Data Driven Mathematical Model of Colon Cancer Progression

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Investigating the spatial interaction of immune cells in colon cancer

The intricate network of interactions between cells and molecules in the tumor microenvironment creates a heterogeneous ecosystem. The proximity of the cells and molecules to their activators and inhibitors is essential in the progression of tumors. Here, we develop a system of partial differential equations coupled with linear elasticity to investigate the effects of spatial interactions on the tumor microenvironment. We observe interesting cell and cytokine distribution patterns, which are heavily affected by macrophages. We also see that cytotoxic T cells get recruited and suppressed at the site of macrophages. Moreover, we observe that anti-tumor macrophages reorganize the patterns in favor of a more spatially restricted cancer and necrotic core. Furthermore, the adjoint-based sensitivity analysis indicates that the most sensitive model's parameters are directly related to macrophages. The results emphasize the widely acknowledged effect of macrophages in controlling cancer cells population and spatially arranging cells in the tumor microenvironment.

Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment

The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level of IL-6 can remarkably slow the tumor's growth.

TumorDecon: A digital cytometry software

There are many experimental methods for characterizing immune profiles of tumors, such as flow and mass cytometry. However, these approaches are time and resource intensive. Thus, several "digital cytometry" methods have been developed to extract cell frequencies from RNA-seq data. Here, we introduce TumorDecon, named for its potential to deconvolve the distribution of cells from the gene expression levels of a bulk of cells, such as a tumor. The Python package provides an accessible way of applying these methods. It includes four deconvolution methods as well as several gene sets, signature matrices, and functions for generating custom signature matrices.

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells' location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells' diffusion and immune cells' influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes' diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

Integrated Analysis of Necroptosis-Related Genes for Prognosis, Immune Microenvironment Infiltration, and Drug Sensitivity in Colon Cancer

Background

Necroptosis, is intimately linked to tumor development and prognosis and has been considered as a target for anticancer therapy. However, the role of necroptosis-related genes (NRGs) in colon cancer is unclear.

Methods

In the present study, we screened 76 NRGs from previous studies and described the landscape of transcriptomic and genetic variation of NRGs in colon cancer (CC) patient samples. Molecular subtypes of necroptosis in colon cancer were identified by clustering analysis, and these molecular subtypes were linked to patient prognosis and TME cell infiltration characteristics. Then, the NRS-score for predicting overall survival (OS) was built based on the TCGA database and validated in the GSE39582 cohort for its predictive power in CC patients. Besides, the ESTIMATE and CIBERSORT algorithms were applied to explore the relationship between NRS-score and tumor immune microenvironment.

Results

We identified two molecular subtypes associated with necroptosis in CC, which have diverse prognosis and immune microenvironment characteristics. Based on the differentially expressed genes between the two molecular subtypes, we further developed a necroptosis risk score signature, referred to as NRS-score. High NRS-score was associated with poor prognosis in CC through immunosuppressive microenvironment and immune escape mechanisms. The nomogram based on NRS-score showed excellent ability to predict prognosis. In addition, NRS-score presented a positive correlation with tumor mutational burden (TMB) and immune checkpoint blockade (ICB) expression and was closely correlated with multiple anticancer agent susceptibility.

Conclusion

This work revealed a close relationship between necroptosis and the prognosis and immune microenvironment of colon cancer. The NRS-score based on the 8-gene signature may be used to predict the sensitivity of immunotherapy and chemotherapy in colon cancer patients, and provides a foundation for future studies targeting necroptosis and its immune microenvironment.

Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model

The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.

One of the outstanding challenges of the mathematical modeling of cancer progression is the existence of many unknown parameters. In this work, we develop a data-driven mathematical model of breast cancer progression by deriving a system of ordinary differential equations for the interaction networks of key cell types and molecules in breast tumors. To overcome the limitations of unknown parameters, we utilize a time course data of a PyMT mice model of breast cancer and estimate parameters using an optimization method. Although the predicted dynamics of cancer and necrotic cells using the obtained values of parameters are in good agreement with the data, the predicted values for a few other variables do not match the data. This might indicate that there are some other key interactions that have not been modeled, and/or there is a noise in the data. The sensitivity and bifurcation analyses show that the most important parameters in controlling the cancer cells population are the proliferation and death rates of cancer cells and adipocytes. These results are in agreement with some biological and clinical studies of breast cancer, which have reported a link between adipocytes and breast cancer progression.

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.

Investigating Optimal Chemotherapy Options for Osteosarcoma Patients through a Mathematical Model

Simple Summary

Osteosarcoma is a rare type of cancer with poor prognoses. However, to the best of our knowledge, there are no mathematical models that study the impact of chemotherapy treatments on the osteosarcoma microenvironment. In this study, we developed a data driven mathematical model to analyze the dynamics of the important players in three groups of osteosarcoma tumors with distinct immune patterns in the presence of the most common chemotherapy drugs. The results indicate that the treatments’ start times and optimal dosages depend on the unique growth rate of the tumor, which implies the necessity of personalized medicine. Furthermore, the developed model can be extended by others to build models that can recommend individual-specific optimal dosages.

Abstract

Since all tumors are unique, they may respond differently to the same treatments. Therefore, it is necessary to study their characteristics individually to find their best treatment options. We built a mathematical model for the interactions between the most common chemotherapy drugs and the osteosarcoma microenvironments of three clusters of tumors with unique immune profiles. We then investigated the effects of chemotherapy with different treatment regimens and various treatment start times on the behaviors of immune and cancer cells in each cluster. Saliently, we suggest the optimal drug dosages for the tumors in each cluster. The results show that abundances of dendritic cells and HMGB1 increase when drugs are given and decrease when drugs are absent. Populations of helper T cells, cytotoxic cells, and IFN-γ grow, and populations of cancer cells and other immune cells shrink during treatment. According to the model, the MAP regimen does a good job at killing cancer, and is more effective than doxorubicin and cisplatin combined or methotrexate alone. The results also indicate that it is important to consider the tumor’s unique growth rate when deciding the treatment details, as fast growing tumors need early treatment start times and high dosages.

Data Driven Mathematical Model of FOLFIRI Treatment for Colon Cancer

Many colon cancer patients show resistance to their treatments. Therefore, it is important to consider unique characteristic of each tumor to find the best treatment options for each patient. In this study, we develop a data driven mathematical model for interaction between the tumor microenvironment and FOLFIRI drug agents in colon cancer. Patients are divided into five distinct clusters based on their estimated immune cell fractions obtained from their primary tumors' gene expression data. We then analyze the effects of drugs on cancer cells and immune cells in each group, and we observe different responses to the FOLFIRI drugs between patients in different immune groups. For instance, patients in cluster 3 with the highest T-reg/T-helper ratio respond better to the FOLFIRI treatment, while patients in cluster 2 with the lowest T-reg/T-helper ratio resist the treatment. Moreover, we use ROC curve to validate the model using the tumor status of the patients at their follow up, and the model predicts well for the earlier follow up days.

Data-Driven Mathematical Model of Osteosarcoma

As the immune system has a significant role in tumor progression, in this paper, we develop a data-driven mathematical model to study the interactions between immune cells and the osteosarcoma microenvironment. Osteosarcoma tumors are divided into three clusters based on their relative abundance of immune cells as estimated from their gene expression profiles. We then analyze the tumor progression and effects of the immune system on cancer growth in each cluster. Cluster 3, which had approximately the same number of naive and M2 macrophages, had the slowest tumor growth, and cluster 2, with the highest population of naive macrophages, had the highest cancer population at the steady states. We also found that the fastest growth of cancer occurred when the anti-tumor immune cells and cytokines, including dendritic cells, helper T cells, cytotoxic cells, and IFN-γ, switched from increasing to decreasing, while the dynamics of regulatory T cells switched from decreasing to increasing. Importantly, the most impactful immune parameters on the number of cancer and total cells were the activation and decay rates of the macrophages and regulatory T cells for all clusters. This work presents the first osteosarcoma progression model, which can be later extended to investigate the effectiveness of various osteosarcoma treatments.

Modeling the Th17 and Tregs Paradigm: Implications for Cancer Immunotherapy

CD4 + T cell differentiation is governed by gene regulatory and metabolic networks, with both networks being highly interconnected and able to adapt to external stimuli. Th17 and Tregs differentiation networks play a critical role in cancer, and their balance is affected by the tumor microenvironment (TME). Factors from the TME mediate recruitment and expansion of Th17 cells, but these cells can act with pro or anti-tumor immunity. Tregs cells are also involved in tumor development and progression by inhibiting antitumor immunity and promoting immunoevasion. Due to the complexity of the underlying molecular pathways, the modeling of biological systems has emerged as a promising solution for better understanding both CD4 + T cell differentiation and cancer cell behavior. In this review, we present a context-dependent vision of CD4 + T cell transcriptomic and metabolic network adaptability. We then discuss CD4 + T cell knowledge-based models to extract the regulatory elements of Th17 and Tregs differentiation in multiple CD4 + T cell levels. We highlight the importance of complementing these models with data from omics technologies such as transcriptomics and metabolomics, in order to better delineate existing Th17 and Tregs bifurcation mechanisms. We were able to recompilate promising regulatory components and mechanisms of Th17 and Tregs differentiation under normal conditions, which we then connected with biological evidence in the context of the TME to better understand CD4 + T cell behavior in cancer. From the integration of mechanistic models with omics data, the transcriptomic and metabolomic reprograming of Th17 and Tregs cells can be predicted in new models with potential clinical applications, with special relevance to cancer immunotherapy.

Immune classification of osteosarcoma

Tumor immune microenvironment has been shown to be important in predicting the tumor progression and the outcome of treatments. This work aims to identify different immune patterns in osteosarcoma and their clinical characteristics. We use the latest and best performing deconvolution method, CIBERSORTx, to obtain the relative abundance of 22 immune cells. Then we cluster patients based on their estimated immune abundance and study the characteristics of these clusters, along with the relationship between immune infiltration and outcome of patients. We find that abundance of CD8 T cells, NK cells and M1 Macrophages have a positive association with prognosis, while abundance of γδ T cells, Mast cells, M0 Macrophages and Dendritic cells have a negative association with prognosis. Accordingly, the cluster with the lowest proportion of CD8 T cells, M1 Macrophages and highest proportion of M0 Macrophages has the worst outcome among clusters. By grouping patients with similar immune patterns, we are also able to suggest treatments that are specific to the tumor microenvironment.