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.

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.

Circulating tumor DNA adds specificity to PET after axicabtagene ciloleucel in large B-cell lymphoma.

We examined the meaning of metabolically active lesions on 1-month restaging nuclear imaging of patients with relapsed/refractory large B-cell lymphoma receiving axicabtagene ciloleucel (axi-cel) by assessing the relationship between total metabolic tumor volume (MTV) on positron emission tomography (PET) scans and circulating tumor DNA (ctDNA) in the plasma. In this prospective multicenter sample collection study, MTV was retrospectively calculated via commercial software at baseline, 1, and 3 months after chimeric antigen receptor (CAR) T-cell therapy; ctDNA was available before and after axi-cel administration. Spearman correlation coefficient (rs) was used to study the relationship between the variables, and a mathematical model was constructed to describe tumor dynamics 1 month after CAR T-cell therapy. The median time between baseline scan and axi-cel infusion was 33 days (range, 1-137 days) for all 57 patients. For 41 of the patients with imaging within 33 days of axi-cel or imaging before that time but no bridging therapy, the correlation at baseline became stronger (rs, 0.61; P < .0001) compared with all patients (rs, 0.38; P = .004). Excluding patients in complete remission with no measurable residual disease, ctDNA and MTV at 1 month did not correlate (rs, 0.28; P = .11) but correlated at 3 months (rs, 0.79; P = .0007). Modeling of tumor dynamics, which incorporated ctDNA and inflammation as part of MTV, recapitulated the outcomes of patients with positive radiologic 1-month scans. Our results suggested that nonprogressing hypermetabolic lesions on 1-month PET represent ongoing treatment responses, and their composition may be elucidated by concurrently examining the ctDNA.

Geospatial characterization of immune cell distributions and dynamics across the microenvironment in clear cell renal cell carcinoma.

INTRODUCTION: In clear cell renal cell carcinoma (ccRCC), tumor-associated macrophage (TAM) induction of CD8+T cells into a terminally exhausted state has been implicated as a major mechanism of immunotherapy resistance, but a deeper biological understanding is necessary. METHODS: Primary ccRCC tumor samples were obtained from 97 patients between 2004 and 2018. Multiplex immunofluorescence using lymphoid and myeloid markers was performed in seven regions of interest per patient across three predefined zones, and geospatial analysis was performed using Ripley's K analysis, a methodology adapted from ecology. RESULTS: Clustering of CD163+M2 like TAMs into the stromal compartment at the tumor-stroma interface was associated with worse clinical stage (tumor/CD163+nK(75): stage I/II: 4.4 (IQR -0.5 to 5.1); stage III: 1.4 (IQR -0.3 to 3.5); stage IV: 0.6 (IQR -2.1 to 2.1); p=0.04 between stage I/II and stage IV), and worse overall survival (OS) and cancer-specific survival (CSS) (tumor/CD163+nK(75): median OS-hi=149 months, lo=86 months, false-discovery rate (FDR)-adj. Cox p<0.001; median CSS-hi=174 months, lo=85 months; FDR-adj. Cox p<0.001). An RNA-seq differential gene expression score was developed using this geospatial metric, and was externally validated in multiple independent cohorts of patients with ccRCC including: TCGA KIRC, and the IMmotion151, IMmotion150, and JAVELIN Renal 101 clinical trials. In addition, this CD163+ geospatial pattern was found to be associated with a higher TIM-3+ proportion of CD8+T cells, indicative of terminal exhaustion (tumor-core: 0.07 (IQR 0.04-0.14) vs 0.40 (IQR 0.15-0.66), p=0.05). CONCLUSIONS: Geospatial clustering of CD163+M2 like TAMs into the stromal compartment at the tumor-stromal interface was associated with poor clinical outcomes and CD8+T cell terminal exhaustion.

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.

Intra-tumor heterogeneity, turnover rate and karyotype space shape susceptibility to missegregation-induced extinction.

The phenotypic efficacy of somatic copy number alterations (SCNAs) stems from their incidence per base pair of the genome, which is orders of magnitudes greater than that of point mutations. One mitotic event stands out in its potential to significantly change a cell's SCNA burden-a chromosome missegregation. A stochastic model of chromosome mis-segregations has been previously developed to describe the evolution of SCNAs of a single chromosome type. Building upon this work, we derive a general deterministic framework for modeling missegregations of multiple chromosome types. The framework offers flexibility to model intra-tumor heterogeneity in the SCNAs of all chromosomes, as well as in missegregation- and turnover rates. The model can be used to test how selection acts upon coexisting karyotypes over hundreds of generations. We use the model to calculate missegregation-induced population extinction (MIE) curves, that separate viable from non-viable populations as a function of their turnover- and missegregation rates. Turnover- and missegregation rates estimated from scRNA-seq data are then compared to theoretical predictions. We find convergence of theoretical and empirical results in both the location of MIE curves and the necessary conditions for MIE. When a dependency of missegregation rate on karyotype is introduced, karyotypes associated with low missegregation rates act as a stabilizing refuge, rendering MIE impossible unless turnover rates are exceedingly high. Intra-tumor heterogeneity, including heterogeneity in missegregation rates, increases as tumors progress, rendering MIE unlikely.

Progenitor Hierarchy of Chronic Myelomonocytic Leukemia Identifies Inflammatory Monocytic-Biased Trajectory Linked to Worse Outcomes.

Myeloblast expansion is a hallmark of disease progression and comprises CD34+ hematopoietic stem and progenitor cells (HSPC). How this compartment evolves during disease progression in chronic myeloid neoplasms is unknown. Using single-cell RNA sequencing and high-parameter flow cytometry, we show that chronic myelomonocytic leukemia (CMML) CD34+ HSPC can be classified into three differentiation trajectories: monocytic, megakaryocyte-erythroid progenitor (MEP), and normal-like. Hallmarks of monocytic-biased trajectory were enrichment of CD120b+ inflammatory granulocyte-macrophage progenitor (GMP)-like cells, activated cytokine receptor signaling, phenotypic hematopoietic stem cell (HSC) depletion, and adverse outcomes. Cytokine receptor diversity was generally an adverse feature and elevated in CD120b+ GMPs. Hypomethylating agents decreased monocytic-biased cells in CMML patients. Given the enrichment of RAS pathway mutations in monocytic-biased cells, NRAS-competitive transplants and LPS-treated xenograft models recapitulated monocytic-biased CMML, suggesting that hematopoietic stress precipitates the monocytic-biased state. Deconvolution of HSPC compartments in other myeloid neoplasms and identifying therapeutic strategies to mitigate the monocytic-biased differentiation trajectory should be explored. SIGNIFICANCE: Our findings establish that multiple differentiation states underlie CMML disease progression. These states are negatively augmented by inflammation and positively affected by hypomethylating agents. Furthermore, we identify HSC depletion and expansion of GMP-like cells with increased cytokine receptor diversity as a feature of myeloblast expansion in inflammatory chronic myeloid neoplasms. This article is highlighted in the In This Issue feature, p. 476.

Autocrine signaling can explain the emergence of Allee effects in cancer cell populations.

In many human cancers, the rate of cell growth depends crucially on the size of the tumor cell population. Low, zero, or negative growth at low population densities is known as the Allee effect; this effect has been studied extensively in ecology, but so far lacks a good explanation in the cancer setting. Here, we formulate and analyze an individual-based model of cancer, in which cell division rates are increased by the local concentration of an autocrine growth factor produced by the cancer cells themselves. We show, analytically and by simulation, that autocrine signaling suffices to cause both strong and weak Allee effects. Whether low cell densities lead to negative (strong effect) or reduced (weak effect) growth rate depends directly on the ratio of cell death to proliferation, and indirectly on cellular dispersal. Our model is consistent with experimental observations from three patient-derived brain tumor cell lines grown at different densities. We propose that further studying and quantifying population-wide feedback, impacting cell growth, will be central for advancing our understanding of cancer dynamics and treatment, potentially exploiting Allee effects for therapy.

Quantification of T- and B-cell Immune Receptor Distribution Diversity Characterizes Immune Cell Infiltration and Lymphocyte Heterogeneity in Clear Cell Renal Cell Carcinoma.

Immune-modulating systemic therapies are often used to treat advanced cancer such as metastatic clear cell renal cell carcinoma (ccRCC). Used alone, sequence-based biomarkers neither accurately capture patient dynamics nor the tumor immune microenvironment. To better understand the tumor ecology of this immune microenvironment, we quantified tumor infiltration across three distinct ccRCC patient tumor cohorts using complementarity determining region-3 (CDR3) sequence recovery counts in tumor-infiltrating lymphocytes and a generalized diversity index (GDI) for CDR3 sequence distributions. GDI can be understood as a curve over a continuum of diversity scales that allows sensitive characterization of distributions to capture sample richness, evenness, and subsampling uncertainty, along with other important metrics that characterize tumor heterogeneity. For example, richness quantified the total unique sequence count, while evenness quantified similarities across sequence frequencies. Significant differences in receptor sequence diversity across gender and race revealed that patients with larger and more clinically aggressive tumors had increased richness of recovered tumoral CDR3 sequences, specifically in those from T-cell receptor alpha and B-cell immunoglobulin lambda light chain. The GDI inflection point (IP) allowed for a novel and robust measure of distribution evenness. High IP values were associated with improved overall survival, suggesting that normal-like sequence distributions lead to better outcomes. These results propose a new quantitative tool that can be used to better characterize patient-specific differences related to immune cell infiltration, and to identify unique characteristics of tumor-infiltrating lymphocyte heterogeneity in ccRCC and other malignancies. SIGNIFICANCE: Assessment of tumor-infiltrating T-cell and B-cell diversity in renal cell carcinoma advances the understanding of tumor-immune system interactions, linking tumor immune ecology with tumor burden, aggressiveness, and patient survival. See related commentary by Krishna and Hakimi, p. 764.

Tipping Cancer Cells Over the Edge: The Context-Dependent Cost of High Ploidy.

Tetraploidy is an aneuploidy-permissive condition that can fuel tumorgenesis. The tip-over hypothesis of cytotoxic therapy sensitivity proposes that therapy is effective if it pushes a cell's aneuploidy above a viable tipping point. But elevated aneuploidy alone may not account for this tipping point. Tissue microenvironments that lack sufficient resources to support tetraploid cells can explain the fitness cost of aneuploidy. Raw materials needed to generate deoxynucleotides, the building blocks of DNA, are candidate rate-limiting factors for the evolution of high-ploidy cancer cells. Understanding the resource cost of high ploidy is key to uncover its therapeutic vulnerabilities across tissue sites with versatile energy supplies.

Geospatial Cellular Distribution of Cancer-Associated Fibroblasts Significantly Impacts Clinical Outcomes in Metastatic Clear Cell Renal Cell Carcinoma.

Cancer-associated fibroblasts (CAF) are highly prevalent cells in the tumor microenvironment in clear cell renal cell carcinoma (ccRCC). CAFs exhibit a pro-tumor effect in vitro and have been implicated in tumor cell proliferation, metastasis, and treatment resistance. Our objective is to analyze the geospatial distribution of CAFs with proliferating and apoptotic tumor cells in the ccRCC tumor microenvironment and determine associations with survival and systemic treatment. Pre-treatment primary tumor samples were collected from 96 patients with metastatic ccRCC. Three adjacent slices were obtained from 2 tumor-core regions of interest (ROI) per patient, and immunohistochemistry (IHC) staining was performed for αSMA, Ki-67, and caspase-3 to detect CAFs, proliferating cells, and apoptotic cells, respectively. H-scores and cellular density were generated for each marker. ROIs were aligned, and spatial point patterns were generated, which were then used to perform spatial analyses using a normalized Ripley's K function at a radius of 25 µm (nK(25)). The survival analyses used an optimal cut-point method, maximizing the log-rank statistic, to stratify the IHC-derived metrics into high and low groups. Multivariable Cox regression analyses were performed accounting for age and International Metastatic RCC Database Consortium (IMDC) risk category. Survival outcomes included overall survival (OS) from the date of diagnosis, OS from the date of immunotherapy initiation (OS-IT), and OS from the date of targeted therapy initiation (OS-TT). Therapy resistance was defined as progression-free survival (PFS) <6 months, and therapy response was defined as PFS >9 months. CAFs exhibited higher cellular clustering with Ki-67+ cells than with caspase-3+ cells (nK(25): Ki-67 1.19; caspase-3 1.05; p = 0.04). The median nearest neighbor (NN) distance from CAFs to Ki-67+ cells was shorter compared to caspase-3+ cells (15 µm vs. 37 µm, respectively; p < 0.001). Multivariable Cox regression analyses demonstrated that both high Ki-67+ density and H-score were associated with worse OS, OS-IT, and OS-TT. Regarding αSMA+CAFs, only a high H-score was associated with worse OS, OS-IT, and OS-TT. For caspase-3+, high H-score and density were associated with worse OS and OS-TT. Patients whose tumors were resistant to targeted therapy (TT) had higher Ki-67 density and H-scores than those who had TT responses. Overall, this ex vivo geospatial analysis of CAF distribution suggests that close proximity clustering of tumor cells and CAFs potentiates tumor cell proliferation, resulting in worse OS and resistance to TT in metastatic ccRCC.

Spatial clustering of CD68+ tumor associated macrophages with tumor cells is associated with worse overall survival in metastatic clear cell renal cell carcinoma.

Immune infiltration is typically quantified using cellular density, not accounting for cellular clustering. Tumor-associated macrophages (TAM) activate oncogenic signaling through paracrine interactions with tumor cells, which may be better reflected by local cellular clustering than global density metrics. Using multiplex immunohistochemistry and digital pathologic analysis we quantified cellular density and cellular clustering for myeloid cell markers in 129 regions of interest from 55 samples from 35 patients with metastatic ccRCC. CD68+ cells were found to be clustered with tumor cells and dispersed from stromal cells, while CD163+ and CD206+ cells were found to be clustered with stromal cells and dispersed from tumor cells. CD68+ density was not associated with OS, while high tumor/CD68+ cell clustering was associated with significantly worse OS. These novel findings would not have been identified if immune infiltrate was assessed using cellular density alone, highlighting the importance of including spatial analysis in studies of immune cell infiltration of tumors. Significance: Increased clustering of CD68+ TAMs and tumor cells was associated with worse overall survival for patients with metastatic ccRCC. This effect would not have been identified if immune infiltrate was assessed using cell density alone, highlighting the importance of including spatial analysis in studies of immune cell infiltration of tumors.

The roles of T cell competition and stochastic extinction events in chimeric antigen receptor T cell therapy.

Chimeric antigen receptor (CAR) T cell therapy is a remarkably effective immunotherapy that relies on in vivo expansion of engineered CAR T cells, after lymphodepletion (LD) by chemotherapy. The quantitative laws underlying this expansion and subsequent tumour eradication remain unknown. We develop a mathematical model of T cell-tumour cell interactions and demonstrate that expansion can be explained by immune reconstitution dynamics after LD and competition among T cells. CAR T cells rapidly grow and engage tumour cells but experience an emerging growth rate disadvantage compared to normal T cells. Since tumour eradication is deterministically unstable in our model, we define cure as a stochastic event, which, even when likely, can occur at variable times. However, we show that variability in timing is largely determined by patient variability. While cure events impacted by these fluctuations occur early and are narrowly distributed, progression events occur late and are more widely distributed in time. We parameterized our model using population-level CAR T cell and tumour data over time and compare our predictions with progression-free survival rates. We find that therapy could be improved by optimizing the tumour-killing rate and the CAR T cells' ability to adapt, as quantified by their carrying capacity. Our tumour extinction model can be leveraged to examine why therapy works in some patients but not others, and to better understand the interplay of deterministic and stochastic effects on outcomes. For example, our model implies that LD before a second CAR T injection is necessary.

The harsh microenvironment in early breast cancer selects for a Warburg phenotype.

The harsh microenvironment of ductal carcinoma in situ (DCIS) exerts strong evolutionary selection pressures on cancer cells. We hypothesize that the poor metabolic conditions near the ductal center foment the emergence of a Warburg Effect (WE) phenotype, wherein cells rapidly ferment glucose to lactic acid, even in normoxia. To test this hypothesis, we subjected low-glycolytic breast cancer cells to different microenvironmental selection pressures using combinations of hypoxia, acidosis, low glucose, and starvation for many months and isolated single clones for metabolic and transcriptomic profiling. The two harshest conditions selected for constitutively expressed WE phenotypes. RNA sequencing analysis of WE clones identified the transcription factor KLF4 as potential inducer of the WE phenotype. In stained DCIS samples, KLF4 expression was enriched in the area with the harshest microenvironmental conditions. We simulated in vivo DCIS phenotypic evolution using a mathematical model calibrated from the in vitro results. The WE phenotype emerged in the poor metabolic conditions near the necrotic core. We propose that harsh microenvironments within DCIS select for a WE phenotype through constitutive transcriptional reprogramming, thus conferring a survival advantage and facilitating further growth and invasion.

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.

Investigating Inter- and Intrasample Diversity of Single-Cell RNA Sequencing Datasets.

Tumor heterogeneity can arise from a variety of extrinsic and intrinsic sources and drives unfavorable outcomes. With recent technological advances, single-cell RNA sequencing has become a way for researchers to easily assay tumor heterogeneity at the transcriptomic level with high resolution. However, ongoing research focuses on different ways to analyze this big data and how to compare across multiple different samples. In this chapter, we provide a practical guide to calculate inter- and intrasample diversity metrics from single-cell RNA sequencing datasets. These measures of diversity are adapted from commonly used metrics in statistics and ecology to quantify and compare sample heterogeneity at single-cell resolution.

Integrating Mathematical Modeling with High-Throughput Imaging Explains How Polyploid Populations Behave in Nutrient-Sparse Environments.

Breast cancer progresses in a multistep process from primary tumor growth and stroma invasion to metastasis. Nutrient-limiting environments promote chemotaxis with aggressive morphologies characteristic of invasion. It is unknown how coexisting cells differ in their response to nutrient limitations and how this impacts invasion of the metapopulation as a whole. In this study, we integrate mathematical modeling with microenvironmental perturbation data to investigate invasion in nutrient-limiting environments inhabited by one or two cancer cell subpopulations. Subpopulations were defined by their energy efficiency and chemotactic ability. Invasion distance traveled by a homogeneous population was estimated. For heterogeneous populations, results suggest that an imbalance between nutrient efficacy and chemotactic superiority accelerates invasion. Such imbalance will spatially segregate the two populations and only one type will dominate at the invasion front. Only if these two phenotypes are balanced, the two subpopulations compete for the same space, which decelerates invasion. We investigate ploidy as a candidate biomarker of this phenotypic heterogeneity and discuss its potential to inform the dose of mTOR inhibitors (mTOR-I) that can inhibit chemotaxis just enough to facilitate such competition. SIGNIFICANCE: This study identifies the double-edged sword of high ploidy as a prerequisite to personalize combination therapies with cytotoxic drugs and inhibitors of signal transduction pathways such as mTOR-Is. GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/80/22/5109/F1.large.jpg.

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.

Time scales and wave formation in non-linear spatial public goods games.

The co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and spatial population structure. As co-evolving populations grow into a spatial domain, their initial spatial arrangement and their growth rate differences are important factors that determine the long-term outcome. We here model producer and free-rider co-evolution in the context of a diffusive public good (PG) that is produced by the producers at a cost but evokes local concentration-dependent growth benefits to all. The benefit of the PG can be non-linearly dependent on public good concentration. We consider the spatial growth dynamics of producers and free-riders in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by the processes of birth, death and diffusion (cell movement and public good distribution). Typically, one population goes extinct, but the time-scale of this process varies with initial conditions and the growth rate functions. We establish that spatial variation is transient regardless of dimensionality, and that structured initial conditions lead to increasing times to get close to an extinction state, called ε-extinction time. Further, we find that uncorrelated initial spatial structures do not influence this ε-extinction time in comparison to a corresponding well-mixed (non-spatial) system. In order to estimate the ε-extinction time of either free-riders or producers we derive a slow manifold solution. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated. Our results provide quantitative predictions for the transient spatial dynamics of cooperative traits under pressure of extinction.