Diversity of dynamics and morphologies of invasive solid tumors

Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction

Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

Diversity of collective migration patterns of invasive breast cancer cells emerging during microtrack invasion

Understanding the mechanisms underlying the diversity of tumor invasion dynamics, including single-cell migration, multicellular streaming, and the emergence of various collective migration patterns, is a long-standing problem in cancer research. Here we have designed and fabricated a series of microchips containing high-throughput microscale tracks using protein repelling coating technology, which were then covered with a thin Matrigel layer. By varying the geometrical confinement (track width) and microenvironment factors (Matrigel concentration), we have reproduced a diversity of collective migration patterns in the chips, which were also observed in vivo. We have further classified the collective patterns and quantified the emergence probability of each class of patterns as a function of microtrack width and Matrigel concentration to devise a quantitive "collective pattern diagram." To elucidate the mechanisms behind the emergence of various collective patterns, we employed cellular automaton simulations, incorporating the effects of both direct cell-cell interactions and microenvironment factors (e.g., chemical gradient and extracellular matrix degradation). Our simulations suggest that tumor cell phenotype heterogeneity, and the associated dynamic selection of a favorable phenotype via cell-microenivronment interactions, are key to the emergence of the observed collective patterns in vitro.

Morphological quantification of proliferation-to-invasion transition in tumor spheroids

BACKGROUND

Metastasis determines the lethality of cancer. In most clinical cases, patients are able to live with tumor proliferation before metastasis. Thus, the transition from tumor proliferation to metastasis/invasion is essential. However, the mechanism is still unclear and especially, the proliferation-to-metastasis/invasion transition point has not been well defined. Therefore, quantitative characterization of this transition is urgently needed.

METHODS

We have successfully developed a home-built living-cell incubation system combined with an inverted optical microscope, and a systematic, quantitative approach to describing the major characteristic morphological parameters for the identification of the critical transition points for tumor-cell spheroids in a collagen fiber scaffold.

RESULTS

The system focuses on in vitro tumor modeling, e.g. the development of tumor-cell spheroids in a collagen fiber scaffold and the monitoring of cell transition from proliferation to invasion. By applying this approach to multiple tumor spheroid models, such as U87 (glioma tumor), H1299 (lung cancer), and MDA-MB-231 (breast cancer) cells, we have obtained quantitative morphological references to evaluate the proliferation-to-invasion transition time, as well as differentiating the invasion potential of tumor cells upon environmental changes, i.e. drug application.

CONCLUSIONS

Our quantitative approach provides a feasible clarification for the proliferation-to-invasion transition of in vitro tumor models (spheroids). Moreover, the transition time is a useful reference for the invasive potential of tumor cells.

GENERAL SIGNIFICANCE

This quantitative approach is potentially applicable to primary tumor cells, and thus has potential applications in the fields of cancer metastasis investigations and clinical diagnostics.

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions

Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.

MET Activation and Physical Dynamics of the Metastatic Process: The Paradigm of Cancers of Unknown Primary Origin

The molecular and cellular mechanisms which drive metastatic spread are the topic of constant debate and scientific research due to the potential implications for cancer patients' prognosis. In addition to genetics and environmental factors, mechanics of single cells and physical interaction with the surrounding environment play relevant role in defining invasive phenotype. Reconstructing the physical properties of metastatic clones may help to clarify still open issues in disease progression as well as to lead to new diagnostic and therapeutic approaches. In this perspective cancer of unknown primary origin (CUP) identify the ideal model to study physical interactions and forces involved in the metastatic process. We have previously demonstrated that MET oncogene is mutated with unexpected high frequency in CUPs. We here analyze and discuss how the MET activation by somatic mutation may affect physical properties in giving rise to such a highly malignant syndrome, as that defined by CUP.

INSIDIA: A FIJI Macro Delivering High-Throughput and High-Content Spheroid Invasion Analysis

Time-series image capture of in vitro 3D spheroidal cancer models embedded within an extracellular matrix affords examination of spheroid growth and cancer cell invasion. However, a customizable, comprehensive and open source solution for the quantitative analysis of such spheroid images is lacking. Here, the authors describe INSIDIA (INvasion SpheroID ImageJ Analysis), an open-source macro implemented as a customizable software algorithm running on the FIJI platform, that enables high-throughput high-content quantitative analysis of spheroid images (both bright-field gray and fluorescent images) with the output of a range of parameters defining the spheroid "tumor" core and its invasive characteristics.

Heterogeneous force network in 3D cellularized collagen networks

Collagen networks play an important role in coordinating and regulating collective cellular dynamics via a number of signaling pathways. Here, we investigate the transmission of forces generated by contractile cells in 3D collagen-I networks. Specifically, the graph (bond-node) representations of collagen networks with collagen concentrations of 1, 2 and 4 mg ml^-1 are derived from confocal microscopy data and used to model the network microstructure. Cell contraction is modeled by applying correlated displacements at specific nodes of the network, representing the focal adhesion sites. A nonlinear elastic model is employed to characterize the mechanical behavior of individual fiber bundles including strain hardening during stretching and buckling under compression. A force-based relaxation method is employed to obtain equilibrium network configurations under cell contraction. We find that for all collagen concentrations, the majority of the forces are carried by a small number of heterogeneous force chains emitted from the contracting cells, which is qualitatively consistent with our experimental observations. The force chains consist of fiber segments that either possess a high degree of alignment before cell contraction or are aligned due to fiber reorientation induced by cell contraction. The decay of the forces along the force chains is significantly slower than the decay of radially averaged forces in the system, suggesting that the fibreous nature of biopolymer network structure can support long-range force transmission. The force chains emerge even at very small cell contractions, and the number of force chains increases with increasing cell contraction. At large cell contractions, the fibers close to the cell surface are in the nonlinear regime, and the nonlinear region is localized in a small neighborhood of the cell. In addition, the number of force chains increases with increasing collagen concentration, due to the larger number of focal adhesion sites in collagen networks with high concentrations.

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

Enhanced invasion of metastatic cancer cells via extracellular matrix interface

Cancer cell invasion is a major component of metastasis and is responsible for extensive cell diffusion into and major destruction of tissues. Cells exhibit complex invasion modes, including a variety of collective behaviors. This phenomenon results in the structural heterogeneity of the extracellular matrix (ECM) in tissues. Here, we systematically investigated the environmental heterogeneity facilitating tumor cell invasion via a combination of in vitro cell migration experiments and computer simulations. Specifically, we constructed an ECM microenvironment in a microfabricated biochip and successfully created a three-dimensional (3D) funnel-like matrigel interface inside. Scanning electron microscopy demonstrated that the interface was at the interior defects of the nano-scale molecular anisotropic orientation and the localized structural density variations in the matrigel. Our results, particularly the correlation of the collective migration pattern with the geometric features of the funnel-like interface, indicate that this heterogeneous in vitro ECM structure strongly guides and promotes aggressive cell invasion in the rigid matrigel space. A cellular automaton model was proposed based on our experimental observations, and the associated quantitative analysis indicated that cell invasion was initiated and controlled by several mechanisms, including microenvironment heterogeneity, long-range cell-cell homotype and gradient-driven directional cellular migration. Our work shows the feasibility of constructing a complex and heterogeneous in vitro 3D ECM microenvironment that mimics the in vivo environment. Moreover, our results indicate that ECM heterogeneity is essential in controlling collective cell invasive behaviors and therefore determining metastasis efficiency.

A cellular automaton model for tumor dormancy: emergence of a proliferative switch

Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a comprehensive understanding of cancer dormancy and the “switch” from a dormant to a proliferative state still needs to be strengthened from both a basic and clinical point of view. Computational modeling enables one to explore a variety of scenarios for possible but realistic microscopic dormancy mechanisms and their predicted outcomes. The aim of this paper is to devise such a predictive computational model of dormancy with an emergent “switch” behavior. Specifically, we generalize a previous cellular automaton (CA) model for proliferative growth of solid tumor that now incorporates a variety of cell-level tumor-host interactions and different mechanisms for tumor dormancy, for example the effects of the immune system. Our new CA rules induce a natural “competition” between the tumor and tumor suppression factors in the microenvironment. This competition either results in a “stalemate” for a period of time in which the tumor either eventually wins (spontaneously emerges) or is eradicated; or it leads to a situation in which the tumor is eradicated before such a “stalemate” could ever develop. We also predict that if the number of actively dividing cells within the proliferative rim of the tumor reaches a critical, yet low level, the dormant tumor has a high probability to resume rapid growth. Our findings may shed light on the fundamental understanding of cancer dormancy.

Evolution and morphology of microenvironment-enhanced malignancy of three-dimensional invasive solid tumors

The emergence of invasive and metastatic behavior in malignant tumors can often lead to fatal outcomes for patients. The collective malignant tumor behavior resulting from the complex tumor-host interactions and the interactions between the tumor cells is currently poorly understood. In this paper, we employ a cellular automaton (CA) model to investigate microenvironment-enhanced malignant behaviors and morphologies of in vitro avascular invasive solid tumors in three dimensions. Our CA model incorporates a variety of microscopic-scale tumor-host interactions, including the degradation of the extracellular matrix by the malignant cells, nutrient-driven cell migration, pressure buildup due to the deformation of the microenvironment by the growing tumor, and its effect on the local tumor-host interface stability. Moreover, the effects of cell-cell adhesion on tumor growth are explicitly taken into account. Specifically, we find that while strong cell-cell adhesion can suppress the invasive behavior of the tumors growing in soft microenvironments, cancer malignancy can be significantly enhanced by harsh microenvironmental conditions, such as exposure to high pressure levels. We infer from the simulation results a qualitative phase diagram that characterizes the expected malignant behavior of invasive solid tumors in terms of two competing malignancy effects: the rigidity of the microenvironment and cell-cell adhesion. This diagram exhibits phase transitions between noninvasive and invasive behaviors. We also discuss the implications of our results for the diagnosis, prognosis, and treatment of malignant tumors.

Quantitative characterization of the microstructure and transport properties of biopolymer networks

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient D(e) and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient D(e) for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient D(e) and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient D(e) as well as the mean survival time τ, which is related to nuclear magnetic resonance relaxation times. Our numerical results for D(e) are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of D(e) for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Torquato and Yeong (1997 J. Chem. Phys. 106 8814). We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed.

Emergent behaviors from a cellular automaton model for invasive tumor growth in heterogeneous microenvironments

Understanding tumor invasion and metastasis is of crucial importance for both fundamental cancer research and clinical practice. In vitro experiments have established that the invasive growth of malignant tumors is characterized by the dendritic invasive branches composed of chains of tumor cells emanating from the primary tumor mass. The preponderance of previous tumor simulations focused on non-invasive (or proliferative) growth. The formation of the invasive cell chains and their interactions with the primary tumor mass and host microenvironment are not well understood. Here, we present a novel cellular automaton (CA) model that enables one to efficiently simulate invasive tumor growth in a heterogeneous host microenvironment. By taking into account a variety of microscopic-scale tumor-host interactions, including the short-range mechanical interactions between tumor cells and tumor stroma, degradation of the extracellular matrix by the invasive cells and oxygen/nutrient gradient driven cell motions, our CA model predicts a rich spectrum of growth dynamics and emergent behaviors of invasive tumors. Besides robustly reproducing the salient features of dendritic invasive growth, such as least-resistance paths of cells and intrabranch homotype attraction, we also predict nontrivial coupling between the growth dynamics of the primary tumor mass and the invasive cells. In addition, we show that the properties of the host microenvironment can significantly affect tumor morphology and growth dynamics, emphasizing the importance of understanding the tumor-host interaction. The capability of our CA model suggests that sophisticated in silico tools could eventually be utilized in clinical situations to predict neoplastic progression and propose individualized optimal treatment strategies.

The goal of the present work is to develop an efficient single-cell based cellular automaton (CA) model that enables one to investigate the growth dynamics and morphology of invasive solid tumors. Recent experiments have shown that highly malignant tumors develop dendritic branches composed of tumor cells that follow each other, which massively invade into the host microenvironment and ultimately lead to cancer metastasis. Previous theoretical/computational cancer modeling neither addressed the question of how such chain-like invasive branches form nor how they interact with the host microenvironment and the primary tumor. Our CA model, which incorporates a variety of microscopic-scale tumor-host interactions (e.g., the mechanical interactions between tumor cells and tumor stroma, degradation of the extracellular matrix by the tumor cells and oxygen/nutrient gradient driven cell motions), can robustly reproduce experimentally observed invasive tumor evolution and predict a wide spectrum of invasive tumor growth dynamics and emergent behaviors in various different heterogeneous environments. Further refinement of our CA model could eventually lead to the development of a powerful simulation tool for clinical purposes capable of predicting neoplastic progression and suggesting individualized optimal treatment strategies.