A Predictive Mathematical Modeling Approach for the Study of Doxorubicin Treatment in Triple Negative Breast Cancer

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.

Nonlinear dynamics of estrogen receptor-positive breast cancer integrating experimental data: A novel spatial modeling approach

Oncology research has focused extensively on estrogen hormones and their function in breast cancer proliferation. Mathematical modeling is essential for the analysis and simulation of breast cancers. This research presents a novel approach to examine the therapeutic and inhibitory effects of hormone and estrogen therapies on the onset of breast cancer. Our proposed mathematical model comprises a nonlinear coupled system of partial differential equations, capturing intricate interactions among estrogen, cytotoxic T lymphocytes, dormant cancer cells, and active cancer cells. The model's parameters are meticulously estimated through experimental studies, and we conduct a comprehensive global sensitivity analysis to assess the uncertainty of these parameter values. Remarkably, our findings underscore the pivotal role of hormone therapy in curtailing breast tumor growth by blocking estrogen's influence on cancer cells. Beyond this crucial insight, our proposed model offers an integrated framework to delve into the complexity of tumor progression and immune response under hormone therapy. We employ diverse experimental datasets encompassing gene expression profiles, spatial tumor morphology, and cellular interactions. Integrating multidimensional experimental data with mathematical models enhances our understanding of breast cancer dynamics and paves the way for personalized treatment strategies. Our study advances our comprehension of estrogen receptor-positive breast cancer and exemplifies a transformative approach that merges experimental data with cutting-edge mathematical modeling. This framework promises to illuminate the complexities of cancer progression and therapy, with broad implications for oncology.

Analysis and modeling of cancer drug responses using cell cycle phase-specific rate effects

Identifying effective therapeutic treatment strategies is a major challenge to improving outcomes for patients with breast cancer. To gain a comprehensive understanding of how clinically relevant anti-cancer agents modulate cell cycle progression, here we use genetically engineered breast cancer cell lines to track drug-induced changes in cell number and cell cycle phase to reveal drug-specific cell cycle effects that vary across time. We use a linear chain trick (LCT) computational model, which faithfully captures drug-induced dynamic responses, correctly infers drug effects, and reproduces influences on specific cell cycle phases. We use the LCT model to predict the effects of unseen drug combinations and confirm these in independent validation experiments. Our integrated experimental and modeling approach opens avenues to assess drug responses, predict effective drug combinations, and identify optimal drug sequencing strategies.

Mathematical Model of Triple-Negative Breast Cancer in Response to Combination Chemotherapies

Triple-negative breast cancer (TNBC) is a heterogenous disease that is defined by its lack of targetable receptors, thus limiting treatment options and resulting in higher rates of metastasis and recurrence. Combination chemotherapy treatments, which inhibit tumor cell proliferation and regeneration, are a major component of standard-of-care treatment of TNBC. In this manuscript, we build a coupled ordinary differential equation model of TNBC with compartments that represent tumor proliferation, necrosis, apoptosis, and immune response to computationally describe the biological tumor affect to a combination of chemotherapies, doxorubicin (DRB) and paclitaxel (PTX). This model is parameterized using longitudinal [18F]-fluorothymidine positron emission tomography (FLT-PET) imaging data which allows for a noninvasive molecular imaging approach to quantify the tumor proliferation and tumor volume measurements for two murine models of TNBC. Animal models include a human cell line xenograft model, MDA-MB-231, and a syngeneic 4T1 mammary carcinoma model. The mathematical models are parameterized and the percent necrosis at the end time point is predicted and validated using histological hematoxylin and eosin (H&E) data. Global Sobol' sensitivity analysis is conducted to further understand the role each parameter plays in the model's goodness of fit to the data. In both the MDA-MB-231 and the 4T1 tumor models, the designed mathematical model can accurately describe both tumor volume changes and final necrosis volume. This can give insight into the ordering, dosing, and timing of DRB and PTX treatment. More importantly, this model can also give insight into future novel combinations of therapies and how the immune system plays a role in therapeutic response to TNBC, due to its calibration to two types of TNBC murine models.

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.

A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation

The mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer’s disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharmacological options to block the mevalonate pathway in cancer cells, one of which is zoledronic acid (ZA) (an N-bisphosphonate (N-BP)), which inhibits the farnesyl pyrophosphate (FPP) synthase enzyme, inducing cell cycle arrest, apoptosis, inhibition of protein prenylation, and cholesterol reduction, as well as leading to the accumulation of isopentenyl pyrophosphate (IPP). We extrapolated the data based on two independently published papers that provide numerical data on the uptake of zoledronic acid (ZA) and the accumulation of IPP (Ag) and its isomer over time by using in vitro human cell line models. Two different mathematical models for IPP kinetics are proposed. The first model (Model 1) is a simpler ordinary differential equation (ODE) compartmental system composed of 3 equations with 10 parameters; the second model (Model 2) is a differential algebraic equation (DAE) system with 4 differential equations, 1 algebraic equation and 13 parameters incorporating the formation of the ZA+enzyme+Ag complex. Each of the two models aims to describe two different experimental situations (continuous and pulse experiments) with the same ZA kinetics. Both models fit the collected data very well. With Model 1, we obtained a prevision accumulation of IPP after 24 h of 169.6 pmol/mgprot/h with an IPP decreasing rate per (pmol/mgprot) of ZA (kXGZ) equal to 13.24/h. With Model 2, we have comprehensive kinetics of IPP upon ZA treatment. We calculate that the IPP concentration was equal to 141.6 pmol/mgprot/h with a decreasing rate/percentage of 0.051 (kXGU). The present study is the first to quantify the influence of ZA on the pharmacodynamics of IPP. While still incorporating a small number of parameters, Model 2 better represents the complexity of the biological behaviour for calculating the IPP produced in different situations, such as studies on γδ T cell-based immunotherapy. In the future, additional clinical studies are warranted to further evaluate and fine-tune dosing approaches.

Combined effects of pioglitazone and doxorubicin on migration and invasion of MDA-MB-231 breast cancer cells

BACKGROUND

Despite antitumor properties, chemotherapy medication can create conditions in tumor cells that work in favor of the tumor. Doxorubicin, commonly prescribed chemotherapy agents, can increase the risk of migration and invasion of tumor cells through overexpression of the CXCR4 gene by affecting downstream signaling pathways. The regulatory role of CXCR7 on CXCR4 function has been demonstrated. Therefore, it is hypothesized that combining doxorubicin with another anticancer drug could be a promising approach.

METHODS

In this research, we evaluated the anti-invasive property of pioglitazone along with antitumor effects of doxorubicin on MDA-MB-231 breast cancer cell lines.

RESULTS

There was no significant difference between two treatment groups in neither the expression nor changes in the expression of CXCR7 and CXCR4 genes (P < 0.05). Pioglitazone-doxorubicin combination reduced cell migration in tumor cells to a significantly higher extent compared to doxorubicin alone (P < 0.05).

CONCLUSIONS

Co-administration of pioglitazone and doxorubicin might reduce cell migration in breast cancer tumor cells, and that cell migration function is independent of some specific proteins.

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.

Acquired chemoresistance is a common cause of treatment failure in cancer. The scheduling of a multi-dose course of chemotherapeutic treatment may influence the dynamics of acquired chemoresistance, and drug schedule optimization may increase the duration of effectiveness of a particular chemotherapeutic agent for a particular patient. Here we present a method for experimentally optimizing an in vitro drug schedule through iterative rounds of experimentation and computational analysis, and demonstrate the method’s ability to improve the performance of doxorubicin treatment in three breast carcinoma cell lines. Specifically, we find that the interval between drug exposures can be optimized while holding drug concentration and number of treatments constant, suggesting that this may be a key variable to explore in future drug schedule optimization efforts. We further use this method’s model calibration and selection process to extract information about the underlying biology of the doxorubicin response, and find that the incorporation of delays on both cell death and regrowth are necessary for accurate parameterization of cell growth data.

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.

Evaluation of Cancer Cell Lines by Four-Point Probe Technique, by Impedance Measurements in Various Frequencies

Cell-based biosensors appear to be an attractive tool for the rapid, simple, and cheap monitoring of chemotherapy effects at a very early stage. In this study, electrochemical measurements using a four-point probe method were evaluated for suspensions of four cancer cell lines of different tissue origins: SK-N-SH, HeLa, MCF-7 and MDA-MB-231, all for two different population densities: 50 K and 100 K cells/500 μL. The anticancer agent doxorubicin was applied for each cell type in order to investigate whether the proposed technique was able to determine specific differences in cell responses before and after drug treatment. The proposed methodology can offer valuable insight into the frequency-dependent bioelectrical responses of various cellular systems using a low frequency range and without necessitating lengthy cell culture treatment. The further development of this biosensor assembly with the integration of specially designed cell/electronic interfaces can lead to novel diagnostic biosensors and therapeutic bioelectronics.

A Quantitative Systems Pharmacology Framework for Optimal Doxorubicin Granulocyte Colony-Stimulating Factor Regimens in Triple-Negative Breast Cancer

INTRODUCTION

To mitigate the risk of neutropenia during chemotherapy treatment of triple-negative breast cancer, prophylactic and supportive therapy with granulocyte colony-stimulating factor (G-CSF) is administered concomitant to chemotherapy. The proper timing of combined chemotherapy and G-CSF is crucial for treatment outcomes.

METHODS

Leveraging our established mathematical model of neutrophil production by G-CSF, we developed quantitative systems pharmacology (QSP) framework to investigate how modulating chemotherapy dose frequency and intensity can maximize antitumour effects. To establish schedules that best control tumour size while minimizing neutropenia, we combined Gompertzian tumour growth with pharmacokinetic/pharmacodynamic models of doxorubicin and G-CSF, and our QSP model of neutrophil production.

RESULTS

We optimized a range of chemotherapeutic cycle lengths and dose sizes to establish regimens that simultaneously reduced tumour burden while minimizing neutropenia. Our results suggest that cytotoxic chemotherapy with doxorubicin 45 mg/m2 every 14 days provides effective control of tumour growth while mitigating neutropenic risks.

CONCLUSION

This work suggests future avenues for optimal regimens of chemotherapy with prophylactic G-CSF support. Importantly, the algorithmic approach that we developed can aid in balancing the anticancer and the neutropenic effects of both drugs, and therefore contributes to rational considerations in clinical decision-making in triple-negative breast cancer.

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.

Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical-experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth-conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

Breast cancer is one of the major causes of mortality in women worldwide. The most aggressive breast cancer subtypes are human epidermal growth factor receptor-positive (HER2+) and triple-negative breast cancers. Therapies targeting HER2 receptors have significantly improved HER2+ breast cancer patient outcomes. However, several recent studies have pointed out the deficiency of existing treatment protocols in combatting disease relapse and improving response rates to treatment. Overriding the inherent actions of the immune system to detect and annihilate cancer via the immune checkpoint pathways is one of the important hallmarks of cancer. Thus, restoration of these pathways by various means of immunomodulation has shown beneficial effects in the management of various types of cancers, including breast. We herein review the recent progress in the management of HER2+ breast cancer via HER2-targeted therapies, and its association with the programmed death receptor-1 (PD-1)/programmed death ligand-1 (PD-L1) axis. In order to link research in the areas of medicine and mathematics and point out specific opportunities for providing efficient theoretical analysis related to HER2+ breast cancer management, we also review mathematical models pertaining to the dynamics of HER2+ breast cancer and immune checkpoint inhibitors.

Experimentally-driven mathematical modeling to improve combination targeted and cytotoxic therapy for HER2+ breast cancer

The goal of this study is to experimentally and computationally investigate combination trastuzumab-paclitaxel therapies and identify potential synergistic effects due to sequencing of the therapies with in vitro imaging and mathematical modeling. Longitudinal alterations in cell confluence are reported for an in vitro model of BT474 HER2+ breast cancer cells following various dosages and timings of paclitaxel and trastuzumab combination regimens. Results of combination drug regimens are evaluated for drug interaction relationships based on order, timing, and quantity of dose of the drugs. Altering the order of treatments, with the same total therapeutic dose, provided significant changes in overall cell confluence (p < 0.001). Two mathematical models are introduced that are constrained by the in vitro data to simulate the tumor cell response to the individual therapies. A collective model merging the two individual drug response models was designed to investigate the potential mechanisms of synergy for paclitaxel-trastuzumab combinations. This collective model shows increased synergy for regimens where trastuzumab is administered prior to paclitaxel and suggests trastuzumab accelerates the cytotoxic effects of paclitaxel. The synergy derived from the model is found to be in agreement with the combination index, where both indicate a spectrum of additive and synergistic interactions between the two drugs dependent on their dose order. The combined in vitro results and development of a mathematical model of drug synergy has potential to evaluate and improve standard-of-care combination therapies in cancer.

Systems biology: perspectives on multiscale modeling in research on endocrine-related cancers

Drawing on concepts from experimental biology, computer science, informatics, mathematics and statistics, systems biologists integrate data across diverse platforms and scales of time and space to create computational and mathematical models of the integrative, holistic functions of living systems. Endocrine-related cancers are well suited to study from a systems perspective because of the signaling complexities arising from the roles of growth factors, hormones and their receptors as critical regulators of cancer cell biology and from the interactions among cancer cells, normal cells and signaling molecules in the tumor microenvironment. Moreover, growth factors, hormones and their receptors are often effective targets for therapeutic intervention, such as estrogen biosynthesis, estrogen receptors or HER2 in breast cancer and androgen receptors in prostate cancer. Given the complexity underlying the molecular control networks in these cancers, a simple, intuitive understanding of how endocrine-related cancers respond to therapeutic protocols has proved incomplete and unsatisfactory. Systems biology offers an alternative paradigm for understanding these cancers and their treatment. To correctly interpret the results of systems-based studies requires some knowledge of how in silico models are built, and how they are used to describe a system and to predict the effects of perturbations on system function. In this review, we provide a general perspective on the field of cancer systems biology, and we explore some of the advantages, limitations and pitfalls associated with using predictive multiscale modeling to study endocrine-related cancers.

Leveraging Mathematical Modeling to Quantify Pharmacokinetic and Pharmacodynamic Pathways: Equivalent Dose Metric

Treatment response assays are often summarized by sigmoidal functions comparing cell survival at a single timepoint to applied drug concentration. This approach has a limited biophysical basis, thereby reducing the biological insight gained from such analysis. In particular, drug pharmacokinetic and pharmacodynamic (PK/PD) properties are overlooked in developing treatment response assays, and the accompanying summary statistics conflate these processes. Here, we utilize mathematical modeling to decouple and quantify PK/PD pathways. We experimentally modulate specific pathways with small molecule inhibitors and filter the results with mechanistic mathematical models to obtain quantitative measures of those pathways. Specifically, we investigate the response of cells to time-varying doxorubicin treatments, modulating doxorubicin pharmacology with small molecules that inhibit doxorubicin efflux from cells and DNA repair pathways. We highlight the practical utility of this approach through proposal of the “equivalent dose metric.” This metric, derived from a mechanistic PK/PD model, provides a biophysically-based measure of drug effect. We define equivalent dose as the functional concentration of drug that is bound to the nucleus following therapy. This metric can be used to quantify drivers of treatment response and potentially guide dosing of combination therapies. We leverage the equivalent dose metric to quantify the specific intracellular effects of these small molecule inhibitors using population-scale measurements, and to compare treatment response in cell lines differing in expression of drug efflux pumps. More generally, this approach can be leveraged to quantify the effects of various pharmaceutical and biologic perturbations on treatment response.

Modelling changes in glutathione homeostasis as a function of quinone redox metabolism

Redox cycling is an understated mechanism of toxicity associated with a plethora of xenobiotics, responsible for preventing the effective treatment of serious conditions such as malaria and cardiomyopathy. Quinone compounds are notorious redox cyclers, present in drugs such as doxorubicin, which is used to treat a host of human cancers. However, the therapeutic index of doxorubicin is undermined by dose-dependent cardiotoxicity, which may be a function of futile redox cycling. In this study, a doxorubicin-specific in silico quinone redox metabolism model is described. Doxorubicin-GSH adduct formation kinetics are thermodynamically estimated from its reduction potential, while the remainder of the model is parameterised using oxygen consumption rate data, indicative of hydroquinone auto-oxidation. The model is then combined with a comprehensive glutathione metabolism model, facilitating the simulation of quinone redox cycling, and adduct-induced GSH depletion. Simulations suggest that glutathione pools are most sensitive to exposure duration at pharmacologically and supra-pharmacologically relevant doxorubicin concentrations. The model provides an alternative method of investigating and quantifying redox cycling induced oxidative stress, circumventing the experimental difficulties of measuring and tracking radical species. This in silico framework provides a platform from which GSH depletion can be explored as a function of a compound’s physicochemical properties.

The impact of tumor receptor heterogeneity on the response to anti-angiogenic cancer treatment

Multiple promoters and inhibitors mediate angiogenesis, the formation of new blood vessels, and these factors represent potential targets for impeding vessel growth in tumors. Vascular endothelial growth factor (VEGF) is a potent angiogenic factor targeted in anti-angiogenic cancer therapies. In addition, thrombospondin-1 (TSP1) is a major endogenous inhibitor of angiogenesis, and TSP1 mimetics are being developed as an alternative type of anti-angiogenic agent. The combination of bevacizumab, an anti-VEGF agent, and ABT-510, a TSP1 mimetic, has been tested in clinical trials to treat advanced solid tumors. However, the patients' responses are highly variable and show disappointing outcomes. To obtain mechanistic insight into the effects of this combination anti-angiogenic therapy, we have constructed a novel whole-body systems biology model including the VEGF and TSP1 reaction networks. Using this molecular-detailed model, we investigated how the combination anti-angiogenic therapy changes the amounts of pro-angiogenic and anti-angiogenic complexes in cancer patients. We particularly focus on answering the question of how the effect of the combination therapy is influenced by tumor receptor expression, one aspect of patient-to-patient variability. Overall, this model complements the clinical administration of combination anti-angiogenic therapy, highlights the role of tumor receptor variability in the heterogeneous responses to anti-angiogenic therapy, and identifies the tumor receptor profiles that correlate with a high likelihood of a positive response to the combination therapy. Our model provides novel understanding of the VEGF-TSP1 balance in cancer patients at the systems-level and could be further used to optimize combination anti-angiogenic therapy.

Mathematical models of tumor cell proliferation: A review of the literature

INTRODUCTION

A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. Areas covered: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. Expert commentary: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

Antitumor properties of Salvianolic acid B against triple-negative and hormone receptor-positive breast cancer cells via ceramide-mediated apoptosis

Triple-negative breast cancer (TNBC) is an aggressive subtype of breast cancer with limited treatment options. It is urgent to develop new therapeutics against this disease. Salvinolic acid B (Sal-B) is a leading bioactive component of Salvia miltiorrhiza Bunge, a well-known Chinese medicine for treating various diseases without appreciable adverse effects. To understand the antitumor properties of Sal-B against TNBC, we analyzed its effects on the cell viability, cell cycle and apoptosis of triple-negative MDA-MB-231 cells with the hormone receptor-positive MCF-7 cells as the control. The in vitro analysis showed that Sal-B could significantly reduce the cell viability and suppress the proliferation of both MDA-MB-231 and MCF-7 cells with decreased cyclin B1 expression, but with no noticeable cell cycle phase change. In mouse models, Sal-B markedly inhibited the growth, decreased the PCNA expression, and increased the cell apoptosis of MDA-MB-231 tumor xenografts. To understand the antitumor mechanisms, we analyzed the expression levels of ceramides, and anti-apoptotic (Bcl-xL and survivin) and pro-apoptotic (caspase-3 and caspase-8) proteins. We found that Sal-B enhanced the ceramide accumulation and inhibited the anti-apoptotic protein expression. Interestingly, the ceramide accumulation was accompanied by decreased expression of glucosylceramide and GM3 synthases, two key enzymes regulating ceramide metabolism. These findings indicate that Sal-B exerts its antitumor effects at least partially by inducing the ceramide accumulation and ceramide-mediated apoptosis via inhibiting the expression of glucosylceramide and GM3 synthases, which was independent of estrogen receptor α. Sal-B appears to be a promising therapeutic agent against TNBC.

Calibration of Multi-Parameter Models of Avascular Tumor Growth Using Time Resolved Microscopy Data

Two of the central challenges of using mathematical models for predicting the spatiotemporal development of tumors is the lack of appropriate data to calibrate the parameters of the model, and quantitative characterization of the uncertainties in both the experimental data and the modeling process itself. We present a sequence of experiments, with increasing complexity, designed to systematically calibrate the rates of apoptosis, proliferation, and necrosis, as well as mobility, within a phase-field tumor growth model. The in vitro experiments characterize the proliferation and death of human liver carcinoma cells under different initial cell concentrations, nutrient availabilities, and treatment conditions. A Bayesian framework is employed to quantify the uncertainties in model parameters. The average difference between the calibration and the data, across all time points is between 11.54% and 14.04% for the apoptosis experiments, 7.33% and 23.30% for the proliferation experiments, and 8.12% and 31.55% for the necrosis experiments. The results indicate the proposed experiment-computational approach is generalizable and appropriate for step-by-step calibration of multi-parameter models, yielding accurate estimations of model parameters related to rates of proliferation, apoptosis, and necrosis.

A multi-state model of chemoresistance to characterize phenotypic dynamics in breast cancer

The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models' ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model's ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.

Variable Cell Line Pharmacokinetics Contribute to Non-Linear Treatment Response in Heterogeneous Cell Populations

We develop a combined experimental-mathematical framework to investigate heterogeneity in the context of breast cancer treated with doxorubicin. We engineer a cell line to over-express the multi-drug resistance 1 protein (MDR1), an ATP-dependent pump that effluxes intracellular drug. Co-culture experiments mixing the MDR1-overexpressing line with its parental line are evaluated via fluorescence microscopy. To quantify the impact of population heterogeneity on therapy response, these data are analyzed with a coupled pharmacokinetics/pharmacodynamics model. The proliferation and death rates of each line vary with co-culture condition (the relative fraction of each cell line at the time of seeding). For example, the death rate in the parental line under low-dose doxorubicin treatment is increased from 0.64 (± 0.22) × 10^-2 to 1.46 (± 0.58) × 10^-2 h^-1 with increasing fractions of MDR1-overexpressing cells. The growth rate of the MDR1-overexpressing line increases 29% as its relative fraction is decreased. Simulations of the pharmacokinetics/pharmacodynamics model suggest increased efflux from MDR1-overexpressing cells contributes to the increased death rate in the parental cells. Experimentally, the death rate of parental cells is constant across co-culture conditions under co-treatment with an MDR1 inhibitor. These data indicate that intercellular pharmacokinetic variability should be considered in analyzing treatment response in heterogeneous populations.

Translational models of tumor angiogenesis: A nexus of in silico and in vitro models

Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.