A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin.

Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.

Cellular barcoding tracks heterogeneous clones through selective pressures and phenotypic transitions.

Genomic DNA barcoding has emerged as a sensitive and flexible tool to measure the fates of clonal subpopulations within a heterogeneous cancer cell population. Coupling cellular barcoding with single-cell transcriptomics permits the longitudinal analysis of molecular mechanisms with detailed clone-level resolution. Numerous recent studies have employed these tools to track clonal cell states in cancer progression and treatment response. With these new technologies comes the opportunity to examine longstanding questions about the origins and contributions of tumor cell heterogeneity and the roles of selection and phenotypic plasticity in disease progression and treatment.

Modeling collective cell behavior in cancer: Perspectives from an interdisciplinary conversation.

Collective cell behavior contributes to all stages of cancer progression. Understanding how collective behavior emerges through cell-cell interactions and decision-making will advance our understanding of cancer biology and provide new therapeutic approaches. Here, we summarize an interdisciplinary discussion on multicellular behavior in cancer, draw lessons from other scientific disciplines, and identify future directions.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics.

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin.

The development of chemoresistance remains a significant cause of treatment failure in breast cancer. We posit that a mathematical understanding of chemoresistance could assist in developing successful treatment strategies. Towards that end, we have developed a model that describes the cytotoxic effects of the standard chemotherapeutic drug doxorubicin on the MCF-7 breast cancer cell line. We assume that treatment with doxorubicin induces a compartmentalization of the breast cancer cell population into surviving cells, which continue proliferating after treatment, and irreversibly damaged cells, which gradually transition from proliferating to treatment-induced death. The model is fit to experimental data including variations in drug concentration, inter-treatment interval, and number of doses. Our model recapitulates tumor cell dynamics in all these scenarios (as quantified by the concordance correlation coefficient, CCC > 0.95). In particular, superior tumor control is observed with higher doxorubicin concentrations, shorter inter-treatment intervals, and a higher number of doses (p < 0.05). Longer inter-treatment intervals require adapting the model parameterization after each doxorubicin dose, suggesting the promotion of chemoresistance. Additionally, we propose promising empirical formulas to describe the variation of model parameters as functions of doxorubicin concentration (CCC > 0.78). Thus, we conclude that our mathematical model could deepen our understanding of the cytotoxic effects of doxorubicin and could be used to explore practical drug regimens achieving optimal tumor control.

Quantification of long-term doxorubicin response dynamics in breast cancer cell lines to direct treatment schedules.

While acquired chemoresistance is recognized as a key challenge to treating many types of cancer, the dynamics with which drug sensitivity changes after exposure are poorly characterized. Most chemotherapeutic regimens call for repeated dosing at regular intervals, and if drug sensitivity changes on a similar time scale then the treatment interval could be optimized to improve treatment performance. Theoretical work suggests that such optimal schedules exist, but experimental confirmation has been obstructed by the difficulty of deconvolving the simultaneous processes of death, adaptation, and regrowth taking place in cancer cell populations. Here we present a method of optimizing drug schedules in vitro through iterative application of experimentally calibrated models, and demonstrate its ability to characterize dynamic changes in sensitivity to the chemotherapeutic doxorubicin in three breast cancer cell lines subjected to treatment schedules varying in concentration, interval between pulse treatments, and number of sequential pulse treatments. Cell populations are monitored longitudinally through automated imaging for 600-800 hours, and this data is used to calibrate a family of cancer growth models, each consisting of a system of ordinary differential equations, derived from the bi-exponential model which characterizes resistant and sensitive subpopulations. We identify a model incorporating both a period of growth arrest in surviving cells and a delay in the death of chemosensitive cells which outperforms the original bi-exponential growth model in Akaike Information Criterion based model selection, and use the calibrated model to quantify the performance of each drug schedule. We find that the inter-treatment interval is a key variable in determining the performance of sequential dosing schedules and identify an optimal retreatment time for each cell line which extends regrowth time by 40%-239%, demonstrating that the time scale of changes in chemosensitivity following doxorubicin exposure allows optimization of drug scheduling by varying this inter-treatment interval.

Functionalized Lineage Tracing for the Study and Manipulation of Heterogeneous Cell Populations.

The ability to track and isolate unique cell lineages from large heterogeneous populations increases the resolution at which cellular processes can be understood under normal and pathogenic states beyond snapshots obtained from single-cell RNA sequencing (scRNA-seq). Here, we describe the Control of Lineages by Barcode Enabled Recombinant Transcription (COLBERT) method in which unique single guide RNA (sgRNA) barcodes are used as functional tags to identify and recall specific lineages of interest. An sgRNA barcode is stably integrated and actively transcribed, such that all cellular progeny will contain the parental barcode and produce a functional sgRNA. The sgRNA barcode has all the benefits of a DNA barcode and added functionalities. Once a barcode pertaining to a lineage of interest is identified, the lineage of interest can be isolated using an activator variant of Cas9 (such as dCas9-VPR) and a barcode-matched sequence upstream of a fluorescent reporter gene. CRISPR activation of the fluorescent reporter will only occur in cells producing the matched sgRNA barcode, allowing precise identification and isolation of lineages of interest from heterogeneous populations.

Multifunctional barcoding with ClonMapper enables high-resolution study of clonal dynamics during tumor evolution and treatment.

Lineage-tracing methods have enabled characterization of clonal dynamics in complex populations, but generally lack the ability to integrate genomic, epigenomic and transcriptomic measurements with live-cell manipulation of specific clones of interest. We developed a functionalized lineage-tracing system, ClonMapper, which integrates DNA barcoding with single-cell RNA sequencing and clonal isolation to comprehensively characterize thousands of clones within heterogeneous populations. Using ClonMapper, we identified subpopulations of a chronic lymphocytic leukemia cell line with distinct clonal compositions, transcriptional signatures and chemotherapy survivorship trajectories; patterns that were also observed in primary human chronic lymphocytic leukemia. The ability to retrieve specific clones before, during and after treatment enabled direct measurements of clonal diversification and durable subpopulation transcriptional signatures. ClonMapper is a powerful multifunctional approach to dissect the complex clonal dynamics of tumor progression and therapeutic response.

Applications of high-resolution clone tracking technologies in cancer.

Tumors are comprised of dynamic, heterogenous cell populations characterized by numerous genetic and non-genetic alterations that accumulate and change with disease progression and treatment. Retrospective analyses of tumor evolution have relied on the measurement of genetic markers (such as copy number variants) to infer clonal dynamics. However, these approaches neglect the critical contributions of non-genetic drivers of disease. Techniques that harness the power of prospective clone tracking via heritable barcode tags provide an alternative strategy. In this review, we discuss methods for high-resolution, quantitative clone tracking, including recent advancements to pair barcode-specific functionality with scRNA-seq, clonal cell isolation, and in situ hybridization and imaging. We discuss these approaches in the context of cancer cell heterogeneity and treatment resistance.

An experimental-mathematical approach to predict tumor cell growth as a function of glucose availability in breast cancer cell lines.

We present the development and validation of a mathematical model that predicts how glucose dynamics influence metabolism and therefore tumor cell growth. Glucose, the starting material for glycolysis, has a fundamental influence on tumor cell growth. We employed time-resolved microscopy to track the temporal change of the number of live and dead tumor cells under different initial glucose concentrations and seeding densities. We then constructed a family of mathematical models (where cell death was accounted for differently in each member of the family) to describe overall tumor cell growth in response to the initial glucose and confluence conditions. The Akaikie Information Criteria was then employed to identify the most parsimonious model. The selected model was then trained on 75% of the data to calibrate the system and identify trends in model parameters as a function of initial glucose concentration and confluence. The calibrated parameters were applied to the remaining 25% of the data to predict the temporal dynamics given the known initial glucose concentration and confluence, and tested against the corresponding experimental measurements. With the selected model, we achieved an accuracy (defined as the fraction of measured data that fell within the 95% confidence intervals of the predicted growth curves) of 77.2 ± 6.3% and 87.2 ± 5.1% for live BT-474 and MDA-MB-231 cells, respectively.

A time-resolved experimental-mathematical model for predicting the response of glioma cells to single-dose radiation therapy.

PURPOSE: To develop and validate a mechanism-based, mathematical model that characterizes 9L and C6 glioma cells' temporal response to single-dose radiation therapy in vitro by explicitly incorporating time-dependent biological interactions with radiation. METHODS: We employed time-resolved microscopy to track the confluence of 9L and C6 glioma cells receiving radiation doses of 0, 2, 4, 6, 8, 10, 12, 14 or 16 Gy. DNA repair kinetics are measured by γH2AX expression via flow cytometry. The microscopy data (814 replicates for 9L, 540 replicates for C6 at various seeding densities receiving doses above) were divided into training (75%) and validation (25%) sets. A mechanistic model was developed, and model parameters were calibrated to the training data. The model was then used to predict the temporal dynamics of the validation set given the known initial confluences and doses. The predictions were compared to the corresponding dynamic microscopy data. RESULTS: For 9L, we obtained an average (± standard deviation, SD) Pearson correlation coefficient between the predicted and measured confluence of 0.87 ± 0.16, and an average (±SD) concordance correlation coefficient of 0.72 ± 0.28. For C6, we obtained an average (±SD) Pearson correlation coefficient of 0.90 ± 0.17, and an average (±SD) concordance correlation coefficient of 0.71 ± 0.24. CONCLUSION: The proposed model can effectively predict the temporal development of 9L and C6 glioma cells in response to a range of single-fraction radiation doses. By developing a mechanism-based, mathematical model that can be populated with time-resolved data, we provide an experimental-mathematical framework that allows for quantitative investigation of cells' temporal response to radiation. Our approach provides two key advances: (i) a time-resolved, dynamic death rate with a clear biological interpretation, and (ii) accurate predictions over a wide range of cell seeding densities and radiation doses.

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology.

We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

A hybrid model of tumor growth and angiogenesis: In silico experiments.

Tumor associated angiogenesis is the development of new blood vessels in response to proteins secreted by tumor cells. These new blood vessels allow tumors to continue to grow beyond what the pre-existing vasculature could support. Here, we construct a mathematical model to simulate tumor angiogenesis by considering each endothelial cell as an agent, and allowing the vascular endothelial growth factor (VEGF) and nutrient fields to impact the dynamics and phenotypic transitions of each tumor and endothelial cell. The phenotypes of the endothelial cells (i.e., tip, stalk, and phalanx cells) are selected by the local VEGF field, and govern the migration and growth of vessel sprouts at the cellular level. Over time, these vessels grow and migrate to the tumor, forming anastomotic loops to supply nutrients, while interacting with the tumor through mechanical forces and the consumption of VEGF. The model is able to capture collapsing and breaking of vessels caused by tumor-endothelial cell interactions. This is accomplished through modeling the physical interaction between the vasculature and the tumor, resulting in vessel occlusion and tumor heterogeneity over time due to the stages of response in angiogenesis. Key parameters are identified through a sensitivity analysis based on the Sobol method, establishing which parameters should be the focus of subsequent experimental efforts. During the avascular phase (i.e., before angiogenesis is triggered), the nutrient consumption rate, followed by the rate of nutrient diffusion, yield the greatest influence on the number and distribution of tumor cells. Similarly, the consumption and diffusion of VEGF yield the greatest influence on the endothelial and tumor cell numbers during angiogenesis. In summary, we present a hybrid mathematical approach that characterizes vascular changes via an agent-based model, while treating nutrient and VEGF changes through a continuum model. The model describes the physical interaction between a tumor and the surrounding blood vessels, explicitly allowing the forces of the growing tumor to influence the nutrient delivery of the vasculature.

Single cell transcriptome profiling of the human alcohol-dependent brain.

Alcoholism remains a prevalent health concern throughout the world. Previous studies have identified transcriptomic patterns in the brain associated with alcohol dependence in both humans and animal models. But none of these studies have systematically investigated expression within the unique cell types present in the brain. We utilized single nucleus RNA sequencing (snRNA-seq) to examine the transcriptomes of over 16 000 nuclei isolated from the prefrontal cortex of alcoholic and control individuals. Each nucleus was assigned to one of seven major cell types by unsupervised clustering. Cell type enrichment patterns varied greatly among neuroinflammatory-related genes, which are known to play roles in alcohol dependence and neurodegeneration. Differential expression analysis identified cell type-specific genes with altered expression in alcoholics. The largest number of differentially expressed genes (DEGs), including both protein-coding and non-coding, were detected in astrocytes, oligodendrocytes and microglia. To our knowledge, this is the first single cell transcriptome analysis of alcohol-associated gene expression in any species and the first such analysis in humans for any addictive substance. These findings greatly advance the understanding of transcriptomic changes in the brain of alcohol-dependent individuals.

Emerging Concepts and Tools in Cell Mechanomemory.

Studying a cell's ability to sense and respond to mechanical cues has emerged as a field unto itself over the last several decades, and this research area is now populated by engineers and biologists alike. As just one example of this cell mechanosensing, fibroblasts on soft substrates have slower growth rates, smaller spread areas, lower traction forces, and slower migration speeds compared to cells on stiff substrates. This phenomenon is not unique to fibroblasts, as these behaviors, and others, on soft substrates has been shown across a variety of cell types, and reproduced in many different labs. Thus far, the field has focused on discerning the mechanisms of cell mechanosensing through ion channels, focal adhesions and integrin-binding sites to the ECM, and the cell cytoskeleton. A relatively new concept in the field is that of mechanical memory, which refers to persistent effects of mechanical stimuli long after they have been removed from said stimulus. Here, we review this literature, provide an overview of emerging substrate fabrication approaches likely to be helpful for the field, and suggest the adaption of genetic tools for studying mechanical memory.

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect.

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

Single-cell RNA sequencing of lung adenocarcinoma reveals heterogeneity of immune response-related genes.

Immunotherapy has emerged as a promising approach to treat cancer. However, partial responses across multiple clinical trials support the significance of characterizing intertumor and intratumor heterogeneity to achieve better clinical results and as potential tools in selecting patients for different types of cancer immunotherapies. Yet, the type of heterogeneity that informs clinical outcome and patient selection has not been fully explored. In particular, the lack of characterization of immune response-related genes in cancer cells hinders the further development of metrics to select and optimize immunotherapy. Therefore, we analyzed single-cell RNA-Seq data from lung adenocarcinoma patients and cell lines to characterize the intratumor heterogeneity of immune response-related genes and demonstrated their potential impact on the efficacy of immunotherapy. We discovered that IFN-γ signaling pathway genes are heterogeneously expressed and coregulated with other genes in single cancer cells, including MHC class II (MHCII) genes. The downregulation of genes in IFN-γ signaling pathways in cell lines corresponds to an acquired resistance phenotype. Moreover, analysis of 2 groups of tumor-restricted antigens, namely neoantigens and cancer testis antigens, revealed heterogeneity in their expression in single cells. These analyses provide a rationale for applying multiantigen combinatorial therapies to prevent tumor escape and establish a basis for future development of prognostic metrics based on intratumor heterogeneity.

Control of Lineage-Specific Gene Expression by Functionalized gRNA Barcodes.

Lineage tracking delivers essential quantitative insight into dynamic, probabilistic cellular processes, such as somatic tumor evolution and differentiation. Methods for high diversity lineage quantitation rely on sequencing a population of DNA barcodes. However, manipulation of specific individual lineages is not possible with this approach. To address this challenge, we developed a functionalized lineage tracing tool, Control of Lineages by Barcode Enabled Recombinant Transcription (COLBERT), that enables high diversity lineage tracing and lineage-specific manipulation of gene expression. This modular platform utilizes expressed barcode gRNAs to both track cell lineages and direct lineage-specific gene expression.