rare intermediate cell states — populations too small and too fleeting to study with bulk methods.

Limitations remain, and the authors are careful to acknowledge them. Correlation-based inference, however sophisticated, cannot fully substitute for direct perturbation; some predicted interactions will prove false when tested experimentally, and some true interactions may be missed if the relevant enhancing activity is rare or condition-specific. Single-cell datasets also under-sample rare cell types, meaning that regulatory maps for those populations will be less complete. Moreover, chromatin accessibility is an imperfect proxy for enhancer activity: an open region is not necessarily an active enhancer, and methods that read out actual enhancer transcription, such as single-cell eRNA detection, could add further resolution in the future. The integration of the computational maps with systematic CRISPR perturbation screens — using the predictions to guide which enhancers to test — represents a promising hybrid strategy that combines scale with causal certainty.

What the study ultimately delivers is a change in the default assumption researchers can make when confronted with a noncoding variant. Where the fallback was once the nearest gene, it can now be a cell-type-specific, confidence-scored list of candidate targets derived from the collective behavior of thousands of single cells. As single-cell atlases continue to grow and as perturbation technologies mature, frameworks like this one are positioned to become standard infrastructure for interpreting the regulatory genome — the layer of DNA that, despite encoding no proteins, orchestrates when, where, and how much every gene is expressed. In bridging the gap between variant catalogs and mechanism, the work brings the field measurably closer to the long-promised era of actionable noncoding genetics.