Bayesian calibration of a stochastic,multiscale agent-based model for predicting in vitro tumor growth

Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.     

Regulation of dual specificity phosphatases in breast cancer during initial treatment with Herceptin: a Boolean model analysis

Background

25% of breast cancer patients suffer from aggressive HER2-positive tumours that are characterised by overexpression of the HER2 protein or by its increased tyrosine kinase activity. Herceptin is a major drug used to treat HER2 positive breast cancer. Understanding the molecular events that occur when breast cancer cells are exposed to Herceptin is therefore of significant importance. Dual specificity phosphatases (DUSPs) are central regulators of cell signalling that function downstream of HER2, but their role in the cellular response to Herceptin is mostly unknown. This study aims to model the initial effects of Herceptin exposure on DUSPs in HER2-positive breast cancer cells using Boolean modelling.

Results

We experimentally measured expression time courses of 21 different DUSPs between 0 and 24 h following Herceptin treatment of human MDA-MB-453 HER2-positive breast cancer cells. We clustered these time courses into patterns of similar dynamics over time. In parallel, we built a series of Boolean models representing the known regulatory mechanisms of DUSPs and then demonstrated that the dynamics predicted by the models is in agreement with the experimental data. Furthermore, we used the models to predict regulatory mechanisms of DUSPs, where these mechanisms were partially known.

Conclusions

Boolean modelling is a powerful technique to investigate and understand signalling pathways. We obtained an understanding of different regulatory pathways in breast cancer and new insights on how these signalling pathways are activated. This method can be generalized to other drugs and longer time courses to better understand how resistance to drugs develops in cancer cells over time.

     

阿霉素抗4T1乳腺癌荷瘤小鼠的免疫调控机制

为了探讨阿霉素 (Adriamycin,ADM) 对4T1乳腺癌荷瘤鼠BALB/c的免疫调节作用,采用定量蛋白质组学串联质量标签 (TMT) 标记技术检测ADM对4T1乳腺癌差异蛋白的影响,利用多重数据库对差异蛋白进行生物信息学分析。根据蛋白质组学结果,寻找差异蛋白中与免疫调节功能相关的靶点,通过酶联免疫吸附测定 (Enzyme linked immunosorbent assay,ELISA) 观察ADM对乳腺癌组织中Th1细胞 (Helper T cells 1,Th1) 和Th2细胞 (Helper T cells 2,Th2) 的影响;通过流式细胞术分析ADM对CD4+ T细胞、CD8+ T细胞和调节性T细胞 (Regulatory T cells,Tregs) 的影响;HE染色观察ADM对4T1乳腺癌荷瘤鼠胸腺的改变。ADM上调170种差异蛋白,下调58种差异蛋白。有73种差异蛋白与免疫调控过程相关,KEGG (Kyoto encyclopedia of genes and genomes,KEGG) 富集于细胞因子及受体相关的重要蛋白通路、白介素17 (Interleukin 17,IL-17) 通路和癌症的转录调控通路。与免疫功能相关的差异蛋白与CD4+ T细胞、CD8+ T细胞和Tregs细胞的功能有关,而这些细胞的分型影响乳腺癌的预后。ADM极显著升高白介素2 (Interleukin 2,IL-2),CD4+ T细胞、CD8+ T淋巴细胞含量 (P<0.01),显著降低Tregs细胞含量 (P<0.05)。ADM抗乳腺癌的免疫调节蛋白有Ighm、Igkc、S100A8、S100A9和Tmsb4x。     

Modeling of Cancer Stem Cell State Transitions Predicts Therapeutic Response

Cancer stem cells (CSCs) possess capacity to both self-renew and generate all cells within a tumor, and are thought to drive tumor recurrence. Targeting the stem cell niche to eradicate CSCs represents an important area of therapeutic development. The complex nature of many interacting elements of the stem cell niche, including both intracellular signals and microenvironmental growth factors and cytokines, creates a challenge in choosing which elements to target, alone or in combination. Stochastic stimulation techniques allow for the careful study of complex systems in biology and medicine and are ideal for the investigation of strategies aimed at CSC eradication. We present a mathematical model of the breast cancer stem cell (BCSC) niche to predict population dynamics during carcinogenesis and in response to treatment. Using data from cell line and mouse xenograft experiments, we estimate rates of interconversion between mesenchymal and epithelial states in BCSCs and find that EMT/MET transitions occur frequently. We examine bulk tumor growth dynamics in response to alterations in the rate of symmetric self-renewal of BCSCs and find that small changes in BCSC behavior can give rise to the Gompertzian growth pattern observed in breast tumors. Finally, we examine stochastic reaction kinetic simulations in which elements of the breast cancer stem cell niche are inhibited individually and in combination. We find that slowing self-renewal and disrupting the positive feedback loop between IL-6, Stat3 activation, and NF-κB signaling by simultaneous inhibition of IL-6 and HER2 is the most effective combination to eliminate both mesenchymal and epithelial populations of BCSCs. Predictions from our model and simulations show excellent agreement with experimental data showing the efficacy of combined HER2 and Il-6 blockade in reducing BCSC populations. Our findings will be directly examined in a planned clinical trial of combined HER2 and IL-6 targeted therapy in HER2-positive breast cancer.     

A unified model of sigmoid tumour growth based on cell proliferation and quiescence

Abstract.   Objectives : A class of sigmoid functions designated generalized von Bertalanffy, Gompertzian and generalized Logistic has been used to fit tumour growth data. Various models have been proposed to explain the biological significance and foundations of these functions. However, no model has been found to fully explain all three or the relationships between them. Materials and Methods : We propose a simple cancer cell population dynamics model that provides a biological interpretation for these sigmoids' ability to represent tumour growth. Results and Conclusions : We show that the three sigmoids can be derived from the model and are in fact a single solution subject to the continuous variation of parameters describing the decay of the proliferation fraction and/or cell quiescence. We use the model to generate proliferation fraction profiles for each sigmoid and comment on the significance of the differences relative to cell cycle-specific and non-cell cycle-specific therapies.     

A structured model and likelihood approach to estimate yeast prion propagon replication rates and their asymmetric transmission

Prion proteins cause a variety of fatal neurodegenerative diseases in mammals but are generally harmless to Baker’s yeast (Saccharomyces cerevisiae). This makes yeast an ideal model organism for investigating the protein dynamics associated with these diseases. The rate of disease onset is related to both the replication and transmission kinetics of propagons, the transmissible agents of prion diseases. Determining the kinetic parameters of propagon replication in yeast is complicated because the number of propagons in an individual cell depends on the intracellular replication dynamics and the asymmetric division of yeast cells within a growing yeast cell colony. We present a structured population model describing the distribution and replication of prion propagons in an actively dividing population of yeast cells. We then develop a likelihood approach for estimating the propagon replication rate and their transmission bias during cell division. We first demonstrate our ability to correctly recover known kinetic parameters from simulated data, then we apply our likelihood approach to estimate the kinetic parameters for six yeast prion variants using propagon recovery data. We find that, under our modeling framework, all variants are best described by a model with an asymmetric transmission bias. This demonstrates the strength of our framework over previous formulations assuming equal partitioning of intracellular constituents during cell division.     

Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments

It is well known that tumor and its microenvironment, or stroma, interact with each other and that this interaction plays a critical role in tumor initiation, growth, and metastasis. This interaction consists of complex relations between tumor cells, stromal cells such as fibroblasts, epithelial cells and immunocytes, the vascular system, the extracellular matrix, and cytokines secreted by the cells. Understanding these relationships may lead to new therapeutic approaches to cancer. In the present paper, we consider tumor-stroma crosstalk in a simple in vitro situation which involves interaction between tumor epithelial cells from breast cancer and a microenvironment consisting of just fibroblasts. The two populations of cells are separated by a semi-permeable membrane that allows only cytokines to cross over. We develop a mathematical model that includes two critical growth factors: TGF-β, produced by the tumor cells, and EGF, secreted by the fibroblasts. The TGF-β modifies the microenvironment by transforming fibroblasts into myofibroblasts. Myofibroblasts secrete higher concentrations of EGF than fibroblasts, thereby, increasing the proliferation of tumor cells. Thus already in this simple setup one sees a mutual interaction between tumor cells and their microenvironment. We conducted experiments which show good agreement with the model’s simulations, hence confirming the model’s ability to predict aspects of tumor cell behavior in response to signaling from fibroblasts.     

Osteoblasts are a major source of inflammatory cytokines in the tumor microenvironment of bone metastatic breast cancer

Metastatic breast cancer cells co‐opt the cells of the bone to increase their production of inflammatory cytokines. Here, we sought to identify key cytokines expressed by osteoblasts in vitro and in vivo in the presence of MDA‐MB‐231 metastatic breast cancer cells, including a bone‐seeking variant. We hypothesized that osteoblast‐derived cytokines increase in the presence of metastatic breast cancer cell conditioned medium (CM), act as chemoattractants for cancer cells, and enhance osteoclast formation. We detected increases in the concentrations of osteoblast‐derived IL‐6, MCP‐1, VEGF, MIP‐2, and KC in vitro in culture supernatants from MC3T3‐E1 cells in the presence of metastatic breast cancer cell CM and from cancer‐bearing femurs ex vivo. A comparison of cancer cell‐ and osteoblast‐derived cytokines revealed that while breast cancer cells expressed the same or equivalent cytokines as the osteoblasts, the breast cancer cells only produced picogram quantities of MCP‐1; osteoblasts expressed nanogram amounts. Bone‐derived MCP‐1 increased in the proximal metaphysis, an area where breast cancer cells preferentially trafficked following intracardiac inoculation in athymic mice. An MDA‐MB‐231 bone‐seeking variant was not different from parental lines. Osteoblast CM was a potent chemoattractant for metastatic breast cancer cells. Furthermore, culture supernatants of osteoblasts treated with breast cancer cell CM enhanced osteoclast formation. These findings suggest that bone metastatic breast cancer cells utilize osteoblast‐derived cytokines to facilitate breast cancer cell colonization and survival upon arrival in the bone microenvironment. J. Cell. Biochem. 111: 1138–1148, 2010. © 2010 Wiley‐Liss, Inc.     

A Poisson mixture model to identify changes in RNA polymerase II binding quantity using high-throughput sequencing technology

We present a mixture model-based analysis for identifying differences in the distribution of RNA polymerase II (Pol II) in transcribed regions, measured using ChIP-seq (chromatin immunoprecipitation following massively parallel sequencing technology). The statistical model assumes that the number of Pol II-targeted sequences contained within each genomic region follows a Poisson distribution. A Poisson mixture model was then developed to distinguish Pol II binding changes in transcribed region using an empirical approach and an expectation-maximization (EM) algorithm developed for estimation and inference. In order to achieve a global maximum in the M-step, a particle swarm optimization (PSO) was implemented. We applied this model to Pol II binding data generated from hormone-dependent MCF7 breast cancer cells and antiestrogen-resistant MCF7 breast cancer cells before and after treatment with 17beta-estradiol (E2). We determined that in the hormone-dependent cells, approximately 9.9% (2527) genes showed significant changes in Pol II binding after E2 treatment. However, only approximately 0.7% (172) genes displayed significant Pol II binding changes in E2-treated antiestrogen-resistant cells. These results show that a Poisson mixture model can be used to analyze ChIP-seq data.     

Serum uPAR as Biomarker in Breast Cancer Recurrence: A Mathematical Model

There are currently over 2.5 million breast cancer survivors in the United States and, according to the American Cancer Society, 10 to 20 percent of these women will develop recurrent breast cancer. Early detection of recurrence can avoid unnecessary radical treatment. However, self-examination or mammography screening may not discover a recurring cancer if the number of surviving cancer cells is small, while biopsy is too invasive and cannot be frequently repeated. It is therefore important to identify non-invasive biomarkers that can detect early recurrence. The present paper develops a mathematical model of cancer recurrence. The model, based on a system of partial differential equations, focuses on tissue biomarkers that include the plasminogen system. Among them, only uPAR is known to have significant correlation to its concentration in serum and could therefore be a good candidate for serum biomarker. The model includes uPAR and other associated cytokines and cells. It is assumed that the residual cancer cells that survived primary cancer therapy are concentrated in the same location within a region with a very small diameter. Model simulations establish a quantitative relation between the diameter of the growing cancer and the total uPAR mass in the cancer. This relation is used to identify uPAR as a potential serum biomarker for breast cancer recurrence.     

Enhanced expression of Rab27A gene by breast cancer cells promoting invasiveness and the metastasis potential by secretion of insulin-like growth factor-II

In addition to the functions of transporting melanosome in melanocytes and releasing contents of lytic granules in CTLs, Rab27A was recently shown to be involved in exocytosis of insulin and chromaffin granules in endocrine cells; it was also reported to be expressed in an exceptionally broad range of specialized secretory cells. As autocrine and paracrine cytokines are essential for invasion and metastasis in some solid tumors, blocking them may be an effective strategy to prevent tumor dissemination. In the present study, we show that Rab27A is associated with invasive and metastatic potentials of human breast cancer cells. The overexpression of Rab27A protein redistributed the cell cycle and increased the invasive and metastatic abilities in breast cancer cells both in vitro and in vivo. We also certified that Rab27A conferred the invasive and metastatic phenotypes on breast cancer cells by promoting the secretion of insulin-like growth factor-II (IGF-II), which regulates the expression of p16, vascular endothelial growth factor, matrix metalloproteinase-9, cathepsin D, cyclin D1, and urokinase-type plasminogen activator. These data provide functional evidence that Rab27A acts as a novel mediator of invasion and metastasis promotion in human breast cancer cells, at least in part, through regulating the secretion of IGF-II, suggesting that synergistic suppression of Rab27A and IGF-II activities holds a promise for preventing breast cancer invasion and metastasis.     

A mathematical model of breast cancer development, local treatment and recurrence

Cancer development is a stepwise process through which normal somatic cells acquire mutations which enable them to escape their normal function in the tissue and become self-sufficient in survival. The number of mutations depends on the patient's age, genetic susceptibility and on the exposure of the patient to carcinogens throughout their life. It is believed that in every malignancy 4-6 crucial similar mutations have to occur on cancer-related genes. These genes are classified as oncogenes and tumour suppressor genes (TSGs) which gain or lose their function respectively, after they have received one mutative hit or both of their alleles have been knocked out. With the acquisition of each of the necessary mutations the transformed cell gains a selective advantage over normal cells, and the mutation will spread throughout the tissue via clonal expansion. We present a simplified model of this mutation and expansion process, in which we assume that the loss of two TSGs is sufficient to give rise to a cancer. Our mathematical model of the stepwise development of breast cancer verifies the idea that the normal mutation rate in genes is only sufficient to give rise to a tumour within a clinically observable time if a high number of breast stem cells and TSGs exist or genetic instability is involved as a driving force of the mutation pathway. Furthermore, our model shows that if a mutation occurred in stem cells pre-puberty, and formed a field of cells with this mutation through clonal formation of the breast, it is most likely that a tumour will arise from within this area. We then apply different treatment strategies, namely surgery and adjuvant external beam radiotherapy and targeted intraoperative radiotherapy (TARGIT) and use the model to identify different sources of local recurrence and analyse their prevention.     

A checkpoint-oriented cell cycle simulation model

Modeling and in silico simulations are of major conceptual and applicative interest in studying the cell cycle and proliferation in eukaryotic cells. In this paper, we present a cell cycle checkpoint-oriented simulator that uses agent-based simulation modeling to reproduce the dynamics of a cancer cell population in exponential growth. Our in silico simulations were successfully validated by experimental in vitro supporting data obtained with HCT116 colon cancer cells. We demonstrated that this model can simulate cell confluence and the associated elongation of the G1 phase. Using nocodazole to synchronize cancer cells at mitosis, we confirmed the model predictivity and provided evidence of an additional and unexpected effect of nocodazole on the overall cell cycle progression. We anticipate that this cell cycle simulator will be a potential source of new insights and research perspectives.     

An ordinary differential equation model for the multistep transformation to cancer

Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the transformation of normal cells to malignant cells. In doing so, we derive an ordinary differential equation model that explores how the balance of angiogenesis, cell death rates, genetic instability, and replication rates give rise to different kinetics in the development of cancer. The key predictions of the model are that cancer develops fastest through a particular ordering of mutations and that mutations in genes that maintain genomic integrity would be the most deleterious type of mutations to inherit. In addition, we perform a sensitivity analysis on the parameters included in the model to determine the probable contribution of each. This paper presents a novel approach to viewing the genetic basis of cancer from a systems biology perspective and provides the groundwork for other models that can be directly tied to clinical and molecular data.