Simulating the impact of a molecular 'decision-process' on cellular phenotype and multicellular patterns in brain tumors

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.

A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously.

METHODS

The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes.

RESULTS

The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades.

CONCLUSIONS

In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.

Synergistic Integration Between Machine Learning and Agent-Based Modeling: A Multidisciplinary Review

Agent-based modeling (ABM) involves developing models in which agents make adaptive decisions in a changing environment. Machine-learning (ML) based inference models can improve sequential decision-making by learning agents' behavioral patterns. With the aid of ML, this emerging area can extend traditional agent-based schemes that hardcode agents' behavioral rules into an adaptive model. Even though there are plenty of studies that apply ML in ABMs, the generalized applicable scenarios, frameworks, and procedures for implementations are not well addressed. In this article, we provide a comprehensive review of applying ML in ABM based on four major scenarios, i.e., microagent-level situational awareness learning, microagent-level behavior intervention, macro-ABM-level emulator, and sequential decision-making. For these four scenarios, the related algorithms, frameworks, procedures of implementations, and multidisciplinary applications are thoroughly investigated. We also discuss how ML can improve prediction in ABMs by trading off the variance and bias and how ML can improve the sequential decision-making of microagent and macrolevel policymakers via a mechanism of reinforced behavioral intervention. At the end of this article, future perspectives of applying ML in ABMs are discussed with respect to data acquisition and quality issues, the possible solution of solving the convergence problem of reinforcement learning, interpretable ML applications, and bounded rationality of ABM.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

Mechanistic characterization of endothelial sprouting mediated by pro-angiogenic signaling

Objective

We aim to quantitatively characterize the crosstalk between VEGF‐ and FGF‐mediated angiogenic signaling and endothelial sprouting, to gain mechanistic insights and identify novel therapeutic strategies.

Methods

We constructed an experimentally validated hybrid agent‐based mathematical model that characterizes endothelial sprouting driven by FGF‐ and VEGF‐mediated signaling. We predicted the total sprout length, number of sprouts, and average length by the mono‐ and co‐stimulation of FGF and VEGF.

Results

The experimentally fitted and validated model predicts that FGF induces stronger angiogenic responses in the long‐term compared with VEGF stimulation. Also, FGF plays a dominant role in the combination effects in endothelial sprouting. Moreover, the model suggests that ERK and Akt pathways and cellular responses contribute differently to the sprouting process. Last, the model predicts that the strategies to modulate endothelial sprouting are context‐dependent, and our model can identify potential effective pro‐ and anti‐angiogenic targets under different conditions and study their efficacy.

Conclusions

The model provides detailed mechanistic insight into VEGF and FGF interactions in sprouting angiogenesis. More broadly, this model can be utilized to identify targets that influence angiogenic signaling leading to endothelial sprouting and to study the effects of pro‐ and anti‐angiogenic therapies.

Navigating Multi-Scale Cancer Systems Biology Towards Model-Driven Clinical Oncology and Its Applications in Personalized Therapeutics

Rapid advancements in high-throughput omics technologies and experimental protocols have led to the generation of vast amounts of scale-specific biomolecular data on cancer that now populates several online databases and resources. Cancer systems biology models built using this data have the potential to provide specific insights into complex multifactorial aberrations underpinning tumor initiation, development, and metastasis. Furthermore, the annotation of these single- and multi-scale models with patient data can additionally assist in designing personalized therapeutic interventions as well as aid in clinical decision-making. Here, we have systematically reviewed the emergence and evolution of (i) repositories with scale-specific and multi-scale biomolecular cancer data, (ii) systems biology models developed using this data, (iii) associated simulation software for the development of personalized cancer therapeutics, and (iv) translational attempts to pipeline multi-scale panomics data for data-driven in silico clinical oncology. The review concludes that the absence of a generic, zero-code, panomics-based multi-scale modeling pipeline and associated software framework, impedes the development and seamless deployment of personalized in silico multi-scale models in clinical settings.

Agent-Based Models Predict Emergent Behavior of Heterogeneous Cell Populations in Dynamic Microenvironments

Computational models are most impactful when they explain and characterize biological phenomena that are non-intuitive, unexpected, or difficult to study experimentally. Countless equation-based models have been built for these purposes, but we have yet to realize the extent to which rules-based models offer an intuitive framework that encourages computational and experimental collaboration. We develop ARCADE, a multi-scale agent-based model to interrogate emergent behavior of heterogeneous cell agents within dynamic microenvironments and demonstrate how complexity of intracellular metabolism and signaling modules impacts emergent dynamics. We perform in silico case studies on context, competition, and heterogeneity to demonstrate the utility of our model for gaining computational and experimental insight. Notably, there exist (i) differences in emergent behavior between colony and tissue contexts, (ii) linear, non-linear, and multimodal consequences of parameter variation on competition in simulated co-cultures, and (iii) variable impact of cell and population heterogeneity on emergent outcomes. Our extensible framework is easily modified to explore numerous biological systems, from tumor microenvironments to microbiomes.

A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth

We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.

On the Impact of Chemo-Mechanically Induced Phenotypic Transitions in Gliomas

Tumor microenvironment is a critical player in glioma progression, and novel therapies for its targeting have been recently proposed. In particular, stress-alleviation strategies act on the tumor by reducing its stiffness, decreasing solid stresses and improving blood perfusion. However, these microenvironmental changes trigger chemo-mechanically induced cellular phenotypic transitions whose impact on therapy outcomes is not completely understood. In this work we analyze the effects of mechanical compression on migration and proliferation of glioma cells. We derive a mathematical model of glioma progression focusing on cellular phenotypic plasticity. Our results reveal a trade-off between tumor infiltration and cellular content as a consequence of stress-alleviation approaches. We discuss how these novel findings increase the current understanding of glioma/microenvironment interactions and can contribute to new strategies for improved therapeutic outcomes.

Integrating in vitro experiments with in silico approaches for Glioblastoma invasion: the role of cell-to-cell adhesion heterogeneity

Glioblastoma cells adopt migration strategies to invade into the brain parenchyma ranging from individual to collective mechanisms, whose role and dynamics are not yet fully understood. In this work, we explore Glioblastoma heterogeneity and recapitulate its invasive patterns both in vitro, by utilizing primary cells along with the U87MG cell line, and in silico, by adopting discrete, individual cell-based mathematics. Glioblastoma cells are cultured three-dimensionally in an ECM-like substrate. The primary Glioblastoma spheroids adopt a novel cohesive pattern, mimicking perivascular invasion in the brain, while the U87MG adopt a typical, starburst invasive pattern under the same experimental setup. Mathematically, we focus on the role of the intrinsic heterogeneity with respect to cell-to-cell adhesion. Our proposed mathematical approach mimics the invasive morphologies observed in vitro and predicts the dynamics of tumour expansion. The role of the proliferation and migration is also explored showing that their effect on tumour morphology is different per cell type. The proposed model suggests that allowing cell-to-cell adhesive heterogeneity within the tumour population is sufficient for variable invasive morphologies to emerge which remain originally undetectable by conventional imaging, indicating that exploration in pathological samples is needed to improve our understanding and reveal potential patient-specific therapeutic targets.

A HYBRID THREE-SCALE MODEL OF TUMOR GROWTH

Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step towards predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction-diffusion equations. At the cell level, we use an agent based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton's second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representating both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Specifically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

Computational Systems Biology in Cancer: Modeling Methods and Applications

In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy.

In Vitro/In Silico Study on the Role of Doubling Time Heterogeneity among Primary Glioblastoma Cell Lines

The application of accurate cancer predictive algorithms validated with experimental data is a field concerning both basic researchers and clinicians, especially regarding a highly aggressive form of cancer, such as Glioblastoma. In an aim to enhance prediction accuracy in realistic patient-specific environments, accounting for both inter- and intratumoral heterogeneity, we use patient-derived Glioblastoma cells from different patients. We focus on cell proliferation using in vitro experiments to estimate cell doubling times and sizes for established primary Glioblastoma cell lines. A preclinically driven mathematical model parametrization is accomplished by taking into account the experimental measurements. As a control cell line we use the well-studied U87MG cells. Both in vitro and in silico results presented support that the variance between tumor staging can be attributed to the differential proliferative capacity of the different Glioblastoma cells. More specifically, the intratumoral heterogeneity together with the overall proliferation reflected in both the proliferation rate and the mechanical cell contact inhibition can predict the in vitro evolution of different Glioblastoma cell lines growing under the same conditions. Undoubtedly, additional imaging techniques capable of providing spatial information of tumor cell physiology and microenvironment will enhance our understanding regarding Glioblastoma nature and verify and further improve our predictability.

A branching process model of heterogeneous DNA damages caused by radiotherapy in in vitro cell cultures

This paper deals with the dynamic modeling and simulation of cell damage heterogeneity and associated mutant cell phenotypes in the therapeutic responses of cancer cell populations submitted to a radiotherapy session during in vitro assays. Each cell is described by a finite number of phenotypic states with possible transitions between them. The population dynamics is then given by an age-dependent multi-type branching process. From this representation, we obtain formulas for the average size of the global survival population as well as the one of subpopulations associated with 10 mutation phenotypes. The proposed model has been implemented into Matlab^© and the numerical results corroborate the ability of the model to reproduce four major types of cell responses: delayed growth, anti-proliferative, cytostatic and cytotoxic.

Advancing Cancer Systems Biology: Introducing the Center for the Development of a Virtual Tumor, CViT

Integrative cancer biology research relies on a variety of data-driven computational modeling and simulation methods and techniques geared towards gaining new insights into the complexity of biological processes that are of critical importance for cancer research. These include the dynamics of gene-protein interaction networks, the percolation of sub-cellular perturbations across scales and the impact they may have on tumorigenesis in both experiments and clinics. Such innovative ‘systems’ research will greatly benefit from enabling Information Technology that is currently under development, including an online collaborative environment, a Semantic Web based computing platform that hosts data and model repositories as well as high-performance computing access. Here, we present one of the National Cancer Institute's recently established Integrative Cancer Biology Programs, i.e. the Center for the Development of a Virtual Tumor, CViT, which is charged with building a cancer modeling community, developing the aforementioned enabling technologies and fostering multi-scale cancer modeling and simulation.

Hybrid multiscale modeling and prediction of cancer cell behavior

Background

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.

Methods

In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.

Results

Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.

Conclusion

Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

The tumor as an organ: comprehensive spatial and temporal modeling of the tumor and its microenvironment

BACKGROUND

Research related to cancer is vast, and continues in earnest in many directions. Due to the complexity of cancer, a better understanding of tumor growth dynamics can be gleaned from a dynamic computational model. We present a comprehensive, fully executable, spatial and temporal 3D computational model of the development of a cancerous tumor together with its environment.

RESULTS

The model was created using Statecharts, which were then connected to an interactive animation front-end that we developed especially for this work, making it possible to visualize on the fly the on-going events of the system's execution, as well as the effect of various input parameters. We were thus able to gain a better understanding of, e.g., how different amounts or thresholds of oxygen and VEGF (vascular endothelial growth factor) affect the progression of the tumor. We found that the tumor has a critical turning point, where it either dies or recovers. If minimum conditions are met at that time, it eventually develops into a full, active, growing tumor, regardless of the actual amount; otherwise it dies.

CONCLUSIONS

This brings us to the conclusion that the tumor is in fact a very robust system: changing initial values of VEGF and oxygen can increase the time it takes to become fully developed, but will not necessarily completely eliminate it.

Mathematical model and its fast numerical method for the tumor growth

In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions.

Agent-based modeling of osteogenic differentiation of mesenchymal stem cells in porous biomaterials

Mesenchymal stem cells (MSC) have shown promise in tissue engineering applications due to their potential for differentiating into mesenchymal tissues such as osteocytes, chondrocytes, and adipocytes and releasing proteins to promote tissue regeneration. One application involves seeding MSCs in biomaterial scaffolds to promote osteogenesis in the repair of bone defects following implantation. However, predicting in vivo survival and differentiation of MSCs in biomaterials is challenging. Rapid and stable vascularization of scaffolds is required to supply nutrients and oxygen that MSCs need to survive as well as to go through osteogenic differentiation. The objective of this study is to develop an agent-based model and simulator that can be used to investigate the effects of using gradient growth factors on survival and differentiation of MSCs seeded in scaffolds. An agent-based model is developed to simulate the MSC behavior. The effect of vascular endothelial growth factor (VEGF) and bone morphogenic protein-2 (BMP-2) on both survival and osteogenic differentiation is studied. Results showed that the survival ratio of MSCs can be enhanced by increasing VEGF concentration. BMP-2 caused a slight increase on survival ratio. Osteogenesis strongly depends on the VEGF concentration as well because of its effect on vascularization. BMP-2 increased the osteogenic differentiation of MSCs.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.

Web-based workflow planning platform supporting the design and execution of complex multiscale cancer models

Significant Virtual Physiological Human efforts and projects have been concerned with cancer modeling, especially in the European Commission Seventh Framework research program, with the ambitious goal to approach personalized cancer simulation based on patient-specific data and thereby optimize therapy decisions in the clinical setting. However, building realistic in silico predictive models targeting the clinical practice requires interactive, synergetic approaches to integrate the currently fragmented efforts emanating from the systems biology and computational oncology communities all around the globe. To further this goal, we propose an intelligent graphical workflow planning system that exploits the multiscale and modular nature of cancer and allows building complex cancer models by intuitively linking/interchanging highly specialized models. The system adopts and extends current standardization efforts, key tools, and infrastructure in view of building a pool of reliable and reproducible models capable of improving current therapies and demonstrating the potential for clinical translation of these technologies.

Fast tracking of co-localization of multiple markers by using the nanozoomer slide scanner and NDPViewer

The detection of co-localization of immunohistochemical markers in tissues or cells requires the application of the confocal laser scanning microscope (CLSM) to multiple immunofluorescence (MIF) stainings. CLSM is operationally sophisticated but requires time-consuming procedures of imaging and reconstruction, and a professional operator is required for manipulation of the microscopic system. Therefore, this technique is less suitable for the examination of many samples in a short time. Moreover, the technique only allows imaging of selected areas of a sample at one time and is not practical for fast panoramic mapping and tracking of whole tissue sections. Here we show a powerful high-throughput and operationally simple histological approach using the Hamamatsu NDP slide scanner (Hamamatsu Nanozoomer 2.0HT) and its viewing platform (NDP.Viewer). The approach not only enables fast mapping and tracking of overlapping spots or regions stained with multiple markers, but also offers panoramic screening of whole tissue sections with fully electronic manipulation for the visualization and analysis of any individual regions.

Identification of crucial parameters in a mathematical multiscale model of glioblastoma growth

Glioblastomas are highly malignant brain tumours. Mathematical models and their analysis provide a tool to support the understanding of the development of these tumours as well as the design of more effective treatment strategies. We have previously developed a multiscale model of glioblastoma progression that covers processes on the cellular and molecular scale. Here, we present a novel nutrient-dependent multiscale sensitivity analysis of this model that helps to identify those reaction parameters of the molecular interaction network that influence the tumour progression on the cellular scale the most. In particular, those parameters are identified that essentially determine tumour expansion and could be therefore used as potential therapy targets. As indicators for the success of a potential therapy target, a deceleration of the tumour expansion and a reduction of the tumour volume are employed. From the results, it can be concluded that no single parameter variation results in a less aggressive tumour. However, it can be shown that a few combined perturbations of two systematically selected parameters cause a slow-down of the tumour expansion velocity accompanied with a decrease of the tumour volume. Those parameters are primarily linked to the reactions that involve the microRNA-451 and the thereof regulated protein MO25.

Cancer systems biology and modeling: microscopic scale and multiscale approaches

Cancer has become known as a complex and systematic disease on macroscopic, mesoscopic and microscopic scales. Systems biology employs state-of-the-art computational theories and high-throughput experimental data to model and simulate complex biological procedures such as cancer, which involves genetic and epigenetic, in addition to intracellular and extracellular complex interaction networks. In this paper, different systems biology modeling techniques such as systems of differential equations, stochastic methods, Boolean networks, Petri nets, cellular automata methods and agent-based systems are concisely discussed. We have compared the mentioned formalisms and tried to address the span of applicability they can bear on emerging cancer modeling and simulation approaches. Different scales of cancer modeling, namely, microscopic, mesoscopic and macroscopic scales are explained followed by an illustration of angiogenesis in microscopic scale of the cancer modeling. Then, the modeling of cancer cell proliferation and survival are examined on a microscopic scale and the modeling of multiscale tumor growth is explained along with its advantages.

WITHDRAWN: Cancer modeling: The holonic agent-based approach

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Investigating biocomplexity through the agent-based paradigm

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex.

A novel method for simulating the extracellular matrix in models of tumour growth

A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typically considered are the nutrient concentration, the extracellular matrix (ECM), and matrix degrading enzymes (MDEs). The in vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. The main contribution of the present work is therefore to describe the processes on the basis of simplified mathematical approaches, which, at the same time, depict realistic results to understand the biological processes. In this work, we discuss if we have to simulate the MDE or if the degraded matrix can be estimated directly with respect to the cancer cell distribution. Additionally, we compare the results for modelling tumour growth using the common and our simplified approach, thereby demonstrating the advantages of the proposed method. Therefore, we introduce variations of the positioning of the nutrient delivering blood vessels and use different initializations of the ECM. We conclude that the novel method, which does not explicitly model the matrix degrading enzymes, provides means for a straightforward and fast implementation for modelling tumour growth.

Multiscale cancer modeling

Simulating cancer behavior across multiple biological scales in space and time, i.e., multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine hypotheses, focus experiments, and enable more accurate predictions. A growing number of examples illustrate the value of this approach in providing quantitative insights in the initiation, progression, and treatment of cancer. In this review, we introduce the most recent and important multiscale cancer modeling works that have successfully established a mechanistic link between different biological scales. Biophysical, biochemical, and biomechanical factors are considered in these models. We also discuss innovative, cutting-edge modeling methods that are moving predictive multiscale cancer modeling toward clinical application. Furthermore, because the development of multiscale cancer models requires a new level of collaboration among scientists from a variety of fields such as biology, medicine, physics, mathematics, engineering, and computer science, an innovative Web-based infrastructure is needed to support this growing community.

Quantitative study of cytotoxic T-lymphocyte immunotherapy for nasopharyngeal carcinoma

BACKGROUND

In clinical practice, the common strategy for immunotherapy of nasopharyngeal carcinoma (NPC) is to infuse cytotoxic T-lymphocyte (CTL) lines several times by intravenous injection, but it is difficult by laboratory research to investigate the relationship between treatment time-point, the amount of CTL added and the therapeutic effect. The objective of this study is to establish a mathematical model to study the therapeutic effect of different treatment time-points and amounts of CTL, and to predict the change in therapeutic effect when the percentage of EBV LMP2-specific CTL is increased from 10% to 20%.

RESULTS

The concentration of epidermal growth factor receptor (EGFR) in the tumor cell cytomembranes increases after CTL is added. Concurrently, there is a marked downward trend of the phosphorylated transforming growth factor-α (TGFα)-EGFR complex in the tumor cell cytomembranes, which indicates restriction of tumor growth after CTL immunotherapy. The relationships among the time of addition of CTL, the amount of CTL added, different CTL specificities for LMP2 and the increment rate k of the total number of tumor cells were evaluated.

CONCLUSIONS

The simulation results quantify the relationships among treatment time-points, amount of CTL added, and the corresponding therapeutic effect of immunotherapy for NPC.

A computational multiscale model of glioblastoma growth: regulation of cell migration and proliferation via microRNA-451, LKB1 and AMPK

A new computational multiscale model of glioblastoma growth is introduced. This model combines an agent-based model for representing processes on the cellular level with a molecular interaction network for each cell on the subcellular scale. The network is based on recently published work on the interaction of microRNA-451, LKB1 and AMPK in the regulation of glioblastoma cell migration and proliferation. We translated this network into a mathematical description by the use of 17 ordinary differential equations. In our model, we furthermore establish a link from the molecular interaction network of a single cell to cellular actions (e.g. chemotactic movement) on the microscopic level. First results demonstrate that the computational model reproduces a tumor cell development comparable to that observed in in vitro experiments.

Developing a multiscale, multi-resolution agent-based brain tumor model by graphics processing units

Multiscale agent-based modeling (MABM) has been widely used to simulate Glioblastoma Multiforme (GBM) and its progression. At the intracellular level, the MABM approach employs a system of ordinary differential equations to describe quantitatively specific intracellular molecular pathways that determine phenotypic switches among cells (e.g. from migration to proliferation and vice versa). At the intercellular level, MABM describes cell-cell interactions by a discrete module. At the tissue level, partial differential equations are employed to model the diffusion of chemoattractants, which are the input factors of the intracellular molecular pathway. Moreover, multiscale analysis makes it possible to explore the molecules that play important roles in determining the cellular phenotypic switches that in turn drive the whole GBM expansion. However, owing to limited computational resources, MABM is currently a theoretical biological model that uses relatively coarse grids to simulate a few cancer cells in a small slice of brain cancer tissue. In order to improve this theoretical model to simulate and predict actual GBM cancer progression in real time, a graphics processing unit (GPU)-based parallel computing algorithm was developed and combined with the multi-resolution design to speed up the MABM. The simulated results demonstrated that the GPU-based, multi-resolution and multiscale approach can accelerate the previous MABM around 30-fold with relatively fine grids in a large extracellular matrix. Therefore, the new model has great potential for simulating and predicting real-time GBM progression, if real experimental data are incorporated.

Non-Markovian models for migration-proliferation dichotomy of cancer cells: anomalous switching and spreading rate

Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the near-core-outer region, where biased migration away from the tumor spheroid core takes place. We suggest non-Markovian switching between the migrating and proliferating phenotypes of tumor cells. Nonlinear master equations for mean densities of cancer cells of both phenotypes are derived. In anomalous switching case we estimate the average size of the near-core-outer region that corresponds to sublinear growth (r(t)) ~ t(μ) for 0 < μ < 1. In model II we consider the outer zone, where the density of cancer cells is very low. We suggest an integrodifferential equation for the total density of cancer cells. For proliferation rate we use the classical logistic growth, while the migration of cells is subdiffusive. The exact formulas for the overall spreading rate of cancer cells are obtained by a hyperbolic scaling and Hamilton-Jacobi techniques.

Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy

Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour remain to be elucidated. Our work is motivated by the migration/proliferation dichotomy (go-or-grow) hypothesis, i.e. the antagonistic migratory and proliferating cellular behaviours in a cell population, which may play a central role in these tumours. In this paper, we formulate a simple go-or-grow model to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density. The model consists of two reaction-diffusion equations describing cell migration, proliferation and a phenotypic switch. We use a combination of numerical and analytical techniques to characterize the development of spatio-temporal instabilities and travelling wave solutions generated by our model. We demonstrate that the density-dependent go-or-grow mechanism can produce complex dynamics similar to those associated with tumour heterogeneity and invasion.

GIV/Girdin is a rheostat that fine-tunes growth factor signals during tumor progression

GIV/Girdin is a multidomain signaling molecule that enhances PI3K-Akt signals downstream of both G protein-coupled and growth factor receptors. We previously reported that GIV triggers cell migration via its C-terminal guanine-nucleotide exchange factor (GEF) motif that activates Gαi. Recently we discovered that GIV's C-terminus directly interacts with the epidermal growth factor receptor (EGFR), and when its GEF function is intact, a Gαi-GIV-EGFR signaling complex assembles. By coupling G proteins to growth factor receptors, GIV is uniquely poised to intercept the incoming receptor-initiated signals and modulate them via G protein intermediates. Subsequent work has revealed that expression of the highly specialized C-terminus of GIV undergoes a bipartite dysregulation during oncogenesis-full length GIV with an intact C-terminus is expressed at levels ~20-50-fold above normal in highly invasive cancer cells and metastatic tumors, but its C-terminus is truncated by alternative splicing in poorly invasive cancer cells and non-invasive tumors. The consequences of such dysregulation on graded signal transduction and cellular phenotypes in the normal epithelium and its implication during tumor progression are discussed herein. Based on the fact that GIV grades incoming signals initiated by ligand-activated receptors by linking them to cyclical activation of G proteins, we propose that GIV is a molecular rheostat for signal transduction.

Agent-based models in translational systems biology

Effective translational methodologies for knowledge representation are needed in order to make strides against the constellation of diseases that affect the world today. These diseases are defined by their mechanistic complexity, redundancy, and nonlinearity. Translational systems biology aims to harness the power of computational simulation to streamline drug/device design, simulate clinical trials, and eventually to predict the effects of drugs on individuals. The ability of agent-based modeling to encompass multiple scales of biological process as well as spatial considerations, coupled with an intuitive modeling paradigm, suggests that this modeling framework is well suited for translational systems biology. This review describes agent-based modeling and gives examples of its translational applications in the context of acute inflammation and wound healing.

A G{alpha}i-GIV molecular complex binds epidermal growth factor receptor and determines whether cells migrate or proliferate

Migrating cells do not proliferate and vice versa, but the mechanism involved remains unknown. Ghosh et al. reveal how this cellular decision is made by showing that a Gα_i–GIV molecular complex interacts with EGF receptor and programs growth factor signaling, triggering migration when assembled and favoring mitosis when assembly is prevented.

Cells respond to growth factors by either migrating or proliferating, but not both at the same time, a phenomenon termed migration-proliferation dichotomy. The underlying mechanism of this phenomenon has remained unknown. We demonstrate here that Gα_i protein and GIV, its nonreceptor guanine nucleotide exchange factor (GEF), program EGF receptor (EGFR) signaling and orchestrate this dichotomy. GIV directly interacts with EGFR, and when its GEF function is intact, a Gα_i–GIV–EGFR signaling complex assembles, EGFR autophosphorylation is enhanced, and the receptor's association with the plasma membrane (PM) is prolonged. Accordingly, PM-based motogenic signals (PI3-kinase-Akt and PLCγ1) are amplified, and cell migration is triggered. In cells expressing a GEF-deficient mutant, the Gαi–GIV-EGFR signaling complex is not assembled, EGFR autophosphorylation is reduced, the receptor's association with endosomes is prolonged, mitogenic signals (ERK 1/2, Src, and STAT5) are amplified, and cell proliferation is triggered. In rapidly growing, poorly motile breast and colon cancer cells and in noninvasive colorectal carcinomas in situ in which EGFR signaling favors mitosis over motility, a GEF-deficient splice variant of GIV was identified. In slow growing, highly motile cancer cells and late invasive carcinomas, GIV is highly expressed and has an intact GEF motif. Thus, inclusion or exclusion of GIV's GEF motif, which activates Gαi, modulates EGFR signaling, generates migration-proliferation dichotomy, and most likely influences cancer progression.

The virtual cell--a candidate co-ordinator for 'middle-out' modelling of biological systems

Understanding the functioning of biological systems depends on tackling complexity spanning spatial scales from genome to organ to whole organism. The basic unit of life, the cell, acts to co-ordinate information received across these scales and processes the myriad of signals to produce an integrated cellular response. Cells interact with and respond to other cells through direct or indirect contact, resulting in emergent structure and function of tissues and organs. Systems biology has traditionally used either a 'top-down' or 'bottom-up' approach. However, neither approach takes account of heterogeneity or 'noise', which is an inherent feature of cellular behaviour and may have significant impact on system level behaviour. We review existing approaches to modelling that use cellular automata or agent-based methodologies, where individual cells are represented as equivalent virtual entities governed by simple rules. These paradigms allow a direct one-to-one mapping between real and virtual cells that can be exploited in terms of acquiring parameters from experimental systems, or for model validation. Such models are inherently extensible and can be integrated with other modelling modalities (e.g. partial or ordinary differential equations) to model multi-scale phenomena. Alternatively, hierarchical agent models may be used to explore the functions of biological systems across temporal and spatial scales. This review examines individual-based models and the application of the paradigm to explore multi-scale phenomena in biology. In so doing, it demonstrates how cellular-based models have begun to play an important role in the development of 'middle-out' models, but with considerable potential for future development.

Multi-scale, multi-resolution brain cancer modeling

In advancing discrete-based computational cancer models towards clinical applications, one faces the dilemma of how to deal with an ever growing amount of biomedical data that ought to be incorporated eventually in one form or another. Model scalability becomes of paramount interest. In an effort to start addressing this critical issue, here, we present a novel multi-scale and multi-resolution agent-based in silico glioma model. While 'multi-scale' refers to employing an epidermal growth factor receptor (EGFR)-driven molecular network to process cellular phenotypic decisions within the micro-macroscopic environment, 'multi-resolution' is achieved through algorithms that classify cells to either active or inactive spatial clusters, which determine the resolution they are simulated at. The aim is to assign computational resources where and when they matter most for maintaining or improving the predictive power of the algorithm, onto specific tumor areas and at particular times. Using a previously described 2D brain tumor model, we have developed four different computational methods for achieving the multi-resolution scheme, three of which are designed to dynamically train on the high-resolution simulation that serves as control. To quantify the algorithms' performance, we rank them by weighing the distinct computational time savings of the simulation runs versus the methods' ability to accurately reproduce the high-resolution results of the control. Finally, to demonstrate the flexibility of the underlying concept, we show the added value of combining the two highest-ranked methods. The main finding of this work is that by pursuing a multi-resolution approach, one can reduce the computation time of a discrete-based model substantially while still maintaining a comparably high predictive power. This hints at even more computational savings in the more realistic 3D setting over time, and thus appears to outline a possible path to achieve scalability for the all-important clinical translation.

Simulating Brain Tumor Heterogeneity with a Multiscale Agent-Based Model: Linking Molecular Signatures, Phenotypes and Expansion Rate

We have extended our previously developed 3D multi-scale agent-based brain tumor model to simulate cancer heterogeneity and to analyze its impact across the scales of interest. While our algorithm continues to employ an epidermal growth factor receptor (EGFR) gene-protein interaction network to determine the cells' phenotype, it now adds an implicit treatment of tumor cell adhesion related to the model's biochemical microenvironment. We simulate a simplified tumor progression pathway that leads to the emergence of five distinct glioma cell clones with different EGFR density and cell 'search precisions'. The in silico results show that microscopic tumor heterogeneity can impact the tumor system's multicellular growth patterns. Our findings further confirm that EGFR density results in the more aggressive clonal populations switching earlier from proliferation-dominated to a more migratory phenotype. Moreover, analyzing the dynamic molecular profile that triggers the phenotypic switch between proliferation and migration, our in silico oncogenomics data display spatial and temporal diversity in documenting the regional impact of tumorigenesis, and thus support the added value of multi-site and repeated assessments in vitro and in vivo. Potential implications from this in silico work for experimental and computational studies are discussed.

In silico cancer modeling: is it ready for prime time?

At the dawn of the era of personalized, systems-driven medicine, computational or in silico modeling and the simulation of disease processes is becoming increasingly important for hypothesis generation and data integration in both experiments and clinics alike. Arguably, the use of these techniques is nowhere more visible than in oncology. To illustrate the field's vast potential, as well as its current limitations, we briefly review selected studies on modeling malignant brain tumors. Implications for clinical practice, and for clinical trial design and outcome prediction, are also discussed.

The role of extracellular matrix in glioma invasion: a cellular Potts model approach

In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion.

Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching

We develop a thermodynamically consistent mixture model for avascular solid tumor growth which takes into account the effects of cell-to-cell adhesion, and taxis inducing chemical and molecular species. The mixture model is well-posed and the governing equations are of Cahn-Hilliard type. When there are only two phases, our asymptotic analysis shows that earlier single-phase models may be recovered as limiting cases of a two-phase model. To solve the governing equations, we develop a numerical algorithm based on an adaptive Cartesian block-structured mesh refinement scheme. A centered-difference approximation is used for the space discretization so that the scheme is second order accurate in space. An implicit discretization in time is used which results in nonlinear equations at implicit time levels. We further employ a gradient stable discretization scheme so that the nonlinear equations are solvable for very large time steps. To solve those equations we use a nonlinear multilevel/multigrid method which is of an optimal order O(N) where N is the number of grid points. Spherically symmetric and fully two dimensional nonlinear numerical simulations are performed. We investigate tumor evolution in nutrient-rich and nutrient-poor tissues. A number of important results have been uncovered. For example, we demonstrate that the tumor may suffer from taxis-driven fingering instabilities which are most dramatic when cell proliferation is low, as predicted by linear stability theory. This is also observed in experiments. This work shows that taxis may play a role in tumor invasion and that when nutrient plays the role of a chemoattractant, the diffusional instability is exacerbated by nutrient gradients. Accordingly, we believe this model is capable of describing complex invasive patterns observed in experiments.

Multiscale agent-based cancer modeling

Agent-based modeling (ABM) is an in silico technique that is being used in a variety of research areas such as in social sciences, economics and increasingly in biomedicine as an interdisciplinary tool to study the dynamics of complex systems. Here, we describe its applicability to integrative tumor biology research by introducing a multi-scale tumor modeling platform that understands brain cancer as a complex dynamic biosystem. We summarize significant findings of this work, and discuss both challenges and future directions for ABM in the field of cancer research.