Evolutionary dynamics of cancer: from epigenetic regulation to cell population dynamics -- mathematical model framework, applications, and open problems
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and heterogeneity in cancer cells. Cancer is a group of diseases involving abnormal cell growth, during which abnormal regulations in stem cell regeneration are essential for the dynamics of cancer development. In general, the dynamics of stem cell regeneration can be simplified as a $\mathrm{G_0}$ phase cell cycle model, which lead to a delay differentiation equation. When cell heterogeneity and plasticity are considered, we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division. The proposed model highlights cell heterogeneity and plasticity, and connects the heterogeneity with cell-to-cell variance in cellular behaviors, e.g. proliferation, apoptosis, and differentiation/senescence, and can be extended to include gene mutation-induced tumor development. Hybrid computations models are developed based on the mathematical model framework, and are applied to the process of inflammation-induced tumorigenesis and tumor relapse after CAR-T therapy. Finally, we give rise to several mathematical problems related to the proposed differential-integral equation. Answers to these problems are crucial for the understanding of the evolutionary dynamics of cancer.
Epigenetic Tracking is a mathematical model of biological cells, originally conceived to study embryonic development. Computer simulations proved the capacity of the model to generate complex 3-dimensional cellular structures, and the potential to reproduce the complexity typical of living beings. The most distinctive feature of this model is the presence in the body of a homogeneous distribution of stem cells, which are dinamically and continuously created during development from non-stem cells and reside in niches. Embryonic stem cells orchestrate early developmental events, adult stem cells…
The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington's landscape, consisting of hills and valleys. The smooth top and valley-strewn bottom of the hill represents their undifferentiated and differentiated states respectively. Although mathematical ideas rooted in nonlinear dynamics and bifurcation theory have been used to quantify this picture, the importance of time delays arising from multistep chemical reactions or cellular shape transformations have been ignored so far. We argue…
We propose a physical model for developmental process at cellular level to discuss the mechanism of epigenetic landscape. In our simplified model, a minimal model, the network of the interaction among cells generates the landscape epigenetically and the differentiation in developmental process is understood as a self-organization. The effect of the regulation by gene expression which is a key ingredient in development is renormalized into the interaction and the environment. At earlier stage of the development the energy landscape of the model is rugged with small amplitude. The state of cells…
Cells are known to sense and respond to their mechanical microenvironment in profound ways. Various evidence has implicated the adhesome, a body of adhesion associated proteins, in several cell fate decisions, including differentiation and proliferation. Furthermore, recent work has demonstrated that substrate topography can modulate the epigenetic state of fibroblasts, facilitate cell reprogramming, and temper inflammation. However, the effectors responsible for such phenomena remain poorly understood. Here we explore the effect of biomaterial design, adhesion, and intracellular forces of the…
The diversity of cell populations is regulated by extracellular and intracellular variability. The latter includes genetic, epigenetic and stochastic variability, all contributing to the experimentally observed heterogeneity in response to external death-inducing stimuli. Studies of sources and regulation of variability in commitment to apoptotic cancer cell death are likely to identify the fundamental features of apoptotic protein networks that are responsible for determining the ultimate cell fate. Systems biology approaches, involving computer simulations of the biochemical reactions accomp…
Stochastic gradient descent on the epigenetic landscape: a unified framework for cellular plasticity, tumor heterogeneity, and the asymptotic irrelevance of fitness
Instituto de Matemática e Computação, Universidade Federal de Itajubá（伊塔朱巴联邦大学数学与计算研究所）；Carl Gustav Carus School of Medicine, Technische Universität Dresden（德累斯顿工业大学卡尔·古斯塔夫·卡斯医学院）
Collective cell migration is a hallmark of developmental and patho-physiological states, including wound healing and invasive cancer growth. The integrity of the expanding epithelial sheets can be influenced by extracellular cues, including cell-cell and cell-matrix interactions. We show the nano-scale topography of the extracellular matrix underlying epithelial cell layers can have a strong effect on the speed and morphology of the fronts of the expanding sheet triggering epithelial-mesenchymal transition (EMT). We further demonstrate that this behavior depends on the mechano-sensitivity of t…
Incorporating stochastic gene expression, signaling-mediated intercellular interactions, and regulated cell proliferation in models of coordinated tissue development
The dynamics of tumor cell populations is hotly debated: do populations derive hierarchically from a subpopulation of cancer stem cells (CSCs), or are stochastic transitions that mutate differentiated cancer cells to CSCs important? Here we argue that regulation must also be important. We sort human melanoma cells using three distinct cancer stem cell (CSC) markers - CXCR6, CD271 and ABCG2 - and observe that the fraction of non-CSC-marked cells first overshoots to a higher level and then returns to the level of unsorted cells. This clearly indicates that the CSC population is homeostatically r…
Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and, when they reach a critical length, the cell will enter permanent cell cycle arrest - a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fu…
Cancer cells can acquire a spectrum of stable hybrid epithelial/mesenchymal (E/M) states during epithelial-mesenchymal transition (EMT). Cells in these hybrid E/M phenotypes often combine epithelial and mesenchymal features and tend to migrate collectively commonly as small clusters. Such collectively migrating cancer cells play a pivotal role in seeding metastases and their presence in cancer patients indicates an adverse prognostic factor. Moreover, cancer cells in hybrid E/M phenotypes tend to be more associated with stemness which endows them with tumor-initiation ability and therapy resis…
BH3 mimetics have been proposed as new anticancer therapeutics. They target anti-apoptotic Bcl-2 proteins, up-regulation of which has been implicated in the resistance of many cancer cells, particularly leukemia and lymphoma cells, to apoptosis. Using probabilistic computational modeling of the mitochondrial pathway of apoptosis, verified by single-cell experimental observations, we develop a model of Bcl-2 inhibition of apoptosis. Our results clarify how Bcl-2 imparts its anti-apoptotic role by increasing the time-to-death and cell-to-cell variability. We also show that although the commitmen…
