Integrated computational and in vivo models reveal Key Insights into macrophage behavior during bone healing.

Myeloid-derived monocyte and macrophages are key cells in the bone that contribute to remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage dynamics and polarization states over time: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. Bone healing is a complex multicellular dynamic process. While traditional in vitro and in vivo experimentation may capture the behavior of select populations with high resolution, they cannot simultaneously track the behavior of multiple populations. To address this, we have used an integrated coupled ordinary differential equations (ODEs)-based framework describing multiple cellular species to in vivo bone injury data in order to identify and test various hypotheses regarding bone cell populations dynamics. Our approach allowed us to infer several biological insights including, but not limited to,: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. In addition, we further tested the robustness of the mathematical model by comparing simulation results to an independent experimental dataset. Taken together, this novel comprehensive mathematical framework allowed us to identify biological mechanisms that best recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. Furthermore, our hypothesis testing methodology could be used in other contexts to decipher mechanisms in complex multicellular processes.

Roadmap on plasticity and epigenetics in cancer.

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

Cancer immunoediting: A game theoretical approach.

The role of the immune system in tumor development increasingly includes the idea of cancer immunoediting. It comprises three phases: elimination, equilibrium, and escape. In the first phase, elimination, transformed cells are recognized and destroyed by immune system. The rare tumor cells that are not destroyed in this phase may then enter the equilibrium phase, where their growth is prevented by immunity mechanisms. The escape phase represents the final phase of this process, where cancer cells begin to grow unconstrained by the immune system. In this study, we describe and analyze an evolutionary game theoretical model of proliferating, quiescent, and immune cells interactions for the first time. The proposed model is evaluated with constant and dynamic approaches. Population dynamics and interactions between the immune system and cancer cells are investigated. Stability of equilibria or critical points are analyzed by applying algebraic analysis. This model allows us to understand the process of cancer development and might help us design better treatment strategies to account for immunoediting.

Hybrid Automata Library: A flexible platform for hybrid modeling with real-time visualization.

The Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL's components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build performant 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on GitHub at https://github.com/MathOnco/HAL under the MIT License. HAL requires the Java JDK version 1.8 or later to compile and run the source code.

Evidence for hypoxia increasing the tempo of evolution in glioblastoma.

BACKGROUND: Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear. METHODS: We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity. RESULTS: Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results. CONCLUSIONS: Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity.

What Is the Storage Effect, Why Should It Occur in Cancers, and How Can It Inform Cancer Therapy?

Intratumor heterogeneity is a feature of cancer that is associated with progression, treatment resistance, and recurrence. However, the mechanisms that allow diverse cancer cell lineages to coexist remain poorly understood. The storage effect is a coexistence mechanism that has been proposed to explain the diversity of a variety of ecological communities, including coral reef fish, plankton, and desert annual plants. Three ingredients are required for there to be a storage effect: (1) temporal variability in the environment, (2) buffered population growth, and (3) species-specific environmental responses. In this article, we argue that these conditions are observed in cancers and that it is likely that the storage effect contributes to intratumor diversity. Data that show the temporal variation within the tumor microenvironment are needed to quantify how cancer cells respond to fluctuations in the tumor microenvironment and what impact this has on interactions among cancer cell types. The presence of a storage effect within a patient's tumors could have a substantial impact on how we understand and treat cancer.

High School Internship Program in Integrated Mathematical Oncology (HIP IMO): Five-Year Experience at Moffitt Cancer Center.

Modern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education traditionally occurs in disciplinary silos, which creates a steep learning curve at the graduate and postdoctoral levels that increasingly bridge multiple disciplines. Numerous colleges have begun to embrace interdisciplinary curricula, but students who double major in mathematics (or other quantitative sciences) and biology (or medicine) remain scarce. We identified the need to educate junior and senior high school students about integrating mathematical and biological skills, through the lens of mathematical oncology, to better prepare students for future careers at the interdisciplinary interface. The High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center has so far trained 59 students between 2015 and 2019. We report here on the program structure, training deliverables, curriculum and outcomes. We hope to promote interdisciplinary educational activities early in a student's career.

Size Matters: Metastatic Cluster Size and Stromal Recruitment in the Establishment of Successful Prostate Cancer to Bone Metastases.

Prostate cancer (PCa) impacts over 180,000 men every year in the USA alone, with 26,000 patients expected to succumb to the disease ( cancer.gov ). The primary cause of death is metastasis, with secondary lesions most commonly occurring in the skeleton. Prostate cancer to bone metastasis is an important, yet poorly understood, process that is difficult to explore with experimental techniques alone. To this end we have utilized a hybrid (discrete-continuum) cellular automaton model of normal bone matrix homeostasis that allowed us to investigate how metastatic PCa can disrupt the bone microenvironment. Our previously published results showed that PCa cells can recruit mesenchymal stem cells (MSCs) that give rise to bone-building osteoblasts. MSCs are also thought to be complicit in the establishment of successful bone metastases (Lu, in Mol Cancer Res 4(4):221-233, 2006). Here we have explored the aspects of early metastatic colonization and shown that the size of PCa clusters needs to be within a specific range to become successfully established: sufficiently large to maximize success, but not too large to risk failure through competition among cancer and stromal cells for scarce resources. Furthermore, we show that MSC recruitment can promote the establishment of a metastasis and compensate for relatively low numbers of PCa cells seeding the bone microenvironment. Combined, our results highlight the utility of biologically driven computational models that capture the complex and dynamic dialogue between cells during the initiation of active metastases.

Preconditioning-Like Properties of Short-Term Hypothermia in Isolated Perfused Rat Liver (IPRL) System.

Hypothermia may attenuate the progression of ischemia-induced damage in liver. Here, we determined the effects of a brief cycle of hypothermic preconditioning applied before an ischemic/reperfusion (I/R) episode in isolated perfused rat liver (IPRL) on tissue damage and oxidative stress. Rats (male, 200-250 g) were anaesthetised with sodium pentobarbital (60 mg·kg-1 i.p) and underwent laparatomy. The liver was removed and perfused in a temperature-regulated non-recirculating system. Livers were randomly divided into two groups (n = 6 each group). In the hypothermia-preconditioned group, livers were perfused with hypothermic buffer (cycle of 10 min at 22 °C plus 10 min at 37 °C) and the other group was perfused at 37 °C. Both groups were then submitted to 40 min of warm ischemia and 20 min of warm reperfusion. The level of tissue-damage indicators (alanine amino transferase, ALT; lactate dehydrogenase, LDH; and proteins), oxidative stress markers (thiobarbituric acid-reactive substances, TBARS; advanced oxidation protein products, AOPP; and glutathione, GSH) were measured in aliquots of perfusate sampled at different time intervals. Histological determinations and oxidative stress biomarkers in homogenized liver (AOPP; TBARS; nitric oxide derivatives, NOx; GSH and glutathione disulphide, GSSG) were also made in the tissue at the end. Results showed that both damage and oxidant indicators significantly decreased while antioxidant increased in hypothermic preconditioned livers. In addition, homogenized liver determinations and histological observations at the end of the protocol corroborate the results in the perfusate, confirming the utility of the perfusate as a non-invasive method. In conclusion, hypothermic preconditioning attenuates oxidative damage and appears to be a promising strategy to protect the liver against IR injury.

Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature.

BACKGROUND: Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment and disease progression. METHODS: We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularisation via vascular endothelial growth factor production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic and aerobic non-angiogenic. RESULTS: We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic; (2) fully angiogenic; or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth factor production in isolation. CONCLUSIONS: The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular normalisation as a neoadjuvant therapy before follow-up with interventions like buffer therapy.

Microenvironmental variables must influence intrinsic phenotypic parameters of cancer stem cells to affect tumourigenicity.

Since the discovery of tumour initiating cells (TICs) in solid tumours, studies focussing on their role in cancer initiation and progression have abounded. The biological interrogation of these cells continues to yield volumes of information on their pro-tumourigenic behaviour, but actionable generalised conclusions have been scarce. Further, new information suggesting a dependence of tumour composition and growth on the microenvironment has yet to be studied theoretically. To address this point, we created a hybrid, discrete/continuous computational cellular automaton model of a generalised stem-cell driven tissue with a simple microenvironment. Using the model we explored the phenotypic traits inherent to the tumour initiating cells and the effect of the microenvironment on tissue growth. We identify the regions in phenotype parameter space where TICs are able to cause a disruption in homeostasis, leading to tissue overgrowth and tumour maintenance. As our parameters and model are non-specific, they could apply to any tissue TIC and do not assume specific genetic mutations. Targeting these phenotypic traits could represent a generalizable therapeutic strategy across cancer types. Further, we find that the microenvironmental variable does not strongly affect the outcomes, suggesting a need for direct feedback from the microenvironment onto stem-cell behaviour in future modelling endeavours.

Current and emerging therapies for bone metastatic castration-resistant prostate cancer.

BACKGROUND: A paucity of therapeutic options is available to treat men with metastatic castration-resistant prostate cancer (mCRPC). However, recent developments in our understanding of the disease have resulted in several new therapies that show promise in improving overall survival rates in this patient population. METHODS: Agents approved for use in the United States and those undergoing clinical trials for the treatment of mCRPC are reviewed. Recent contributions to the understanding of prostate biology and bone metastasis are discussed as well as how the underlying mechanisms may represent opportunities for therapeutic intervention. New challenges to delivering effective mCRPC treatment will also be examined. RESULTS: New and emerging treatments that target androgen synthesis and utilization or the microenvironment may improve overall survival rates for men diagnosed with mCRPC. Determining how factors derived from the primary tumor can promote the development of premetastatic niches and how prostate cancer cells parasitize niches in the bone microenvironment, thus remaining dormant and protected from systemic therapy, could yield new therapies to treat mCRPC. Challenges such as intratumoral heterogeneity and patient selection can potentially be circumvented via computational biology approaches. CONCLUSIONS: The emergence of novel treatments for mCRPC, combined with improved patient stratification and optimized therapy sequencing, suggests that significant gains may be made in terms of overall survival rates for men diagnosed with this form of cancer.

A seven-step guide to spatial, agent-based modelling of tumour evolution.

Spatial agent-based models are frequently used to investigate the evolution of solid tumours subject to localized cell-cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, spatial computational models are predicted to become ever more necessary for making sense of complex clinical and experimental data sets, for predicting clinical outcomes, and for optimizing treatment strategies. Here we present a non-technical step by step guide to developing such a model from first principles. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off-lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterization, visualization and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasize the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system. Our guide is aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of the models on which major cancer studies now so often depend.

Dissecting the Spatially Restricted Effects of Microenvironment-Mediated Resistance on Targeted Therapy Responses.

The response of tumors to anti-cancer therapies is defined not only by cell-intrinsic therapy sensitivities but also by local interactions with the tumor microenvironment. Fibroblasts that make tumor stroma have been shown to produce paracrine factors that can strongly reduce the sensitivity of tumor cells to many types of targeted therapies. Moreover, a high stroma/tumor ratio is generally associated with poor survival and reduced therapy responses. However, in contrast to advanced knowledge of the molecular mechanisms responsible for stroma-mediated resistance, its effect on the ability of tumors to escape therapeutic eradication remains poorly understood. To a large extent, this gap of knowledge reflects the challenge of accounting for the spatial aspects of microenvironmental resistance, especially over longer time frames. To address this problem, we integrated spatial inferences of proliferation-death dynamics from an experimental animal model of targeted therapy responses with spatial mathematical modeling. With this approach, we dissected the impact of tumor/stroma distribution, magnitude and distance of stromal effects. While all of the tested parameters affected the ability of tumor cells to resist elimination, spatial patterns of stroma distribution within tumor tissue had a particularly strong impact.

The bone ecosystem facilitates multiple myeloma relapse and the evolution of heterogeneous drug resistant disease.

Multiple myeloma (MM) is an osteolytic malignancy that is incurable due to the emergence of treatment resistant disease. Defining how, when and where myeloma cell intrinsic and extrinsic bone microenvironmental mechanisms cause relapse is challenging with current biological approaches. Here, we report a biology-driven spatiotemporal hybrid agent-based model of the MM-bone microenvironment. Results indicate MM intrinsic mechanisms drive the evolution of treatment resistant disease but that the protective effects of bone microenvironment mediated drug resistance (EMDR) significantly enhances the probability and heterogeneity of resistant clones arising under treatment. Further, the model predicts that targeting of EMDR deepens therapy response by eliminating sensitive clones proximal to stroma and bone, a finding supported by in vivo studies. Altogether, our model allows for the study of MM clonal evolution over time in the bone microenvironment and will be beneficial for optimizing treatment efficacy so as to significantly delay disease relapse.

Peristromal niches protect lung cancers from targeted therapies through a combined effect of multiple molecular mediators.

Targeted therapies directed against oncogenic signaling addictions, such as inhibitors of ALK in ALK+ NSCLC often induce strong and durable clinical responses. However, they are not curative in metastatic cancers, as some tumor cells persist through therapy, eventually developing resistance. Therapy sensitivity can reflect not only cell-intrinsic mechanisms but also inputs from stromal microenvironment. Yet, the contribution of tumor stroma to therapeutic responses in vivo remains poorly defined. To address this gap of knowledge, we assessed the contribution of stroma-mediated resistance to therapeutic responses to the frontline ALK inhibitor alectinib in xenograft models of ALK+ NSCLC. We found that stroma-proximal tumor cells are partially protected against cytostatic effects of alectinib. This effect is observed not only in remission, but also during relapse, indicating the strong contribution of stroma-mediated resistance to both persistence and resistance. This therapy-protective effect of the stromal niche reflects a combined action of multiple mechanisms, including growth factors and extracellular matrix components. Consequently, despite improving alectinib responses, suppression of any individual resistance mechanism was insufficient to fully overcome the protective effect of stroma. Focusing on shared collateral sensitivity of persisters offered a superior therapeutic benefit, especially when using an antibody-drug conjugate with bystander effect to limit therapeutic escape. These findings indicate that stroma-mediated resistance might be the major contributor to both residual and progressing disease and highlight the limitation of focusing on suppressing a single resistance mechanism at a time.

Paracrine enhancement of tumor cell proliferation provides indirect stroma-mediated chemoresistance via acceleration of tumor recovery between chemotherapy cycles.

The ability of tumors to survive therapy reflects both cell-intrinsic and microenvironmental mechanisms. Across many cancers, including triple-negative breast cancer (TNBC), a high stroma/tumor ratio correlates with poor survival. In many contexts, this correlation can be explained by the direct reduction of therapy sensitivity by stroma-produced paracrine factors. We sought to explore whether this direct effect contributes to the link between stroma and poor responses to chemotherapies. Our in vitro studies with panels of TNBC cell line models and stromal isolates failed to detect a direct modulation of chemoresistance. At the same time, consistent with prior studies, we observed treatment-independent enhancement of tumor cell proliferation by fibroblast-produced secreted factors. Using spatial statistics analyses, we found that proximity to stroma is often associated with enhanced tumor cell proliferation in vivo . Based on these observations, we hypothesized an indirect link between stroma and chemoresistance, where stroma-augmented proliferation potentiates the recovery of residual tumors between chemotherapy cycles. To evaluate the feasibility of this hypothesis, we developed a spatial agent-based model of stroma impact on proliferation/death dynamics. The model was quantitatively parameterized using inferences from histological analyses and experimental studies. We found that the observed enhancement of tumor cell proliferation within stroma-proximal niches can enable tumors to avoid elimination over multiple chemotherapy cycles. Therefore, our study supports the existence of a novel, indirect mechanism of environment-mediated chemoresistance that might contribute to the negative correlation between stromal content and poor therapy outcomes.

Stroma-Mediated Breast Cancer Cell Proliferation Indirectly Drives Chemoresistance by Accelerating Tumor Recovery between Chemotherapy Cycles.

The ability of tumors to survive therapy reflects both cell-intrinsic and microenvironmental mechanisms. Across many cancers, including triple-negative breast cancer (TNBC), a high stroma/tumor ratio correlates with poor survival. In many contexts, this correlation can be explained by the direct reduction of therapy sensitivity induced by stroma-produced paracrine factors. We sought to explore whether this direct effect contributes to the link between stroma and poor responses to chemotherapies. In vitro studies with panels of TNBC cell line models and stromal isolates failed to detect a direct modulation of chemoresistance. At the same time, consistent with prior studies, fibroblast-produced secreted factors stimulated treatment-independent enhancement of tumor cell proliferation. Spatial analyses indicated that proximity to stroma is often associated with enhanced tumor cell proliferation in vivo. These observations suggested an indirect link between stroma and chemoresistance, where stroma-augmented proliferation potentiates the recovery of residual tumors between chemotherapy cycles. To evaluate this hypothesis, a spatial agent-based model of stroma impact on proliferation/death dynamics was developed that was quantitatively parameterized using inferences from histologic analyses and experimental studies. The model demonstrated that the observed enhancement of tumor cell proliferation within stroma-proximal niches could enable tumors to avoid elimination over multiple chemotherapy cycles. Therefore, this study supports the existence of an indirect mechanism of environment-mediated chemoresistance that might contribute to the negative correlation between stromal content and poor therapy outcomes. SIGNIFICANCE: Integration of experimental research with mathematical modeling reveals an indirect microenvironmental chemoresistance mechanism by which stromal cells stimulate breast cancer cell proliferation and highlights the importance of consideration of proliferation/death dynamics. See related commentary by Wall and Echeverria, p. 3667.

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation.

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Exploiting evolution to treat drug resistance: combination therapy and the double bind.

Although many anticancer therapies are successful in killing a large percentage of tumor cells when initially administered, the evolutionary dynamics underpinning tumor progression mean that, often, resistance is an inevitable outcome. Research in the field of ecology suggests that an evolutionary double bind could be an effective way to treat tumors. In an evolutionary double bind two therapies are used in combination such that evolving resistance to one leaves individuals more susceptible to the other. In this paper we present a general evolutionary game theory framework of a double bind to study the effect that such an approach would have in cancer. Furthermore we use this mathematical framework to understand recent experimental results that suggest a synergistic effect between a p53 cancer vaccine and chemotherapy. Our model recapitulates the latest experimental data and provides an explanation for its effectiveness based on the commensalistic relationship between the tumor phenotypes.