Temporal tissue dynamics from a spatial snapshot

Quantifying cell-state densities in single-cell phenotypic landscapes using Mellon

Cell-state density characterizes the distribution of cells along phenotypic landscapes and is crucial for unraveling the mechanisms that drive diverse biological processes. Here, we present Mellon, an algorithm for estimation of cell-state densities from high-dimensional representations of single-cell data. We demonstrate Mellon’s efficacy by dissecting the density landscape of differentiating systems, revealing a consistent pattern of high-density regions corresponding to major cell types intertwined with low-density, rare transitory states. We present evidence implicating enhancer priming and the activation of master regulators in emergence of these transitory states. Mellon offers the flexibility to perform temporal interpolation of time-series data, providing a detailed view of cell-state dynamics during developmental processes. Mellon facilitates density estimation across various single-cell data modalities, scaling linearly with the number of cells. Our work underscores the importance of cell-state density in understanding the differentiation processes, and the potential of Mellon to provide insights into mechanisms guiding biological trajectories.

Integrated computational and in vivo models reveal Key Insights into macrophage behavior during bone healing

Myeloid-derived monocyte and macrophages are key cells in the bone that contribute to remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage dynamics and polarization states over time: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. Bone healing is a complex multicellular dynamic process. While traditional in vitro and in vivo experimentation may capture the behavior of select populations with high resolution, they cannot simultaneously track the behavior of multiple populations. To address this, we have used an integrated coupled ordinary differential equations (ODEs)-based framework describing multiple cellular species to in vivo bone injury data in order to identify and test various hypotheses regarding bone cell populations dynamics. Our approach allowed us to infer several biological insights including, but not limited to,: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. In addition, we further tested the robustness of the mathematical model by comparing simulation results to an independent experimental dataset. Taken together, this novel comprehensive mathematical framework allowed us to identify biological mechanisms that best recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. Furthermore, our hypothesis testing methodology could be used in other contexts to decipher mechanisms in complex multicellular processes.

Comparing phenotypic manifolds with Kompot: Detecting differential abundance and gene expression at single-cell resolution

Single-cell studies are frequently designed to compare across conditions such as health and disease. However, existing computational approaches typically rely on grouping cells into discrete populations before making comparisons, which can limit resolution for detecting state-dependent changes. Here, we introduce Kompot, a statistical framework for comparative analysis of multi-condition single-cell data. Kompot quantifies both differential abundance, capturing how cells redistribute across the phenotypic space, and differential expression, identifying condition-specific transcriptional changes that may be localized, heterogeneous, or oppositely regulated across states. By modeling cell density and gene expression as continuous functions over a shared cell-state representation, Kompot enables single-cell–resolution inference with principled uncertainty estimates, without requiring predefined clusters or cell types. Applying Kompot to aging murine bone marrow, we identified a continuum of shifts in hematopoietic stem cell and mature cell states, transcriptional remodeling of monocytes independent of compositional changes, and divergent regulation of oxidative stress response genes across cell types. We demonstrate the utility of Kompot in disease settings by identifying cell-state and gene expression changes associated with improved efficacy of combinatorial immunotherapy in melanoma. Additionally, Kompot enables multi-sample comparative analysis by accounting for sample-to-sample heterogeneity. By capturing both global and cell-state–specific effects of perturbation, the Kompot framework is broadly applicable to dissecting condition-specific effects in complex single-cell landscapes. ### Competing Interest Statement The authors have declared no competing interest. National Institutes of Health, R35GM147125, R01CA292932, T32GM136534, S10OD028685 The Mark Foundation for Cancer Research, https://ror.org/00v7th354, Endeavor Award Edward P. Evans Foundation, https://ror.org/03h22gm35, Discovery Research Grant Brotman Baty Institute, https://ror.org/03jxvbk42, Pilot Award

Modeling Osteocyte Network Formation: Healthy and Cancerous Environments

Advanced cancers, such as prostate and breast cancers, commonly metastasize to bone. In the bone matrix, dendritic osteocytes form a spatial network allowing communication between osteocytes and the osteoblasts located on the bone surface. This communication network facilitates coordinated bone remodelling. In the presence of a cancerous microenvironment, the morphology of this network changes. Commonly osteocytes appear to be either overdifferentiated (i.e., there are more dendrites than healthy bone) or underdeveloped(i.e., dendrites do not fully form). In addition to structural changes, histological sections from metastatic breast cancer xenografted mice show that number of osteocytes per unit area is different between healthy bone and cancerous bone. We present a stochastic agent-based model for bone formation incorporating osteoblasts and osteocytes that allows us to probe both network structure and density of osteocytes in bone. Our model both allows for the simulation of our spatial network model and analysis of mean-field equations in the form of integro-partial differential equations. We considered variations of our model to study specific physiological hypotheses related to osteoblast differentiation; for example predicting how changing biological parameters, such as rates of bone secretion, rates of cancer formation and rates of osteoblast differentiation can allow for qualitatively different network morphologies. We then used our model to explore how commonly applied therapies such as bisphosphonates (e.g. zoledronic acid) impact osteocyte network formation.

An Integrated Computational Model of the Bone Microenvironment in Bone-Metastatic Prostate Cancer

Abstract Bone metastasis will impact most men with advanced prostate cancer. The vicious cycle of bone degradation and formation driven by metastatic prostate cells in bone yields factors that drive cancer growth. Mechanistic insights into this vicious cycle have suggested new therapeutic opportunities, but complex temporal and cellular interactions in the bone microenvironment make drug development challenging. We have integrated biologic and computational approaches to generate a hybrid cellular automata model of normal bone matrix homeostasis and the prostate cancer-bone microenvironment. The model accurately reproduces the basic multicellular unit bone coupling process, such that introduction of a single prostate cancer cell yields a vicious cycle similar in cellular composition and pathophysiology to models of prostate-to-bone metastasis. Notably, the model revealed distinct phases of osteolytic and osteogenic activity, a critical role for mesenchymal stromal cells in osteogenesis, and temporal changes in cellular composition. To evaluate the robustness of the model, we assessed the effect of established bisphosphonate and anti-RANKL therapies on bone metastases. At approximately 100% efficacy, bisphosphonates inhibited cancer progression while, in contrast with clinical observations in humans, anti-RANKL therapy fully eradicated metastases. Reducing anti-RANKL yielded clinically similar results, suggesting that better targeting or dosing could improve patient survival. Our work establishes a computational model that can be tailored for rapid assessment of experimental therapies and delivery of precision medicine to patients with prostate cancer with bone metastases. Cancer Res; 74(9); 2391–401. ©2014 AACR.

Computational Modeling of Interactions between Multiple Myeloma and the Bone Microenvironment

Multiple Myeloma (MM) is a B-cell malignancy that is characterized by osteolytic bone lesions. It has been postulated that positive feedback loops in the interactions between MM cells and the bone microenvironment form reinforcing ‘vicious cycles’, resulting in more bone resorption and MM cell population growth in the bone microenvironment. Despite many identified MM-bone interactions, the combined effect of these interactions and their relative importance are unknown. In this paper, we develop a computational model of MM-bone interactions and clarify whether the intercellular signaling mechanisms implemented in this model appropriately drive MM disease progression. This new computational model is based on the previous bone remodeling model of Pivonka et al. [1], and explicitly considers IL-6 and MM-BMSC (bone marrow stromal cell) adhesion related pathways, leading to formation of two positive feedback cycles in this model. The progression of MM disease is simulated numerically, from normal bone physiology to a well established MM disease state. Our simulations are consistent with known behaviors and data reported for both normal bone physiology and for MM disease. The model results suggest that the two positive feedback cycles identified for this model are sufficient to jointly drive the MM disease progression. Furthermore, quantitative analysis performed on the two positive feedback cycles clarifies the relative importance of the two positive feedback cycles, and identifies the dominant processes that govern the behavior of the two positive feedback cycles. Using our proposed quantitative criteria, we identify which of the positive feedback cycles in this model may be considered to be ‘vicious cycles’. Finally, key points at which to block the positive feedback cycles in MM-bone interactions are identified, suggesting potential drug targets.

Mathematical Discovery of Potential Therapeutic Targets: Application to Rare Melanomas

Patients with rare types of melanoma such as acral, mucosal, or uveal melanoma, have lower survival rates than patients with cutaneous melanoma; these lower survival rates reflect the lower objective response rates to immunotherapy compared to cutaneous melanoma. Understanding tumor-immune dynamics in rare melanomas is critical for the development of new therapies and for improving response rates to current cancer therapies. Progress has been hindered by the lack of clinical data and the need for better preclinical models of rare melanomas. Canine melanoma provides a valuable comparative oncology model for rare types of human melanomas. We analyzed RNA sequencing data from canine melanoma patients and combined this with literature information to create a novel mechanistic mathematical model of melanoma-immune dynamics. Sensitivity analysis of the mathematical model indicated influential pathways in the dynamics, providing support for potential new therapeutic targets and future combinations of therapies. We share our learnings from this work, to help enable the application of this proof-of-concept workflow to other rare disease settings with sparse available data.

VAPOR: A variational autoencoder with transport operators to disentangle cellular gene expression dynamics of co-occurring biological processes in time and space

Abstract Single-cell and spatial transcriptomics enable the analysis of cellular states and dynamics in gene expression, revealing how diverse biological processes relate to these states over time and space. To study these dynamics, trajectory inference methods order cells along computationally inferred paths to reconstruct gradual transitions in cell states. However, by encouraging smooth and continuous trajectories, these approaches tend to conflate co-occurring processes-such as proliferation, maturation, and spatial organization-that are jointly reflected in gene expression, potentially overlooking process-specific gene expression dynamics. To address this, we developed VAPOR, which integrates a variational autoencoder with transport operators to model and disentangle cellular gene expression dynamics for potentially co-occurring biological processes. VAPOR inputs single-cell (or spatial) gene expression data into a variational autoencoder (VAE) to learn the latent states of cells and then models their latent dynamics as an ordinary differential equation. The latent dynamics are further decomposed into process-specific components parameterized by transport operators (TOs) and their corresponding process weights. Each TO defines a process-specific dynamics, and its weight for each cell quantifies the process's contribution to the cell dynamics. After assessment by simulation studies, we applied VAPOR with benchmarking to real data, including time-course scRNA-seq from postconceptual human brain development, spatial transcriptomics of the mouse hippocampus, and cross-species scRNA-seq spanning human and macaque first-trimester forebrain development. In these applications, VAPOR has identified a variety of temporal and spatial co-occurring processes, such as cell cycle, gliogenesis, neurogenesis, and neuronal migration, along with associated dynamic genes, including those species-specific to human and macaque development. VAPOR is available as an open-source tool for general-purpose use. ### Competing Interest Statement The authors have declared no competing interest.

Patient-derived model capturing hypoxia and extracellular matrix remodelling of immunologically cold high-grade serous tumours

High-grade serous carcinoma tumours present poor survival rates, often associated with immunologically excluded environments driven by hypoxia and extensive extracellular matrix remodelling that disrupt tumour-stromal-immune interactions. Current experimental models fail to fully capture these microenvironmental features, limiting understanding of tumour-immune dynamics and drug development. Here, we present bioengineered patient-derived tumour-immune models to mimic physiologically relevant oxygen levels and extracellular matrix remodelling. Cancer cells are co-cultured with cancer-associated fibroblasts within human plasma-3D matrices or grown on decellularized human ovaries. Immune cells are either included within the 3D constructs to study multi-cellular interactions or challenged to infiltrate the matrices. We demonstrate that intratumoural hypoxia acts as a friend and a foe enhancing the activation and cytotoxicity of CD8 + T cells while inducing stromal/matrix dysregulation associated with impaired immune infiltration. Targeting TGF-β signalling attenuates the hypoxia-driven stromal-mediated immune exclusion. These relevant models may aid the development of targeted therapies to transform immunologically cold tumours into immunogenic to benefit female patients.

Towards a new spatial representation of bone remodeling

Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology. Different approaches to modeling give insight into different aspects of a phenomena so it is useful to have an arsenal of various computational and mathematical models. Here we develop a mathematical representation of bone remodeling that can effectively describe many aspects of the complicated geometries and spatial behavior observed.    There is a sharp interface between bone and marrow regions. Also the surface of bone moves in and out, i.e. in the normal direction, due to remodeling. Based on these observations we employ the use of a level-set function to represent the spatial behavior of remodeling. We elaborate on a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes.    We exhibit simulations based on our computational model that show the motion of the interface between bone and marrow as a consequence of bone remodeling. The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo.    By employing the level set approach it is possible to develop computational and mathematical representations of the spatialbehavior of bone remodeling. By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo. This makes it possible to perform in silica experiments more closely resembling experimental observations.

A unified network systems approach uncovers a core program underlying T follicular helper cell differentiation

Characterizing multi-scale processes underlying immune-state progression is critical for defining their function. This becomes pertinent for functionally diverse and plastic immune cells, such as T follicular helper (Tfh) cells. Here, we adopt a multi-scale network-systems approach that incorporates both regulatory and protein-protein interactions. This approach integrates diverse data types, captures regulation across levels of immune system organization, and recapitulates known Tfh differentiation drivers. Further, we present CoreNet, a core Tfh gene set that is conserved between humans and mice, across tissue types and disease contexts, and is consistent across data modalities. Using CoreNet, we implicate NR3C1 and interleukin (IL)-12 in the regulation of Tfh differentiation. Notably, IL-12 is permissive for differentiation of Tfh precursors but blocks differentiation into germinal center Tfh cells. Overall, this work elucidates networks with unexplored roles governing Tfh differentiation across species and tissues, while providing a generalizable framework. CoreNet is accessible through an interactive web server: https://pitt-csi.shinyapps.io/tfhcorenet/.

Optimizing the dynamics of bone turnover with genetic algorithm

Control systems and the modeling strategies are not only limited to engineering problems. These approaches can be used in the field of bio-mathematics as well and modern studies have promoted this approach to a great extent. The computational modeling and simulation of bone metastasis is painful yet critical after cancer invades the body. This vicious cycle is complex, and several research centers worldwide are devoted to understanding the dynamics and setting up a treatment strategy for this life-threatening behavior of cancer. Cancerous cells activation and the corresponding process of metastasis is reported to boost during the periodic waves of COVID-19, due to the inflammatory nature of the infection associated with SARS-2 and its variants. The bone cells are comprised of two types of cells responsible for bone formation and resorption. The computational framework of such cells, in spatial form, can help the researchers forecast the bone dynamics in a robust manner where the impact of cancer is incorporated into the computational model as a source of perturbation. A series of computational models are presented to explore the complex behavior of bone metastasis with COVID-19 induced infection. The finite difference algorithm is used to simulate the nonlinear computational model. The results obtained are in close agreement with the experimental findings. The computational results can help explore the vicious cycle’s fate and help set up control strategies through drug therapies.

Hierarchical classification of immune cell transcriptomes at population-scale

Accurate immune cell classification is essential for interpreting single-cell RNA sequencing (scRNA-seq) data. However, progress is constrained by the lack of independent, high-resolution benchmarks, as the routine integration of datasets introduces statistical dependencies that artificially inflate model generalizability. Here, we present the single-cell universal classification omnibus (Suco), a resource of independent, uniform expert annotations, and Compocyte, a modular hierarchical classifier. Together, they establish a framework designed for the scale of human population immunology. This approach substantially outperforms existing classifiers while facilitating expert review of ambiguous annotations. Applying Compocyte across 50 studies, including three newly generated datasets, we classified 15.6 million leukocytes from 3,965 patients. Within this expansive cohort, we identified a new tumor-associated resorptive macrophage phenotype, a non-canonical monocyte subtype in subclinical cytokine release syndrome, and the programmatic erosion of T cell memory stemness across metastatic sites. Suco and Compocyte thus provide a generalizable architecture and benchmark capable of sustaining high-resolution annotation across massive clinical cohorts. ### Competing Interest Statement CMR has consulted regarding oncology drug development with Amgen, AstraZeneca, Daiichi Sankyo, Genentech, Merck, and Novartis, and has received licensing and royalty payments for DLL3-directed therapeutics. T.W. reports stock ownership for Roche, Astra Zeneca, Bayer, Innate Pharma, Kyntra, Illumina, 10x Genomics, and Merck KGaA as well as research funding from Atrandi Biosciences, Vilnius, Lithuania; CanVirex AG, Basel Switzerland; and Institut fuer Klinische Krebsforschung GmbH, Frankfurt, Germany, and travel funding from Roche, Basel, Switzerland. S.Z. reports advisory board membership and honoraria from Amgen, Astellas, AstraZeneca, Bayer, Bristol-Myers Squibb, Daiichi Sankyo, Eisai, EUSA, Gilead, Ipsen, Johnson&Johnson, Lilly, MedSir, Medtoday, Merck, MSD, Novartis, Pfizer, Roche, Sanofi Aventis, StreamedUp, Urotrials, Urotube, Zentiva and resarch funding from Eisai. S.Z. reports clinical trial support from Amgen, AstraZeneca, AVEO, Bayer, Biontech, Bristol-Myers Squibb, Calithera, Exelixis, Gilead, Lilly, MSD, Novartis, Pfizer, Roche, Seagen/Astellas, Urotrials and travels & conference support from Amgen, Astellas, AstraZeneca, Bayer, EISAI, Ipsen, Johnson&Johnson, Merck, MSD, Pfizer. All remaining authors declare no relevant competing interests. Spanish Association Against Cancer, PI049999 Federal Ministry of Research, Technology and Space, 001001KT2322 National Cancer Institute, R35 CA263816 National Cancer Institute, U24 CA213274 National Cancer Institute, P30 CA008748 Research Council of Lithuania, P-MIP-24-93

Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle

Bone is a common site for cancer metastasis. To create space for their growth, cancer cells stimulate bone resorbing osteoclasts. Cytokine RANKL is a key osteoclast activator, while osteoprotegerin (OPG) is a RANKL decoy receptor and an inhibitor of osteoclastogenesis. Consistently, systemic application of OPG decreases metastatic tumor burden in bone. However, OPG produced locally by cancer cells was shown to enhance osteolysis and tumor growth. We propose that OPG produced by cancer cells causes a local reduction in RANKL levels, inducing a steeper RANKL gradient away from the tumor and towards the bone tissue, resulting in faster resorption and tumor expansion. We tested this hypothesis using a mathematical model of nonlinear partial differential equations describing the spatial dynamics of OPG, RANKL, PTHrP, osteoclasts, tumor and bone mass. We demonstrate that at lower expression rates, tumor-derived OPG enhances the chemotactic RANKL gradient and osteolysis, whereas at higher expression rates OPG broadly inhibits RANKL and decreases osteolysis and tumor burden. Moreover, tumor expression of a soluble mediator inducing RANKL in the host tissue, such as PTHrP, is important for correct orientation of the RANKL gradient. A meta-analysis of OPG, RANKL and PTHrP expression in normal prostate, carcinoma and metastatic tissues demonstrated an increase in expression of OPG, but not RANKL, in metastatic prostate cancer, and positive correlation between OPG and PTHrP in metastatic prostate cancer. The proposed mechanism highlights the importance of the spatial distribution of receptors, decoys and ligands, and can be applied to other systems involving regulation of spatially anisotropic processes.

A mathematical model for describing the metastasis of cancer in bone tissue

Metastasis is the rapid proliferation of cancer cells (secondary tumour) at a specific place, generally leading to death. This occurs at anatomical parts providing the necessary environment for vas...

The evolving concept of cell identity in the single cell era

Summary: This Spotlight explores emerging technologies that are enabling the systematic and unbiased quantification of cell identity, and how these efforts will enable the construction of high-resolution, dynamic cell atlases.