The mechanics of metastasis: insights from a computational model

A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation

Introduction

Colorectal cancer (CRC) is a major cause of cancer related deaths in the United States, with CRC metastasis to the liver being a common occurrence. The development of an optimal metastatic environment is essential process prior to tumor metastasis. This process, called pre-metastatic niche (PMN) formation, involves activation of key resident liver cells, including fibroblast-like stellate cells and macrophages such as Kupffer cells. Tumor-mediated factors introduced to this environment transform resident cells that secrete additional growth factors and remodel the extracellular matrix (ECM), which is thought to promote tumor colonization and metastasis in the secondary environment.

Methods

To investigate the underlying mechanisms of these dynamics, we developed a multicellular computational model to characterize the spatiotemporal dynamics of the PMN formation in tissue. This modeling framework integrates intracellular and extracellular signaling, and traction and junctional forces into a Cellular Potts model, and represents multiple cell types with varying levels of cellular activation. We perform numerical experiments to investigate the role of key factors in PMN formation and tumor invasiveness, including growth factor concentration, timing of tumor arrival, relative composition of resident cells, and the size of invading tumor cluster.

Results

These parameter studies identified growth factor availability and ECM concentration in the environment as two of the key determinants of tumor invasiveness. We further predict that both the ECM concentration potential and growth factor sensitivity of the stellate cells are key drivers of the PMN formation and associated ECM concentration.

Conclusions

Overall, this modeling framework represents a significant step towards simulating cancer metastasis and investigating the role of key factors on PMN formation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00831-0.

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

Haemodynamic-dependent arrest of circulating tumour cells at large blood vessel bifurcations as new model for metastasis

Homing of circulating tumour cells (CTC) at distant sites represents a critical event in metastasis dissemination. In addition to physical entrapment, probably responsible of the majority of the homing events, the vascular system provides with geometrical factors that govern the flow biomechanics and impact on the fate of the CTC. Here we mathematically explored the distribution of velocities and the corresponding streamlines at the bifurcations of large blood vessel and characterized an area of low-velocity at the carina of bifurcation that favours the residence of CTC. In addition to this fluid physics effect, the adhesive capabilities of the CTC provide with a biological competitive advantage resulting in a marginal but systematic arrest as evidenced by dynamic in vitro recirculation in Y-microchannels and by perfusion in in vivo mice models. Our results also demonstrate that viscosity, as a main determinant of the Reynolds number that define flow biomechanics, may be modulated to limit or impair CTC accumulation at the bifurcation of blood vessels, in agreement with the apparent positive effect observed in the clinical setting by anticoagulants in advanced oncology disease.

Adhesion modulates cell morphology and migration within dense fibrous networks

One of the most fundamental abilities required for the sustainability of complex life forms is active cell migration, since it is essential in diverse processes from morphogenesis to leukocyte chemotaxis in immune response. The movement of a cell is the result of intricate mechanisms, that involve the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In particular, epithelial cancer cells have to employ mechanical strategies in order to migrate through the tissue's basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. We have performed a systematic analysis using a phase-field model and we propose a novel approach to simulate cell migration with dissipative particle dynamics modelling. With this purpose we have measured in our simulation the cell's velocity and quantified its morphology as a function of the fibre density and of its adhesiveness to the matrix fibres. Furthermore, we have compared our results to a previousin vitromigration assay of fibrosarcoma cells in fibrous matrices. The results show good agreement between the two methodologies and experiments in the literature, which indicates that these minimalist descriptions are able to capture the main features of the system. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. In addition, our analysis suggests that matrix metalloproteinases (MMPs) play an important role as adhesiveness modulators. We propose that new assays should be carried out to address the role of adhesion and the effect of different MMPs in cell migration under confined conditions.

Computational analysis of adhesion between a cancer cell and a white blood cell in a bifurcated microvessel

BACKGROUND AND OBJECTIVE

Cancer is one of the diseases caused by irregular and uncontrolled growth of cells and their propagation into various parts of the body. The motion and adhesion of cancer cells in a blood vessel is a critical step in tumor progression that depends on some vascular parameters such as vessel branching. In this study, effect of microvessel branching on the bonds between a cancer cell and a white blood has been investigated as compared to an analogous problem in a straight vessel.

METHODS

The analysis is performed using finite elements and fluid-structure interaction methods. Moreover, the equations for adhesion of the cancer cell to white blood cell are coded in MATLAB for calculating forces between them and the code is coupled directly and simultaneously with the COMSOL software. For fluid-structure interaction analysis, it is assumed that the properties of the blood and the cells are homogeneous and the fluid is incompressible and Newtonian. Cancer cell is modeled as a rigid body and white blood cell is assumed as linear elastic.

RESULTS

The results show that although the geometry of the vessel does not affect on the separation distance of cancer cell considerably, but at the area near a bifurcation, high fluctuations in cancer cell velocity is occurred due to increasing in number of bond formation between the cancer cell and the white blood cell. Accordingly, it can be predicted that higher concentration of adhered particles occurs near the bifurcations. Moreover, shear stress at the point of contact of the cancer cell and the white blood cell in the branched vessel is greater than that in the straight path. In addition to, the probability of breaking of the bond between the cancer cell and the white blood cell increases in the branched vessel.

CONCLUSIONS

Through consideration in the adhesion charts of this study along with observations from medical interventions such as drug delivery to cancer patients, considerable developments on the treatment or prevention of cancer metastasis may be achieved.

GPER Activation Inhibits Cancer Cell Mechanotransduction and Basement Membrane Invasion via RhoA

The invasive properties of cancer cells are intimately linked to their mechanical phenotype, which can be regulated by intracellular biochemical signalling. Cell contractility, induced by mechanotransduction of a stiff fibrotic matrix, and the epithelial-mesenchymal transition (EMT) promote invasion. Metastasis involves cells pushing through the basement membrane into the stroma-both of which are altered in composition with cancer progression. Agonists of the G protein-coupled oestrogen receptor (GPER), such as tamoxifen, have been largely used in the clinic, and interest in GPER, which is abundantly expressed in tissues, has greatly increased despite a lack of understanding regarding the mechanisms which promote its multiple effects. Here, we show that specific activation of GPER inhibits EMT, mechanotransduction and cell contractility in cancer cells via the GTPase Ras homolog family member A (RhoA). We further show that GPER activation inhibits invasion through an in vitro basement membrane mimic, similar in structure to the pancreatic basement membrane that we reveal as an asymmetric bilayer, which differs in composition between healthy and cancer patients.

Development of label-free biophysical markers in osteogenic maturation

The spatial and temporal changes of morphological and mechanical properties of living cells reflect complex functionally-associated processes. Monitoring these modifications could provide a direct information on the cellular functional state. Here we present an integrated biophysical approach to the quantification of the morphological and mechanical phenotype of single cells along a maturation pathway. Specifically, quantitative phase microscopy and single cell biomechanical testing were applied to the characterization of the maturation of human foetal osteoblasts, demonstrating the ability to identify effective label-free biomarkers along this fundamental biological process.

Biophysical Phenotyping and Modulation of ALDH+ Inflammatory Breast Cancer Stem-Like Cells

Cancer stem-like cells (CSCs) have been shown to initiate tumorigenesis and cancer metastasis in many cancer types. Although identification of CSCs through specific marker expression helps define the CSC compartment, it does not directly provide information on how or why this cancer cell subpopulation is more metastatic or tumorigenic. In this study, the functional and biophysical characteristics of aggressive and lethal inflammatory breast cancer (IBC) CSCs at the single-cell level are comprehensively profiled using multiple microengineered tools. Distinct functional (cell migration, growth, adhesion, invasion and self-renewal) and biophysical (cell deformability, adhesion strength and contractility) properties of ALDH+ SUM149 IBC CSCs are found as compared to their ALDH- non-CSC counterpart, providing biophysical insights into why CSCs has an enhanced propensity to metastasize. It is further shown that the cellular biophysical phenotype can predict and determine IBC cells' tumorigenic ability. SUM149 and SUM159 IBC cells selected and modulated through biophysical attributes-adhesion and stiffness-show characteristics of CSCs in vitro and enhance tumorigenicity in in vivo murine models of primary tumor growth. Overall, the multiparametric cellular biophysical phenotyping and modulation of IBC CSCs yields a new understanding of IBC's metastatic properties and how they might develop and be targeted for therapeutic interventions.

Intraglomerular crosstalk elaborately regulates podocyte injury and repair in diabetic patients: insights from a 3D multiscale modeling study

Podocytes are mainly involved in the regulation of glomerular filtration rate (GFR) under physiological condition. Podocyte depletion is a crucial pathological alteration in diabetic nephropathy (DN) and results in a broad spectrum of clinical syndromes such as protein urine and renal insufficiency. Recent studies indicate that depleted podocytes can be regenerated via differentiation of the parietal epithelial cells (PECs), which serve as the local progenitors of podocytes. However, the podocyte regeneration process is regulated by a complicated mechanism of cell-cell interactions and cytokine stimulations, which has been studied in a piecemeal manner rather than systematically. To address this gap, we developed a high-resolution multi-scale multi-agent mathematical model in 3D, mimicking the in situ glomerulus anatomical structure and micro-environment, to simulate the podocyte regeneration process under various cytokine perturbations in healthy and diabetic conditions. Our model showed that, treatment with pigment epithelium derived factor (PEDF) or insulin-like growth factor-1 (IGF-1) alone merely ameliorated the glomerulus injury, while co-treatment with both cytokines replenished the damaged podocyte population gradually. In addition, our model suggested that continuous administration of PEDF instead of a bolus injection sustained the regeneration process of podocytes. Part of the results has been validated by our in vivo experiments. These results indicated that amelioration of the glomerular stress by PEDF and promotion of PEC differentiation by IGF-1 are equivalently critical for podocyte regeneration. Our 3D multi-scale model represents a powerful tool for understanding the signaling regulation and guiding the design of cytokine therapies in promoting podocyte regeneration.

The mechanical properties of individual cell spheroids

The overall physical properties of tissues emerge in a complex manner from the properties of the component cells and other constituent materials from which the tissue is formed, across multiple length scales ranging from nanometres to millimetres. Recent studies have suggested that interfacial tension between cells contributes significantly to the mechanical properties of tissues and that the overall surface tension is determined by the ratio of adhesion tension to cortical tension. Using cavitation rheology (CR), we have measured the interfacial properties and the elastic modulus of spheroids formed from HEK cells. By comparing the work of bubble formation with deformation of the cell spheroid at different length scales, we have estimated the cortical tension for HEK cells. This innovative approach to understanding the fundamental physical properties associated with tissue mechanics may guide new approaches for the generation of materials to replace or regenerate damaged or diseased tissues.

Bubbly vertex dynamics: A dynamical and geometrical model for epithelial tissues with curved cell shapes

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.

CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries

Mechanical forces play a key role in a wide range of biological processes, from embryogenesis to cancer metastasis, and there is considerable interest in the intuitive question, "Can cellular forces be inferred from cell shapes?" Although several groups have posited affirmative answers to this stimulating question, nagging issues remained regarding equation structure, solution uniqueness and noise sensitivity. Here we show that the mechanical and mathematical factors behind these issues can be resolved by using curved cell edges rather than straight ones. We present a new package of force-inference equations and assessment tools and denote this new package CellFIT, the Cellular Force Inference Toolkit. In this approach, cells in an image are segmented and equilibrium equations are constructed for each triple junction based solely on edge tensions and the limiting angles at which edges approach each junction. The resulting system of tension equations is generally overdetermined. As a result, solutions can be obtained even when a modest number of edges need to be removed from the analysis due to short length, poor definition, image clarity or other factors. Solving these equations yields a set of relative edge tensions whose scaling must be determined from data external to the image. In cases where intracellular pressures are also of interest, Laplace equations are constructed to relate the edge tensions, curvatures and cellular pressure differences. That system is also generally overdetermined and its solution yields a set of pressures whose offset requires reference to the surrounding medium, an open wound, or information external to the image. We show that condition numbers, residual analyses and standard errors can provide confidence information about the inferred forces and pressures. Application of CellFIT to several live and fixed biological tissues reveals considerable force variability within a cell population, significant differences between populations and elevated tensions along heterotypic boundaries.

Investigation of the essential role of platelet-tumor cell interactions in metastasis progression using an agent-based model

BACKGROUND

Metastatic tumors are a major source of morbidity and mortality for most cancers. Interaction of circulating tumor cells with endothelium, platelets and neutrophils play an important role in the early stages of metastasis formation. These complex dynamics have proven difficult to study in experimental models. Prior computational models of metastases have focused on tumor cell growth in a host environment, or prediction of metastasis formation from clinical data. We used agent-based modeling (ABM) to dynamically represent hypotheses of essential steps involved in circulating tumor cell adhesion and interaction with other circulating cells, examine their functional constraints, and predict effects of inhibiting specific mechanisms.

METHODS

We developed an ABM of Early Metastasis (ABMEM), a descriptive semi-mechanistic model that replicates experimentally observed behaviors of populations of circulating tumor cells, neutrophils, platelets and endothelial cells while incorporating representations of known surface receptor, autocrine and paracrine interactions. Essential downstream cellular processes were incorporated to simulate activation in response to stimuli, and calibrated with experimental data. The ABMEM was used to identify potential points of interdiction through examination of dynamic outcomes such as rate of tumor cell binding after inhibition of specific platelet or tumor receptors.

RESULTS

The ABMEM reproduced experimental data concerning neutrophil rolling over endothelial cells, inflammation-induced binding between neutrophils and platelets, and tumor cell interactions with these cells. Simulated platelet inhibition with anti-platelet drugs produced unstable aggregates with frequent detachment and re-binding. The ABMEM replicates findings from experimental models of circulating tumor cell adhesion, and suggests platelets play a critical role in this pre-requisite for metastasis formation. Similar effects were observed with inhibition of tumor integrin αV/β3. These findings suggest that anti-platelet or anti-integrin therapies may decrease metastasis by preventing stable circulating tumor cell adhesion.

CONCLUSION

Circulating tumor cell adhesion is a complex, dynamic process involving multiple cell-cell interactions. The ABMEM successfully captures the essential interactions necessary for this process, and allows for in-silico iterative characterization and invalidation of proposed hypotheses regarding this process in conjunction with in-vitro and in-vivo models. Our results suggest that anti-platelet therapies and anti-integrin therapies may play a promising role in inhibiting metastasis formation.

Tackling the cancer signal transduction “Labyrinth”: A combinatorial use of biochemical tools with mathematical models will enhance the identification of optimal targets for each molecular defect

Unraveling cancer‐associated molecular defects is crucial for further pharmacological targeting. Although novel techniques are being developed to elucidate genomic, proteomic, and transcriptomic alterations, the map of protein interactions and aberrations in normal but also in malignant cells is still obscure. It has been recently shown that many of the events in signaling cascades might be revealed using mathematical models. Transcriptional regulation still represents the main obstacle for the design of truly molecularly‐targeted agents, mainly due to its enormous plasticity and heterogeneity in cells and tissues. Systematic mapping of signaling networks and application of new computational algorithms will reinforce the use of novel research tools in this venue. The case of epidermal growth factor receptor family proteins and their intracellular cross‐talk interactions and downstream molecules is used as a representative paradigm. Cancer 2014;120:316–322. © 2013 American Cancer Society.

Modeling the mechanics of cancer: effect of changes in cellular and extra-cellular mechanical properties

Malignant transformation, though primarily driven by genetic mutations in cells, is also accompanied by specific changes in cellular and extra-cellular mechanical properties such as stiffness and adhesivity. As the transformed cells grow into tumors, they interact with their surroundings via physical contacts and the application of forces. These forces can lead to changes in the mechanical regulation of cell fate based on the mechanical properties of the cells and their surrounding environment. A comprehensive understanding of cancer progression requires the study of how specific changes in mechanical properties influences collective cell behavior during tumor growth and metastasis. Here we review some key results from computational models describing the effect of changes in cellular and extra-cellular mechanical properties and identify mechanistic pathways for cancer progression that can be targeted for the prediction, treatment, and prevention of cancer.

A multiscale road map of cancer spheroids – incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.