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.

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.

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.

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.

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.

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.

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?

Computational modeling reveals a key role for polarized myeloid cells in controlling osteoclast activity during bone injury repair.

Bone-forming osteoblasts and -resorbing osteoclasts control bone injury repair, and myeloid-derived cells such as monocytes and macrophages are known to influence their behavior. However, precisely how these multiple cell types coordinate and regulate each other over time within the bone marrow to restore bone is difficult to dissect using biological approaches. Conversely, mathematical modeling lends itself well to this challenge. Therefore, we generated an ordinary differential equation (ODE) model powered by experimental data (osteoblast, osteoclast, bone volume, pro- and anti-inflammatory myeloid cells) obtained from intra-tibially injured mice. Initial ODE results using only osteoblast/osteoclast populations demonstrated that bone homeostasis could not be recovered after injury, but this issue was resolved upon integration of pro- and anti-inflammatory myeloid population dynamics. Surprisingly, the ODE revealed temporal disconnects between the peak of total bone mineralization/resorption, and osteoblast/osteoclast numbers. Specifically, the model indicated that osteoclast activity must vary greatly (> 17-fold) to return the bone volume to baseline after injury and suggest that osteoblast/osteoclast number alone is insufficient to predict bone the trajectory of bone repair. Importantly, the values of osteoclast activity fall within those published previously. These data underscore the value of mathematical modeling approaches to understand and reveal new insights into complex biological processes.

Quantification and Optimization of Standard-of-Care Therapy to Delay the Emergence of Resistant Bone Metastatic Prostate Cancer.

BACKGROUND: Bone metastatic prostate cancer (BMPCa), despite the initial responsiveness to androgen deprivation therapy (ADT), inevitably becomes resistant. Recent clinical trials with upfront treatment of ADT combined with chemotherapy or novel hormonal therapies (NHTs) have extended overall patient survival. These results indicate that there is significant potential for the optimization of standard-of-care therapies to delay the emergence of progressive metastatic disease. METHODS: Here, we used data extracted from human bone metastatic biopsies pre- and post-abiraterone acetate/prednisone to generate a mathematical model of bone metastatic prostate cancer that can unravel the treatment impact on disease progression. Intra-tumor heterogeneity in regard to ADT and chemotherapy resistance was derived from biopsy data at a cellular level, permitting the model to track the dynamics of resistant phenotypes in response to treatment from biological first-principles without relying on data fitting. These cellular data were mathematically correlated with a clinical proxy for tumor burden, utilizing prostate-specific antigen (PSA) production as an example. RESULTS: Using this correlation, our model recapitulated the individual patient response to applied treatments in a separate and independent cohort of patients (n = 24), and was able to estimate the initial resistance to the ADT of each patient. Combined with an intervention-decision algorithm informed by patient-specific prediction of initial resistance, we propose to optimize the sequence of treatments for each patient with the goal of delaying the evolution of resistant disease and limit cancer cell growth, offering evidence for an improvement against retrospective data. CONCLUSIONS: Our results show how minimal but widely available patient information can be used to model and track the progression of BMPCa in real time, offering a clinically relevant insight into the patient-specific evolutionary dynamics of the disease and suggesting new therapeutic options for intervention. TRIAL REGISTRATION: NCT # 01953640. FUNDING: Funded by an NCI U01 (NCI) U01CA202958-01 and a Moffitt Team Science Award. CCL and DB were partly funded by an NCI PSON U01 (U01CA244101). AA was partly funded by a Department of Defense Prostate Cancer Research Program (W81XWH-15-1-0184) fellowship. LC was partly funded by a postdoctoral fellowship (PF-13-175-01-CSM) from the American Cancer Society.

Spontaneous cell fusions as a mechanism of parasexual recombination in tumour cell populations.

The initiation and progression of cancers reflect the underlying process of somatic evolution, in which the diversification of heritable phenotypes provides a substrate for natural selection, resulting in the outgrowth of the most fit subpopulations. Although somatic evolution can tap into multiple sources of diversification, it is assumed to lack access to (para)sexual recombination-a key diversification mechanism throughout all strata of life. On the basis of observations of spontaneous fusions involving cancer cells, the reported genetic instability of polypoid cells and the precedence of fusion-mediated parasexual recombination in fungi, we asked whether cell fusions between genetically distinct cancer cells could produce parasexual recombination. Using differentially labelled tumour cells, we found evidence of low-frequency, spontaneous cell fusions between carcinoma cells in multiple cell line models of breast cancer both in vitro and in vivo. While some hybrids remained polyploid, many displayed partial ploidy reduction, generating diverse progeny with heterogeneous inheritance of parental alleles, indicative of partial recombination. Hybrid cells also displayed elevated levels of phenotypic plasticity, which may further amplify the impact of cell fusions on the diversification of phenotypic traits. Using mathematical modelling, we demonstrated that the observed rates of spontaneous somatic cell fusions may enable populations of tumour cells to amplify clonal heterogeneity, thus facilitating the exploration of larger areas of the adaptive landscape (relative to strictly asexual populations), which may substantially accelerate a tumour's ability to adapt to new selective pressures.

Selection-driven tumor evolution with public goods leads to patterns of clonal expansion consistent with neutral growth.

Cancers are the result of eco-evolutionary processes fueled by heritable phenotypic diversification and driven by environmentally dependent selection. Space represents a key growth-limiting ecological resource, the ability to explore this resource is likely under strong selection. Using agent-based modeling, we explored the interplay between phenotypic strategies centered on gaining access to new space through cell-extrinsic degradation of extracellular matrix barriers and the exploitation of this resource through maximizing cell proliferation. While cell proliferation is a cell-intrinsic property, newly accessed space represents a public good, which can benefit both producers and non-producers. We found that this interplay results in ecological succession, enabling emergence of large, heterogeneous, and highly proliferative populations. Even though in our simulations both remodeling and proliferation strategies were under strong positive selection, their interplay led to sub-clonal architecture that could be interpreted as evidence for neutral evolution, warranting cautious interpretation of inferences from sequencing of cancer genomes.

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.

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.

Modeling Osteocyte Network Formation: Healthy and Cancerous Environments.

Advanced cancers, such as prostate and breast cancers, commonly metastasize to bone. In the bone matrix, dendritic osteocytes form a spatial network allowing communication between osteocytes and the osteoblasts located on the bone surface. This communication network facilitates coordinated bone remodeling. In the presence of a cancerous microenvironment, the topology of this network changes. In those situations, osteocytes often appear to be either overdifferentiated (i.e., there are more dendrites than healthy bone) or underdeveloped (i.e., dendrites do not fully form). In addition to structural changes, histological sections from metastatic breast cancer xenografted mice show that number of osteocytes per unit area is different between healthy bone and cancerous bone. We present a stochastic agent-based model for bone formation incorporating osteoblasts and osteocytes that allows us to probe both network structure and density of osteocytes in bone. Our model both allows for the simulation of our spatial network model and analysis of mean-field equations in the form of integro-partial differential equations. We considered variations of our model to study specific physiological hypotheses related to osteoblast differentiation; for example predicting how changing biological parameters, such as rates of bone secretion, rates of cancer formation, and rates of osteoblast differentiation can allow for qualitatively different network topologies. We then used our model to explore how commonly applied therapies such as bisphosphonates (e.g., zoledronic acid) impact osteocyte network formation.

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.

Stromal reactivity differentially drives tumour cell evolution and prostate cancer progression.

Prostate cancer (PCa) progression is a complex eco-evolutionary process driven by the feedback between evolving tumour cell phenotypes and microenvironmentally driven selection. To better understand this relationship, we used a multiscale mathematical model that integrates data from biology and pathology on the microenvironmental regulation of PCa cell behaviour. Our data indicate that the interactions between tumour cells and their environment shape the evolutionary dynamics of PCa cells and explain overall tumour aggressiveness. A key environmental determinant of this aggressiveness is the stromal ecology, which can be either inhibitory, highly reactive (supportive) or non-reactive (neutral). Our results show that stromal ecology correlates directly with tumour growth but inversely modulates tumour evolution. This suggests that aggressive, environmentally independent PCa may be a result of poor stromal ecology, supporting the concept that purely tumour epithelium-centric metrics of aggressiveness may be incomplete and that incorporating markers of stromal ecology would improve prognosis.

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.