Breast and prostate cancers are both hormone-driven adenocarcinomas that undergo analogous invasion programs. Using lightsheet microscopy on intact tumors, we identified transitional junctions between precancerous and invasive regions. We then developed a multimodal serial-section workflow integrating volumetric reconstruction with spatial transcriptomics. Analysis of 319 spatial assays from 51 cases revealed gene expression features and novel structural insights defining the shift from precancer to invasive disease. In breast cancer, loss of MGP and PLAT was associated with invasive transition and promoted tumorigenesis in functional assays. In prostate cancer, GDF15, ALDH1A3, ANPEP, and FASN were upregulated along invasive progression, and their knockdown in PC-3 cells suppressed proliferation and migration. Enrichment of tumor-associated macrophages (SPP1+ and MS4A6A+) along non-triple-negative breast cancer breast cancer transitions highlights immune involvement as a potential driver of invasiveness. SIGNIFICANCE:Our method of defining precise spatial locations of invasive transition allows for the direct interrogation of transition drivers, presenting new therapeutic targets for the two most prevalent cancers and providing a framework for studying spatially defined mechanisms of tumor progression. See related commentary by Jing and Li, p. 1720.

Motivation Recent spatial technologies measure the transcriptome, epigenome, proteome, metabolome, and other modalities from thousands of cells across a tissue. Most assays typically profile only one modality from a tissue slice, raising the question of how to align spatial data from heterogeneous feature spaces. While multiple approaches have been developed for multi-modal integration of single-cell datasets, few existing techniques perform spatial alignment across arbitrary modalities incorporating both spatial and feature information.Results We introduce Manifold Gromov-Wasserstein (MGW), a metric-learning framework that exploits the product structure of spatial multiomics to infer modality-specific Riemannian pull-back metrics with neural fields. MGW aligns Riemannian distances induced by these metrics via Gromov-Wasserstein optimal transport, yielding a hyperparameter-free cost across arbitrary modalities sharing a spatial base. The formulation enjoys theoretical invariances-including orthogonal transformations of the spatial and feature domains as well as global feature scalings. We demonstrate the advantages of MGW on multiple alignment tasks, including Stereo-Seq spatiotemporal transcriptomics of mouse embryo, Xenium and Visium spatial transcriptomics of colorectal cancer, and spatial metabolomics-transcriptomics from human striatum and kidney cancer. MGW recovers biologically meaningful correspondences and spatially coherent tissue structures, outperforming existing OT and non-OT based multi-modal baselines.Availability and implementation Software is available at https://github.com/raphael-group/MGW.

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport explicitly constrains the rank of the transport plan to infer latent structure. This improves statistical stability and robustness, yields sharper parametric rates for estimating Wasserstein distances adaptive to the intrinsic rank, and generalizes K-means to co-clustering. These advantages, however, come at the cost of a non-convex and NP-hard optimization problem. We introduce transport clustering, an algorithm to compute a low-rank OT plan that reduces low-rank OT to a clustering problem on correspondences obtained from a full-rank transport registration step. We prove that this reduction yields polynomial-time, constant-factor approximation algorithms for low-rank OT: specifically, a (1+γ) approximation for negative-type metrics and a (1+γ+√(2γ) ) approximation for kernel costs, where γ∈ [0,1] denotes the approximation ratio of the optimal full-rank solution relative to the low-rank optimal. Empirically, transport clustering outperforms existing low-rank OT solvers on synthetic benchmarks and large-scale, high-dimensional datasets.

Recent efforts to build comprehensive tissue and tumor atlases leverage diverse spatial technologies to measure transcriptomic, proteomic, epigenetic, and other modalities with hundreds to thousands of features at thousands to millions of spatially resolved locations in a tissue slice. Integrating such data across spatial technologies that differ in molecular features, spatial resolution, and tissue morphology remains a major challenge. We introduce MultimOdal Spatial Alignment and Integration with Coordinate neural Field (MOSAICField), a unified framework for aligning spatial slices across arbitrary combinations of experimental modalities. MOSAICField computes two types of spatial alignments across multiple slices from the same tissue: physical alignment, which reconstructs a contiguous 3D model of the original tissue, and morphological alignment, which maps distinct morphological or anatomical structures, such as ducts, veins, or neurons, that may traverse the tissue at different angles relative to the direction of slicing. MOSAICField computes both alignments using a deep neural network that estimates a nonlinear deformation field with a multimodal feature loss. We evaluate MOSAICField on simulated data and a prostate cancer sample from the Human Tumor Atlas Network (HTAN), containing more than a dozen spatial slices with multimodal profiling data. MOSAICField constructs an accurate 3D tumor model, tracks the architecture of the prostatic ductal system, and improves analysis of features within and across modalities, outperforming existing methods.

Most evolutionary studies on pancreatic cancer rely on bulk sequencing, yet clonal evolution happens at the single-cell level. We used single-nucleus DNA sequencing to study 137,491 single nuclei from 24 pancreatic neoplasms reflecting various clinical scenarios. We found higher frequencies of somatic alterations to driver genes that bulk studies indicate; many manifest as copy number alterations and account for the majority of spatial heterogeneity. In pancreatic cancers with canonical KRAS oncogenic mutations, we found likely varied dependence on the genotype that may signify differential response to KRAS inhibition. In pancreatic cancers with germline heterozygous BRCA2 mutations, we discovered varied mechanisms and timing of inactivation of the wild-type allele that sculpted differential evolutionary trajectories. Inactivation of tumor-intrinsic response to transforming growth factor-β happens through various mechanisms, takes place after oncogenesis and coincides with invasion and metastasis, reflecting increasing selective pressure for the phenotype later in pancreatic ductal adenocarcinoma development. This study uses single-cell DNA sequencing to analyze genomic evolution in pancreatic cancer using a cohort of multiregionally and longitudinally sampled patients’ tissues across various clinical contexts.

MOTIVATION:Recent dynamic lineage tracing technologies use genome editing to induce heritable mutations, or edits, that accumulate across successive cell divisions. These edits are measured using single-cell sequencing or imaging, providing data to reconstruct cell lineages at single-cell resolution. Current computational approaches to infer cell lineage trees, or phylogenies, from these data perform two separate steps: (i) Identify each cell's edits (genotype) from the raw sequencing or imaging data; (ii) Infer a cell lineage tree from the cell genotypes. However, genotyping cells is an inexact process and genotype errors can yield an inaccurate lineage tree. For example, using fluorescence based-imaging to measure edits results in a high fraction (≈25%-50%) of uncertain or erroneous genotypes. RESULTS:We introduce Lineage Analysis via Maximum Likelihood with PRobabilistic Observations (LAML-Pro), an algorithm that jointly infers cell genotypes and a cell lineage tree. LAML-Pro is based on the Probabilistic Mixed-type Missing Observation (PMMO) model, which we derive to describe both the genome editing and genotype observation processes. LAML-Pro constructs lineage trees from thousands of cells in under an hour by leveraging the sparsity of transitions under the PMMO model. On simulated data, we demonstrate that LAML-Pro corrects genotype errors and infers substantially more accurate trees than existing methods which are vulnerable to genotype errors. Applied to data from two recent imaging-based lineage tracing systems, LAML-Pro reduces genotype errors by 5-fold and produces more spatially coherent lineage trees compared to existing methods. AVAILABILITY AND IMPLEMENTATION:LAML-Pro is implemented in C++ and is available as both a command-line interface and as a Python library at: github.com/raphael-group/LAML-Pro.

Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However, Sinkhorn has quadratic space and time complexity in the number of points, limiting scalability to larger datasets. Low-rank OT achieves linear complexity, but by definition, cannot compute a one-to-one correspondence between points. When the optimal transport problem is an assignment problem between datasets then an optimal mapping, known as the Monge map, is guaranteed to be a bijection. In this setting, we show that the factors of an optimal low-rank coupling co-cluster each point with its image under the Monge map. We leverage this invariant to derive an algorithm, Hierarchical Refinement (HiRef), that dynamically constructs a multiscale partition of each dataset using low-rank OT subproblems, culminating in the bijective Monge map. Hierarchical Refinement runs in log-linear time and linear space, retaining the advantages of low-rank OT while overcoming its limited resolution. We demonstrate the advantages of Hierarchical Refinement on several datasets, including ones containing over a million points, scaling full-rank OT to problems previously beyond Sinkhorn's reach.

During development, cells differentiate through a hierarchy of increasingly restricted cell types, a process that is summarized by a cell differentiation map. Recent technologies profile lineages and cell types at scale, but existing methods to infer cell differentiation maps from these data rely on heuristic models with restrictive assumptions about the developmental process. Here we introduce a quantitative framework to evaluate cell differentiation maps and develop an algorithm, called Carta, that infers an optimal differentiation map from single-cell lineage tracing data. The key insight in Carta is to balance the tradeoff between the complexity of the map and the number of unobserved cell type transitions on the lineage tree. We show that, in models of mammalian trunk development and mouse hematopoiesis, Carta identifies important features of development that are not revealed by other methods, including convergent differentiation of cell types, progenitor differentiation dynamics and new intermediate progenitors.

MOTIVATION:Gene expression varies across a tissue due to both the organization of the tissue into spatial domains, i.e. discrete regions of a tissue with distinct cell type composition, and continuous spatial gradients of gene expression within different spatial domains. Spatially resolved transcriptomics (SRT) technologies provide high-throughput measurements of gene expression in a tissue slice, enabling the characterization of spatial gradients and domains. However, existing computational methods for quantifying spatial variation in gene expression either model only spatial domains-and do not account for continuous gradients of expression-or require restrictive geometric assumptions on the spatial domains and spatial gradients that do not hold for many complex tissues. RESULTS:We introduce GASTON-Mix, a machine learning algorithm to identify both spatial domains and spatial gradients within each domain from SRT data. GASTON-Mix extends the mixture-of-experts (MoE) deep learning framework to a spatial MoE model, combining the clustering component of the MoE model with a neural field model that learns a separate 1D coordinate ("isodepth") within each domain. The spatial MoE is capable of representing any geometric arrangement of spatial domains in a tissue, and the isodepth coordinates define continuous gradients of gene expression within each domain. We show using simulations and real data that GASTON-Mix identifies spatial domains and spatial gradients of gene expression more accurately than existing methods. GASTON-Mix reveals spatial gradients in the striatum and lateral septum that regulate complex social behavior, and GASTON-Mix reveals localized spatial gradients of hypoxia and TNF-α signaling in the tumor microenvironment. AVAILABILITY AND IMPLEMENTATION:GASTON-Mix is available at https://github.com/raphael-group/GASTON-Mix.

Digitized healthcare data, high-throughput profiling technologies, and data repositories have facilitated the emergence of a new era of cancer research. Each data stream requires specialized analysis methods for interpretation. The data-driven era of cancer research requires the development, enhancement, and sustainment of informatics technology software infrastructure, including fundamental methodology development in artificial intelligence and data science. We review current and emerging informatics technology developments for cancer research and discovery, spanning molecular and cellular characterizations, image analysis, informatics, and therapeutics. Summarizing the diverse methods and applications of informatics throughout cancer research identifies themes and emerging areas for the next generation of cancer research. This article is part of a special series: Driving Cancer Discoveries with Computational Research, Data Science, and Machine Learning/AI.

SIGNIFICANCE:Although the pancreatic cancer genome has been described, it has not been explored with respect to stages of diagnosis or treatment bottlenecks. We now describe and quantify the genomic features of PDAC in the context of evolutionary metrics and in doing so have identified a novel prognostic biomarker.

Mammalian brain cell identity is shaped by intrinsic factors and external context. We present a spatially resolved transcriptomic and gene regulatory atlas of cell types found across all subcortical brain regions in a primate - the marmoset monkey. Dense sampling and cross-species integrations revealed spatially precise neuronal assemblies, including in complex structures such as hypothalamus. We find chromatin accessibility and transcriptional identity are spatially tuned within and across subcortical structures. Spatial gradients within subfields of the hippocampal formation are predominantly orchestrated by graded transcription factors coupled with graded enhancers. The primate-expanded population of GABAergic neurons in the thalamus shares transcriptional and regulatory syntax with neurons in superior colliculus, reflecting an evolutionary adaptation compared with rodents. We show that unexpected transcriptional convergence, such as between striatal GABAergic medium spiny neurons and telencephalic glutamatergic neurons, can arise when distinct gene regulatory networks impinge on the same downstream genes. ### Competing Interest Statement The authors have declared no competing interest. National Institute of Mental Health, https://ror.org/04xeg9z08, UM1MH130981 Netherlands Organization for Scientific Research, NWO:024.004.012

Castration-resistant prostate cancer (CRPC) is an aggressive disease exhibiting multiple epigenomic subtypes: androgen receptor-dependent CRPC-AR, and lineage plastic subtypes CRPC-SCL (stem cell-like), CRPC-WNT (Wnt-dependent), and CRPC-NE (neuroendocrine). By transcriptomic profiling of tissue, and whole-genome sequencing (WGS) of tissue and cell-free DNA (cfDNA) from 500 samples, we relate genomic variants with epigenomic state. We find lineage plasticity is associated with higher epigenomic and genomic heterogeneity. Samples with CRPC-SCL show higher chromosomal instability. We find DNA alterations, particularly chromosomal rearrangements, in the YAP/TAZ pathway associated with CRPC-SCL. For example, complex rearrangements on chromosome 4, which are supported by patient-matched 3D genome architecture data, decrease promoter interactions of MOB1B , a YAP/TAZ pathway inhibitor, with its enhancers. Together, the genomic variants in the pathway can predict CRPC-SCL with 79% accuracy. We show the utility of cfDNA WGS for joint inference of epigenomic state and genomic variants, which can guide patient stratification for clinical decisions. Significance:This study reveals genomic variants associated with the presence of lineage-plastic CRPC stem cell-like state. We leverage the utility of minimally invasive cfDNA sequencing to obtain genomic and epigenomic insights about CRPC heterogeneity, which have implications for patient stratification for treatment decisions.

Castration resistant prostate cancer (CRPC) is an aggressive, highly plastic, late-stage disease. We previously showed that the two histological subtypes, adenocarcinoma (CRPC-Adeno) and neuroendocrine (CRPC-NE), show four epigenetic and transcriptomic subtypes: CRPC-AR depends on the androgen receptor pathway, CRPC-SCL is stem-cell like, CRPC-WNT is dependent on the WNT pathway, and CRPC-NE has high expression of neuroendocrine markers. Here, by analyzing data from 500 patients with tissue and/or liquid biopsies, we uncover the landscape of molecular heterogeneity in patient tumors. Analysis of whole-genome sequencing revealed genomic variants associated with CRPC-SCL and allowed development of a computational classifier which can predict presence of CRPC-SCL in patient tumors solely using genomic alterations with 81% accuracy. In particular, analysis of matched chromatin conformation data (Hi-C) showed a complex rearrangement on chromosome 4 disrupts enhancer - promoter contacts leading to downregulation of MOB1B, which can lead to upregulation of the YAP/TAZ pathway that is characteristic of CRPC-SCL. Joint computational inference of epigenomic state and genomic variants from cell-free DNA collected at multiple points during the evolution of resistance to AR signaling inhibitors allowed investigation of genomic and epigenomic co-evolution at an unprecedented resolution. We discuss the current limits of detection for tumoral epigenomic and genomic states using cell-free DNA for clinical application. Importantly, our study demonstrates the utility of liquid biopsies for discovery of basic biological mechanisms leading to treatment resistance, beyond their use for biomarkers. Marjorie Roskes, Alexander Martinez-Fundichely, Weiling Li, Sandra Cohen, Hao Xu, Shahd ElNaggar, Anisha Tehim, Metin Balabin, Chen Khuan Wong, Yu Chen, Ben Raphael, Ekta Khurana. Evolution of genomic and epigenomic heterogeneity in prostate cancer from tissue and liquid biopsies [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2025; Part 1 (Regular Abstracts); 2025 Apr 25-30; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2025;85(8_Suppl_1):Abstract nr 3883.

scATAC-seq data presents unprecedented opportunities to identify somatic mutations in regulatory regions. However, existing tools struggle to reliably detect somatic mutations from scATAC-seq data due to the unbalanced coverage between tumor and normal cells. To address this, we developed scVar, a pipeline designed to detect somatic mutations from scATAC-seq data. Applying scVar to snATAC-Seq data from about 200 tumor samples spanning 10 cancer types, we identified over 70, 000 somatic mutations, with 95% located in non-coding regions. Comparison with bulk WGS and WXS data demonstrated that scVar achieves high accuracy in detecting somatic mutations. Notably, scVar effectively recaptured the UV mutational signature in skin cancer. Variant allele frequency (VAF) analysis revealed an increase in VAF in snATAC-seq data compared to WXS data. For tumor suppressor genes such as TP53, VHL, BAP1, CDH1, CBFB, TGIF1, and ZNF750, homozygous mutations with VAFs approaching 1 were consistently detected in snATAC-seq data, emphasizing the critical role of biallelic variants in tumor initiation. We also observed recurrent TERT promoter mutations across 20 samples, with VAFs close to 1, which were associated with increased chromatin accessibility and expression in glioblastoma, but not in skin cancer. Additionally, novel promoter mutations, such as in CDK12, were linked to increased gene expression. These findings highlight the utility of scVar in uncovering somatic mutations and their functional effects in non-coding regions from scATAC-seq data. Song Cao, Liting Zhang, Alla Karpova, Fernanda M. Rodrigues, Yingduo Song, Nadezhda V. Terekhanova, Benjamin J. Raphael, Ryan C. Fields, Feng Chen, Li Ding. Discovery of non-coding somatic driver mutations in single-cell chromatin accessibility data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2025; Part 1 (Regular Abstracts); 2025 Apr 25-30; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2025;85(8_Suppl_1):Abstract nr 2385.

Viral infections and cancers are driven by evolution of populations of highly mutable genomic variants. A key evolutionary process in these populations is their migration or spread via transmission or metastasis. Understanding this process is crucial for research, clinical practice, and public health, yet tracing spread pathways is challenging. Phylogenetics offers the main methodological framework for this problem, with challenges including determining the conditions when a phylogenetic tree reflects the underlying migration tree structure, and balancing computational efficiency, flexibility, and biological realism. We tackle these challenges using the powerful machinery of graph homomorphisms, a mathematical concept describing how one graph can be mapped onto another while preserving its structure. We focus on metastatic migrations and viral host-to-host transmissions in outbreak settings. We investigate how structural constraints on migration patterns influence the relationship between phylogenetic and migration trees and propose algorithms to evaluate trees consistency under varying conditions. Leveraging our findings, we introduce a framework for inferring transmission/migration trees by sampling potential solutions from a prior random tree distribution and identifying a subsample consistent with a given phylogeny. By varying the prior distribution, this approach generalizes several existing models, offering a versatile strategy applicable in diverse settings.

The properties of mammalian cells depend on their location within organs. Gene expression in the liver varies between periportal and pericentral hepatocytes1-3, and in the intestine from crypts to villus tips4,5. A key element of tissue spatial organization is probably metabolic, but direct assessments of spatial metabolism remain limited. Here we map spatial metabolic gradients in the mouse liver and intestine. We develop an integrated experimental-computational workflow using matrix-assisted laser desorption/ionization (MALDI) imaging mass spectrometry (IMS), isotope tracing and deep-learning artificial intelligence. Most measured metabolites (>90%) showed significant spatial concentration gradients in the liver lobules and intestinal villi. In the liver, tricarboxylic acid (TCA)-cycle metabolites and their isotope labelling from both glutamine and lactate localized periportally. Energy-stress metabolites, including adenosine monophosphate (AMP), also localized periportally, consistent with a high periportal energy demand. In the intestine, the TCA intermediates malate (tip) and citrate (crypt) showed opposite spatial patterns, aligning with higher glutamine catabolism in tips and lactate oxidation in crypts based on isotope tracing. Finally, we mapped the fate of the obesogenic dietary sugar fructose. In the intestine, oral fructose was catabolized faster in the villus bottom than in the tips. In the liver, fructose-derived carbon accumulated pericentrally as fructose-1-phosphate and triggered pericentral adenosine triphosphate (ATP) depletion. Thus, we both provide foundational knowledge regarding intestine and liver metabolic organization and identify fructose-induced focal derangements in liver metabolism.

Dynamic lineage tracing technologies combine genome editing with single-cell sequencing to track cell divisions. We introduce Lineage Analysis via Maximum Likelihood (LAML) to infer a maximum likelihood time-resolved cell lineage tree under the Probabilistic Mixed-type Missing model, which we derive to describe key features of dynamic lineage tracing systems. LAML produces accurate tree topologies with branch lengths representing experimental time between ancestral cells. LAML outperforms existing methods in terms of accuracy and scalability on simulated data, and calculates the timing of cell migrations to metastatic sites in a mouse model of lung adenocarcinoma, revealing distinct epochs of metastasis progression.

Deriving the sequence of transitions between cell types, or differentiation events, that occur during organismal development is one of the fundamental challenges in developmental biology. Single-cell and spatial sequencing of samples from different developmental timepoints provide data to investigate differentiation but inferring a sequence of differentiation events requires: (1) finding trajectories, or ancestor:descendant relationships, between cells from consecutive timepoints; (2) coarse-graining these trajectories into a differentiation map, or collection of transitions between cell types, rather than individual cells. We introduce Hidden-Markov Optimal Transport (HM-OT), an algorithm that simultaneously groups cells into cell types and learns transitions between these cell types from single-cell or spatial developmental time series. HM-OT uses low-rank optimal transport to simultaneously align samples in a time series and learn a sequence of clusterings and a differentiation map with minimal total transport cost.

A common problem in phylogeny is to reconstruct the ancestral states of a feature measured at the present time. The classic Fitch-Hartigan and Sankoff algorithms compute the most parsimonious or most likely reconstruction. However, these approaches do not readily extend to structured ancestral reconstruction problems, such as those encountered when inferring the routes of metastases in cancer, deriving the transmission history of viruses, or detecting horizontal gene transfer in phylogenetic networks. We develop a combinatorial optimization approach to ancestral reconstruction problems based on the tree-labeling polytope, a geometric object whose vertices represent the ancestral labelings of a tree. We derive algorithms for three structured ancestral reconstruction problems: parsimonious migration history, softwired small parsimony, and convex recoloring. We apply these algorithms to analyze routes of metastasis in a mouse model of lung adenocarcinoma using lineage-tracing data from thousands of single cells.