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.

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.

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.

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.

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.

Non-cell-autonomous driving of tumour growth supports sub-clonal heterogeneity.

Cancers arise through a process of somatic evolution that can result in substantial sub-clonal heterogeneity within tumours. The mechanisms responsible for the coexistence of distinct sub-clones and the biological consequences of this coexistence remain poorly understood. Here we used a mouse xenograft model to investigate the impact of sub-clonal heterogeneity on tumour phenotypes and the competitive expansion of individual clones. We found that tumour growth can be driven by a minor cell subpopulation, which enhances the proliferation of all cells within a tumour by overcoming environmental constraints and yet can be outcompeted by faster proliferating competitors, resulting in tumour collapse. We developed a mathematical modelling framework to identify the rules underlying the generation of intra-tumour clonal heterogeneity. We found that non-cell-autonomous driving of tumour growth, together with clonal interference, stabilizes sub-clonal heterogeneity, thereby enabling inter-clonal interactions that can lead to new phenotypic traits.

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.

Mathematical modeling of erythrocyte chimerism informs genetic intervention strategies for sickle cell disease.

Recent advances in gene therapy and genome-engineering technologies offer the opportunity to correct sickle cell disease (SCD), a heritable disorder caused by a point mutation in the ß-globin gene. The developmental switch from fetal γ-globin to adult ß-globin is governed in part by the transcription factor (TF) BCL11A. This TF has been proposed as a therapeutic target for reactivation of γ-globin and concomitant reduction of ß-sickle globin. In this and other approaches, genetic alteration of a portion of the hematopoietic stem cell (HSC) compartment leads to a mixture of sickling and corrected red blood cells (RBCs) in periphery. To reverse the sickling phenotype, a certain proportion of corrected RBCs is necessary; the degree of HSC alteration required to achieve a desired fraction of corrected RBCs remains unknown. To address this issue, we developed a mathematical model describing aging and survival of sickle-susceptible and normal RBCs; the former can have a selective survival advantage leading to their overrepresentation. We identified the level of bone marrow chimerism required for successful stem cell-based gene therapies in SCD. Our findings were further informed using an experimental mouse model, where we transplanted mixtures of Berkeley SCD and normal murine bone marrow cells to establish chimeric grafts in murine hosts. Our integrative theoretical and experimental approach identifies the target frequency of HSC alterations required for effective treatment of sickling syndromes in humans. Our work replaces episodic observations of such target frequencies with a mathematical modeling framework that covers a large and continuous spectrum of chimerism conditions. Am. J. Hematol. 91:931-937, 2016. © 2016 Wiley Periodicals, Inc.

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.

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.

Adult stem cell activity in naked mole rats for long-term tissue maintenance.

The naked mole rat (NMR), Heterocephalus glaber, the longest-living rodent, provides a unique opportunity to explore how evolution has shaped adult stem cell (ASC) activity and tissue function with increasing lifespan. Using cumulative BrdU labelling and a quantitative imaging approach to track intestinal ASCs (Lgr5+) in their native in vivo state, we find an expanded pool of Lgr5+ cells in NMRs, and these cells specifically at the crypt base (Lgr5+CBC) exhibit slower division rates compared to those in short-lived mice but have a similar turnover as human LGR5+CBC cells. Instead of entering quiescence (G0), NMR Lgr5+CBC cells reduce their division rates by prolonging arrest in the G1 and/or G2 phases of the cell cycle. Moreover, we also observe a higher proportion of differentiated cells in NMRs that confer enhanced protection and function to the intestinal mucosa which is able to detect any chemical imbalance in the luminal environment efficiently, triggering a robust pro-apoptotic, anti-proliferative response within the stem/progenitor cell zone.

The mechanics of stochastic slowdown in evolutionary games.

We study the stochastic dynamics of evolutionary games, and focus on the so-called 'stochastic slowdown' effect, previously observed in Altrock et al. (2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a beneficial mutation may take longer to fixate than a neutral one. More precisely, the fixation time conditioned on the mutant taking over can show a maximum at intermediate selection strength. We show that this phenomenon is present in the Prisoner's Dilemma, and also discuss counterintuitive slowdown and speedup in coexistence games. In order to establish the microscopic origins of these phenomena, we calculate the average sojourn times. This allows us to identify the transient states which contribute most to the slowdown effect, and enables us to provide an understanding of slowdown in the takeover of a small group of cooperators by defectors in the Prisoner's Dilemma: Defection spreads fast initially, but the final steps to takeover can be delayed substantially. The analysis of coexistence games reveals even more intricate non-monotonic behavior. In small populations, the conditional average fixation time can show multiple extrema as a function of the selection strength, e.g., slowdown, speedup, and slowdown again. We classify generic 2×2 games with respect to the possibility to observe non-monotonic behavior of the conditional average fixation time as a function of selection strength.

Stability properties of underdominance in finite subdivided populations.

IN ISOLATED populations underdominance leads to bistable evolutionary dynamics: below a certain mutant allele frequency the wildtype succeeds. Above this point, the potentially underdominant mutant allele fixes. In subdivided populations with gene flow there can be stable states with coexistence of wildtypes and mutants: polymorphism can be maintained because of a migration-selection equilibrium, i.e., selection against rare recent immigrant alleles that tend to be heterozygous. We focus on the stochastic evolutionary dynamics of systems where demographic fluctuations in the coupled populations are the main source of internal noise. We discuss the influence of fitness, migration rate, and the relative sizes of two interacting populations on the mean extinction times of a group of potentially underdominant mutant alleles. We classify realistic initial conditions according to their impact on the stochastic extinction process. Even in small populations, where demographic fluctuations are large, stability properties predicted from deterministic dynamics show remarkable robustness. Fixation of the mutant allele becomes unlikely but the time to its extinction can be long.