An Interplay Between Reaction-Diffusion and Cell-Matrix Adhesion Regulates Multiscale Invasion in Early Breast Carcinomatosis

Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation

Computational models are not just appealing because they can simulate and predict the development of biological phenomena across multiple spatial and temporal scales, but also because they can integrate information from well-established in vitro and in vivo models and test new hypotheses in cancer biomedicine. Agent-based models and simulations are especially interesting candidates among computational modeling procedures in cancer research due to the capability to, for instance, recapitulate the dynamics of neoplasia and tumor - host interactions. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature that explores strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on verification approached as simulation calibration. We consolidate our review with an outline of modern approaches for agent-based models' validation and provide an ambitious outlook toward rigorous and reliable calibration.

Synergistic Effects of Matrix Biophysical Properties on Gastric Cancer Cell Behavior via Integrin-Mediated Cell-ECM Interactions

The biophysical properties of the extracellular matrix (ECM) play a pivotal role in modulating cancer progression via cell-ECM interactions. However, the biophysical properties specific to gastric cancer (GC) remain largely unexplored. Pertinently, GC ECM shows significantly heterogeneous metamorphoses, such as matrix stiffening and intricate restructuring. By combining collagen I and alginate, this study designs an in vitro biomimetic hydrogel platform to independently modulate matrix stiffness and structure across a physiological stiffness spectrum while preserving consistent collagen concentration and fiber topography. With this platform, this study assesses the impacts of matrix biophysical properties on cell proliferation, migration, invasion, and other pivotal dynamics of AGS. The findings spotlight a compelling interplay between matrix stiffness and structure, influencing both cellular responses and ECM remodeling. Furthermore, this investigation into the integrin/actin-collagen interplay reinforces the central role of integrins in mediating cell-ECM interactions, reciprocally sculpting cell conduct, and ECM adaptation. Collectively, this study reveals a previously unidentified role of ECM biophysical properties in GC malignant potential and provides insight into the bidirectional mechanical cell-ECM interactions, which may facilitate the development of novel therapeutic horizons.

An Endosomal Acid-Regulatory Feedback System Rewires Cytosolic cAMP Metabolism and Drives Tumor Progression

Although suppressed cAMP levels have been linked to cancer for nearly five decades, the molecular basis remains uncertain. Here, we identify endosomal pH as a novel regulator of cytosolic cAMP homeostasis and a promoter of transformed phenotypic traits in colorectal cancer. Combining experiments and computational analysis, we show that the Na+/H+ exchanger NHE9 contributes to proton leak and causes luminal alkalinization, which induces resting [Ca2+], and in consequence, represses cAMP levels, creating a feedback loop that echoes nutrient deprivation or hypoxia. Higher NHE9 expression in cancer epithelia is associated with a hybrid epithelial-mesenchymal (E/M) state, poor prognosis, tumor budding, and invasive growth in vitro and in vivo. These findings point to NHE9-mediated cAMP suppression as a pseudostarvation-induced invasion state and potential therapeutic vulnerability in colorectal cancer. Our observations lay the groundwork for future research into the complexities of endosome-driven metabolic reprogramming and phenotype switching and the biology of cancer progression.

IMPLICATIONS

Endosomal pH regulator NHE9 actively controls cytosolic Ca2+ levels to downregulate the adenylate cyclase-cAMP system, enabling colorectal cancer cells to acquire hybrid E/M characteristics and promoting metastatic progression.

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

Extracellular matrix dynamics: A key regulator of cell migration across length-scales and systems

The interactions between cells and their surrounding extracellular matrix (ECM) are dynamic and play critical roles in cell migration during development, health, and diseases. Recent advances have highlighted the complexity and diversity of ECM compositions, or "matrisomes", of tissues resulting in ECMs of different physical, mechanical, and biochemical properties. Investigating the effects of these properties on cell-ECM interactions in the context of cell migration have led to a better understanding of the principles underlying tissue morphogenesis, wound healing, immune response, or cancer metastasis. These new insights into the interplay between ECM dynamics and cell migration can lead to the identification of unique opportunities for therapeutic interventions.

The senescent mesothelial matrix accentuates colonization by ovarian cancer cells

Ovarian cancer is amongst the most morbid of gynecological malignancies due to its diagnosis at an advanced stage, a transcoelomic mode of metastasis, and rapid transition to chemotherapeutic resistance. Like all other malignancies, the progression of ovarian cancer may be interpreted as an emergent outcome of the conflict between metastasizing cancer cells and the natural defense mounted by microenvironmental barriers to such migration. Here, we asked whether senescence in coelom-lining mesothelia, brought about by drug exposure, affects their interaction with disseminated ovarian cancer cells. We observed that cancer cells adhered faster on senescent human and murine mesothelial monolayers than on non-senescent controls. Time-lapse epifluorescence microscopy showed that mesothelial cells were cleared by a host of cancer cells that surrounded the former, even under sub-confluent conditions. A multiscale computational model predicted that such colocalized mesothelial clearance under sub-confluence requires greater adhesion between cancer cells and senescent mesothelia. Consistent with the prediction, we observed that senescent mesothelia expressed an extracellular matrix with higher levels of fibronectin, laminins and hyaluronan than non-senescent controls. On senescent matrix, cancer cells adhered more efficiently, spread better, and moved faster and persistently, aiding the spread of cancer. Inhibition assays using RGD cyclopeptides suggested the adhesion was predominantly contributed by fibronectin and laminin. These findings led us to propose that the senescence-associated matrisomal phenotype of peritoneal barriers enhances the colonization of invading ovarian cancer cells contributing to the metastatic burden associated with the disease.

Extracellular matrix remodeling in tumor progression and immune escape: from mechanisms to treatments

The malignant tumor is a multi-etiological, systemic and complex disease characterized by uncontrolled cell proliferation and distant metastasis. Anticancer treatments including adjuvant therapies and targeted therapies are effective in eliminating cancer cells but in a limited number of patients. Increasing evidence suggests that the extracellular matrix (ECM) plays an important role in tumor development through changes in macromolecule components, degradation enzymes and stiffness. These variations are under the control of cellular components in tumor tissue via the aberrant activation of signaling pathways, the interaction of the ECM components to multiple surface receptors, and mechanical impact. Additionally, the ECM shaped by cancer regulates immune cells which results in an immune suppressive microenvironment and hinders the efficacy of immunotherapies. Thus, the ECM acts as a barrier to protect cancer from treatments and supports tumor progression. Nevertheless, the profound regulatory network of the ECM remodeling hampers the design of individualized antitumor treatment. Here, we elaborate on the composition of the malignant ECM, and discuss the specific mechanisms of the ECM remodeling. Precisely, we highlight the impact of the ECM remodeling on tumor development, including proliferation, anoikis, metastasis, angiogenesis, lymphangiogenesis, and immune escape. Finally, we emphasize ECM "normalization" as a potential strategy for anti-malignant treatment.

Interplay of adherens junctions and matrix proteolysis determines the invasive pattern and growth of squamous cell carcinoma

Cancers, such as squamous cell carcinoma, frequently invade as multicellular units. However, these invading units can be organised in a variety of ways, ranging from thin discontinuous strands to thick 'pushing' collectives. Here we employ an integrated experimental and computational approach to identify the factors that determine the mode of collective cancer cell invasion. We find that matrix proteolysis is linked to the formation of wide strands but has little effect on the maximum extent of invasion. Cell-cell junctions also favour wide strands, but our analysis also reveals a requirement for cell-cell junctions for efficient invasion in response to uniform directional cues. Unexpectedly, the ability to generate wide invasive strands is coupled to the ability to grow effectively when surrounded by extracellular matrix in three-dimensional assays. Combinatorial perturbation of both matrix proteolysis and cell-cell adhesion demonstrates that the most aggressive cancer behaviour, both in terms of invasion and growth, is achieved at high levels of cell-cell adhesion and high levels of proteolysis. Contrary to expectation, cells with canonical mesenchymal traits - no cell-cell junctions and high proteolysis - exhibit reduced growth and lymph node metastasis. Thus, we conclude that the ability of squamous cell carcinoma cells to invade effectively is also linked to their ability to generate space for proliferation in confined contexts. These data provide an explanation for the apparent advantage of retaining cell-cell junctions in squamous cell carcinomas.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

Galectin-9 Signaling Drives Breast Cancer Invasion through Extracellular Matrix

Aberrations in glycan and lectin expression and function represent one of the earliest hallmarks of cancer. Among galectins, a conserved family of β-galactoside-binding lectins, the role of Galectin-9 in immune-tumor interactions is well-established, although its effect on cancer cell behavior remains unclear. In this study, we assayed for, and observed, an association between Galectin-9 expression and invasiveness of breast cancer cells in vitro and in vivo. Genetic perturbation and pharmacological inhibition using novel cognate inhibitors confirmed a positive correlation between Galectin-9 levels and the adhesion of invasive cancer cells to─and their invasion through─constituted organomimetic extracellular matrix microenvironments. Signaling experiments and unbiased quantitative proteomics revealed Galectin-9 induction of Focal Adhesion Kinase activity and S100A4 expression, respectively. FAK inhibition decreased S100A4 mRNA levels. Our results provide crucial insights into how elevated Galectin-9 expression potentiates the invasiveness of breast cancer cells during early steps of invasion.

Extracellular matrix as a driver for intratumoral heterogeneity

The architecture of an organ is built through interactions between its native cells and its connective tissue consisting of stromal cells and the extracellular matrix (ECM). Upon transformation through tumorigenesis, such interactions are disrupted and replaced by a new set of intercommunications between malignantly transformed parenchyma, an altered stromal cell population, and a remodeled ECM. In this perspective, we propose that the intratumoral heterogeneity of cancer cell phenotypes is an emergent property of such reciprocal intercommunications, both biochemical and mechanical-physical, which engender and amplify the diversity of cell behavioral traits. An attempt to assimilate such findings within a framework of phenotypic plasticity furthers our understanding of cancer progression.

Size matters: tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens

The reaction-diffusion model constitutes one of the most influential mathematical models to study distribution of morphogens in tissues. Despite its widespread use, the effect of finite tissue size on model-predicted spatio-temporal morphogen distributions has not been completely elucidated. In this study, we analytically investigated the spatio-temporal distributions of morphogens predicted by a reaction-diffusion model in a finite one-dimensional domain, as a proxy for a biological tissue, and compared it with the solution of the infinite-domain model. We explored the reduced parameter, the tissue length in units of a characteristic reaction-diffusion length, and identified two reaction-diffusion regimes separated by a crossover tissue size estimated in approximately three characteristic reaction-diffusion lengths. While above this crossover the infinite-domain model constitutes a good approximation, it breaks below this crossover, whereas the finite-domain model faithfully describes the entire parameter space. We evaluated whether the infinite-domain model renders accurate estimations of diffusion coefficients when fitted to finite spatial profiles, a procedure typically followed in fluorescence recovery after photobleaching (FRAP) experiments. We found that the infinite-domain model overestimates diffusion coefficients when the domain is smaller than the crossover tissue size. Thus, the crossover tissue size may be instrumental in selecting the suitable reaction-diffusion model to study tissue morphogenesis.

Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales

The metastasis of malignant epithelial tumors begins with the egress of transformed cells from the confines of their basement membrane (BM) to their surrounding collagen-rich stroma. Invasion can be morphologically diverse: when breast cancer cells are separately cultured within BM-like matrix, collagen I (Coll I), or a combination of both, they exhibit collective-, dispersed mesenchymal-, and a mixed collective-dispersed (multimodal)- invasion, respectively. In this paper, we asked how distinct these invasive modes are with respect to the cellular and microenvironmental cues that drive them. A rigorous computational exploration of invasion was performed within an experimentally motivated Cellular Potts-based modeling environment. The model comprised of adhesive interactions between cancer cells, BM- and Coll I-like extracellular matrix (ECM), and reaction-diffusion-based remodeling of ECM. The model outputs were parameters cognate to dispersed- and collective- invasion. A clustering analysis of the output distribution curated through a careful examination of subsumed phenotypes suggested at least four distinct invasive states: dispersed, papillary-collective, bulk-collective, and multimodal, in addition to an indolent/non-invasive state. Mapping input values to specific output clusters suggested that each of these invasive states are specified by distinct input signatures of proliferation, adhesion and ECM remodeling. In addition, specific input perturbations allowed transitions between the clusters and revealed the variation in the robustness between the invasive states. Our systems-level approach proffers quantitative insights into how the diversity in ECM microenvironments may steer invasion into diverse phenotypic modes during early dissemination of breast cancer and contributes to tumor heterogeneity.

Recent advances in understanding the role of metabolic heterogeneities in cell migration

Migration is an energy-intensive, multi-step process involving cell adhesion, protrusion, and detachment. Each of these steps require cells to generate and consume energy, regulating their morphological changes and force generation. Given the need for energy to move, cellular metabolism has emerged as a critical regulator of both single cell and collective migration. Recently, metabolic heterogeneity has been highlighted as a potential determinant of collective cell behavior, as individual cells may play distinct roles in collective migration. Several tools and techniques have been developed and adapted to study cellular energetics during migration including live-cell probes to characterize energy utilization and metabolic state and methodologies to sort cells based on their metabolic profile. Here, we review the recent advances in techniques, parsing the metabolic heterogeneities inherent in cell populations and their contributions to cell migration.

Heterogeneity in 2,6-Linked Sialic Acids Potentiates Invasion of Breast Cancer Epithelia

Heterogeneity in phenotypes of malignantly transformed cells and aberrant glycan expression on their surface are two prominent hallmarks of cancers that have hitherto not been linked to each other. In this paper, we identify differential levels of a specific glycan linkage: α2,6-linked sialic acids within breast cancer cells in vivo and in culture. Upon sorting out two populations with moderate, and relatively higher, cell surface α2,6-linked sialic acid levels from the triple-negative breast cancer cell line MDA-MB-231, both populations (denoted as medium and high 2,6-Sial cells, respectively) stably retained their levels in early passages. Upon continuous culturing, medium 2,6-Sial cells recapitulated the heterogeneity of the unsorted line whereas high 2,6-Sial cells showed no such tendency. Compared with high 2,6-Sial cells, the medium 2,6-Sial counterparts showed greater adhesion to reconstituted extracellular matrices (ECMs) and invaded faster as single cells. The level of α2,6-linked sialic acids in the two sublines was found to be consistent with the expression of a specific glycosyl transferase, ST6GAL1. Stably knocking down ST6GAL1 in the high 2,6-Sial cells enhanced their invasiveness. When cultured together, medium 2,6-Sial cells differentially migrated to the edge of growing tumoroid-like cocultures, whereas high 2,6-Sial cells formed the central bulk. Multiscale simulations in a Cellular Potts model-based computational environment calibrated to our experimental findings suggest that differential levels of cell-ECM adhesion, likely regulated by α2,6-linked sialic acids, facilitate niches of highly invasive cells to efficiently migrate centrifugally as the invasive front of a malignant breast tumor.

Nanomotors Sense Local Physicochemical Heterogeneities in Tumor Microenvironments*

The invasion of cancer is brought about by continuous interaction of malignant cells with their surrounding tissue microenvironment. Investigating the remodeling of local extracellular matrix (ECM) by invading cells can thus provide fundamental insights into the dynamics of cancer progression. In this paper, we use an active untethered nanomechanical tool, realized as magnetically driven nanomotors, to locally probe a 3D tissue culture environment. We observed that nanomotors preferentially adhere to the cancer-proximal ECM and magnitude of the adhesive force increased with cell lines of higher metastatic ability. We experimentally confirmed that sialic acid linkage specific to cancer-secreted ECM makes it differently charged, which causes this adhesion. In an assay consisting of both cancerous and non-cancerous epithelia, that mimics the in vivo histopathological milieu of a malignant breast tumor, we find that nanomotors preferentially decorate the region around the cancer cells.