Connecting Agent-Based Models with High-Dimensional Parameter Spaces to Multidimensional Data Using SMoRe ParS: A Surrogate Modeling Approach.

Across a broad range of disciplines, agent-based models (ABMs) are increasingly utilized for replicating, predicting, and understanding complex systems and their emergent behavior. In the biological and biomedical sciences, researchers employ ABMs to elucidate complex cellular and molecular interactions across multiple scales under varying conditions. Data generated at these multiple scales, however, presents a computational challenge for robust analysis with ABMs. Indeed, calibrating ABMs remains an open topic of research due to their own high-dimensional parameter spaces. In response to these challenges, we extend and validate our novel methodology, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), arriving at a computationally efficient framework for connecting high dimensional ABM parameter spaces with multidimensional data. Specifically, we modify SMoRe ParS to initially confine high dimensional ABM parameter spaces using unidimensional data, namely, single time-course information of in vitro cancer cell growth assays. Subsequently, we broaden the scope of our approach to encompass more complex ABMs and constrain parameter spaces using multidimensional data. We explore this extension with in vitro cancer cell inhibition assays involving the chemotherapeutic agent oxaliplatin. For each scenario, we validate and evaluate the effectiveness of our approach by comparing how well ABM simulations match the experimental data when using SMoRe ParS-inferred parameters versus parameters inferred by a commonly used direct method. In so doing, we show that our approach of using an explicitly formulated surrogate model as an interlocutor between the ABM and the experimental data effectively calibrates the ABM parameter space to multidimensional data. Our method thus provides a robust and scalable strategy for leveraging multidimensional data to inform multiscale ABMs and explore the uncertainty in their parameters.

Integrating a dynamic central metabolism model of cancer cells with a hybrid 3D multiscale model for vascular hepatocellular carcinoma growth.

We develop here a novel modelling approach with the aim of closing the conceptual gap between tumour-level metabolic processes and the metabolic processes occurring in individual cancer cells. In particular, the metabolism in hepatocellular carcinoma derived cell lines (HEPG2 cells) has been well characterized but implementations of multiscale models integrating this known metabolism have not been previously reported. We therefore extend a previously published multiscale model of vascular tumour growth, and integrate it with an experimentally verified network of central metabolism in HEPG2 cells. This resultant combined model links spatially heterogeneous vascular tumour growth with known metabolic networks within tumour cells and accounts for blood flow, angiogenesis, vascular remodelling and nutrient/growth factor transport within a growing tumour, as well as the movement of, and interactions between normal and cancer cells. Model simulations report for the first time, predictions of spatially resolved time courses of core metabolites in HEPG2 cells. These simulations can be performed at a sufficient scale to incorporate clinically relevant features of different tumour systems using reasonable computational resources. Our results predict larger than expected temporal and spatial heterogeneity in the intracellular concentrations of glucose, oxygen, lactate pyruvate, f16bp and Acetyl-CoA. The integrated multiscale model developed here provides an ideal quantitative framework in which to study the relationship between dosage, timing, and scheduling of anti-neoplastic agents and the physiological effects of tumour metabolism at the cellular level. Such models, therefore, have the potential to inform treatment decisions when drug response is dependent on the metabolic state of individual cancer cells.

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.

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.

Modeling hepatitis C virus protein and p53 interactions in hepatocytes: Implications for carcinogenesis.

Hepatitis C virus (HCV) infection has reached epidemic proportions worldwide. Individuals with chronic HCV infection and without access to treatment are at high risk for developing hepatocellular carcinoma (HCC), a liver cancer that is rapidly fatal after diagnosis. A number of factors have been identified that contribute to HCV-driven carcinogenesis such as scarring of the liver, and chronic inflammation. Recent evidence indicates a direct role for HCV-encoded proteins themselves in oncogenesis of infected hepatocytes. The viral protein HCV core has been shown to interact directly with the host tumor suppressor protein p53, and to modulate p53-activity in a biphasic manner. Here, biochemically-motivated mathematical models of HCV-p53 interactions are developed to elucidate the mechanisms underlying this phenomenon. We show that by itself, direct interaction between HCV core and p53 is insufficient to recapitulate the experimental data. We postulate the existence of an additional factor, activated by HCV core that inhibits p53 function. We present experimental evidence in support of this hypothesis. The model including this additional factor reproduces the experimental results, validating our assumptions. Finally, we investigate what effect HCV core-p53 interactions could have on the capacity of an infected hepatocyte to repair damage to its DNA. Integrating our model with an existing model of the oscillatory response of p53 to DNA damage predicts a biphasic relationship between HCV core and the transformative potential of infected hepatocytes. In addition to providing mechanistic insights, these results suggest a potential biomarker that could help in identifying those HCV patients most at risk of progression to HCC.

Exploiting the synergy between carboplatin and ABT-737 in the treatment of ovarian carcinomas.

Platinum drug-resistance in ovarian cancers mediated by anti-apoptotic proteins such as Bcl-xL is a major factor contributing to the chemotherapeutic resistance of recurrent disease. Consequently, concurrent inhibition of Bcl-xL in combination with chemotherapy may improve treatment outcomes for patients. Here, we develop a mathematical model to investigate the potential of combination therapy with ABT-737, a small molecule inhibitor of Bcl-xL, and carboplatin, a platinum-based drug, on a simulated tumor xenograft. The model is calibrated against in vivo experimental data, wherein xenografts established in mice were treated with ABT-737 and/or carboplatin on a fixed periodic schedule. The validated model is used to predict the minimum drug load that will achieve a predetermined level of tumor growth inhibition, thereby maximizing the synergy between the two drugs. Our simulations suggest that the infusion-duration of each carboplatin dose is a critical parameter, with an 8-hour infusion of carboplatin given weekly combined with a daily bolus dose of ABT-737 predicted to minimize residual disease. The potential of combination therapy to prevent or delay the onset of carboplatin-resistance is also investigated. When resistance is acquired as a result of aberrant DNA-damage repair in cells treated with carboplatin, drug delivery schedules that induce tumor remission with even low doses of combination therapy can be identified. Intrinsic resistance due to pre-existing cohorts of resistant cells precludes tumor regression, but dosing strategies that extend disease-free survival periods can still be identified. These results highlight the potential of our model to accelerate the development of novel therapeutics such as BH3 mimetics.

A partial differential equation model of metastasized prostatic cancer.

Biochemically failing metastatic prostate cancer is typically treated with androgen ablation. However, due to the emergence of castration-resistant cells that can survive in low androgen concentrations, such therapy eventually fails. Here, we develop a partial differential equation model of the growth and response to treatment of prostate cancer that has metastasized to the bone. Existence and uniqueness results are derived for the resulting free boundary problem. In particular, existence and uniqueness of solutions for all time are proven for the radially symmetric case. Finally, numerical simulations of a tumor growing in 2-dimensions with radial symmetry are carried in order to evaluate the therapeutic potential of different treatment strategies. These simulations are able to reproduce a variety of clinically observed responses to treatment, and suggest treatment strategies that may result in tumor remission, underscoring our model's potential to make a significant contribution in the field of prostate cancer therapeutics.

Modeling stem/progenitor cell-induced neovascularization and oxygenation around solid implants.

Tissue engineering constructs and other solid implants with biomedical applications, such as drug delivery devices or bioartificial organs, need oxygen (O(2)) to function properly. To understand better the vascular integration of such devices, we recently developed a novel model sensor containing O(2)-sensitive crystals, consisting of a polymeric capsule limited by a nanoporous filter. The sensor was implanted in mice with hydrogel alone (control) or hydrogel embedded with mouse CD117/c-kit+ bone marrow progenitor cells in order to stimulate peri-implant neovascularization. The sensor provided local partial O(2) pressure (pO(2)) using noninvasive electron paramagnetic resonance signal measurements. A consistently higher level of peri-implant oxygenation was observed in the cell-treatment case than in the control over a 10-week period. To provide a mechanistic explanation of these experimental observations, we present in this article a mathematical model, formulated as a system of coupled partial differential equations, that simulates peri-implant vascularization. In the control case, vascularization is considered to be the result of a foreign body reaction, while in the cell-treatment case, adipogenesis in response to paracrine stimuli produced by the stem cells is assumed to induce neovascularization. The model is validated by fitting numerical predictions of local pO(2) to measurements from the implanted sensor. The model is then used to investigate further the potential for using stem cell treatment to enhance the vascular integration of biomedical implants. We thus demonstrate how mathematical modeling combined with experimentation can be used to infer how vasculature develops around biomedical implants in control and stem cell-treated cases.

Mathematical modeling of prostate cancer progression in response to androgen ablation therapy.

Prostate cancer progression depends in part on the complex interactions between testosterone, its active metabolite DHT, and androgen receptors. In a metastatic setting, the first line of treatment is the elimination of testosterone. However, such interventions are not curative because cancer cells evolve via multiple mechanisms to a castrate-resistant state, allowing progression to a lethal outcome. It is hypothesized that administration of antiandrogen therapy in an intermittent, as opposed to continuous, manner may bestow improved disease control with fewer treatment-related toxicities. The present study develops a biochemically motivated mathematical model of antiandrogen therapy that can be tested prospectively as a predictive tool. The model includes "personalized" parameters, which address the heterogeneity in the predicted course of the disease under various androgen-deprivation schedules. Model simulations are able to capture a variety of clinically observed outcomes for "average" patient data under different intermittent schedules. The model predicts that in the absence of a competitive advantage of androgen-dependent cancer cells over castration-resistant cancer cells, intermittent scheduling can lead to more rapid treatment failure as compared to continuous treatment. However, increasing a competitive advantage for hormone-sensitive cells swings the balance in favor of intermittent scheduling, delaying the acquisition of genetic or epigenetic alterations empowering androgen resistance. Given the near universal prevalence of antiandrogen treatment failure in the absence of competing mortality, such modeling has the potential of developing into a useful tool for incorporation into clinical research trials and ultimately as a prognostic tool for individual patients.

The molecular basis of synergism between carboplatin and ABT-737 therapy targeting ovarian carcinomas.

Resistance to standard chemotherapy (carboplatin + paclitaxel) is one of the leading causes of therapeutic failure in ovarian carcinomas. Emergence of chemoresistance has been shown to be mediated in part by members of the Bcl family of proteins including the antiapoptotic protein Bcl-x(L), whose expression is correlated with shorter disease-free intervals in recurrent disease. ABT-737 is an example of one of the first small-molecule inhibitors of Bcl-2/Bcl-x(L) that has been shown to increase the sensitivity of ovarian cancer cells to carboplatin. To exploit the therapeutic potential of these two drugs and predict optimal doses and dose scheduling, it is essential to understand the molecular basis of their synergistic action. Here, we build and calibrate a mathematical model of ABT-737 and carboplatin action on an ovarian cancer cell line (IGROV-1). The model suggests that carboplatin treatment primes cells for ABT-737 therapy because of an increased dependence of cells with DNA damage on Bcl-x(L) for survival. Numerical simulations predict the existence of a threshold of Bcl-x(L) below which these cells are unable to recover. Furthermore, co- plus posttreatment of ABT-737 with carboplatin is predicted to be the best strategy to maximize synergism between these two drugs. A critical challenge in chemotherapy is to strike a balance between maximizing cell-kill while minimizing patient drug load. We show that the model can be used to compute minimal doses required for any desired fraction of cell kill. These results underscore the potential of the modeling work presented here as a valuable quantitative tool to aid in the translation of novel drugs such as ABT-737 from the experimental to clinical setting and highlight the need for close collaboration between modelers and experimental scientists.

Quantification of endothelial cell-targeted anti-Bcl-2 therapy and its suppression of tumor growth and vascularization.

Proapoptotic and antiapoptotic proteins in the Bcl family are key regulators of programmed cell death. It is the interaction between these molecules that determines cellular response to apoptotic signals, making them attractive targets for therapeutic intervention. In recent experiments designed to study tumor angiogenesis, Bcl-2 upregulation in endothelial cells was shown to be a critical mediator of vascular development. In this article, we develop a mathematical model that explicitly incorporates the response of endothelial cells to variations in proapoptotic and antiapoptotic proteins in the Bcl family, as well as the administration of specific antiangiogenic therapies targeted against Bcl-2. The model is validated by comparing its predictions to in vitro experimental data that reports microvessel density prior to and following the administration of 0.05 to 5.0 micromol/L of BL193, a promising small molecule inhibitor of Bcl-2. Numerical simulations of in vivo treatment of tumors predict the existence of a threshold for the amount of therapy required for successful treatment and quantify how this threshold varies with the stage of tumor growth. Furthermore, the model shows how rapidly the least effective dosage of BL193 decreases if an even moderately better inhibitor of Bcl-2 is used and predicts that increasing cell wall permeability of endothelial cells to BL193 does not significantly affect this threshold. A critical challenge of experimental therapeutics for cancer is to decide which drugs are the best candidates for clinical trials. These results underscore the potential of mathematical modeling to guide the development of novel antiangiogenic therapies and to direct drug design.