Multiscale models of breast cancer progression

Agent-based approaches for biological modeling in oncology: A literature review

CONTEXT

Computational modeling involves the use of computer simulations and models to study and understand real-world phenomena. Its application is particularly relevant in the study of potential interactions between biological elements. It is a promising approach to understand complex biological processes and predict their behavior under various conditions.

METHODOLOGY

This paper is a review of the recent literature on computational modeling of biological systems. Our study focuses on the field of oncology and the use of artificial intelligence (AI) and, in particular, agent-based modeling (ABM), between 2010 and May 2023.

RESULTS

Most of the articles studied focus on improving the diagnosis and understanding the behaviors of biological entities, with metaheuristic algorithms being the models most used. Several challenges are highlighted regarding increasing and structuring knowledge about biological systems, developing holistic models that capture multiple scales and levels of organization, reproducing emergent behaviors of biological systems, validating models with experimental data, improving computational performance of models and algorithms, and ensuring privacy and personal data protection are discussed.

A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

Understanding the Targeting Mechanisms of Multi-Specific Biologics in Immunotherapy with Multiscale Modeling

Immunotherapeutics are frequently associated with adverse side effects due to the elicitation of global immune modulation. To lower the risk of these side effects, recombinant DNA technology is employed to enhance the selectivity of cell targeting by genetically fusing different biomolecules, yielding new species referred to as multi-specific biologics. The design of new multi-specific biologics is a central challenge for the realization of new immunotherapies. To understand the molecular determinants responsible for regulating the binding between multi-specific biologics and surface-bound membrane receptors, we developed a multiscale computational framework that integrates various simulation approaches covering different timescales and spatial resolutions. Our model system of multi-specific biologics contains two natural ligands of immune receptors, which are covalently tethered by a peptide linker. Using this method, a number of interesting features of multi-specific biologics were identified. Our study therefore provides an important strategy to design the next-generation biologics for immunotherapy.

•

Two proteins are connected by different linkers as a model of bispecific biologics

•

Conformational dynamics of biologics are captured by microsecond MD simulations

•

Coarse-grained simulations are used to test binding between biologics and receptors

•

Biologics with long and flexible linkers are more efficient in targeting receptors

A Multiscale Model for the Self-Assembly of Coat Proteins in Bacteriophage MS2

The self-assembly of viral capsids is an essential step to the formation of infectious viruses. Elucidating the kinetic mechanisms of how a capsid or virus-like particle assembles could advance our knowledge about the viral lifecycle, as well as the general principles in self-assembly of biomaterials. However, current understanding of capsid assembly remains incomplete for many viruses due to the fact that the transient intermediates along the assembling pathways are experimentally difficult to be detected. In this paper, we constructed a new multiscale computational framework to simulate the self-assembly of virus-like particles. We applied our method to the coat proteins of bacteriophage MS2 as a specific model system. This virus-like particle of bacteriophage MS2 has a unique feature that its 90 sequence-identical dimers can be classified into two structurally various groups: one is the symmetric CC dimer, and the other is the asymmetric AB dimer. The homotypic interactions between AB dimers result in a 5-fold symmetric contact, while the heterotypic interactions between AB and CC dimers result in 6-fold symmetric contact. We found that the assembly can be described as a physical process of phase transition that is regulated by various factors such as concentration and specific stoichiometry between AB and CC dimers. Our simulations also demonstrate that heterotypic and homotypic interfaces play distinctive roles in modulating the assembling kinetics. The interaction between AB and CC dimers is much more dynamic than that between two AB dimers. We therefore suggest that the alternate growth of viral capsid through the heterotypic dimer interactions dominates the assembling pathways. This is, to the best of our knowledge, the first multiscale model to simulate the assembling process of coat proteins in bacteriophage MS2. The generality of this approach opens the door to its further applications in assembly of other viral capsids, virus-like particles, and novel drug delivery systems.

Agent-based model of multicellular tumor spheroid evolution including cell metabolism

Computational models aiming at the spatio-temporal description of cancer evolution are a suitable framework for testing biological hypotheses from experimental data, and generating new ones. Building on our recent work (J. Theor. Biol. 389, 146 (2016)) we develop a 3D agent-based model, capable of tracking hundreds of thousands of interacting cells, over time scales ranging from seconds to years. Cell dynamics is driven by a Monte Carlo solver, incorporating partial differential equations to describe chemical pathways and the activation/repression of "genes", leading to the up- or down-regulation of specific cell markers. Each cell-agent of different kind (stem, cancer, stromal etc.) runs through its cycle, undergoes division, can exit to a dormant, senescent, necrotic state, or apoptosis, according to the inputs from its systemic network. The basic network at this stage describes glucose/oxygen/ATP cycling, and can be readily extended to cancer-cell specific markers. Eventual accumulation of chemical/radiation damage to each cell's DNA is described by a Markov chain of internal states, and by a damage-repair network, whose evolution is linked to the cell systemic network. Aimed at a direct comparison with experiments of tumorsphere growth from stem cells, the present model will allow to quantitatively study the role of transcription factors involved in the reprogramming and variable radio-resistance of simulated cancer-stem cells, evolving in a realistic computer simulation of a growing multicellular tumorsphere.

Integrating Structural Information to Study the Dynamics of Protein-Protein Interactions in Cells

The information of how two proteins interact is embedded in the atomic details of their binding interfaces. These interactions, spatial-temporally coordinating each other as a network in a variable cytoplasmic environment, dominate almost all biological functions. A feasible and reliable computational model is highly demanded to realistically simulate these cellular processes and unravel the complexities beneath them. We therefore present a multiscale framework that integrates simulations on two different scales. The higher-resolution model incorporates structural information of proteins and energetics of their binding, while the lower-resolution model uses a highly simplified representation of proteins to capture the long-time-scale dynamics of a system with multiple proteins. Through a systematic benchmark test and two practical applications of biomolecular systems with specific cellular functions, we demonstrated that this method could be a powerful approach to understand molecular mechanisms of dynamic interactions between biomolecules and their functional impacts with high computational efficiency.

Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System

Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.

Understanding the Connection between Nanoparticle Uptake and Cancer Treatment Efficacy using Mathematical Modeling

Nanoparticles have shown great promise in improving cancer treatment efficacy while reducing toxicity and treatment side effects. Predicting the treatment outcome for nanoparticle systems by measuring nanoparticle biodistribution has been challenging due to the commonly unmatched, heterogeneous distribution of nanoparticles relative to free drug distribution. We here present a proof-of-concept study that uses mathematical modeling together with experimentation to address this challenge. Individual mice with 4T1 breast cancer were treated with either nanoparticle-delivered or free doxorubicin, with results demonstrating improved cancer kill efficacy of doxorubicin loaded nanoparticles in comparison to free doxorubicin. We then developed a mathematical theory to render model predictions from measured nanoparticle biodistribution, as determined using graphite furnace atomic absorption. Model analysis finds that treatment efficacy increased exponentially with increased nanoparticle accumulation within the tumor, emphasizing the significance of developing new ways to optimize the delivery efficiency of nanoparticles to the tumor microenvironment.

A Brownian dynamics tumor progression simulator with application to glioblastoma

Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1-2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 μm), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.

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.

Modeling of the metabolic energy dissipation for restricted tumor growth

Energy dissipation mostly represents unwanted outcome but in the biochemical processes it may alter the biochemical pathways. However, it is rarely considered in the literature although energy dissipation and its alteration due to the changes in cell microenvironment may improve methods for guiding chemical and biochemical processes in the desired directions. Deeper insight into the changes of metabolic activity of tumor cells exposed to osmotic stress or irradiation may offer the possibility of tumor growth reduction. In this work effects of the osmotic stress and irradiation on the thermodynamical affinity of tumor cells and their damping effects on metabolic energy dissipation were investigated and modeled. Although many various models were applied to consider the tumor restrictive growth they have not considered the metabolic energy dissipation. In this work a pseudo rheological model in the form of "the metabolic spring-pot element" is formulated to describe theoretically the metabolic susceptibility of tumor spheroid. This analog model relates the thermodynamical affinity of cell growth with the volume expansion of tumor spheroid under isotropic loading conditions. Spheroid relaxation induces anomalous nature of the metabolic energy dissipation which causes the damping effects on cell growth. The proposed model can be used for determining the metabolic energy "structure" in the context of restrictive cell growth as well as for predicting optimal doses for cancer curing in order to tailor the clinical treatment for each person and each type of cancer.

Application of pharmacometrics and quantitative systems pharmacology to cancer therapy: The example of luminal a breast cancer

Breast cancer (BC) is the most common cancer in women, and the second most frequent cause of cancer-related deaths in women worldwide. It is a heterogeneous disease composed of multiple subtypes with distinct morphologies and clinical implications. Quantitative systems pharmacology (QSP) is an emerging discipline bridging systems biology with pharmacokinetics (PK) and pharmacodynamics (PD) leveraging the systematic understanding of drugs' efficacy and toxicity. Despite numerous challenges in applying computational methodologies for QSP and mechanism-based PK/PD models to biological, physiological, and pharmacological data, bridging these disciplines has the potential to enhance our understanding of complex disease systems such as BC. In QSP/PK/PD models, various sources of data are combined including large, multi-scale experimental data such as -omics (i.e. genomics, transcriptomics, proteomics, and metabolomics), biomarkers (circulating and bound), PK, and PD endpoints. This offers a means for a translational application from pre-clinical mathematical models to patients, bridging the bench to bedside paradigm. Not only can these models be applied to inform and advance BC drug development, but they also could aid in optimizing combination therapies and rational dosing regimens for BC patients. Here, we review the current literature pertaining to the application of QSP and pharmacometrics-based pharmacotherapy in BC including bottom-up and top-down modeling approaches. Bottom-up modeling approaches employ mechanistic signal transduction pathways to predict the behavior of a biological system. The ones that are addressed in this review include signal transduction and homeostatic feedback modeling approaches. Alternatively, top-down modeling techniques are bioinformatics reconstruction techniques that infer static connections between molecules that make up a biological network and include (1) Bayesian networks, (2) co-expression networks, and (3) module-based approaches. This review also addresses novel techniques which utilize the principles of systems biology, synthetic lethality and tumor priming, both of which are discussed in relationship to novel drug targets and existing BC therapies. By utilizing QSP approaches, clinicians may develop a platform for improved dose individualization for subpopulation of BC patients, strengthen rationale in treatment designs, and explore mechanism elucidation for improving future treatments in BC medicine.

An agent-based model of triple-negative breast cancer: the interplay between chemokine receptor CCR5 expression, cancer stem cells, and hypoxia

Background

Triple-negative breast cancer lacks estrogen, progesterone, and HER2 receptors and is thus not possible to treat with targeted therapies for these receptors. Therefore, a greater understanding of triple-negative breast cancer is necessary for the treatment of this cancer type. In previous work from our laboratory, we found that chemokine ligand-receptor CCL5-CCR5 axis is important for the metastasis of human triple-negative breast cancer cell MDA-MB-231 to the lymph nodes and lungs, in a mouse xenograft model. We collected relevant experimental data from our and other laboratories for numbers of cancer stem cells, numbers of CCR5+ cells, and cell migration rates for different breast cancer cell lines and different experimental conditions.

Results

Using these experimental data we developed an in silico agent-based model of triple-negative breast cancer that considers surface receptor CCR5-high and CCR5-low cells and breast cancer stem cells, to predict the tumor growth rate and spatio-temporal distribution of cells in primary tumors. We find that high cancer stem cell percentages greatly increase tumor growth. We find that anti-stem cell treatment decreases tumor growth but may not lead to dormancy unless all stem cells get eliminated. We further find that hypoxia increases overall tumor growth and treatment with a CCR5 inhibitor maraviroc slightly decreases overall tumor growth. We also characterize 3D shapes of solid and invasive tumors using several shape metrics.

Conclusions

Breast cancer stem cells and CCR5+ cells affect the overall growth and morphology of breast tumors. In silico drug treatments demonstrate limited efficacy of incomplete inhibition of cancer stem cells after which tumor growth recurs, and CCR5 inhibition causes only a slight reduction in tumor growth.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0445-x) contains supplementary material, which is available to authorized users.

Multiscalar cellular automaton simulates in-vivo tumour-stroma patterns calibrated from in-vitro assay data

BACKGROUND

The tumour stroma -or tumour microenvironment- is an important constituent of solid cancers and it is thought to be one of the main obstacles to quantitative translation of drug activity between the preclinical and clinical phases of drug development. The tumour-stroma relationship has been described as being both pro- and antitumour in multiple studies. However, the causality of this complex biological relationship between the tumour and stroma has not yet been explored in a quantitative manner in complex tumour morphologies.

METHODS

To understand how these stromal and microenvironmental factors contribute to tumour physiology and how oxygen distributes within them, we have developed a lattice-based multiscalar cellular automaton model. This model uses principles of cytokine and oxygen diffusion as well as cell motility and plasticity to describe tumour-stroma landscapes. Furthermore, to calibrate the model, we propose an innovative modelling platform to extract model parameters from multiple in-vitro assays. This platform provides a novel way to extract meta-data that can be used to complement in-vivo studies and can be further applied in other contexts.

RESULTS

Here we show the necessity of the tumour-stroma opposing relationship for the model simulations to successfully describe the in-vivo stromal patterns of the human lung cancer cell lines Calu3 and Calu6, as models of clinical and preclinical tumour-stromal topologies. This is especially relevant to drugs that target the tumour microenvironment, such as antiangiogenics, compounds targeting the hedgehog pathway or immune checkpoint inhibitors, and is potentially a key platform to understand the mechanistic drivers for these drugs.

CONCLUSION

The tumour-stroma automaton model presented here enables the interpretation of complex in-vitro data and uses it to parametrise a model for in-vivo tumour-stromal relationships.

Polymeric Biomaterials for In Vitro Cancer Tissue Engineering and Drug Testing Applications

Biomimetic polymers and materials have been widely used in tissue engineering for regeneration and replication of diverse types of both normal and diseased tissues. Cancer, being a prevalent disease throughout the world, has initiated substantial interest in the creation of tissue-engineered models for anticancer drug testing. The development of these in vitro three-dimensional (3D) culture models using novel biomaterials has facilitated the investigation of tumorigenic and associated biological phenomena with a higher degree of complexity and physiological context than that provided by established two-dimensional culture models. In this review, an overview of a wide range of natural, synthetic, and hybrid biomaterials used for 3D cancer cell culture and investigation of cancer cell behavior is presented. The role of these materials in modulating cell-matrix interactions and replicating specific tumorigenic characteristics is evaluated. In addition, recent advances in biomaterial design, synthesis, and fabrication are also assessed. Finally, the advantages of incorporating polymeric biomaterials in 3D cancer models for obtaining efficacy data in anticancer drug testing applications are highlighted.

Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success

Hierarchical processes spanning several orders of magnitude of both space and time underlie nearly all cancers. Multi-scale statistical, mathematical, and computational modeling methods are central to designing, implementing and assessing treatment strategies that account for these hierarchies. The basic science underlying these modeling efforts is maturing into a new discipline that is close to influencing and facilitating clinical successes. The purpose of this review is to capture the state-of-the-art as well as the key barriers to success for multi-scale modeling in clinical oncology. We begin with a summary of the long-envisioned promise of multi-scale modeling in clinical oncology, including the synthesis of disparate data types into models that reveal underlying mechanisms and allow for experimental testing of hypotheses. We then evaluate the mathematical techniques employed most widely and present several examples illustrating their application as well as the current gap between pre-clinical and clinical applications. We conclude with a discussion of what we view to be the key challenges and opportunities for multi-scale modeling in clinical oncology.

Epigenetic modifications, chromatin distribution and TP53 transcription in a model of breast cancer progression

In the present paper we aimed to characterize epigenetic aspects and analyze TP53 transcription in the 21 T series, composed of breast cell lines: non-cancerous H16N2; Atypical Ductal Hyperplasia 21PT; Ductal Carcinoma in situ 21NT and Invasive Metastatic Carcinoma 21MT1. We detected a global genomic hypomethylation in 21NT and 21MT1. The histone modification markers analysis showed an important global decrease of the active chromatin mark H4Ac in 21MT1 relative to the other cell lines while the repressive mark H3K9Me3 were not significantly altered. The mRNA levels of DNA methylation and histone modification key enzymes are consistent with the observed genomic hypomethylation and histone hypoacetylation. The expression of DNMT3A/B increased at the initial stages of oncogenesis and the expression of DNMT1 and HAT1 decreased at the advanced stages of breast cancer. Using a confocal immunofluorescent assay, we observed that H4Ac was mostly located at the periphery and the repressive mark H3K9Me3, at the center of 21NT and 21MT1 cells nuclei. TP53 P1 promoter was found to be in an open chromatin state, with a relatively high enrichment of H4Ac and similar TP53 transcription levels in all 21 T cell lines. In conclusion, we observed epigenetic alterations (global genome hypomethylation, global hypoacetylation and accumulation of pericentric heterochromatin) in metastatic breast cancer cells of the 21 T series. These alterations may act at later stages of breast cancer progression and may not affect TP53 transcription at the P1 promoter.

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.

Systems Medicine: The Future of Medical Genomics, Healthcare, and Wellness

Recent advances in genomics have led to the rapid and relatively inexpensive collection of patient molecular data including multiple types of omics data. The integration of these data with clinical measurements has the potential to impact on our understanding of the molecular basis of disease and on disease management. Systems medicine is an approach to understanding disease through an integration of large patient datasets. It offers the possibility for personalized strategies for healthcare through the development of a new taxonomy of disease. Advanced computing will be an important component in effectively implementing systems medicine. In this chapter we describe three computational challenges associated with systems medicine: disease subtype discovery using integrated datasets, obtaining a mechanistic understanding of disease, and the development of an informatics platform for the mining, analysis, and visualization of data emerging from translational medicine studies.

3-D individual cell based computational modeling of tumor cell-macrophage paracrine signaling mediated by EGF and CSF-1 gradients

High density of macrophages in mammary tumors has been associated with a higher risk of metastasis and thus increased mortality in women. The EGF/CSF-1 paracrine signaling increases the number of invasive tumor cells by both recruiting tumor cells further away and manipulating the macrophages' innate ability to open up a passage into blood vessels thus promoting intravasation and finally metastasis. A 3-D individual-cell-based model is introduced, to better understand the tumor cell-macrophage interactions, and to explore how changing parameters of the paracrine signaling system affects the number of invasive tumor cells. The simulation data and videos of the cell movements correlated well with findings from both in vitro and in vivo experimental results. The model demonstrated how paracrine signaling is necessary to achieve co-migration of tumor cells and macrophages towards a specific signaling source. We showed how the paracrine signaling enhances the number of both invasive tumor cells and macrophages. The simulations revealed that for the in vitro experiments the imposed no-flux boundary condition might be affecting the results, and that changing the setup might lead to different experimental findings. In our simulations, the 3 : 1 tumor cell/macrophage ratio, observed in vivo, was robust for many parameters but sensitive to EGF signal strength and fraction of macrophages in the tumor. The model can be used to identify new agents for targeted therapy and we suggest that a successful strategy to prevent or limit invasion of tumor cells would be to block the tumor cell-macrophage paracrine signaling. This can be achieved by either blocking the EGF or CSF-1 receptors or supressing the EGF or CSF-1 signal.

Ductal carcinoma in situ of the breast: the importance of morphologic and molecular interactions

Ductal carcinoma in situ (DCIS) of the breast is a lesion characterized by significant heterogeneity, in terms of morphology, immunohistochemical staining, molecular signatures, and clinical expression. For some patients, surgical excision provides adequate treatment, but a subset of patients will experience recurrence of DCIS or progression to invasive ductal carcinoma (IDC). Recent years have seen extensive research aimed at identifying the molecular events that characterize the transition from normal epithelium to DCIS and IDC. Tumor epithelial cells, myoepithelial cells, and stromal cells undergo alterations in gene expression, which are most important in the early stages of breast carcinogenesis. Epigenetic modifications, such as DNA methylation, together with microRNA alterations, play a major role in these genetic events. In addition, tumor proliferation and invasion is facilitated by the lesional microenvironment, which includes stromal fibroblasts and macrophages that secrete growth factors and angiogenesis-promoting substances. Characterization of DCIS on a molecular level may better account for the heterogeneity of these lesions and how this manifests as differences in patient outcome and response to therapy. Molecular assays originally developed for assessing likelihood of recurrence in IDC are recently being applied to DCIS, with promising results. In the future, the classification of DCIS will likely incorporate molecular findings along with histologic and immunohistochemical features, allowing for personalized prognostic information and therapeutic options for patients with DCIS. This review summarizes current data regarding the molecular characterization of DCIS and discusses the potential clinical relevance.

An agent-based model of cancer stem cell initiated avascular tumour growth and metastasis: the effect of seeding frequency and location

It is very important to understand the onset and growth pattern of breast primary tumours as well as their metastatic dissemination. In most cases, it is the metastatic disease that ultimately kills the patient. There is increasing evidence that cancer stem cells are closely linked to the progression of the metastatic tumour. Here, we investigate stem cell seeding to an avascular tumour site using an agent-based stochastic model of breast cancer metastatic seeding. The model includes several important cellular features such as stem cell symmetric and asymmetric division, migration, cellular quiescence, senescence, apoptosis and cell division cycles. It also includes external features such as stem cell seeding frequency and location. Using this model, we find that cell seeding rate and location are important features for tumour growth. We also define conditions in which the tumour growth exhibits decremented and exponential growth patterns. Overall, we find that seeding, senescence and division limit affect not only the number of stem cells, but also their spatial and temporal distribution.

Simulation predicts IGFBP2-HIF1α interaction drives glioblastoma growth

Tremendous strides have been made in improving patients’ survival from cancer with one glaring exception: brain cancer. Glioblastoma is the most common, aggressive and highly malignant type of primary brain tumor. The average overall survival remains less than 1 year. Notably, cancer patients with obesity and diabetes have worse outcomes and accelerated progression of glioblastoma. The root cause of this accelerated progression has been hypothesized to involve the insulin signaling pathway. However, while the process of invasive glioblastoma progression has been extensively studied macroscopically, it has not yet been well characterized with regards to intracellular insulin signaling. In this study we connect for the first time microscale insulin signaling activity with macroscale glioblastoma growth through the use of computational modeling. Results of the model suggest a novel observation: feedback from IGFBP2 to HIF1α is integral to the sustained growth of glioblastoma. Our study suggests that downstream signaling from IGFI to HIF1α, which has been the target of many insulin signaling drugs in clinical trials, plays a smaller role in overall tumor growth. These predictions strongly suggest redirecting the focus of glioma drug candidates on controlling the feedback between IGFBP2 and HIF1α.

Current treatment for glioblastoma patients is limited to nonspecific methods: surgery followed by a combination of radio- and chemotherapy. With these methods, glioma patient survival is less than one year post-diagnosis. Targeting specific protein signaling pathways offers potentially more potent therapies. One promising potential target is the insulin signaling pathway, which is known to contribute to glioblastoma progression. However, drugs targeting this pathway have shown mixed results in clinical trials, and the detailed mechanisms of how the insulin signaling pathway promotes glioblastoma growth remain to be elucidated. Here, we developed a computational model of insulin signaling in glioblastoma in order to study this pathway’s role in tumor progression. Using the model, we systematically test contributions of different insulin signaling protein interactions on glioblastoma growth. Our model highlights a key driver for the growth of glioblastoma: IGFBP2-HIF1α feedback. This interaction provides a target that could open the door for new therapies in glioma and other solid tumors.

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.

Applications of systems science in biomedical research regarding obesity and noncommunicable chronic diseases: opportunities, promise, and challenges

Interest in the application of systems science (SS) in biomedical research, particularly regarding obesity and noncommunicable chronic disease (NCD) research, has been growing rapidly over the past decade. SS is a broad term referring to a family of research approaches that include modeling. As an emerging approach being adopted in public health, SS focuses on the complex dynamic interaction between agents (e.g., people) and subsystems defined at different levels. SS provides a conceptual framework for interdisciplinary and transdisciplinary approaches that address complex problems. SS has unique advantages for studying obesity and NCD problems in comparison to the traditional analytic approaches. The application of SS in biomedical research dates back to the 1960s with the development of computing capacity and simulation software. In recent decades, SS has been applied to addressing the growing global obesity epidemic. There is growing appreciation and support for using SS in the public health field, with many promising opportunities. There are also many challenges and uncertainties, including methodologic, funding, and institutional barriers. Integrated efforts by stakeholders that address these challenges are critical for the successful application of SS in the future.

Mathematical modeling for novel cancer drug discovery and development

INTRODUCTION

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments.

AREAS COVERED

This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment.

EXPERT OPINION

Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

Dynamic expression patterns of differential proteins during early invasion of hepatocellular carcinoma

Background

Tumor cell invasion into the surrounding matrix has been well documented as an early event of metastasis occurrence. However, the dynamic expression patterns of proteins during early invasion of hepatocellular carcinoma (HCC) are largely unknown. Using a three-dimensional HCC invasion culture model established previously, we investigated the dynamic expression patterns of identified proteins during early invasion of HCC.

Materials and Methods

Highly metastatic MHCC97H cells and a liver tissue fragment were long-term co-cultured in a rotating wall vessel (RWV) bioreactor to simulate different pathological states of HCC invasion. The established spherical co-cultures were collected on days 0, 5, 10, and 15 for dynamic expression pattern analysis. Significantly different proteins among spheroids at different time points were screened and identified using quantitative proteomics of iTRAQ labeling coupled with LC–MS/MS. Dynamic expression patterns of differential proteins were further categorized by K-means clustering. The expression modes of several differentially expressed proteins were confirmed by Western blot and qRT–PCR.

Results

Time course analysis of invasion/metastasis gene expressions (MMP2, MMP7, MMP9, CD44, SPP1, CXCR4, CXCL12, and CDH1) showed remarkable, dynamic alterations during the invasion process of HCC. A total of 1,028 proteins were identified in spherical co-cultures collected at different time points by quantitative proteomics. Among these proteins, 529 common differential proteins related to HCC invasion were clustered into 25 types of expression patterns. Some proteins displayed significant dynamic alterations during the early invasion process of HCC, such as upregulation at the early invasion stage and downregulation at the late invasion stage (e.g., MAPRE1, PHB2, cathepsin D, etc.) or continuous upregulation during the entire invasion process (e.g., vitronectin, Met, clusterin, ICAM1, GSN, etc.).

Conclusions

Dynamic expression patterns of candidate proteins during the early invasion process of HCC facilitate the discovery of new molecular targets for early intervention to prevent HCC invasion and metastasis.

The role of engineering approaches in analysing cancer invasion and metastasis

In the past decade, novel materials, probes and tools have enabled fundamental and applied cancer researchers to take a fresh look at the complex problem of tumour invasion and metastasis. These new tools, which include imaging modalities, controlled but complex in vitro culture conditions, and the ability to model and predict complex processes in vivo, represent an integration of traditional with novel engineering approaches; and their potential effect on quantitatively understanding tumour progression and invasion looks promising.

Microengineered tumor models: insights & opportunities from a physical sciences-oncology perspective

Prevailing evidence has established the fundamental role of microenvironmental conditions in tumorigenesis. However, the ability to identify, interrupt, and translate the underlying cellular and molecular mechanisms into meaningful therapies remains limited, due in part to a lack of organotypic culture systems that accurately recapitulate tumor physiology. Integration of tissue engineering with microfabrication technologies has the potential to address this challenge and mimic tumor heterogeneity with pathological fidelity. Specifically, this approach allows recapitulating global changes of tissue-level phenomena, while also controlling microscale variability of various conditions including spatiotemporal presentation of soluble signals, biochemical and physical characteristics of the extracellular matrix, and cellular composition. Such platforms have continued to elucidate the role of the microenvironment in cancer pathogenesis and significantly improve drug discovery and screening, particularly for therapies that target tumor-enabling stromal components. This review discusses some of the landmark efforts in the field of micro-tumor engineering with a particular emphasis on deregulated tissue organization and mass transport phenomena in the tumor microenvironment.

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

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