A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment.

Targeting key regulators of the cancer stem cell phenotype to overcome their critical influence on tumor growth is a promising new strategy for cancer treatment. Here we present a modeling framework that operates at both the cellular and molecular levels, for investigating IL-6 mediated, cancer stem cell driven tumor growth and targeted treatment with anti-IL6 antibodies. Our immediate goal is to quantify the influence of IL-6 on cancer stem cell self-renewal and survival, and to characterize the subsequent impact on tumor growth dynamics. By including the molecular details of IL-6 binding, we are able to quantify the temporal changes in fractional occupancies of bound receptors and their influence on tumor volume. There is a strong correlation between the model output and experimental data for primary tumor xenografts. We also used the model to predict tumor response to administration of the humanized IL-6R monoclonal antibody, tocilizumab (TCZ), and we found that as little as 1mg/kg of TCZ administered weekly for 7 weeks is sufficient to result in tumor reduction and a sustained deceleration of tumor growth.

Modeling head and neck cancer stem cell-mediated tumorigenesis.

A large body of literature has emerged supporting the importance of cancer stem cells (CSCs) in the pathogenesis of head and neck cancers. CSCs are a subpopulation of cells within a tumor that share the properties of self-renewal and multipotency with stem cells from normal tissue. Their functional relevance to the pathobiology of cancer arises from the unique properties of tumorigenicity, chemotherapy resistance, and their ability to metastasize and invade distant tissues. Several molecular profiles have been used to discriminate a stem cell from a non-stem cell. CSCs can be grown for study and further enriched using a number of in vitro techniques. An evolving option for translational research is the use of mathematical and computational models to describe the role of CSCs in complex tumor environments. This review is focused discussing the evidence emerging from modeling approaches that have clarified the impact of CSCs to the biology of cancer.

A phase II trial of the BCL-2 homolog domain 3 mimetic AT-101 in combination with docetaxel for recurrent, locally advanced, or metastatic head and neck cancer.

BACKGROUND: AT-101 is a BCL-2 Homolog domain 3 mimetic previously demonstrated to have tumoricidal effects in advanced solid organ malignancies. Given the evidence of activity in xenograft models, treatment with AT-101 in combination with docetaxel is a therapeutic doublet of interest in metastatic head and neck squamous cell carcinoma. PATIENTS AND METHODS: Patients included in this trial had unresectable, recurrent, or distantly metastatic head and neck squamous cell carcinoma (R/M HNSCC) not amenable to curative radiation or surgery. This was an open label randomized, phase II trial in which patients were administered AT-101 in addition to docetaxel. The three treatment arms were docetaxel, docetaxel plus pulse dose AT-101, and docetaxel plus metronomic dose AT-101. The primary endpoint of this trial was overall response rate. RESULTS: Thirty-five patients were registered and 32 were evaluable for treatment response. Doublet therapy with AT-101 and docetaxel was well tolerated with only 2 patients discontinuing therapy due to treatment related toxicities. The overall response rate was 11 % (4 partial responses) with a clinical benefit rate of 74 %. Median progression free survival was 4.3 months (range: 0.7-13.7) and overall survival was 5.5 months (range: 0.4-24). No significant differences were noted between dosing strategies. CONCLUSION: Although met with a favorable toxicity profile, the addition of AT-101 to docetaxel in R/M HNSCC does not appear to demonstrate evidence of efficacy.

Dysregulated FGFR3 signaling alters the immune landscape in bladder cancer and presents therapeutic possibilities in an agent-based model.

Bladder cancer is an increasingly prevalent global disease that continues to cause morbidity and mortality despite recent advances in treatment. Immune checkpoint inhibitors (ICI) and fibroblast growth factor receptor (FGFR)-targeted therapeutics have had modest success in bladder cancer when used as monotherapy. Emerging data suggests that the combination of these two therapies could lead to improved clinical outcomes, but the optimal strategy for combining these agents remains uncertain. Mathematical models, specifically agent-based models (ABMs), have shown recent successes in uncovering the multiscale dynamics that shape the trajectory of cancer. They have enabled the optimization of treatment methods and the identification of novel therapeutic strategies. To assess the combined effects of anti-PD-1 and anti-FGFR3 small molecule inhibitors (SMI) on tumor growth and the immune response, we built an ABM that captures key facets of tumor heterogeneity and CD8+ T cell phenotypes, their spatial interactions, and their response to therapeutic pressures. Our model quantifies how tumor antigenicity and FGFR3 activating mutations impact disease trajectory and response to anti-PD-1 antibodies and anti-FGFR3 SMI. We find that even a small population of weakly antigenic tumor cells bearing an FGFR3 mutation can render the tumor resistant to combination therapy. However, highly antigenic tumors can overcome therapeutic resistance mediated by FGFR3 mutation. The optimal therapy depends on the strength of the FGFR3 signaling pathway. Under certain conditions, ICI alone is optimal; in others, ICI followed by anti-FGFR3 therapy is best. These results indicate the need to quantify FGFR3 signaling and the fitness advantage conferred on bladder cancer cells harboring this mutation. This ABM approach may enable rationally designed treatment plans to improve clinical outcomes.

Haematopoietic stem cells do not asymmetrically segregate chromosomes or retain BrdU.

Stem cells are proposed to segregate chromosomes asymmetrically during self-renewing divisions so that older ('immortal') DNA strands are retained in daughter stem cells whereas newly synthesized strands segregate to differentiating cells. Stem cells are also proposed to retain DNA labels, such as 5-bromo-2-deoxyuridine (BrdU), either because they segregate chromosomes asymmetrically or because they divide slowly. However, the purity of stem cells among BrdU-label-retaining cells has not been documented in any tissue, and the 'immortal strand hypothesis' has not been tested in a system with definitive stem cell markers. Here we tested these hypotheses in haematopoietic stem cells (HSCs), which can be highly purified using well characterized markers. We administered BrdU to newborn mice, mice treated with cyclophosphamide and granulocyte colony-stimulating factor, and normal adult mice for 4 to 10 days, followed by 70 days without BrdU. In each case, less than 6% of HSCs retained BrdU and less than 0.5% of all BrdU-retaining haematopoietic cells were HSCs, revealing that BrdU has poor specificity and poor sensitivity as an HSC marker. Sequential administration of 5-chloro-2-deoxyuridine and 5-iodo-2-deoxyuridine indicated that all HSCs segregate their chromosomes randomly. Division of individual HSCs in culture revealed no asymmetric segregation of the label. Thus, HSCs cannot be identified on the basis of BrdU-label retention and do not retain older DNA strands during division, indicating that these are not general properties of stem cells.

Phenotype switching in a global method for agent-based models of biological tissue.

Agent-based models (ABMs) are an increasingly important tool for understanding the complexities presented by phenotypic and spatial heterogeneity in biological tissue. The resolution a modeler can achieve in these regards is unrivaled by other approaches. However, this comes at a steep computational cost limiting either the scale of such models or the ability to explore, parameterize, analyze, and apply them. When the models involve molecular-level dynamics, especially cell-specific dynamics, the limitations are compounded. We have developed a global method for solving these computationally expensive dynamics significantly decreases the computational time without altering the behavior of the system. Here, we extend this method to the case where cells can switch phenotypes in response to signals in the microenvironment. We find that the global method in this context preserves the temporal population dynamics and the spatial arrangements of the cells while requiring markedly less simulation time. We thus add a tool for efficiently simulating ABMs that captures key facets of the molecular and cellular dynamics in heterogeneous tissue.

Mathematical model predicts tumor control patterns induced by fast and slow cytotoxic T lymphocyte killing mechanisms.

Immunotherapy has dramatically transformed the cancer treatment landscape largely due to the efficacy of immune checkpoint inhibitors (ICIs). Although ICIs have shown promising results for many patients, the low response rates in many cancers highlight the ongoing challenges in cancer treatment. Cytotoxic T lymphocytes (CTLs) execute their cell-killing function via two distinct mechanisms: a fast-acting, perforin-mediated process and a slower, Fas ligand (FasL)-driven pathway. Evidence also suggests that the preferred killing mechanism of CTLs depends on the antigenicity of tumor cells. To determine the critical factors affecting responses to ICIs, we construct an ordinary differential equation model describing in vivo tumor-immune dynamics in the presence of active or blocked PD-1/PD-L1 immune checkpoint. Specifically, we identify important aspects of the tumor-immune landscape that affect tumor size and composition in the short and long term. We also generate a virtual cohort of mice with diverse tumor and immune attributes to simulate the outcomes of immune checkpoint blockade in a heterogeneous population. By identifying key tumor and immune characteristics associated with tumor elimination, dormancy, and escape, we predict which fraction of a population potentially responds well to ICIs and ways to enhance therapeutic outcomes with combination therapy.

Implementing a global approach for efficiently simulating molecular dynamics in agent-based models of biological tissue.

This protocol explains how to take an agent-based model (ABM) with molecular dynamics and set it up to solve the molecular dynamics with a global approach. It can be used to speed up simulations significantly while retaining high levels of accuracy with the original ABM. Two options are presented for implementing this global approach, depending on the desired spatial variability in molecular concentrations. Both options coarse-grain the molecular dynamics in space by dividing the microenvironment into regions with uniform concentrations. For complete details on the use and execution of this protocol, please refer to Bergman et al. (2022).

A global method for fast simulations of molecular dynamics in multiscale agent-based models of biological tissues.

Agent-based models (ABMs) are a natural platform for capturing the multiple time and spatial scales in biological processes. However, these models are computationally expensive, especially when including molecular-level effects. The traditional approach to simulating this type of multiscale ABM is to solve a system of ordinary differential equations for the molecular events per cell. This significantly adds to the computational cost of simulations as the number of agents grows, which contributes to many ABMs being limited to around 10 5 cells. We propose an approach that requires the same computational time independent of the number of agents. This speeds up the entire simulation by orders of magnitude, allowing for more thorough explorations of ABMs with even larger numbers of agents. We use two systems to show that the new method strongly agrees with the traditionally used approach. This computational strategy can be applied to a wide range of biological investigations.

SMoRe ParS: A novel methodology for bridging modeling modalities and experimental data applied to 3D vascular tumor growth.

Multiscale systems biology is having an increasingly powerful impact on our understanding of the interconnected molecular, cellular, and microenvironmental drivers of tumor growth and the effects of novel drugs and drug combinations for cancer therapy. Agent-based models (ABMs) that treat cells as autonomous decision-makers, each with their own intrinsic characteristics, are a natural platform for capturing intratumoral heterogeneity. Agent-based models are also useful for integrating the multiple time and spatial scales associated with vascular tumor growth and response to treatment. Despite all their benefits, the computational costs of solving agent-based models escalate and become prohibitive when simulating millions of cells, making parameter exploration and model parameterization from experimental data very challenging. Moreover, such data are typically limited, coarse-grained and may lack any spatial resolution, compounding these challenges. We address these issues by developing a first-of-its-kind method that leverages explicitly formulated surrogate models (SMs) to bridge the current computational divide between agent-based models and experimental data. In our approach, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), we quantify the uncertainty in the relationship between agent-based model inputs and surrogate model parameters, and between surrogate model parameters and experimental data. In this way, surrogate model parameters serve as intermediaries between agent-based model input and data, making it possible to use them for calibration and uncertainty quantification of agent-based model parameters that map directly onto an experimental data set. We illustrate the functionality and novelty of Surrogate Modeling for Reconstructing Parameter Surfaces by applying it to an agent-based model of 3D vascular tumor growth, and experimental data in the form of tumor volume time-courses. Our method is broadly applicable to situations where preserving underlying mechanistic information is of interest, and where computational complexity and sparse, noisy calibration data hinder model parameterization.

An Agent-Based Model of Combination Oncolytic Viral Therapy and Anti-PD-1 Immunotherapy Reveals the Importance of Spatial Location When Treating Glioblastoma.

Oncolytic viral therapies and immunotherapies are of growing clinical interest due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. These treatment modalities provide promising alternatives to the standard of care, particularly for cancers with poor prognoses, such as the lethal brain tumor glioblastoma (GBM). However, uncertainty remains regarding optimal dosing strategies, including how the spatial location of viral doses impacts therapeutic efficacy and tumor landscape characteristics that are most conducive to producing an effective immune response. We develop a three-dimensional agent-based model (ABM) of GBM undergoing treatment with a combination of an oncolytic Herpes Simplex Virus and an anti-PD-1 immunotherapy. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We utilize the spatially explicit nature of the ABM to determine optimal viral dosing in both the temporal and spatial contexts. After proposing an adaptive viral dosing strategy that chooses to dose sites at the location of highest tumor cell density, we find that, in most cases, this adaptive strategy produces a more effective treatment outcome than repeatedly dosing in the center of the tumor.

Standing Variations Modeling Captures Inter-Individual Heterogeneity in a Deterministic Model of Prostate Cancer Response to Combination Therapy.

Sipuleucel-T (Provenge) is the first live cell vaccine approved for advanced, hormonally refractive prostate cancer. However, survival benefit is modest and the optimal combination or schedule of sipuleucel-T with androgen depletion remains unknown. We employ a nonlinear dynamical systems approach to modeling the response of hormonally refractive prostate cancer to sipuleucel-T. Our mechanistic model incorporates the immune response to the cancer elicited by vaccination, and the effect of androgen depletion therapy. Because only a fraction of patients benefit from sipuleucel-T treatment, inter-individual heterogeneity is clearly crucial. Therefore, we introduce our novel approach, Standing Variations Modeling, which exploits inestimability of model parameters to capture heterogeneity in a deterministic model. We use data from mouse xenograft experiments to infer distributions on parameters critical to tumor growth and to the resultant immune response. Sampling model parameters from these distributions allows us to represent heterogeneity, both at the level of the tumor cells and the individual (mouse) being treated. Our model simulations explain the limited success of sipuleucel-T observed in practice, and predict an optimal combination regime that maximizes predicted efficacy. This approach will generalize to a range of emerging cancer immunotherapies.

A validated mathematical model of FGFR3-mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer.

Bladder cancer is a common malignancy with over 80,000 estimated new cases and nearly 18,000 deaths per year in the United States alone. Therapeutic options for metastatic bladder cancer had not evolved much for nearly four decades, until recently, when five immune checkpoint inhibitors were approved by the U.S. Food and Drug Administration (FDA). Despite the activity of these drugs in some patients, the objective response rate for each is less than 25%. At the same time, fibroblast growth factor receptors (FGFRs) have been attractive drug targets for a variety of cancers, and in 2019 the FDA approved the first therapy targeted against FGFR3 for bladder cancer. Given the excitement around these new receptor tyrosine kinase and immune checkpoint targeted strategies, and the challenges they each may face on their own, emerging data suggest that combining these treatment options could lead to improved therapeutic outcomes. In this paper, we develop a mathematical model for FGFR3-mediated tumor growth and use it to investigate the impact of the combined administration of a small molecule inhibitor of FGFR3 and a monoclonal antibody against the PD-1/PD-L1 immune checkpoint. The model is carefully calibrated and validated with experimental data before survival benefits, and dosing schedules are explored. Predictions of the model suggest that FGFR3 mutation reduces the effectiveness of anti-PD-L1 therapy, that there are regions of parameter space where each monotherapy can outperform the other, and that pretreatment with anti-PD-L1 therapy always results in greater tumor reduction even when anti-FGFR3 therapy is the more effective monotherapy.

Receptor cross-talk in angiogenesis: mapping environmental cues to cell phenotype using a stochastic, Boolean signaling network model.

Cancer invasion and metastasis depend on tumor-induced angiogenesis, the means by which cancer cells attract and maintain a blood supply. During angiogenesis, cellular processes are tightly coordinated by signaling molecules and their receptors. Understanding how endothelial cells synthesize multiple biochemical signals can catalyze the development of novel therapeutic strategies to combat cancer. This study is the first to propose a signal transduction model highlighting the cross-talk between key receptors involved in angiogenesis, namely the VEGF, integrin, and cadherin receptors. From experimental data, we construct a network model of receptor cross-talk and analyze its dynamics. We identify relationships between receptor activation combinations and cellular function, and show that cross-talk is crucial to phenotype determination. The network converges to a unique set of output states that correspond to known cell phenotypes: migratory, proliferating, quiescent, apoptotic, and it predicts one phenotype that challenges the "go or grow" hypothesis. Finally, we use the model to study protein inhibition and to suggest molecular targets for anti-angiogenic therapies.

Topography of extracellular matrix mediates vascular morphogenesis and migration speeds in angiogenesis.

The extracellular matrix plays a critical role in orchestrating the events necessary for wound healing, muscle repair, morphogenesis, new blood vessel growth, and cancer invasion. In this study, we investigate the influence of extracellular matrix topography on the coordination of multi-cellular interactions in the context of angiogenesis. To do this, we validate our spatio-temporal mathematical model of angiogenesis against empirical data, and within this framework, we vary the density of the matrix fibers to simulate different tissue environments and to explore the possibility of manipulating the extracellular matrix to achieve pro- and anti-angiogenic effects. The model predicts specific ranges of matrix fiber densities that maximize sprout extension speed, induce branching, or interrupt normal angiogenesis, which are independently confirmed by experiment. We then explore matrix fiber alignment as a key factor contributing to peak sprout velocities and in mediating cell shape and orientation. We also quantify the effects of proteolytic matrix degradation by the tip cell on sprout velocity and demonstrate that degradation promotes sprout growth at high matrix densities, but has an inhibitory effect at lower densities. Our results are discussed in the context of ECM targeted pro- and anti-angiogenic therapies that can be tested empirically.

Modeling Oncolytic Viral Therapy, Immune Checkpoint Inhibition, and the Complex Dynamics of Innate and Adaptive Immunity in Glioblastoma Treatment.

Oncolytic viruses are of growing interest to cancer researchers and clinicians, due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. The immune response to an oncolytic virus plays a critical role in treatment efficacy. However, uncertainty remains regarding the circumstances under which the immune system either assists in eliminating tumor cells or inhibits treatment via rapid viral clearance, leading to the cessation of the immune response. In this work, we develop an ordinary differential equation model of treatment for a lethal brain tumor, glioblastoma, using an oncolytic Herpes Simplex Virus. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy (OVT), and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We focus on the tradeoff between viral clearance by innate immune cells and the innate immune cell-mediated recruitment of antiviral and antitumor adaptive immune cells. Our model suggests that when a tumor is treated with OVT alone, the innate immune cells' ability to clear the virus quickly after administration has a much larger impact on the treatment outcome than the adaptive immune cells' antitumor activity. Even in a highly antigenic tumor with a strong innate immune response, the faster recruitment of antitumor adaptive immune cells is not sufficient to offset the rapid viral clearance. This motivates our subsequent incorporation of an immunotherapy that inhibits the PD-1/PD-L1 checkpoint pathway by blocking PD-1, which we combine with OVT within the model. The combination therapy is most effective for a highly antigenic tumor or for intermediate levels of innate immune localization. Extreme levels of innate immune cell activity either clear the virus too quickly or fail to activate a sufficiently strong adaptive response, yielding ineffective combination therapy of GBM. Hence, we show that the innate and adaptive immune interactions significantly influence treatment response and that combining OVT with an immune checkpoint inhibitor expands the range of immune conditions that allow for tumor size reduction or clearance.

In Silico Models Accurately Predict In Vivo Response for IL6 Blockade in Head and Neck Cancer.

Malignant features of head and neck squamous cell carcinoma (HNSCC) may be derived from the presence of stem-like cells that are characterized by uniquely high tumorigenic potential. These cancer stem cells (CSC) function as putative drivers of tumor initiation, therapeutic evasion, metastasis, and recurrence. Although they are an appealing conceptual target, CSC-directed cancer therapies remain scarce. One promising CSC target is the IL6 pathway, which is strongly correlated with poor patient survival. In this study we created and validated a multiscale mathematical model to investigate the impact of cross-talk between tumor cell- and endothelial cell (EC)-secreted IL6 on HNSCC growth and the CSC fraction. We then predicted and analyzed the responses of HNSCC to tocilizumab (TCZ) and cisplatin combination therapy. The model was validated with in vivo experiments involving human ECs coimplanted with HNSCC cell line xenografts. Without artificial tuning to the laboratory data, the model showed excellent predictive agreement with the decrease in tumor volumes observed in TCZ-treated mice, as well as a decrease in the CSC fraction. This computational platform provides a framework for preclinical cisplatin and TCZ dose and frequency evaluation to be tested in future clinical studies. SIGNIFICANCE: A mathematical model is used to rapidly evaluate dosing strategies for IL6 pathway modulation. These results may lead to nonintuitive dosing or timing treatment schedules to optimize synergism between drugs.

Mechanistic Deconvolution of Oral Absorption Model with Dynamic Gastrointestinal Fluid to Predict Regional Rate and Extent of GI Drug Dissolution.

Multiple approaches such as mathematical deconvolution and mechanistic oral absorption models have been used to predict in vivo drug dissolution in the gastrointestinal (GI) tract. However, these approaches are often validated by plasma pharmacokinetic profiles, but not by in vivo drug dissolution due to the limited data available regarding the local GI environment. It is also challenging to predict and validate in vivo dissolution in different regions of the GI tract (stomach, duodenum, jejunum, and ileum). In this study, the dynamic fluid compartment absorption and transport (DFCAT) model was used to predict the in vivo dissolution profiles of ibuprofen, which was administered as an 800-mg immediate-release tablet to healthy subjects, in different regions of the GI tract. The prediction was validated with concentration time-courses of ibuprofen (BCS class 2a) in different regions of the GI tract that we have obtained over the past few years. The computational model predicted that the dissolution of ibuprofen was minimal in the stomach (2%), slightly more in the duodenum (6.3%), and primarily dissolved in the jejunum (63%) and the ileum (25%). The detailed model prediction of drug dissolution in different regions of GI can provide a quantitative reference of in vivo dissolution that may provide valuable insight in developing in vitro tests for drug product optimization and quality.

Breast cancer stem cells-research opportunities utilizing mathematical modeling.

There is increasing evidence for the "cancer stem cell hypothesis" which holds that cancers originate in tissue stem cells or progenitor cells. As a result of this, cancers are driven by a cellular subcomponent that retains stem cell properties. Among these properties are self-renewal and multi-lineage differentiation. The biological processes which account for stem cell properties are currently being elucidated. Cancer stem cells maintain many of the same characteristics of their normal counterparts. The combination of biological research with mathematical modeling may provide for a greater understanding of the complex picture of breast cancer stem cells and assist cancer biologists and clinical oncologists in designing and testing novel therapeutic strategies.

Patient-derived xenograft (PDX) tumors increase growth rate with time.

Patient-derived xenograft (PDX) models are frequently used for translational cancer research, and are assumed to behave consistently as the tumor ages. However, growth rate constancy as a function of time is unclear. Notably, variable PDX growth rates over time might have implications for the interpretation of translational studies. We characterized four PDX models through several in vivo passages from primary human head and neck squamous cell carcinoma and salivary gland adenoid cystic carcinoma. We developed a mathematical approach to merge growth data from different passages into a single measure of relative tumor volume normalized to study initiation size. We analyzed log-relative tumor volume increase with linear mixed effect models. Two oral pathologists analyzed the PDX tissues to determine if histopathological feature changes occurred over in vivo passages. Tumor growth rate increased over time. This was determined by repeated measures linear regression statistical analysis in four different PDX models. A quadratic statistical model for the temporal effect predicted the log-relative tumor volume significantly better than a linear time effect model. We found a significant correlation between passage number and histopathological features of higher tumor grade. Our mathematical treatment of PDX data allows statistical analysis of tumor growth data over long periods of time, including over multiple passages. Non-linear tumor growth in our regression models revealed the exponential growth rate increased over time. The dynamic tumor growth rates correlated with quantifiable histopathological changes that related to passage number in multiple types of cancer.