Mathematical Models of Cancer Cell Plasticity

From Crypts to Cancer: A Holistic Perspective on Colorectal Carcinogenesis and Therapeutic Strategies

Colorectal cancer (CRC) represents a significant global health burden, with high incidence and mortality rates worldwide. Recent progress in research highlights the distinct clinical and molecular characteristics of colon versus rectal cancers, underscoring tumor location's importance in treatment approaches. This article provides a comprehensive review of our current understanding of CRC epidemiology, risk factors, molecular pathogenesis, and management strategies. We also present the intricate cellular architecture of colonic crypts and their roles in intestinal homeostasis. Colorectal carcinogenesis multistep processes are also described, covering the conventional adenoma-carcinoma sequence, alternative serrated pathways, and the influential Vogelstein model, which proposes sequential APC, KRAS, and TP53 alterations as drivers. The consensus molecular CRC subtypes (CMS1-CMS4) are examined, shedding light on disease heterogeneity and personalized therapy implications.

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.

Metastasis Models: Thermodynamics and Complexity

The thermodynamic formalism of nonequilibrium systems together with the theory of complex systems and systems biology offer an appropriate theoretical framework to explain the complexity observed at the macroscopic level in physiological phenomena. In turn, they allow the establishment of an appropriate conceptual and operational framework to address the study of phenomena such as the emergence and evolution of cancer.This chapter is organized as follows: In Subheading 1, an integrated vision of these disciplines is offered for the characterization of the emergence and evolution of cancer, seen as a nonlinear dynamic system, temporally and spatially self-organized out of thermodynamic equilibrium. The development of the various mathematical models and different techniques and approaches used in the characterization of cancer metastasis is presented in Subheading 2. Subheading 3 is devoted to the time course of cancer metastasis, with particular emphasis on the epithelial-mesenchymal transition (EMT henceforth) as well as chronotherapeutic treatments. In Subheading 4, models of the spatial evolution of cancer metastasis are presented. Finally, in Subheading 5, some conclusions and remarks are presented.

Multiscale model of the different modes of cancer cell invasion

MOTIVATION

Mathematical models of biological processes altered in cancer are built using the knowledge of complex networks of signaling pathways, detailing the molecular regulations inside different cell types, such as tumor cells, immune and other stromal cells. If these models mainly focus on intracellular information, they often omit a description of the spatial organization among cells and their interactions, and with the tumoral microenvironment.

RESULTS

We present here a model of tumor cell invasion simulated with PhysiBoSS, a multiscale framework, which combines agent-based modeling and continuous time Markov processes applied on Boolean network models. With this model, we aim to study the different modes of cell migration and to predict means to block it by considering not only spatial information obtained from the agent-based simulation but also intracellular regulation obtained from the Boolean model.

Our multiscale model integrates the impact of gene mutations with the perturbation of the environmental conditions and allows the visualization of the results with 2D and 3D representations. The model successfully reproduces single and collective migration processes and is validated on published experiments on cell invasion. In silico experiments are suggested to search for possible targets that can block the more invasive tumoral phenotypes.

AVAILABILITY AND IMPLEMENTATION

https://github.com/sysbio-curie/Invasion_model_PhysiBoSS.

Data-driven spatio-temporal modelling of glioblastoma

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

Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios

Mathematical Oncology has emerged as a research field that applies either continuous or discrete models to mathematically describe cancer-related phenomena. Such methods are usually expressed in terms of differential equations, however tumor composition involves specific cellular structure and can demonstrate probabilistic nature, often requiring tailor-made approaches. In this context, cell-based models allow monitoring independent single parameters, which might vary in both time and space. By relying on extant tumor growth models in the literature, this study introduces cellular-automata simulation strategies that admit heterogeneous cell population while capturing both single-cell and cluster-cell behaviors. In this agent-based computational model, tumor cells are limited to follow four possible courses of action, namely: proliferation, migration, apoptosis or quiescence. Despite the apparent simplicity of those actions, the model can represent different complex tumor features depending on parameter settings. This study virtualized five different scenarios, showcasing model capabilities of representing tumor dynamics including alternate dormancy periods, cell death instability and cluster formation. Implementation techniques are also explored together with prospective model expansion towards deterministic features. The proposed stochastic cellular automaton model is able to effectively simulate different scenarios regarding tumor growth effectively, figuring as an interesting tool for in silico modeling, with promising capabilities of expansion to support research in mathematical oncology, thus improving diagnosis tools and/or personalized treatment.

Roadmap on plasticity and epigenetics in cancer

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

The matrix-dependent 3D spheroid model of the migration of non-small cell lung cancer: a step towards a rapid automated screening

In vitro 3D cell culture systems utilizing multicellular tumor spheroids (MCTS) are widely used in translational oncology, including for studying cell migration and in personalized therapy. However, early stages of cellular migration from MCTS and cross-talk between spheroids are overlooked, which was addressed in the current study. Here, we investigated cell migration from MCTS derived from human non-small cell lung cancer (NSCLC) cell line A549 cultured on different substrates, collagen gel or plastic, at different time points. We found that migration starts at 4–16 h time points after the seeding and its speed is substrate-dependent. We also demonstrated that co-culture of two NSCLC-derived MCTS on collagen gel, but not on plastic, facilitates cell migration compared with single MTCS. This finding should be considered when designing MCTS-based functional assays for personalized therapeutic approach and drug screenings. Overall, our work characterizes the in vitro 3D cell culture model resembling NSCLC cell migration from the clusters of CTCs into surgical wound, and describes microscopy-based tools and approaches for image data analysis with a potential for further automation. These tools and approaches also might be used to predict patterns of CTCs migration based on ex vivo analysis of patient biopsy in a 3D culture system.

Non-local multiscale approach for the impact of go or grow hypothesis on tumour-viruses interactions

We propose and study computationally a novel non-local multiscale moving boundary mathematical model for tumour and oncolytic virus (OV) interactions when we consider the go or grow hypothesis for cancer dynamics. This spatio-temporal model focuses on two cancer cell phenotypes that can be infected with the OV or remain uninfected, and which can either move in response to the extracellular-matrix (ECM) density or proliferate. The interactions between cancer cells, those among cancer cells and ECM, and those among cells and OV occur at the macroscale. At the micro-scale, we focus on the interactions between cells and matrix degrading enzymes (MDEs) that impact the movement of tumour boundary. With the help of this multiscale model we explore the impact on tumour invasion patterns of two different assumptions that we consider in regard to cell-cell and cell-matrix interactions. In particular we investigate model dynamics when we assume that cancer cell fluxes are the result of local advection in response to the density of extracellular matrix (ECM), or of non-local advection in response to cell-ECM adhesion. We also investigate the role of the transition rates between mainly-moving and mainly-growing cancer cell sub-populations, as well as the role of virus infection rate and virus replication rate on the overall tumour dynamics.

Fractional Mathematical Oncology: On the potential of non-integer order calculus applied to interdisciplinary models

Mathematical Oncology investigates cancer-related phenomena through mathematical models as comprehensive as possible. Accordingly, an interdisciplinary approach involving concepts from biology to materials science can provide a deeper understanding of biological systems pertaining the disease. In this context, fractional calculus (also referred to as non-integer order) is a branch in mathematical analysis whose tools can describe complex phenomena comprising different time and space scales. Fractional-order models may allow a better description and understanding of oncological particularities, potentially contributing to decision-making in areas of interest such as tumor evolution, early diagnosis techniques and personalized treatment therapies. By following a phenomenological (i.e. mechanistic) approach, the present study surveys and explores different aspects of Fractional Mathematical Oncology, reviewing and discussing recent developments in view of their prospective applications.

Are we on the cusp of a new paradigm for biology? The illogic of molecular developmental biology versus Janus-faced control of embryogenesis via differentiation waves

The logic of molecular developmental biology fails to explain embryogenesis. A new approach, Janus-faced control, involving both top-down control by differentiation waves and bottom-up control via the mechanical consequences of cell differentiations, may be needed. This obviates problems inherent in reductionism with an explicit, testable mechanism.