The effects of EGF-receptor density on multiscale tumor growth patterns

Modeling Physical Forces Experienced by Cancer and Stromal Cells Within Different Organ-Specific Tumor Tissue

Mechanical force exerted on cancer cells by their microenvironment have been reported to drive cells toward invasive phenotypes by altering cells' motility, proliferation, and apoptosis. These mechanical forces include compressive, tensile, hydrostatic, and shear forces. The importance of forces is then hypothesized to be an alteration of cancer cells' and their microenvironment's biophysical properties as the indicator of a tumor's malignancy state. Our objective is to investigate and quantify the correlation between a tumor's malignancy state and forces experienced by the cancer cells and components of the microenvironment. In this study, we have developed a multicomponent, three-dimensional model of tumor tissue consisting of a cancer cell surrounded by fibroblasts and extracellular matrix (ECM). Our results on three different organs including breast, kidney, and pancreas show that: A) the stresses within tumor tissue are impacted by the organ specific ECM's biophysical properties, B) more invasive cancer cells experience higher stresses, C) in pancreas which has a softer ECM (Young modulus of 1.0 kPa) and stiffer cancer cells (Young modulus of 2.4 kPa and 1.7 kPa) than breast and kidney, cancer cells experienced significantly higher stresses, D) cancer cells in contact with ECM experienced higher stresses compared to cells surrounded by fibroblasts but the area of tumor stroma experiencing high stresses has a maximum length of 40 μm when the cancer cell is surrounded by fibroblasts and 12 μm for when the cancer cell is in vicinity of ECM. This study serves as an important first step in understanding of how the stresses experienced by cancer cells, fibroblasts, and ECM are associated with malignancy states of cancer cells in different organs. The quantification of forces exerted on cancer cells by different organ-specific ECM and at different stages of malignancy will help, first to develop theranostic strategies, second to predict accurately which tumors will become highly malignant, and third to establish accurate criteria controlling the progression of cancer cells malignancy. Furthermore, our in silico model of tumor tissue can yield critical, useful information for guiding ex vivo or in vitro experiments, narrowing down variables to be investigated, understanding what factors could be impacting cancer treatments or even biomarkers to be looking for.

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.

A Spatial Quantitative Systems Pharmacology Platform spQSP-IO for Simulations of Tumor-Immune Interactions and Effects of Checkpoint Inhibitor Immunotherapy

Simple Summary

Mathematical and computational models, such as quantitative systems pharmacology (QSP) models, are becoming a popular tool in drug discovery. The advancement of imaging techniques creates a unique opportunity to further expand these models and enhance their predictive power by incorporating characteristics of individual patients embedded in the image data obtained from tissue samples. The aim of this study is to develop a platform which combines the strength of QSP models and spatially resolved agent-based models (ABM), and create a model of cancer development in the context of anti-cancer immunity and immune checkpoint inhibition therapy. The model can be applied in virtual clinical trials and biomarker discovery to help refine trial design.

Abstract

Quantitative systems pharmacology (QSP) models have become increasingly common in fundamental mechanistic studies and drug discovery in both academic and industrial environments. With imaging techniques widely adopted and other spatial quantification of tumor such as spatial transcriptomics gaining traction, it is crucial that these data reflecting tumor spatial heterogeneity be utilized to inform the QSP models to enhance their predictive power. We developed a hybrid computational model platform, spQSP-IO, to extend QSP models of immuno-oncology with spatially resolved agent-based models (ABM), combining their powers to track whole patient-scale dynamics and recapitulate the emergent spatial heterogeneity in the tumor. Using a model of non-small-cell lung cancer developed based on this platform, we studied the role of the tumor microenvironment and cancer–immune cell interactions in tumor development and applied anti-PD-1 treatment to virtual patients and studied how the spatial distribution of cells changes during tumor growth in response to the immune checkpoint inhibition treatment. Using parameter sensitivity analysis and biomarker analysis, we are able to identify mechanisms and pretreatment measurements correlated with treatment efficacy. By incorporating spatial data that highlight both heterogeneity in tumors and variability among individual patients, spQSP-IO models can extend the QSP framework and further advance virtual clinical trials.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling

MOTIVATION

Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell).

RESULTS

PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen.

AVAILABILITY AND IMPLEMENTATION

PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Modelling multi-scale cell-tissue interaction of tissue-engineered muscle constructs

Expectation on engineered tissue substitute continues to grow, and for an effective development of a functional tissue and to control its quality, cellular mechanoresponse plays a key role. Although the mechanoresponse – in terms of cell–tissue interaction across scales – has been understood better in recent years, there are still technical limitations to quantitatively monitor the processes involved in the development of both native and engineered tissues. Computational (in silico) studies have been utilised to complement the experimental limitations and successfully applied to the prediction of tissue growth. We here review recent activities in the area of combined experimental and computational analyses of tissue growth, especially in the tissue engineering context, and highlight the advantages of such an approach for the future of the tissue engineering, using our own case study of predicting musculoskeletal tissue engineering construct development.

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.

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.

Extracellular region of epidermal growth factor receptor: a potential target for anti-EGFR drug discovery

The epidermal growth factor receptor (EGFR) is a transmembrane receptor with tyrosine kinase activity involved in regulation of cellular multiplication, survival, differentiation and metastasis. Our knowledge about function and complex management of these receptors has driving the development of specific and targeted treatment modalities for human cancers in the last 20 years. EGFR is the first receptor target against which monoclonal antibodies (mAb) have been evolved for cancer treatment. Here we review the biology of ErbB receptors, including their architecture, signaling, regulation and therapeutic strategies and the mechanisms of resistances offered by the receptors against small-molecule tyrosine kinases and resistance overcome implications of mAbs. The efficacy of EGFR-specific mAb in cancer depends on site specific extracellular region of EGFR, which has crucial role in process of dimerization and activation. This review highlights evolution of various resistance mechanisms due to consequences of current small-molecule anti-EGFR therapies.

Integrating Multiscale Modeling with Drug Effects for Cancer Treatment

In this paper, we review multiscale modeling for cancer treatment with the incorporation of drug effects from an applied system's pharmacology perspective. Both the classical pharmacology and systems biology are inherently quantitative; however, systems biology focuses more on networks and multi factorial controls over biological processes rather than on drugs and targets in isolation, whereas systems pharmacology has a strong focus on studying drugs with regard to the pharmacokinetic (PK) and pharmacodynamic (PD) relations accompanying drug interactions with multiscale physiology as well as the prediction of dosage-exposure responses and economic potentials of drugs. Thus, it requires multiscale methods to address the need for integrating models from the molecular levels to the cellular, tissue, and organism levels. It is a common belief that tumorigenesis and tumor growth can be best understood and tackled by employing and integrating a multifaceted approach that includes in vivo and in vitro experiments, in silico models, multiscale tumor modeling, continuous/discrete modeling, agent-based modeling, and multiscale modeling with PK/PD drug effect inputs. We provide an example application of multiscale modeling employing stochastic hybrid system for a colon cancer cell line HCT-116 with the application of Lapatinib drug. It is observed that the simulation results are similar to those observed from the setup of the wet-lab experiments at the Translational Genomics Research Institute.

Agent-Based Modeling in Systems Pharmacology

Modeling and simulation (M&S) techniques provide a platform for knowledge integration and hypothesis testing to gain insights into biological systems that would not be possible a priori. Agent‐based modeling (ABM) is an M&S technique that focuses on describing individual components rather than homogenous populations. This tutorial introduces ABM to systems pharmacologists, using relevant case studies to highlight how ABM‐specific strengths have yielded success in the area of preclinical mechanistic modeling.

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.

Analysis of gene expression of secreted factors associated with breast cancer metastases in breast cancer subtypes

Breast cancer is a heterogeneous disease, having multiple subtypes with different malignant phenotypes. The triple-negative breast cancer, or basal breast cancer, is highly aggressive, metastatic, and difficult to treat. Previously, we identified that key molecules (IL6, CSF2, CCL5, VEGFA, and VEGFC) secreted by tumor cells and stromal cells in basal breast cancer can promote metastasis. It remains to assess whether these molecules function similarly in other subtypes of breast cancer. Here, we characterize the relative gene expression of the five secreted molecules and their associated receptors (GP130, GMRA, GMRB, CCR5, VEGFR2, NRP1, VEGFR3, NRP2) in the basal, HER2 (human epidermal growth factor receptor 2) positive, luminal A, and luminal B subtypes using high throughput data from tumor samples in The Cancer Genome Atlas (TCGA) and Molecular Taxonomy of Breast Cancer International Consortium (METABRIC). IL6 and CCL5 gene expression are basal breast cancer specific, whereas high gene expression of GP130 was observed in luminal A/B. VEGFA/C and CSF2 mRNA are overexpressed in HER2 positive breast cancer, with VEGFA and CSF2 also overexpressed in basal breast cancer. Further study of the specific protein function of these factors within their associated cancer subtypes may yield personalized biomarkers and treatment modalities.

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.

A leak pathway for luminal protons in endosomes drives oncogenic signalling in glioblastoma

Epidermal growth factor receptor (EGFR) signalling is a potent driver of glioblastoma, a malignant and lethal form of brain cancer. Disappointingly, inhibitors targeting receptor tyrosine kinase activity are not clinically effective and EGFR persists on the plasma membrane to maintain tumour growth and invasiveness. Here we show that endolysosomal pH is critical for receptor sorting and turnover. By functioning as a leak pathway for protons, the Na(+)/H(+) exchanger NHE9 limits luminal acidification to circumvent EGFR turnover and prolong downstream signalling pathways that drive tumour growth and migration. In glioblastoma, NHE9 expression is associated with stem/progenitor characteristics, radiochemoresistance, poor prognosis and invasive growth in vitro and in vivo. Silencing or inhibition of NHE9 in brain tumour-initiating cells attenuates tumoursphere formation and improves efficacy of EGFR inhibitor. Thus, NHE9 mediates inside-out control of oncogenic signalling and is a highly druggable target for pan-specific receptor clearance in cancer therapy.

Lymphatic endothelial cells support tumor growth in breast cancer

Tumor lymphatic vessels (LV) serve as a conduit of tumor cell dissemination, due to their leaky nature and secretion of tumor-recruiting factors. Though lymphatic endothelial cells (LEC) lining the LV express distinct factors (also called lymphangiocrine factors), these factors and their roles in the tumor microenvironment are not well understood. Here we employ LEC, microvascular endothelial cells (MEC), and human umbilical vein endothelial cells (HUVEC) cultured in triple-negative MDA-MB-231 tumor-conditioned media (TCM) to determine the factors that may be secreted by various EC in the MDA-MB-231 breast tumor. These factors will serve as endothelium derived signaling molecules in the tumor microenvironment. We co-injected these EC with MDA-MB-231 breast cancer cells into animals and showed that LEC support tumor growth, HUVEC have no significant effect on tumor growth, whereas MEC suppress it. Focusing on LEC-mediated tumor growth, we discovered that TCM-treated LEC (‘tumor-educated LEC') secrete high amounts of EGF and PDGF-BB, compared to normal LEC. LEC-secreted EGF promotes tumor cell proliferation. LEC-secreted PDGF-BB induces pericyte infiltration and angiogenesis. These lymphangiocrine factors may support tumor growth in the tumor microenvironment. This study shows that LV serve a novel role in the tumor microenvironment apart from their classical role as conduits of metastasis.

Modeling of liver metastatic disease with applied drug therapy

Colorectal carcinoma is acknowledged as the second leading cause of total cancer-related death in the European Region. The majority of deaths related to colorectal carcinoma are connected with liver metastatic disease. Approximately, in 25% of all patients, liver metastatic disease is diagnosed at the same time as the primary diagnosis, while up to a quarter of others would develop liver metastases in the course of the illness. In this study, we developed reaction-diffusion model and analyzed the effect of drug therapy on liver metastatic disease for a specific patient. Tumor volumes in specific time points were obtained using CT scan images. The nonlinear function for cell proliferation rate as well as data about clinically applied drug therapy was included in the model. Fitting procedure was used for parameter estimation. Good agreement of numerical and experimental results shows the feasibility and efficacy of the proposed system.

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.

Multiscale models of breast cancer progression

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

Integrating intracellular dynamics using CompuCell3D and Bionetsolver: applications to multiscale modelling of cancer cell growth and invasion

In this paper we present a multiscale, individual-based simulation environment that integrates CompuCell3D for lattice-based modelling on the cellular level and Bionetsolver for intracellular modelling. CompuCell3D or CC3D provides an implementation of the lattice-based Cellular Potts Model or CPM (also known as the Glazier-Graner-Hogeweg or GGH model) and a Monte Carlo method based on the metropolis algorithm for system evolution. The integration of CC3D for cellular systems with Bionetsolver for subcellular systems enables us to develop a multiscale mathematical model and to study the evolution of cell behaviour due to the dynamics inside of the cells, capturing aspects of cell behaviour and interaction that is not possible using continuum approaches. We then apply this multiscale modelling technique to a model of cancer growth and invasion, based on a previously published model of Ramis-Conde et al. (2008) where individual cell behaviour is driven by a molecular network describing the dynamics of E-cadherin and β-catenin. In this model, which we refer to as the centre-based model, an alternative individual-based modelling technique was used, namely, a lattice-free approach. In many respects, the GGH or CPM methodology and the approach of the centre-based model have the same overall goal, that is to mimic behaviours and interactions of biological cells. Although the mathematical foundations and computational implementations of the two approaches are very different, the results of the presented simulations are compatible with each other, suggesting that by using individual-based approaches we can formulate a natural way of describing complex multi-cell, multiscale models. The ability to easily reproduce results of one modelling approach using an alternative approach is also essential from a model cross-validation standpoint and also helps to identify any modelling artefacts specific to a given computational approach.

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.

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.

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.

Cancer stem cell, niche and EGFR decide tumor development and treatment response: A bio-computational simulation study

Recent research in cancer biology has suggested the hypothesis that tumors are initiated and driven by a small group of cancer stem cells (CSCs). Furthermore, cancer stem cell niches have been found to be essential in determining fates of CSCs, and several signaling pathways have been proven to play a crucial role in cellular behavior, which could be two important factors in cancer development. To better understand the progression, heterogeneity and treatment response of breast cancer, especially in the context of CSCs, we propose a mathematical model based on the cell compartment method. In this model, three compartments of cellular subpopulations are constructed: CSCs, progenitor cells (PCs), and terminal differentiated cells (TCs). Moreover, (1) the cancer stem cell niche is, considered by modeling its effect on division patterns (symmetric or asymmetric) of CSCs, and (2) the EGFR signaling pathway is integrated by modeling its role in cell proliferation, apoptosis. Our simulation results indicate that (1) a higher probability for symmetric division of CSC may result in a faster expansion of tumor population, and for a larger number of niches, the tumor grows at a slower rate, but the final tumor volume is larger; (2) higher EGFR expression correlates to tumors with larger volumes while a saturation function is observed, and (3) treatments that inhibit tyrosine kinase activity of EGFR may not only repress the tumor volume, but also decrease the CSCs percentages by shifting CSCs from symmetric divisions to asymmetric divisions. These findings suggest that therapies should be designed to effectively control or eliminate the symmetric division of CSCs and to reduce or destroy the CSC niches.

A systems biology view of cancer

In order to understand how a cancer cell is functionally different from a normal cell it is necessary to assess the complex network of pathways involving gene regulation, signaling, and cell metabolism, and the alterations in its dynamics caused by the several different types of mutations leading to malignancy. Since the network is typically complex, with multiple connections between pathways and important feedback loops, it is crucial to represent it in the form of a computational model that can be used for a rigorous analysis. This is the approach of systems biology, made possible by new -omics data generation technologies. The goal of this review is to illustrate this approach and its utility for our understanding of cancer. After a discussion of recent progress using a network-centric approach, three case studies related to diagnostics, therapy, and drug development are presented in detail. They focus on breast cancer, B-cell lymphomas, and colorectal cancer. The discussion is centered on key mathematical and computational tools common to a systems biology approach.

Multiparameter computational modeling of tumor invasion

Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A wealth of qualitative empirical evidence links disease progression with tumor morphology, histopathology, invasion, and associated molecular phenomena. However, the quantitative contribution of each of the known parameters in this progression remains elusive. Mathematical modeling can provide the capability to quantify the connection between variables governing growth, prognosis, and treatment outcome. By quantifying the link between the tumor boundary morphology and the invasive phenotype, this work provides a quantitative tool for the study of tumor progression and diagnostic/prognostic applications. This establishes a framework for monitoring system perturbation towards development of therapeutic strategies and correlation to clinical outcome for prognosis.

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.

A new concept for cancer therapy: out-competing the aggressor

Cancer expansion depends on host organ conditions that permit growth. Since such microenvironmental nourishment is limited we argue here that an autologous, therapeutically engineered and faster metabolizing cell strain could potentially out-compete native cancer cell populations for available resources which in turn should contain further cancer growth. This hypothesis aims on turning cancer progression, and its microenvironmental dependency, into a therapeutic opportunity. To illustrate our concept, we developed a three-dimensional computational model that allowed us to investigate the growth dynamics of native tumor cells mixed with genetically engineered cells that exhibit a higher proliferation rate. The simulation results confirm in silico efficacy of such therapeutic cells to combating cancer cells on site in that they can indeed control tumor growth once their proliferation rate exceeds a certain level. While intriguing from a theoretical perspective, this bold, innovative ecology-driven concept bears some significant challenges that warrant critical discussion in the community for further refinement.

Quantitative modeling perspectives on the ErbB system of cell regulatory processes

The complexities of the processes involved in ErbB-mediated regulation of cellular phenotype are broadly appreciated, so much so that it might be reasonably argued that this highly studied system provided significant impetus for the systems perspective on cell signaling processes in general. Recent years have seen major advances in the level of characterization of the ErbB system as well as our ability to make measurements of the system. This new data provides significant new insight, while at the same time creating new challenges for making quantitative statements and predictions with certainty. Here, we discuss recent advances in each of these directions and the interplay between them, with a particular focus on quantitative modeling approaches to interpret data and provide predictive power. Our discussion follows the sequential order of ErbB pathway activation, beginning with considerations of receptor/ligand interactions and dynamics, proceeding to the generation of intracellular signals, and ending with determination of cellular phenotype. As discussed herein, these processes become increasingly difficult to describe or interpret in terms of traditional models, and we review emerging methodologies to address this complexity.

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.

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.

semCDI: a query formulation for semantic data integration in caBIG

OBJECTIVES

To develop mechanisms to formulate queries over the semantic representation of cancer-related data services available through the cancer Biomedical Informatics Grid (caBIG).

DESIGN

The semCDI query formulation uses a view of caBIG semantic concepts, metadata, and data as an ontology, and defines a methodology to specify queries using the SPARQL query language, extended with Horn rules. semCDI enables the joining of data that represent different concepts through associations modeled as object properties, and the merging of data representing the same concept in different sources through Common Data Elements (CDE) modeled as datatype properties, using Horn rules to specify additional semantics indicating conditions for merging data. Validation In order to validate this formulation, a prototype has been constructed, and two queries have been executed against currently available caBIG data services.

DISCUSSION

The semCDI query formulation uses the rich semantic metadata available in caBIG to build queries and integrate data from multiple sources. Its promise will be further enhanced as more data services are registered in caBIG, and as more linkages can be achieved between the knowledge contained within caBIG's NCI Thesaurus and the data contained in the Data Services.

CONCLUSION

semCDI provides a formulation for the creation of queries on the semantic representation of caBIG. This constitutes the foundation to build a semantic data integration system for more efficient and effective querying and exploratory searching of cancer-related data.

Using magnetic resonance microscopy to study the growth dynamics of a glioma spheroid in collagen I: A case study

BACKGROUND

Highly malignant gliomas are characterized by rapid growth, extensive local tissue infiltration and the resulting overall dismal clinical outcome. Gaining any additional insights into the complex interaction between this aggressive brain tumor and its microenvironment is therefore critical. Currently, the standard imaging modalities to investigate the crucial interface between tumor growth and invasion in vitro are light and confocal laser scanning microscopy. While immensely useful in cell culture, integrating these modalities with this cancer's clinical imaging method of choice, i.e. MRI, is a non-trivial endeavour. However, this integration is necessary, should advanced computational modeling be able to utilize these in vitro data to eventually predict growth behaviour in vivo. We therefore argue that employing the same imaging modality for both the experimental setting and the clinical situation it represents should have significant value from a data integration perspective. In this case study, we have investigated the feasibility of using a specific form of MRI, i.e. magnetic resonance microscopy or MRM, to study the expansion dynamics of a multicellular tumor spheroid in a collagen type I gel.

METHODS

An U87mEGFR human giloblastoma multicellular spheroid (MTS) containing approximately 4.103 cells was generated and pipetted into a collagen I gel. The sample was then imaged using a T2-weighted 3D spoiled gradient echo pulse sequence on a 14T MRI scanner over a period of 12 hours with a temporal resolution of 3 hours at room temperature. Standard histopathology was performed on the MRM sample, as well as on control samples.

RESULTS

We were able to acquire three-dimensional MR images with a spatial resolution of 24 x 24 x 24 microm3. Our MRM data successfully documented the volumetric growth dynamics of an MTS in a collagen I gel over the 12-hour period. The histopathology results confirmed cell viability in the MRM sample, yet displayed distinct patterns of cell proliferation and invasion as compared to control.

CONCLUSION

In this study, we demonstrate that a specific form of MRI, i.e. magnetic resonance microscopy or MRM, can be used to study the dynamic growth of a multicellular tumor spheroid (MTS) with a single cell scale spatial resolution that approaches the level of light microscopy. We argue that MRM can be employed as a complementary non-invasive tool to characterize microscopic MTS expansion, and thus, together with integrative computational modeling, may allow bridging of the experimental and clinical scales more readily.

Simulating non-small cell lung cancer with a multiscale agent-based model

BACKGROUND

The epidermal growth factor receptor (EGFR) is frequently overexpressed in many cancers, including non-small cell lung cancer (NSCLC). In silico modeling is considered to be an increasingly promising tool to add useful insights into the dynamics of the EGFR signal transduction pathway. However, most of the previous modeling work focused on the molecular or the cellular level only, neglecting the crucial feedback between these scales as well as the interaction with the heterogeneous biochemical microenvironment.

RESULTS

We developed a multiscale model for investigating expansion dynamics of NSCLC within a two-dimensional in silico microenvironment. At the molecular level, a specific EGFR-ERK intracellular signal transduction pathway was implemented. Dynamical alterations of these molecules were used to trigger phenotypic changes at the cellular level. Examining the relationship between extrinsic ligand concentrations, intrinsic molecular profiles and microscopic patterns, the results confirmed that increasing the amount of available growth factor leads to a spatially more aggressive cancer system. Moreover, for the cell closest to nutrient abundance, a phase-transition emerges where a minimal increase in extrinsic ligand abolishes the proliferative phenotype altogether.

CONCLUSION

Our in silico results indicate that in NSCLC, in the presence of a strong extrinsic chemotactic stimulus (and depending on the cell's location) downstream EGFR-ERK signaling may be processed more efficiently, thereby yielding a migration-dominant cell phenotype and overall, an accelerated spatio-temporal expansion rate.

The complexity of targeting EGFR signalling in cancer: from expression to turnover

The epidermal growth factor receptor (ErbB1 or EGFR) has been found to be altered in a variety of human cancers. A number of agents targeting these receptors, including specific antibodies directed against the ligand-binding domain of the receptor and small molecules that inhibit kinase activity are either in clinical trials or are already approved for clinical treatment. However, identifying patients that are likely to respond to such treatments has been challenging. As a consequence, it still remains important to identify additional alterations of the tumor cell that contribute to the response to EGFR-targeted agents. While EGFR-mediated signalling pathways have been well established, there is still a rather limited understanding of how intracellular protein-protein interactions, ubiquitination, endocytosis and subsequent degradation of EGFR contribute to the determination of sensitivity to EGFR targeting agents and are emerging areas of investigation. This review primarily focuses on the basic signal transduction pathways mediated through activated membrane bound and/or endosomal EGFR and emphasizes the need to co-target additional proteins that function either upstream or downstream of EGFR to improve cancer therapy.