Modeling of self-organized avascular tumor growth with a hybrid cellular automaton

Pattern formation in multicellular spheroids is addressed with a hybrid lattice-gas cellular automaton model. Multicellular spheroids serve as experimental model system for the study of avascular tumor growth. Typically, multicellular spheroids consist of a necrotic core surrounded by rings of quiescent and proliferating tumor cells, respectively. Furthermore, after an initial exponential growth phase further spheroid growth is significantly slowed down even if further nutrient is supplied. The cellular automaton model explicitly takes into account mitosis, apoptosis and necrosis as well as nutrient consumption and a diffusible signal that is emitted by cells becoming necrotic. All cells follow identical interaction rules. The necrotic signal induces a chemotactic migration of tumor cells towards maximal signal concentrations. Starting from a small number of tumor cells automaton simulations exhibit the self-organized formation of a layered structure consisting of a necrotic core, a ring of quiescent tumor cells and a thin outer ring of proliferating tumor cells.     

Influence of dental restorative materials on ESR biodosimetry in tooth enamel

Using an experimental model and PENELOPE Monte Carlo simulations, the effects of resin and amalgam on the absorbed doses in tooth enamel were studied to evaluate the feasibility of using restored teeth in electron spin resonance (ESR) dose reconstruction. The model consisted of a phantom containing a plate of these restorative materials placed between powered enamel layers exposed to X rays and a ??Co beam. The experimental results and simulations agreed, showing that the attenuation produced by amalgam and resin with a thickness of 1, 2, and 4 mm is similar to that produced by the enamel itself in the case of the radiation sources employed. For X rays and ??Co γ radiation the attenuation reached almost 100% and 40%, respectively. These results show that for ESR dose reconstruction, the use of all available enamel of a tooth leads to errors in the estimated dose due to attenuation effects in both healthy and restored teeth. Thus the importance of an enamel selection from different sides of the tooth surface to apply ESR dose reconstruction in the case of a practical situation is shown.     

PPAR??激动剂罗格列酮对人乳腺癌细胞生长 抑制及诱导凋亡作用研究

目的:观察氧化酶体激活物增殖受体(PPARγ)激动剂罗格列酮(ROZ)在体外激活PPARγ后对MCF-7细胞的生长抑制及诱导凋亡作用。方法:MTT法检测ROZ对MCF-7细胞的生长抑制作用;集落形成实验观察ROZ对MCF-7细胞集落形成的影响;不同浓度ROZ作用72h,Hoechst33342染色观察MCF-7细胞的形态变化,流式细胞光度分析术(FCM)检测凋亡细胞百分率以及ROZ对细胞周期的影响;Western blot方法检测ROZ对MCF-7细胞Bcl-2、Caspase-3表达的影响。结果:ROZ可呈剂量依赖性抑制MCF-7细胞的生长及集落形成。ROZ浓度为6×10-5M和3×10-4M时则G1期细胞数明显增加,S期相应减少。Hoechst33342染色经ROZ处理的肿瘤细胞染色质呈颗粒状,且有凋亡小体出现。FCM检测结果显示,ROZ作用72h凋亡细胞数达22.05%。Western blot提示ROZ可抑制Bcl-2表达,促进Caspase3表达。结论:ROZ在体外可抑制MCF-7细胞的增殖并诱导其凋亡,这可能与其抑制Bcl-2表达、促进caspase3表达有关。提示ROZ有望成为乳腺癌治疗药或肿瘤治疗的辅助用药,PPARγ有潜力成为肿瘤治疗的新靶点。     

Musashi1, an evolutionarily conserved neural RNA-binding protein, is a versatile marker of human glioma cells in determining their cellular origin, malignancy, and proliferative activity.

Tumor cells often express phenotypic markers that are specific to the cells from which they originated. A neural RNA-binding protein, Musashil, is an evolutionarily well-conserved marker for neural stem cells/ progenitor cells. To examine the origin of gliomas, we examined the expression of the human Musashil homolog, MSI1, in human glioma tissues and in normal human adult and fetal brains. As we had seen previously in rodents, in the normal human brain, MSI1 was expressed in cells located in the ventricular and subventricular zones, in GFAP-negative glial cells, and in GFAP-positive astrocytes. In glioblastomas, MSI1 was expressed in GFAP-negative tumor cells forming foci that were clearly demarcated and surrounded by GFAP-positive cells. Tumor cells arranged in pseudopalisades were also strongly immunoreactive with MSI1 antibodies. The percentage of MSI1-labeled tumor cells increased in higher-grade astrocytomas and correlated with proliferative activity, as estimated by an MIB-1 staining index. Our results indicate that MSI1 is an excellent marker for neural progenitor cells including neural stem cells in normal human brains. Furthermore, the expression of MSI1 correlates well with the immature nature as well as the malignancy of tumor cells in human gliomas. Thus, we expect the analysis of MSI1 expression to contribute to the understanding of the cellular origin and biology of human gliomas.     

Optimal pathways control fixation of multiple mutations during cancer initiation

Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.     

Origins and evolution of cell phenotypes in breast tumors

This study presents a stochastic model that correlates genomic instability with tumor formation. The model describes the time- and space-variant volumetric concentrations of cancer cells of various phenotypes in a breast tumor. The cells of epithelial origin in the cancerous breast tissue are classified into four different phenotypes, normal epithelial cells and the grade 1, grade 2 and grade 3 cancer cell types with increasing potential for growth and invasion. Equations governing the time course of volumetric concentrations of cell phenotypes are derived by using the principle of conservation of mass. Cell migration into and from the stroma is taken into account. The transformations between cell phenotypes are due to genetic inheritance and chromosome aberrations. These transformations are assumed to be stochastic functions of the local cell concentration. The simulations of the model for planar geometry replicate the shapes of human breast tumors and capture the time history of tumor growth in animal models. Simulations point to transformation of tumor cell population from heterogeneous compositions to a single phenotype at advanced stages of invasive tumors. Systematic variations of model parameters in the computations indicate the important roles the migration capacity, proliferation rate, and phenotype transition probability play in tumor growth. The model developed provides realistic simulations for standard breast cancer therapies and can be used in the optimization studies of chemotherapy, radiotherapy, hormone therapy and emerging individualized therapies for cancer.     

Mitochondria in relation to cancer metastasis: introduction to a mini-review series

This introductory article and those that follow focus on the roles that mitochondria may have in cancer metastasis (spreading) that all too frequently leads to death of cancer patients. The history of cancer dates back in time to several thousand years BC and continues to this day. Although billions of dollars have been invested, numerous cancer researchers/scientists and oncologist located at universities, hospitals, cancer centers, commercial entities (companies), and government agencies have been unable to discover ??magic bullets?? to quickly silence most cancers. That is, agents that are effective not only in eradicating the primary tumor at its site of origin, but eradicating also distant tumors that have arisen therefrom via metastatic cells. Fortunately, in recent years some researchers have obtained evidence that the mitochondria of cancer cells are involved not only in providing in part the necessary energy (ATP) to fuel their growth, but hold the secrets to their immortality, and propensity to metastasize (spread) from their original site of origin to other body locations. This introductory article, as well as those that follow, focus on the possible roles of mitochondria in cancer metastasis as well as strategies to arrest cancer metastasis based on this knowledge. Ideally, for a patient to become ??cancer free?? the anticancer agent/agents used must 1) eradicate the primary tumor at its site of origin, 2) eradicate any tumors at other body locations that have arisen via metastasis, and 3) eradicate any tumor cells that remain in the blood, i.e., circulating tumor cells. One such agent that holds promise for doing all three is the small molecule 3-bromopyruvate (3BP) discovered in the author??s laboratory by Dr. Young H. Ko near the turn of the century to be a potent anti-cancer agent [Ko et al.(2001) Can Lett 173:83?C91].     

Phase separation and bistability in a three-dimensional model for protein domain formation at biomembranes

Proteins in living cells interact with membranes. They may bind to or unbind from the membrane to the cytosol depending on the lipid composition of the membrane and their interaction with cytosolic enzymes. Moreover, proteins can accumulate at the membrane and assemble in spatial domains. Here, a simple model of protein cycling at biomembranes is studied, when the total number of proteins is conserved. Specifically, we consider the spatio-temporal dynamics of MARCKS proteins and their interactions with enzymes facilitating translocation from and rebinding to the membrane. The model exhibits two qualitatively different mechanisms of protein domain formation: phase separation related to a long-wave instability of a membrane state with homogeneous protein coverage and stable coexistence of two states with different homogeneous protein coverage in bistable media. We evaluate the impact of the cytosolic volume on the occurrence of protein pattern formation by simulations in a three-dimensional model. We show that the explicit treatment of the volume in the model leads to an effective rescaling of the reaction rates. For a simplified model of protein cycling, we can derive analytical expressions for the rescaling coefficients and verify them by direct simulations with the complete three-dimensional model.     

Isologous diversification for robust development of cell society.

Isologous diversification, proposed for cell differentiation, is shown to be stable against molecular and other external fluctuations, where amplification of noise-induced slight difference between cells leads to a noise-tolerant society with differentiated cell types. It is a general consequence of interacting cells with biochemical networks and cell divisions, as is confirmed by several model simulations. According to the theory, differentiation proceeds first by loss of synchrony of intracellular oscillations as the number of cells increases. Then the chemical composition of the cells is differentiated. The differentiated compositions become inherited by the next generation, and lead to determined cell types. As a result of successive occurrence of the cell differentiation, the cell society will be composed of different cell types. The whole developmental process is robust not only against molecular fluctuations but also against the removal of a cluster of cells. This robustness is a remarkable feature of isologous diversification, in contrast to the conventional threshold-type mechanism for development. As a testable consequence of the theory, we also discuss interaction-dependent tumor formation and negative correlation between growth speed and chemical diversity.     

A mechanical model of tumor encapsulation and transcapsular spread

In this paper, a mathematical modeling framework is presented which describes the growth, encapsulation, and transcapsular spread of solid tumors. The model is based on the physical forces and cellular interactions involved in tumorigenesis and is used to test and compare the active (foreign body hypothesis) and passive (expansive growth hypothesis) hypotheses of capsule formation, such investigations being ideally suited to our mechanical model. The model simulations lead us to predict that, although an active response can successfully control tumor growth via the deposition of large amounts of collagen, this alone is insufficient for capsule formation. In contrast, a solely passive responsive is capable of producing an encapsulated tumor with minimal accumulation of connective tissue within the tumor. When both responses are active, a denser capsule forms and there is a significant increase in connective tissue within the tumor. Using a modified version of the model, in which tumor cells are assumed to produce degradative proteases at a rate which depends on the pressure they experience, it is also possible to show that transcapsular spread or invasion of the tumor may be due to the production by the tumor cells of proteases and their subsequent action.     

Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth,Pre-Existing Vessel Co-Option,Angiogenesis and Blood Perfusion

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.     

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.     

Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue

We propose a multiscale chemo-mechanical model of cancer tumor development in epithelial tissue. The model is based on the transformation of normal cells into a cancerous state triggered by a local failure of spatial synchronization of the circadian rhythm. The model includes mechanical interactions and a chemical signal exchange between neighboring cells, as well as a division of cells and intercalation that allows for modification of the respective parameters following transformation into the cancerous state. The numerical simulations reproduce different dephasing patterns—spiral waves and quasistationary clustering, with the latter being conducive to cancer formation. Modification of mechanical properties reproduces a distinct behavior of invasive and localized carcinoma.     

A sclerostin-based theory for strain-induced bone formation

Bone formation responds to mechanical loading, which is believed to be mediated by osteocytes. Previous theories assumed that loading stimulates osteocytes to secrete signals that stimulate bone formation. In computer simulations this 'stimulatory' theory successfully produced load-aligned trabecular structures. In recent years, however, it was discovered that osteocytes inhibit bone formation via the protein sclerostin. To reconcile this with strain-induced bone formation, one must assume that sclerostin secretion decreases with mechanical loading. This leads to a new 'inhibitory' theory in which loading inhibits osteocytes from inhibiting bone formation. Here we used computer simulations to show that a sclerostin-based model is able to produce a load-aligned trabecular architecture. An important difference appeared when we compared the response of the stimulatory and inhibitory models to loss of osteocytes, and found that the inhibitory pathway prevents the loss of trabeculae that is seen with the stimulatory model. Further, we demonstrated with combined stimulatory/inhibitory models that the two pathways can work side-by-side to achieve a load-adapted bone architecture.     

Continuous and discrete mathematical models of tumor-induced angiogenesis

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial-cell migration, and organize themselves into a dendritic structure. Subsequent cell proliferation near the sprout tip permits further extension of the capillary and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumors. In this paper we present both continuous and discrete mathematical models which describe the formation of the capillary sprout network in response to chemical stimuli (tumor angiogenic factors, TAF) supplied by a solid tumor. The models also take into account essential endothelial cell-extracellular matrix interactions via the inclusion of the matrix macromolecule fibronectin. The continuous model consists of a system of nonlinear partial differential equations describing the initial migratory response of endothelial cells to the TAF and the fibronectin. Numerical simulations of the system, using parameter values based on experimental data, are presented and compared qualitatively with in vivo experiments. We then use a discretized form of the partial differential equations to develop a biased random-walk model which enables us to track individual endothelial cells at the sprout tips and incorporate anastomosis, mitosis and branching explicitly into the model. The theoretical capillary networks generated by computer simulations of the discrete model are compared with the morphology of capillary networks observed in in vivo experiments.     

Fibroblast Growth Factor Receptor 1 Activation in Mammary Tumor Cells Promotes Macrophage Recruitment in a CX3CL1-Dependent Manner

Tumor formation is an extensive process requiring complex interactions that involve both tumor cell-intrinsic pathways and soluble mediators within the microenvironment. Tumor cells exploit the intrinsic functions of many soluble molecules, including chemokines and their receptors, to regulate pro-tumorigenic phenotypes that are required for growth and progression of the primary tumor. Previous studies have shown that activation of inducible FGFR1 (iFGFR1) in mammary epithelial cells resulted in increased proliferation, migration, and invasion in vitro and tumor formation in vivo. These studies also demonstrated that iFGFR1 activation stimulated recruitment of macrophages to the epithelium where macrophages contributed to iFGFR1-mediated epithelial cell proliferation and angiogenesis. The studies presented here further utilize this model to identify the mechanisms that regulate FGFR1-induced macrophage recruitment. Results from this study elucidate a novel role for the inflammatory chemokine CX3CL1 in FGFR1-induced macrophage migration. Specifically, we illustrate that activation of both the inducible FGFR1 construct in mouse mammary epithelial cells and endogenous FGFR in the triple negative breast cancer cell line, HS578T, leads to expression of the chemokine CX3CL1. Furthermore, we demonstrate that FGFR-induced CX3CL1 is sufficient to recruit CX3CR1-expressing macrophages in vitro. Finally, blocking CX3CR1 in vivo leads to decreased iFGFR1-induced macrophage recruitment, which correlates with decreased angiogenesis. While CX3CL1 is a known target of FGF signaling in the wound healing environment, these studies demonstrate that FGFR activation also leads to induction of CX3CL1 in a tumor setting. Furthermore, these results define a novel role for CX3CL1 in promoting macrophage recruitment during mammary tumor formation, suggesting that the CX3CL1/CX3CR1 axis may represent a potential therapeutic approach for targeting breast cancers associated with high levels of tumor-associated macrophages.     

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels’ growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development—the avascular and vascular phases—and in each stage two cases are considered—with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).     

Simulating PDGF-Driven Glioma Growth and Invasion in an Anatomically Accurate Brain Domain

Gliomas are the most common of all primary brain tumors. They are characterized by their diffuse infiltration of the brain tissue and are uniformly fatal, with glioblastoma being the most aggressive form of the disease. In recent years, the over-expression of platelet-derived growth factor (PDGF) has been shown to produce tumors in experimental rodent models that closely resemble this human disease, specifically the proneural subtype of glioblastoma. We have previously modeled this system, focusing on the key attribute of these experimental tumors—the “recruitment” of oligodendroglial progenitor cells (OPCs) to participate in tumor formation by PDGF-expressing retrovirally transduced cells—in one dimension, with spherical symmetry. However, it has been observed that these recruitable progenitor cells are not uniformly distributed throughout the brain and that tumor cells migrate at different rates depending on the material properties in different regions of the brain. Here we model the differential diffusion of PDGF-expressing and recruited cell populations via a system of partial differential equations with spatially variable diffusion coefficients and solve the equations in two spatial dimensions on a mouse brain atlas using a flux-differencing numerical approach. Simulations of our in silico model demonstrate qualitative agreement with the observed tumor distribution in the experimental animal system. Additionally, we show that while there are higher concentrations of OPCs in white matter, the level of recruitment of these plays little role in the appearance of “white matter disease,” where the tumor shows a preponderance for white matter. Instead, simulations show that this is largely driven by the ratio of the diffusion rate in white matter as compared to gray. However, this ratio has less effect on the speed of tumor growth than does the degree of OPC recruitment in the tumor. It was observed that tumor simulations with greater degrees of recruitment grow faster and develop more nodular tumors than if there is no recruitment at all, similar to our prior results from implementing our model in one dimension. Combined, these results show that recruitment remains an important consideration in understanding and slowing glioma growth.     

Maspin is an angiogenesis inhibitor

Maspin, a unique member of the serpin family, is a secreted protein encoded by a class II tumor suppressor gene whose downregulation is associated with the development of breast and prostate cancers. Overexpression of maspin in breast tumor cells limits their growth and metastases in vivo. In this report we demonstrate that maspin is an effective inhibitor of angiogenesis. In vitro, it acted directly on cultured endothelial cells to stop their migration towards basic fibroblast growth factor and vascular endothelial growth factor and to limit mitogenesis and tube formation. In vivo, it blocked neovascularization in the rat cornea pocket model. Maspin derivatives mutated in the serpin reactive site lost their ability to inhibit the migration of fibroblasts, keratinocytes, and breast cancer cells but were still able to block angiogenesis in vitro and in vivo. When maspin was delivered locally to human prostate tumor cells in a xenograft mouse model, it blocked tumor growth and dramatically reduced the density of tumor-associated microvessels. These data suggest that the tumor suppressor activity of maspin may depend in large part on its ability to inhibit angiogenesis and raise the possibility that maspin and similar serpins may be excellent leads for the development of drugs that modulate angiogenesis.