Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach

Examining the Influence of Nondimensionalization on Partial Rank Correlation Coefficient Results when Modeling the Epithelial Mesenchymal Transition

Partial Rank Correlation Coefficient (PRCC) is a powerful type of global sensitivity analysis. Usually performed following Latin Hypercube Sampling (LHS), this analysis can highlight the parameters in a mathematical model producing the observed results, a crucial step when using models to understand real-world phenomena and guide future experiments. Recently, Gasior et al. performed LHS and PRCC when modeling the influence of cell-cell contact and TGF- β signaling on the epithelial mesenchymal transition (Gasior et al. in J Theor Biol 546:111160, 2022). Though their analysis provided insight into how these tumor-level factors can impact intracellular signaling during the transition, their results were potentially impacted by nondimensionalizing the model prior to performing sensitivity analysis. This work seeks to understand the true impact of nondimensionalization on sensitivity analysis by performing LHS and PRCC on both the original model that Gasior et al. proposed and seven different nondimensionalizations. Parameter ranges were kept small to capture shifts in the values that originally produced bistable behavior. By comparing these eight different iterations, this work shows that the issues from performing sensitivity analysis following nondimensionalization are two-fold: (1) nondimensionalization can obscure or exclude important parameters from in-depth analysis and (2) how a model is nondimensionalized can, potentially, change analysis results. Ultimately, this work cautions against using nondimensionalization prior to sensitivity analysis if the subsequent results are meant to guide future experiments.

A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation

Introduction

Colorectal cancer (CRC) is a major cause of cancer related deaths in the United States, with CRC metastasis to the liver being a common occurrence. The development of an optimal metastatic environment is essential process prior to tumor metastasis. This process, called pre-metastatic niche (PMN) formation, involves activation of key resident liver cells, including fibroblast-like stellate cells and macrophages such as Kupffer cells. Tumor-mediated factors introduced to this environment transform resident cells that secrete additional growth factors and remodel the extracellular matrix (ECM), which is thought to promote tumor colonization and metastasis in the secondary environment.

Methods

To investigate the underlying mechanisms of these dynamics, we developed a multicellular computational model to characterize the spatiotemporal dynamics of the PMN formation in tissue. This modeling framework integrates intracellular and extracellular signaling, and traction and junctional forces into a Cellular Potts model, and represents multiple cell types with varying levels of cellular activation. We perform numerical experiments to investigate the role of key factors in PMN formation and tumor invasiveness, including growth factor concentration, timing of tumor arrival, relative composition of resident cells, and the size of invading tumor cluster.

Results

These parameter studies identified growth factor availability and ECM concentration in the environment as two of the key determinants of tumor invasiveness. We further predict that both the ECM concentration potential and growth factor sensitivity of the stellate cells are key drivers of the PMN formation and associated ECM concentration.

Conclusions

Overall, this modeling framework represents a significant step towards simulating cancer metastasis and investigating the role of key factors on PMN formation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00831-0.

Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues

The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis. We analyze the spatial architecture in biopsy tissues stained with multiplex immunofluorescence. We derive a two-point correlation function and the corresponding spatial power spectral distribution. We show that this data-deduced power spectral distribution can fit the power spectrum of the solution of reaction-diffusion equations that can then identify patient-specific tumor growth and invasion rates. This approach allows the measurement of patient-specific critical tumor dynamical properties from routinely available biopsy material at a single snapshot in time.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Wnt signaling in cell adhesion, development, and colon cancer

Wnt signaling is essential for embryonic development, influencing processes such as axis formation, cell proliferation and differentiation, cell fate decisions, and axon guidance. It also plays a role in maintaining tissue homeostasis in adult organisms. The loss of normal cell polarity and adhesion caused by Wnt signaling activation is a fundamental step for tumor progression and metastasis. Activating the canonical Wnt pathway is a driving force in many human cancers, especially colorectal, hepatocellular, and mammary carcinomas. Wnt causes the stabilization and nuclear transport of newly synthesized transcriptional regulator β-catenin. The generally accepted view is that the canonical effects of Wnt growth factors are caused by the transcription of β-catenin target genes. Here, we review recent findings that indicate Wnt is a regulator of many other cellular physiological activities, such as macropinocytosis, endosome trafficking, protein stability, focal adhesions, and lysosomal activity. Some of these regulatory responses occur within minutes and do not require new protein synthesis, indicating that there is much more to Wnt beyond the well-established transcriptional role of β-catenin. The main conclusion that emerges from these studies is that in basal cell conditions, the activity of the key protein kinase GSK3, which is inhibited by Wnt pathway activation, normally represses the actin machinery that orchestrates macropinocytosis with implications in cancer. These contributions expand our understanding of the multifaceted roles of Wnt signaling in cellular processes, development, and cancer, providing insights into potential therapeutic targets and strategies.

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

Multiscale computational modeling of aortic valve calcification

Calcific aortic valve disease (CAVD) is a common cardiovascular disease that affects millions of people worldwide. The disease is characterized by the formation of calcium nodules on the aortic valve leaflets, which can lead to stenosis and heart failure if left untreated. The pathogenesis of CAVD is still not well understood, but involves several signaling pathways, including the transforming growth factor beta (TGF β ) pathway. In this study, we developed a multiscale computational model for TGF β -stimulated CAVD. The model framework comprises cellular behavior dynamics, subcellular signaling pathways, and tissue-level diffusion fields of pertinent chemical species, where information is shared among different scales. Processes such as endothelial to mesenchymal transition (EndMT), fibrosis, and calcification are incorporated. The results indicate that the majority of myofibroblasts and osteoblast-like cells ultimately die due to lack of nutrients as they become trapped in areas with higher levels of fibrosis or calcification, and they subsequently act as sources for calcium nodules, which contribute to a polydispersed nodule size distribution. Additionally, fibrosis and calcification processes occur more frequently in regions closer to the endothelial layer where the cell activity is higher. Our results provide insights into the mechanisms of CAVD and TGF β signaling and could aid in the development of novel therapeutic approaches for CAVD and other related diseases such as cancer. More broadly, this type of modeling framework can pave the way for unraveling the complexity of biological systems by incorporating several signaling pathways in subcellular models to simulate tissue remodeling in diseases involving cellular mechanobiology.

Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics

We here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differential equations (PDEs). A differential equation finally governs the local degradation of the extracellular matrix (ECM) by the malignant mass. Numerical realizations of the model are run to reproduce tumor growth and invasion in a number scenarios that differ for cell properties (adhesiveness, duplication potential, proteolytic activity) and/or environmental conditions (level of tissue oxygenation and matrix density pattern). In particular, our simulations suggest that tumor aggressiveness, in terms of invasive depth and extension of necrotic tissue, can be reduced by (i) stable cell-cell contact interactions, (ii) poor tendency of malignant agents to chemotactically move upon oxygen gradients, and (iii) presence of an overdense matrix, if coupled by a disrupted proteolytic activity of the disease.

Computational simulations of bispecific T cell engagers by a multiscale model

The use of bispecific antibodies as T cell engagers can bypass the normal T cell receptor-major histocompatibility class interaction, redirect the cytotoxic activity of T cells, and lead to highly efficient tumor cell killing. However, this immunotherapy also causes significant on-target off-tumor toxicologic effects, especially when it is used to treat solid tumors. To avoid these adverse events, it is necessary to understand the fundamental mechanisms involved in the physical process of T cell engagement. We developed a multiscale computational framework to reach this goal. The framework combines simulations on the intercellular and multicellular levels. On the intercellular level, we simulated the spatial-temporal dynamics of three-body interactions among bispecific antibodies, CD3 and tumor-associated antigens (TAAs). The derived number of intercellular bonds formed between CD3 and TAAs was further transferred to the multicellular simulations as the input parameter of adhesive density between cells. Through the simulations under various molecular and cellular conditions, we were able to gain new insights into how to adopt the most appropriate strategy to maximize the drug efficacy and avoid the off-target effect. For instance, we discovered that the low antibody-binding affinity resulted in the formation of large clusters at the cell-cell interface, which could be important to control the downstream signaling pathways. We also tested different molecular architectures of the bispecific antibody and suggested the existence of an optimal length in regulating the T cell engagement. Overall, the current multiscale simulations serve as a proof-of-concept study to help in the future design of new biological therapeutics.

Phenotype-structured model of intra-clonal heterogeneity and drug resistance in multiple myeloma

Multiple myeloma (MM) is a genetically complex hematological cancer characterized by the abnormal proliferation of malignant plasma cells in the bone marrow. This disease progresses from a premalignant condition known as monoclonal gammopathy of unknown significance (MGUS) through sequential genetic alterations involving various genes. These genetic changes contribute to the uncontrolled growth of multiple clones of plasma cells. In this study, we present a phenotype-structured model that captures the intra-clonal heterogeneity and drug resistance in multiple myeloma (MM). The model accurately reproduces the branching evolutionary pattern observed in MM progression, aligning with a previously developed multiscale model. Numerical simulations reveal that higher mutation rates enhance tumor phenotype diversity, while access to growth factors accelerates tumor evolution and increases its final size. Interestingly, the model suggests that further increasing growth factor access primarily amplifies tumor size rather than altering clonal dynamics. Additionally, the model emphasizes that higher mutation frequencies and growth factor availability elevate the chances of drug resistance and relapse. It indicates that the timing of the treatment could trajectory of tumor evolution and clonal emergence in the case of branching evolutionary pattern. Given its low computational cost, our model is well-suited for quantitative studies on MM clonal heterogeneity and its interaction with chemotherapeutic treatments.

Dynamics and functions of E-cadherin complexes in epithelial cell and tissue morphogenesis

Cell-cell adhesion is at the center of structure and dynamics of epithelial tissue. E-cadherin-catenin complexes mediate Ca2+-dependent trans-homodimerization and constitute the kernel of adherens junctions. Beyond the basic function of cell-cell adhesion, recent progress sheds light the dynamics and interwind interactions of individual E-cadherin-catenin complex with E-cadherin superclusters, contractile actomyosin and mechanics of the cortex and adhesion. The nanoscale architecture of E-cadherin complexes together with cis-interactions and interactions with cortical actomyosin adjust to junctional tension and mechano-transduction by reinforcement or weakening of specific features of the interactions. Although post-translational modifications such as phosphorylation and glycosylation have been implicated, their role for specific aspects of in E-cadherin function has remained unclear. Here, we provide an overview of the E-cadherin complex in epithelial cell and tissue morphogenesis focusing on nanoscale architectures by super-resolution approaches and post-translational modifications from recent, in particular in vivo, studies. Furthermore, we review the computational modelling in E-cadherin complexes and highlight how computational modelling has contributed to a deeper understanding of the E-cadherin complexes.

Understanding the General Principles of T Cell Engagement by Multiscale Computational Simulations

The use of bispecific antibodies as T cell engagers can bypass the normal TCR-MHC interaction, redirect the cytotoxic activity of T-cells, and lead to highly efficient tumor cell killing. However, this immunotherapy also causes significant on-target off-tumor toxicologic effects, especially when they were used to treat solid tumors. In order to avoid these adverse events, it is necessary to understand the fundamental mechanisms during the physical process of T cell engagement. We developed a multiscale computational framework to reach this goal. The framework combines simulations on the intercellular and multicellular levels. On the intercellular level, we simulated the spatial-temporal dynamics of three-body interactions among bispecific antibodies, CD3 and TAA. The derived number of intercellular bonds formed between CD3 and TAA were further transferred into the multicellular simulations as the input parameter of adhesive density between cells. Through the simulations under various molecular and cellular conditions, we were able to gain new insights of how to adopt the most appropriate strategy to maximize the drug efficacy and avoid the off-target effect. For instance, we discovered that the low antibody binding affinity resulted in the formation of large clusters at the cell-cell interface, which could be important to control the downstream signaling pathways. We also tested different molecular architectures of the bispecific antibody and suggested the existence of an optimal length in regulating the T cell engagement. Overall, the current multiscale simulations serve as a prove-of-concept study to help the future design of new biological therapeutics.

SIGNIFICANCE

T-cell engagers are a class of anti-cancer drugs that can directly kill tumor cells by bringing T cells next to them. However, current treatments using T-cell engagers can cause serious side-effects. In order to reduce these effects, it is necessary to understand how T cells and tumor cells interact together through the connection of T-cell engagers. Unfortunately, this process is not well studied due to the limitations in current experimental techniques. We developed computational models on two different scales to simulate the physical process of T cell engagement. Our simulation results provide new insights into the general properties of T cell engagers. The new simulation methods can therefore serve as a useful tool to design novel antibodies for cancer immunotherapy.

Digital twin demonstrates significance of biomechanical growth control in liver regeneration after partial hepatectomy

Partial liver removal is an important therapy option for liver cancer. In most patients within a few weeks, the liver is able to fully regenerate. In some patients, however, regeneration fails with often severe consequences. To better understand the control mechanisms of liver regeneration, experiments in mice were performed, guiding the creation of a spatiotemporal 3D model of the regenerating liver. The model represents cells and blood vessels within an entire liver lobe, a macroscopic liver subunit. The model could reproduce the experimental data only if a biomechanical growth control (BGC)-mechanism, inhibiting cell cycle entrance at high compression, was taken into account and predicted that BGC may act as a short-range growth inhibitor minimizing the number of proliferating neighbor cells of a proliferating cell, generating a checkerboard-like proliferation pattern. Model-predicted cell proliferation patterns in pigs and mice were found experimentally. The results underpin the importance of biomechanical aspects in liver growth control.

A computational modeling approach for predicting multicell spheroid patterns based on signaling-induced differential adhesion

Physiological and pathological processes including embryogenesis and tumorigenesis rely on the ability of individual cells to work collectively to form multicell patterns. In these heterogeneous multicell systems, cell-cell signaling induces differential adhesion between cells that leads to tissue-level patterning. However, the sensitivity of pattern formation to changes in the strengths of signaling or cell adhesion processes is not well understood. Prior work has explored these issues using synthetically engineered heterogeneous multicell spheroid systems, in which cell subpopulations engage in bidirectional intercellular signaling to regulate the expression of different cadherins. While engineered cell systems provide excellent experimental tools to observe pattern formation in cell populations, computational models of these systems may be leveraged to explore more systematically how specific combinations of signaling and adhesion parameters can drive the emergence of unique patterns. We developed and validated two- and three-dimensional agent-based models (ABMs) of spheroid patterning for previously described cells engineered with a bidirectional signaling circuit that regulates N- and P-cadherin expression. Systematic exploration of model predictions, some of which were experimentally validated, revealed how cell seeding parameters, the order of signaling events, probabilities of induced cadherin expression, and homotypic adhesion strengths affect pattern formation. Unsupervised clustering was also used to map combinations of signaling and adhesion parameters to these unique spheroid patterns predicted by the ABM. Finally, we demonstrated how the model may be deployed to design new synthetic cell signaling circuits based on a desired final multicell pattern.

Modeling the influence of cell-cell contact and TGF-β signaling on the epithelial mesenchymal transition in MCF7 breast carcinoma cells

The epithelial mesenchymal transition (EMT) is a process by which cells lose their adhesive nature and gain the migratory properties associated with mesenchymal cells. This transition allows cells to migrate away from a primary tumor while maintaining their newly acquired invasive behavior, suggesting that there is a bistable switch between the epithelial and mesenchymal phenotypes. In recent experimental work, we found evidence of this bistability in the MCF7 breast carcinoma cell line (Gasior et al., 2019). Underlying the complex processes governing EMT, we identify a feedback loop between E-cadherin, a protein involved in cellular adhesion, and Slug, a transcription factor that is upregulated during EMT. Here, we present a simple mathematical model that examines the relationship between E-cadherin and Slug in response to pro-epithelial and pro-mesenchymal factors, cell-cell contact and TGF-β, respectively. We hypothesize that cell-cell contact is a critical component in the transition from the epithelial to the mesenchymal phenotype and that it is possible to initiate EMT with the loss of cell-cell contact or the activation of the TGF-β signaling pathway. We propose a reversible bistable switch in response to a loss of cell-cell contact but an irreversible bistable switch when the cell is exposed to TGF-β. Taken together, this model shows that acquiring and retaining invasive behavior by cells with high levels of cell-cell contact is not impossible but, instead, depends on the cooperation between the two switches. The predictions of this model for E-cadherin and Slug levels were compared against relative gene expression data from our recent experiments with MCF7 cells (Gasior et al., 2019). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments, while also highlighting issues that arise when comparing in vitro experimental results to theoretical predictions.

A 3D multi-agent-based model for lumen morphogenesis: the role of the biophysical properties of the extracellular matrix

The correct function of many organs depends on proper lumen morphogenesis, which requires the orchestration of both biological and mechanical aspects. However, how these factors coordinate is not yet fully understood. Here, we focus on the development of a mechanistic model for computationally simulating lumen morphogenesis. In particular, we consider the hydrostatic pressure generated by the cells' fluid secretion as the driving force and the density of the extracellular matrix as regulators of the process. For this purpose, we develop a 3D agent-based-model for lumen morphogenesis that includes cells' fluid secretion and the density of the extracellular matrix. Moreover, this computer-based model considers the variation in the biological behavior of cells in response to the mechanical forces that they sense. Then, we study the formation of the lumen under different-mechanical scenarios and conclude that an increase in the matrix density reduces the lumen volume and hinders lumen morphogenesis. Finally, we show that the model successfully predicts normal lumen morphogenesis when the matrix density is physiological and aberrant multilumen formation when the matrix density is excessive.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00366-022-01654-1.

Nrf2 Modulates the Hybrid Epithelial/Mesenchymal Phenotype and Notch Signaling During Collective Cancer Migration

Hybrid epithelial/mesenchymal cells (E/M) are key players in aggressive cancer metastasis. It remains a challenge to understand how these cell states, which are mostly non-existent in healthy tissue, become stable phenotypes participating in collective cancer migration. The transcription factor Nrf2, which is associated with tumor progression and resistance to therapy, appears to be central to this process. Here, using a combination of immunocytochemistry, single cell biosensors, and computational modeling, we show that Nrf2 functions as a phenotypic stability factor for hybrid E/M cells by inhibiting a complete epithelial-mesenchymal transition (EMT) during collective cancer migration. We also demonstrate that Nrf2 and EMT signaling are spatially coordinated near the leading edge. In particular, computational analysis of an Nrf2-EMT-Notch network and experimental modulation of Nrf2 by pharmacological treatment or CRISPR/Cas9 gene editing reveal that Nrf2 stabilizes a hybrid E/M phenotype which is maximally observed in the interior region immediately behind the leading edge. We further demonstrate that the Nrf2-EMT-Notch network enhances Dll4 and Jagged1 expression at the leading edge, which correlates with the formation of leader cells and protruding tips. Altogether, our results provide direct evidence that Nrf2 acts as a phenotypic stability factor in restricting complete EMT and plays an important role in coordinating collective cancer migration.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Inverse problem approaches for mutation laws in heterogeneous tumours with local and nonlocal dynamics

Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to the transformation of a primary tumour cell population into a secondary, more aggressive cell population. We focus on local and nonlocal mathematical models for cell dynamics and movement, and identify these mutation laws from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. In a local cancer invasion model, we first reconstruct the mutation law when we assume that the mutations depend only on the surrounding cancer cells (i.e., the ECM plays no role in mutations). Second, we assume that the mutations depend on the ECM only, and we reconstruct the mutation law in this case. Third, we reconstruct the mutation when we assume that there is no prior knowledge about the mutations. Finally, for the nonlocal cancer invasion model, we reconstruct the mutation law that depends on the cancer cells and on the ECM. For these numerical reconstructions, our approximations are based on the finite difference method combined with the finite elements method. As the inverse problem is ill-posed, we use the Tikhonov regularisation technique in order to regularise the solution. Stability of the solution is examined by adding additive noise into the measurements.

Relating simulation studies by provenance-Developing a family of Wnt signaling models

For many biological systems, a variety of simulation models exist. A new simulation model is rarely developed from scratch, but rather revises and extends an existing one. A key challenge, however, is to decide which model might be an appropriate starting point for a particular problem and why. To answer this question, we need to identify entities and activities that contributed to the development of a simulation model. Therefore, we exploit the provenance data model, PROV-DM, of the World Wide Web Consortium and, building on previous work, continue developing a PROV ontology for simulation studies. Based on a case study of 19 Wnt/β-catenin signaling models, we identify crucial entities and activities as well as useful metadata to both capture the provenance information from individual simulation studies and relate these forming a family of models. The approach is implemented in WebProv, a web application for inserting and querying provenance information. Our specialization of PROV-DM contains the entities Research Question, Assumption, Requirement, Qualitative Model, Simulation Model, Simulation Experiment, Simulation Data, and Wet-lab Data as well as activities referring to building, calibrating, validating, and analyzing a simulation model. We show that most Wnt simulation models are connected to other Wnt models by using (parts of) these models. However, the overlap, especially regarding the Wet-lab Data used for calibration or validation of the models is small. Making these aspects of developing a model explicit and queryable is an important step for assessing and reusing simulation models more effectively. Exposing this information helps to integrate a new simulation model within a family of existing ones and may lead to the development of more robust and valid simulation models. We hope that our approach becomes part of a standardization effort and that modelers adopt the benefits of provenance when considering or creating simulation models.

We revise a provenance ontology for simulation studies of cellular biochemical models. Provenance information is useful for understanding the creation of a simulation model because it not only contains information about the entities and activities that have led to a simulation model but also their relations, all of which can be visualized. It provides additional structure by explicitly recording research questions, assumptions, and requirements and relating them along with data, qualitative models, simulation models, and simulation experiments through a small set of predefined but extensible activities.

We have applied our concept to a family of 19 Wnt signaling models and implemented a web-based tool (WebProv) to store the provenance information from these studies. The resulting provenance graph visualizes the story line of simulation studies and demonstrates the creation and calibration of simulation models, the successive attempts of validation and extension, and shows, beyond an individual simulation study, how the Wnt models are related. Thereby, the steps and sources that contributed to a simulation model are made explicit.

Our approach complements other approaches aimed at facilitating the reuse and assessment of simulation products in systems biology such as model repositories as well as annotation and documentation guidelines.

Immunofluorescence Image Feature Analysis and Phenotype Scoring Pipeline for Distinguishing Epithelial-Mesenchymal Transition

Epithelial–mesenchymal transition (EMT) is an essential biological process, also implicated in pathological settings such as cancer metastasis, in which epithelial cells transdifferentiate into mesenchymal cells. We devised an image analysis pipeline to distinguish between tissues comprised of epithelial and mesenchymal cells, based on extracted features from immunofluorescence images of differing biochemical markers. Mammary epithelial cells were cultured with 0 (control), 2, 4, or 10 ng/mL TGF-β1, a well-established EMT-inducer. Cells were fixed, stained, and imaged for E-cadherin, actin, fibronectin, and nuclei via immunofluorescence microscopy. Feature selection was performed on different combinations of individual cell markers using a Bag-of-Features extraction. Control and high-dose images comprised the training data set, and the intermediate dose images comprised the testing data set. A feature distance analysis was performed to quantify differences between the treatment groups. The pipeline was successful in distinguishing between control (epithelial) and the high-dose (mesenchymal) groups, as well as demonstrating progress along the EMT process in the intermediate dose groups. Validation using quantitative PCR (qPCR) demonstrated that biomarker expression measurements were well-correlated with the feature distance analysis. Overall, we identified image pipeline characteristics for feature extraction and quantification of immunofluorescence images to distinguish progression of EMT.

Computational systems-biology approaches for modeling gene networks driving epithelial-mesenchymal transitions

Epithelial-mesenchymal transition (EMT) is an important biological process through which epithelial cells undergo phenotypic transitions to mesenchymal cells by losing cell-cell adhesion and gaining migratory properties that cells use in embryogenesis, wound healing, and cancer metastasis. An important research topic is to identify the underlying gene regulatory networks (GRNs) governing the decision making of EMT and develop predictive models based on the GRNs. The advent of recent genomic technology, such as single-cell RNA sequencing, has opened new opportunities to improve our understanding about the dynamical controls of EMT. In this article, we review three major types of computational and mathematical approaches and methods for inferring and modeling GRNs driving EMT. We emphasize (1) the bottom-up approaches, where GRNs are constructed through literature search; (2) the top-down approaches, where GRNs are derived from genome-wide sequencing data; (3) the combined top-down and bottom-up approaches, where EMT GRNs are constructed and simulated by integrating bioinformatics and mathematical modeling. We discuss the methodologies and applications of each approach and the available resources for these studies.

The role of mechanical interactions in EMT

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-β, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales

The metastasis of malignant epithelial tumors begins with the egress of transformed cells from the confines of their basement membrane (BM) to their surrounding collagen-rich stroma. Invasion can be morphologically diverse: when breast cancer cells are separately cultured within BM-like matrix, collagen I (Coll I), or a combination of both, they exhibit collective-, dispersed mesenchymal-, and a mixed collective-dispersed (multimodal)- invasion, respectively. In this paper, we asked how distinct these invasive modes are with respect to the cellular and microenvironmental cues that drive them. A rigorous computational exploration of invasion was performed within an experimentally motivated Cellular Potts-based modeling environment. The model comprised of adhesive interactions between cancer cells, BM- and Coll I-like extracellular matrix (ECM), and reaction-diffusion-based remodeling of ECM. The model outputs were parameters cognate to dispersed- and collective- invasion. A clustering analysis of the output distribution curated through a careful examination of subsumed phenotypes suggested at least four distinct invasive states: dispersed, papillary-collective, bulk-collective, and multimodal, in addition to an indolent/non-invasive state. Mapping input values to specific output clusters suggested that each of these invasive states are specified by distinct input signatures of proliferation, adhesion and ECM remodeling. In addition, specific input perturbations allowed transitions between the clusters and revealed the variation in the robustness between the invasive states. Our systems-level approach proffers quantitative insights into how the diversity in ECM microenvironments may steer invasion into diverse phenotypic modes during early dissemination of breast cancer and contributes to tumor heterogeneity.

Measuring and Modelling the Epithelial- Mesenchymal Hybrid State in Cancer: Clinical Implications

The epithelial-mesenchymal (E/M) hybrid state has emerged as an important mediator of elements of cancer progression, facilitated by epithelial mesenchymal plasticity (EMP). We review here evidence for the presence, prognostic significance, and therapeutic potential of the E/M hybrid state in carcinoma. We further assess modelling predictions and validation studies to demonstrate stabilised E/M hybrid states along the spectrum of EMP, as well as computational approaches for characterising and quantifying EMP phenotypes, with particular attention to the emerging realm of single-cell approaches through RNA sequencing and protein-based techniques.

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.

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

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Conformational dynamics of biologics are captured by microsecond MD simulations

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

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

A hybrid model of intercellular tension and cell-matrix mechanical interactions in a multicellular geometry

Epithelial cells form continuous sheets of cells that exist in tensional homeostasis. Homeostasis is maintained through cell-to-cell junctions that distribute tension and balance forces between cells and their underlying matrix. Disruption of tensional homeostasis can lead to epithelial-mesenchymal transition (EMT), a transdifferentiation process in which epithelial cells adopt a mesenchymal phenotype, losing cell-cell adhesion and enhancing cellular motility. This process is critical during embryogenesis and wound healing, but is also dysregulated in many disease states. To further understand the role of intercellular tension in spatial patterning of epithelial cell monolayers, we developed a multicellular computational model of cell-cell and cell-substrate forces. This work builds on a hybrid cellular Potts model (CPM)-finite element model to evaluate cell-matrix mechanical feedback of an adherent multicellular cluster. Cellular movement is governed by thermodynamic constraints from cell volume, cell-cell and cell-matrix contacts, and durotaxis, which arises from cell-generated traction forces on a finite element substrate. Junction forces at cell-cell contacts balance these traction forces, thereby producing a mechanically stable epithelial monolayer. Simulations were compared to in vitro experiments using fluorescence-based junction force sensors in clusters of cells undergoing EMT. Results indicate that the multicellular CPM model can reproduce many aspects of EMT, including epithelial monolayer formation dynamics, changes in cell geometry, and spatial patterning of cell-cell forces in an epithelial tissue.

An in-silico study of cancer cell survival and spatial distribution within a 3D microenvironment

3D cell cultures are in-vitro models representing a significant improvement with respect to traditional monolayers. Their diffusion and applicability, however, are hampered by the complexity of 3D systems, that add new physical variables for experimental analyses. In order to account for these additional features and improve the study of 3D cultures, we here present SALSA (ScAffoLd SimulAtor), a general purpose computational tool that can simulate the behavior of a population of cells cultured in a 3D scaffold. This software allows for the complete customization of both the polymeric template structure and the cell population behavior and characteristics. In the following the technical description of SALSA will be presented, together with its validation and an example of how it could be used to optimize the experimental analysis of two breast cancer cell lines cultured in collagen scaffolds. This work contributes to the growing field of integrated in-silico/in-vitro analysis of biological systems, which have great potential for the study of complex cell population behaviours and could lead to improve and facilitate the effectiveness and diffusion of 3D cell culture models.

Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments

Cancers present with high variability across patients and tumors; thus, cancer care, in terms of disease prevention, detection, and control, can highly benefit from a personalized approach. For a comprehensive personalized oncology practice, this personalization should ideally consider data gathered from various information levels, which range from the macroscale population level down to the microscale tumor level, without omission of the central patient level. Appropriate data mined from each of these levels can significantly contribute in devising personalized treatment plans tailored to the individual patient and tumor. Mathematical models of solid tumors, combined with patient-specific tumor profiles, present a unique opportunity to personalize cancer treatments after detection using a bottom-up approach. Here, we discuss how information harvested from mathematical models and from corresponding in silico experiments can be implemented in preclinical and clinical applications. To conceptually illustrate the power of these models, one such model is presented, and various pertinent tumor and treatment scenarios are demonstrated in silico. The presented model, specifically a multiscale, hybrid cellular automaton, has been fully validated in vitro using multiple cell-line-specific data. We discuss various insights provided by this model and other models like it and their role in designing predictive tools that are both patient, and tumor specific. After refinement and parametrization with appropriate data, such in silico tools have the potential to be used in a clinical setting to aid in treatment protocols and decision making.

Computational models to explore the complexity of the epithelial to mesenchymal transition in cancer

Epithelial to mesenchymal transition (EMT) is a complex biological process that plays a key role in cancer progression and metastasis formation. Its activation results in epithelial cells losing adhesion and polarity and becoming capable of migrating from their site of origin. At this step the disease is generally considered incurable. As EMT execution involves several individual molecular components, connected by nontrivial relations, in vitro techniques are often inadequate to capture its complexity. Computational models can be used to complement experiments and provide additional knowledge difficult to build up in a wetlab. Indeed in silico analysis gives the user total control on the system, allowing to identify the contribution of each independent element. In the following, two kinds of approaches to the computational study of EMT will be presented. The first relies on signal transduction networks description and details how changes in gene expression could influence this process, both focusing on specific aspects of the EMT and providing a general frame for this phenomenon easily comparable with experimental data. The second integrates single cell and population level descriptions in a multiscale model that can be considered a more accurate representation of the EMT. The advantages and disadvantages of each approach will be highlighted, together with the importance of coupling computational and experimental results. Finally, the main challenges that need to be addressed to improve our knowledge of the role of EMT in the neoplastic disease and the scientific and translational value of computational models in this respect will be presented. This article is categorized under: Analytical and Computational Methods > Computational Methods.

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.

Continuous Dynamic Modeling of Regulated Cell Adhesion: Sorting, Intercalation, and Involution

Cell-cell adhesion is essential for tissue growth and multicellular pattern formation and crucial for the cellular dynamics during embryogenesis and cancer progression. Understanding the dynamical gene regulation of cell adhesion molecules (CAMs) responsible for the emerging spatial tissue behaviors is a current challenge because of the complexity of these nonlinear interactions and feedback loops at different levels of abstraction-from genetic regulation to whole-organism shape formation. To extend our understanding of cell and tissue behaviors due to the regulation of adhesion molecules, here we present a novel, to our knowledge, model for the spatial dynamics of cellular patterning, growth, and shape formation due to the differential expression of CAMs and their regulation. Capturing the dynamic interplay between genetic regulation, CAM expression, and differential cell adhesion, the proposed continuous model can explain the complex and emergent spatial behaviors of cell populations that change their adhesion properties dynamically because of inter- and intracellular genetic regulation. This approach can demonstrate the mechanisms responsible for classical cell-sorting behaviors, cell intercalation in proliferating populations, and the involution of germ layer cells induced by a diffusing morphogen during gastrulation. The model makes predictions on the physical parameters controlling the amplitude and wavelength of a cellular intercalation interface, as well as the crucial role of N-cadherin regulation for the involution and migration of cells beyond the gradient of the morphogen Nodal during zebrafish gastrulation. Integrating the emergent spatial tissue behaviors with the regulation of genes responsible for essential cellular properties such as adhesion will pave the way toward understanding the genetic regulation of large-scale complex patterns and shapes formation in developmental, regenerative, and cancer biology.

Tuning intercellular adhesion with membrane-anchored oligonucleotides

Adhesive interactions between cells play an integral role in development, differentiation and regeneration. Existing methods for controlling cell-cell cohesion and adhesion by manipulating protein expression are constrained by biological interdependencies, e.g. coupling of cadherins to actomyosin force-feedback mechanisms. We use oligonucleotides conjugated to PEGylated lipid anchors (ssDNAPEGDPPE) to introduce artificial cell-cell adhesion that is largely decoupled from the internal cytoskeleton. We describe cell-cell doublets with a mechanical model based on isotropic, elastic deformation of spheres to estimate the adhesion at the cell-cell interface. Physical manipulation of adhesion by modulating the PEG-lipid to ssDNAPEGDPPE ratio, and conversely treating with actin-depolymerizing cytochalasin D, resulted in decreases and increases in doublet contact area, respectively. Our data are relevant to the ongoing discussion over mechanisms of tissue surface tension and in agreement with models based on opposing cortical and cohesive forces. PEG-lipid modulation of doublet geometries resulted in a well-defined curve indicating continuity, enabling prescriptive calibration for controlling doublet geometry. Our study demonstrates tuning of basic doublet adhesion, laying the foundation for more complex multicellular adhesion control independent of protein expression.

Volumetric imaging parameters are significant for predicting the pathological complete response of preoperative concurrent chemoradiotherapy in local advanced rectal cancer

Preoperative concurrent chemoradiotherapy (CCRT) as the standard treatment for locally advanced rectal cancer (LARC) has been widely used in clinic. Its efficiency influences the prognosis and the selection of subsequent treatment. The current criteria for evaluating the prognosis of patients with extremely sensitive preoperative CCRT include the clinical complete remission response (cCR) and pathological complete response (pCR), but those with cCR may not necessarily achieve pCR, and the pCR can be confirmed only after surgery. Some scholars believe that patients with pCR after CCRT can be categorized as 'watch and wait'. Therefore, it is extremely important to find a way to predict the pCR status of patients before therapy. In this study, we examined the expression of stem cell markers and obtained direct and derivative volumetric imaging parameters before treatment. Subsequently, these factors and the general clinical data were adopted into a regression model, and the correlation between them and the pCR was analyzed. We found that the pCR of LARC was positively correlated with tumor compactness (TC), whereas it was negatively correlated with approximate tumor volume (ATV), real tumor volume (RTV), total surface area of the tumor (TSA) and tumor maximum longitudinal length (TML). In these meaningful predictors, the positive predictive values and the negative predictive values of TC were 74.73% and 94.61%, respectively. Compared with other possible predictors, TC is the most encouraging predictor of pCR. Our findings provide a way for clinicians to predict the sensitivity of preoperative CCRT and will help to select individualized treatment options for LARC patients.

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. As a tumour increases in malignancy, the cancer cells adopt the ability to mutate into secondary cell subpopulations giving rise to a heterogeneous tumour. This new cell subpopulation often carries higher invasive abilities and permits a quicker spread of the tumour. Building upon the recent multiscale modelling framework for cancer invasion within a fibrous ECM introduced in Shuttleworth and Trucu, (2019), in this paper we consider the process of local invasion by a heterotypic tumour consisting of two cancer cell populations mixed with a two-phase ECM. To that end, we address the double feedback link between the tissue-scale cancer dynamics and the cell-scale molecular processes through the development of a two-part modelling framework that crucially incorporates the multiscale dynamic redistribution of oriented fibres occurring within a two-phase extra-cellular matrix and combines this with the multiscale leading edge dynamics exploring key matrix-degrading enzymes molecular processes along the tumour interface that drive the movement of the cancer boundary. The modelling framework will be accompanied by computational results that explore the effects of the underlying fibre network on the overall pattern of cancer invasion.

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.

A 3D Multiscale Model to Explore the Role of EGFR Overexpression in Tumourigenesis

The epidermal growth factor receptor (EGFR) signalling cascade is one of the main pathways that regulate the survival and division of mammalian cells. It is also one of the most altered transduction pathways in cancer. Acquired mutations in the EGFR/ERK pathway can cause the overexpression of EGFR on the surface of the cell, while others downregulate the inactivation of switched on intracellular proteins such as Ras and Raf. This upregulates the activity of ERK and promotes cell division. We develop a 3D multiscale model to explore the role of EGFR overexpression on tumour initiation. In this model, cells are described as individual objects that move, interact, divide, proliferate, and die by apoptosis. We use Brownian Dynamics to describe the extracellular and intracellular regulations of cells as well as the spatial and stochastic effects influencing them. The fate of each cell depends on the number of active transcription factors in the nucleus. We use numerical simulations to investigate the individual and combined effects of mutations on the intracellular regulation of individual cells. Next, we show that the distance between active receptors increase the level of EGFR/ERK signalling. We demonstrate the usefulness of the model by quantifying the impact of mutational alterations in the EGFR/ERK pathway on the growth rate of in silico tumours.

MMP Secretion Rate and Inter-invadopodia Spacing Collectively Govern Cancer Invasiveness

Invadopodia are micron-sized invasive structures that mediate extracellular matrix (ECM) degradation through a combination of membrane-bound and soluble matrix metalloproteinases (MMPs). However, how such localized degradation is converted into pores big enough for cancer cells to invade, and the relative contributions of membrane-bound versus soluble MMPs to this process remain unclear. In this article, we address these questions by combining experiments and simulations. We show that in MDA-MB-231 cells, an increase in ECM density enhances invadopodia-mediated ECM degradation and decreases inter-invadopodia spacing. ECM degradation is mostly mediated by soluble MMPs, which are activated by membrane-bound MT1-MMP. We present a computational model of invadopodia-mediated ECM degradation, which recapitulates the above observations and identifies MMP secretion rate as an important regulator of invadopodia stability. Simulations with multiple invadopodia suggest that inter-invadopodia spacing and MMP secretion rate collectively dictate the size of the degraded zones. Taken together, our results suggest that for creating pores conducive for cancer invasion, cells must tune inter-invadopodia spacing and MMP secretion rate in an ECM density-dependent manner, thereby striking a balance between invadopodia penetration and ECM degradation.

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.

Scalable population-level modelling of biological cells incorporating mechanics and kinetics in continuous time

The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this detailed knowledge of the individual cell to be able to explain at the population level how cells interact and respond with each other and their environment. In particular, the goal is to understand how organisms develop, maintain and repair functional tissues and organs. In this paper, we propose a novel computational framework for modelling populations of interacting cells. Our framework incorporates mechanistic, constitutive descriptions of biomechanical properties of the cell population, and uses a coarse-graining approach to derive individual rate laws that enable propagation of the population through time. Thanks to its multiscale nature, the resulting simulation algorithm is extremely scalable and highly efficient. As highlighted in our computational examples, the framework is also very flexible and may straightforwardly be coupled with continuous-time descriptions of biochemical signalling within, and between, individual cells.

Model Prediction and Validation of an Order Mechanism Controlling the Spatiotemporal Phenotype of Early Hepatocellular Carcinoma

Recently, hepatocyte-sinusoid alignment (HSA) has been identified as a mechanism that supports the coordination of hepatocytes during liver regeneration to reestablish a functional micro-architecture (Hoehme et al. in Proc Natl Acad Sci 107(23):10371-10376, 2010). HSA means that hepatocytes preferentially align along the closest micro-vessels. Here, we studied whether this mechanism is still active in early hepatocellular tumors. The same agent-based spatiotemporal model that previously correctly predicted HSA in liver regeneration was further developed to simulate scenarios in early tumor development, when individual initiated hepatocytes gain increased proliferation capacity. The model simulations were performed under conditions of realistic liver micro-architectures obtained from 3D reconstructions of confocal laser scanning micrographs. Interestingly, the established model predicted that initiated hepatocytes at first arrange in elongated patterns. Only when the tumor progresses to cell numbers of approximately 4000, does it adopt spherical structures. This prediction may have relevant consequences, since elongated tumors may reach critical structures faster, such as larger vessels, compared to a spherical tumor of similar cell number. Interestingly, this model prediction was confirmed by analysis of the spatial organization of initiated hepatocytes in a rat liver tumor initiation study using single doses of 250 mg/kg of the genotoxic carcinogen N-nitrosomorpholine (NNM). Indeed, small clusters of GST-P positive cells induced by NNM were elongated, almost columnar, while larger GDT-P positive foci of approximately the size of liver lobuli adopted spherical shapes. From simulations testing numerous possible mechanisms, only HSA could explain the experimentally observed initial deviation from spherical shape. The present study demonstrates that the architecture of small cell clusters of hepatocytes early after initiation is still controlled by physiological mechanisms. However, this coordinating influence is lost when the tumor grows to approximately 4000 cells, leading to further growth in spherical shape. Our findings stress the potential importance of organ micro-architecture in understanding tumor phenotypes.

Creation of Three-Dimensional Liver Tissue Models from Experimental Images for Systems Medicine

In this chapter, we illustrate how three-dimensional liver tissue models can be created from experimental image modalities by utilizing a well-established processing chain of experiments, microscopic imaging, image processing, image analysis and model construction. We describe how key features of liver tissue architecture are quantified and translated into model parameterizations, and show how a systematic iteration of experiments and model simulations often leads to a better understanding of biological phenomena in systems biology and systems medicine.