Understanding and leveraging phenotypic plasticity during metastasis formation.

Cancer metastasis is the process of detrimental systemic spread and the primary cause of cancer-related fatalities. Successful metastasis formation requires tumor cells to be proliferative and invasive; however, cells cannot be effective at both tasks simultaneously. Tumor cells compensate for this trade-off by changing their phenotype during metastasis formation through phenotypic plasticity. Given the changing selection pressures and competitive interactions that tumor cells face, it is poorly understood how plasticity shapes the process of metastasis formation. Here, we develop an ecology-inspired mathematical model with phenotypic plasticity and resource competition between phenotypes to address this knowledge gap. We find that phenotypically plastic tumor cell populations attain a stable phenotype equilibrium that maintains tumor cell heterogeneity. Considering treatment types inspired by chemo- and immunotherapy, we highlight that plasticity can protect tumors against interventions. Turning this strength into a weakness, we corroborate current clinical practices to use plasticity as a target for adjuvant therapy. We present a parsimonious view of tumor plasticity-driven metastasis that is quantitative and experimentally testable, and thus potentially improving the mechanistic understanding of metastasis at the cell population level, and its treatment consequences.

Promoting extinction or minimizing growth? The impact of treatment on trait trajectories in evolving populations.

When cancers or bacterial infections establish, small populations of cells have to free themselves from homoeostatic regulations that prevent their expansion. Trait evolution allows these populations to evade this regulation, escape stochastic extinction and climb up the fitness landscape. In this study, we analyze this complex process and investigate the fate of a cell population that underlies the basic processes of birth, death, and mutation. We find that the shape of the fitness landscape dictates a circular adaptation trajectory in the trait space spanned by birth and death rates. We show that successful adaptation is less likely for parental populations with higher turnover (higher birth and death rates). Including density- or trait-affecting treatment we find that these treatment types change the adaptation dynamics in agreement with a geometrical analysis of fitness gradients. Treatment strategies that simultaneously target birth and death rates are most effective, but also increase evolvability. By mapping physiological adaptation pathways and molecular drug mechanisms to traits and treatments with clear eco-evolutionary consequences, we can achieve a much better understanding of the adaptation dynamics and the eco-evolutionary mechanisms at play in the dynamics of cancer and bacterial infections.

Multiscale heterogeneity in gastric adenocarcinoma evolution is an obstacle to precision medicine.

BACKGROUND: Cancer is a somatic evolutionary disease and adenocarcinomas of the stomach and gastroesophageal junction (GC) may serve as a two-dimensional model of cancer expansion, in which tumor subclones are not evenly mixed during tumor progression but rather spatially separated and diversified. We hypothesize that precision medicine efforts are compromised when clinical decisions are based on a single-sample analysis, which ignores the mechanisms of cancer evolution and resulting intratumoral heterogeneity. Using multiregional whole-exome sequencing, we investigated the effect of somatic evolution on intratumoral heterogeneity aiming to shed light on the evolutionary biology of GC. METHODS: The study comprised a prospective discovery cohort of 9 and a validation cohort of 463 GCs. Multiregional whole-exome sequencing was performed using samples form 45 primary tumors and 3 lymph node metastases (range 3-10 tumor samples/patient) of the discovery cohort. RESULTS: In total, the discovery cohort harbored 16,537 non-synonymous mutations. Intratumoral heterogeneity of somatic mutations and copy number variants were present in all tumors of the discovery cohort. Of the non-synonymous mutations, 53-91% were not present in each patient's sample; 399 genes harbored 2-4 different non-synonymous mutations in the same patient; 175 genes showed copy number variations, the majority being heterogeneous, including CD274 (PD-L1). Multi-sample tree-based analyses provided evidence for branched evolution being most complex in a microsatellite instable GC. The analysis of the mode of evolution showed a high degree of heterogeneity in deviation from neutrality within each tumor. We found evidence of parallel evolution and evolutionary trajectories: different mutations of SMAD4 aligned with different subclones and were found only in TP53 mutant GCs. CONCLUSIONS: Neutral and non-neutral somatic evolution shape the mutational landscape in GC along its lateral expansions. It leads to complex spatial intratumoral heterogeneity, where lymph node metastases may stem from different areas of the primary tumor, synchronously. Our findings may have profound effects on future patient management. They illustrate the risk of mis-interpreting tumor genetics based on single-sample analysis and open new avenues for an evolutionary classification of GC, i.e., the discovery of distinct evolutionary trajectories which can be utilized for precision medicine.

Sex or cannibalism: Polyphenism and kin recognition control social action strategies in nematodes.

Resource polyphenisms, where single genotypes produce alternative feeding strategies in response to changing environments, are thought to be facilitators of evolutionary novelty. However, understanding the interplay between environment, morphology, and behavior and its significance is complex. We explore a radiation of Pristionchus nematodes with discrete polyphenic mouth forms and associated microbivorous versus cannibalistic traits. Notably, comparing 29 Pristionchus species reveals that reproductive mode strongly correlates with mouth-form plasticity. Male-female species exhibit the microbivorous morph and avoid parent-offspring conflict as indicated by genetic hybrids. In contrast, hermaphroditic species display cannibalistic morphs encouraging competition. Testing predation between 36 co-occurring strains of the hermaphrodite P. pacificus showed that killing inversely correlates with genomic relatedness. These empirical data together with theory reveal that polyphenism (plasticity), kin recognition, and relatedness are three major factors that shape cannibalistic behaviors. Thus, developmental plasticity influences cooperative versus competitive social action strategies in diverse animals.

The impact of phenotypic heterogeneity of tumour cells on treatment and relapse dynamics.

Intratumour heterogeneity is increasingly recognized as a frequent problem for cancer treatment as it allows for the evolution of resistance against treatment. While cancer genotyping becomes more and more established and allows to determine the genetic heterogeneity, less is known about the phenotypic heterogeneity among cancer cells. We investigate how phenotypic differences can impact the efficiency of therapy options that select on this diversity, compared to therapy options that are independent of the phenotype. We employ the ecological concept of trait distributions and characterize the cancer cell population as a collection of subpopulations that differ in their growth rate. We show in a deterministic model that growth rate-dependent treatment types alter the trait distribution of the cell population, resulting in a delayed relapse compared to a growth rate-independent treatment. Whether the cancer cell population goes extinct or relapse occurs is determined by stochastic dynamics, which we investigate using a stochastic model. Again, we find that relapse is delayed for the growth rate-dependent treatment type, albeit an increased relapse probability, suggesting that slowly growing subpopulations are shielded from extinction. Sequential application of growth rate-dependent and growth rate-independent treatment types can largely increase treatment efficiency and delay relapse. Interestingly, even longer intervals between decisions to change the treatment type may achieve close-to-optimal efficiencies and relapse times. Monitoring patients at regular check-ups may thus provide the temporally resolved guidance to tailor treatments to the changing cancer cell trait distribution and allow clinicians to cope with this dynamic heterogeneity.

The invasion of de-differentiating cancer cells into hierarchical tissues.

Many fast renewing tissues are characterized by a hierarchical cellular architecture, with tissue specific stem cells at the root of the cellular hierarchy, differentiating into a whole range of specialized cells. There is increasing evidence that tumors are structured in a very similar way, mirroring the hierarchical structure of the host tissue. In some tissues, differentiated cells can also revert to the stem cell phenotype, which increases the risk that mutant cells lead to long lasting clones in the tissue. However, it is unclear under which circumstances de-differentiating cells will invade a tissue. To address this, we developed mathematical models to investigate how de-differentiation is selected as an adaptive mechanism in the context of cellular hierarchies. We derive thresholds for which de-differentiation is expected to emerge, and it is shown that the selection of de-differentiation is a result of the combination of the properties of cellular hierarchy and de-differentiation patterns. Our results suggest that de-differentiation is most likely to be favored provided stem cells having the largest effective self-renewal rate. Moreover, jumpwise de-differentiation provides a wider range of favorable conditions than stepwise de-differentiation. Finally, the effect of de-differentiation on the redistribution of self-renewal and differentiation probabilities also greatly influences the selection for de-differentiation.

Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time.

Population structure can be modeled by evolutionary graphs, which can have a substantial influence on the fate of mutants. Individuals are located on the nodes of these graphs, competing to take over the graph via the links. Applications for this framework range from the ecology of river systems and cancer initiation in colonic crypts to biotechnological search for optimal mutations. In all these applications, both the probability of fixation and the associated time are of interest. We study this problem for all undirected and unweighted graphs up to a certain size. We devise a genetic algorithm to find graphs with high or low fixation probability and short or long fixation time and study their structure searching for common themes. Our work unravels structural properties that maximize or minimize fixation probability and time, which allows us to contribute to a first map of the universe of evolutionary graphs.

How many samples are needed to infer truly clonal mutations from heterogenous tumours?

BACKGROUND: Modern cancer treatment strategies aim to target tumour specific genetic (or epigenetic) alterations. Treatment response improves if these alterations are clonal, i.e. present in all cancer cells within tumours. However, the identification of truly clonal alterations is impaired by the tremendous intra-tumour genetic heterogeneity and unavoidable sampling biases. METHODS: Here, we investigate the underlying causes of these spatial sampling biases and how the distribution and sizes of biopsies in sampling protocols can be optimised to minimize such biases. RESULTS: We find that in the ideal case, less than a handful of samples can be enough to infer truly clonal mutations. The frequency of the largest sub-clone at diagnosis is the main factor determining the accuracy of truncal mutation estimation in structured tumours. If the first sub-clone is dominating the tumour, higher spatial dispersion of samples and larger sample size can increase the accuracy of the estimation. In such an improved sampling scheme, fewer samples will enable the detection of truly clonal alterations with the same probability. CONCLUSIONS: Taking spatial tumour structure into account will decrease the probability to misclassify a sub-clonal mutation as clonal and promises better informed treatment decisions.

Replicative cellular age distributions in compartmentalized tissues.

The cellular age distribution of hierarchically organized tissues can reveal important insights into the dynamics of cell differentiation and self-renewal and associated cancer risks. Here, we examine the effect of progenitor compartments with varying differentiation and self-renewal capacities on the resulting observable distributions of replicative cellular ages. We find that strongly amplifying progenitor compartments, i.e. compartments with high self-renewal capacities, substantially broaden the age distributions which become skewed towards younger cells with a long tail of few old cells. For several of these strongly amplifying compartments, the age distribution becomes virtually independent of the influx from the stem cell compartment. By contrast, if tissues are organized into many downstream compartments with low self-renewal capacity, the shape of the replicative cell distribution in more differentiated compartments is dominated by stem cell dynamics with little added variation. In the limiting case of a strict binary differentiation tree without self-renewal, the shape of the output distribution becomes indistinguishable from that of the input distribution. Our results suggest that a comparison of cellular age distributions between healthy and cancerous tissues may inform about dynamical changes within the hierarchical tissue structure, i.e. an acquired increased self-renewal capacity in certain tumours. Furthermore, we compare our theoretical results to telomere length distributions in granulocyte populations of 10 healthy individuals across different ages, highlighting that our theoretical expectations agree with experimental observations.

Modeling treatment-dependent glioma growth including a dormant tumor cell subpopulation.

BACKGROUND: Tumors comprise a variety of specialized cell phenotypes adapted to different ecological niches that massively influence the tumor growth and its response to treatment. METHODS: In the background of glioblastoma multiforme, a highly malignant brain tumor, we consider a rapid proliferating phenotype that appears susceptible to treatment, and a dormant phenotype which lacks this pronounced proliferative ability and is not affected by standard therapeutic strategies. To gain insight in the dynamically changing proportions of different tumor cell phenotypes under different treatment conditions, we develop a mathematical model and underline our assumptions with experimental data. RESULTS: We show that both cell phenotypes contribute to the distinct composition of the tumor, especially in cycling low and high dose treatment, and therefore may influence the tumor growth in a phenotype specific way. CONCLUSION: Our model of the dynamic proportions of dormant and rapidly growing glioblastoma cells in different therapy settings suggests that phenotypically different cells should be considered to plan dose and duration of treatment schedules.

Detecting truly clonal alterations from multi-region profiling of tumours.

Modern cancer therapies aim at targeting tumour-specific alterations, such as mutations or neo-antigens, and maximal treatment efficacy requires that targeted alterations are present in all tumour cells. Currently, treatment decisions are based on one or a few samples per tumour, creating uncertainty on whether alterations found in those samples are actually present in all tumour cells. The probability of classifying clonal versus sub-clonal alterations from multi-region profiling of tumours depends on the earliest phylogenetic branching event during tumour growth. By analysing 181 samples from 10 renal carcinoma and 11 colorectal cancers we demonstrate that the information gain from additional sampling falls onto a simple universal curve. We found that in colorectal cancers, 30% of alterations identified as clonal with one biopsy proved sub-clonal when 8 samples were considered. The probability to overestimate clonal alterations fell below 1% in 7/11 patients with 8 samples per tumour. In renal cell carcinoma, 8 samples reduced the list of clonal alterations by 40% with respect to a single biopsy. The probability to overestimate clonal alterations remained as high as 92% in 7/10 renal cancer patients. Furthermore, treatment was associated with more unbalanced tumour phylogenetic trees, suggesting the need of denser sampling of tumours at relapse.

Should tissue structure suppress or amplify selection to minimize cancer risk?

BACKGROUND: It has been frequently argued that tissues evolved to suppress the accumulation of growth enhancing cancer inducing mutations. A prominent example is the hierarchical structure of tissues with high cell turnover, where a small number of tissue specific stem cells produces a large number of specialized progeny during multiple differentiation steps. Another well known mechanism is the spatial organization of stem cell populations and it is thought that this organization suppresses fitness enhancing mutations. However, in small populations the suppression of advantageous mutations typically also implies an increased accumulation of deleterious mutations. Thus, it becomes an important question whether the suppression of potentially few advantageous mutations outweighs the combined effects of many deleterious mutations. RESULTS: We argue that the distribution of mutant fitness effects, e.g. the probability to hit a strong driver compared to many deleterious mutations, is crucial for the optimal organization of a cancer suppressing tissue architecture and should be taken into account in arguments for the evolution of such tissues. CONCLUSION: We show that for systems that are composed of few cells reflecting the typical organization of a stem cell niche, amplification or suppression of selection can arise from subtle changes in the architecture. Moreover, we discuss special tissue structures that can suppress most types of non-neutral mutations simultaneously. REVIEWERS: This article was reviewed by Benjamin Allen, Andreas Deutsch and Ignacio Rodriguez-Brenes. For the full reviews, please go to the Reviewers' comments section.

The Cancer Stem Cell Fraction in Hierarchically Organized Tumors Can Be Estimated Using Mathematical Modeling and Patient-Specific Treatment Trajectories.

Many tumors are hierarchically organized and driven by a subpopulation of tumor-initiating cells (TIC), or cancer stem cells. TICs are uniquely capable of recapitulating the tumor and are thought to be highly resistant to radio- and chemotherapy. Macroscopic patterns of tumor expansion before treatment and tumor regression during treatment are tied to the dynamics of TICs. Until now, the quantitative information about the fraction of TICs from macroscopic tumor burden trajectories could not be inferred. In this study, we generated a quantitative method based on a mathematical model that describes hierarchically organized tumor dynamics and patient-derived tumor burden information. The method identifies two characteristic equilibrium TIC regimes during expansion and regression. We show that tumor expansion and regression curves can be leveraged to infer estimates of the TIC fraction in individual patients at detection and after continued therapy. Furthermore, our method is parameter-free; it solely requires the knowledge of a patient's tumor burden over multiple time points to reveal microscopic properties of the malignancy. We demonstrate proof of concept in the case of chronic myeloid leukemia (CML), wherein our model recapitulated the clinical history of the disease in two independent patient cohorts. On the basis of patient-specific treatment responses in CML, we predict that after one year of targeted treatment, the fraction of TICs increases 100-fold and continues to increase up to 1,000-fold after 5 years of treatment. Our novel framework may significantly influence the implementation of personalized treatment strategies and has the potential for rapid translation into the clinic. Cancer Res; 76(7); 1705-13. ©2016 AACR.

Ontogenic growth as the root of fundamental differences between childhood and adult cancer.

Cancer, the unregulated proliferation of cells, can occur at any age and may arise from almost all cell types. However, the incidence and types of cancer differ with age. Some cancers are predominantly observed in children, others are mostly restricted to older ages. Treatment strategies of some cancers are very successful and cure is common in childhood, while treatment of the same cancer type is much more challenging in adults. Here, we develop a stochastic model of stem cell proliferation that considers both tissue development and homeostasis and discuss the disturbance of such a system by mutations. Due to changes in population size, mutant fitness becomes context dependent and consequently the effects of mutations on the stem cell population can vary with age. We discuss different mutant phenotypes and show the age dependency of their expected abundances. Most importantly, fitness of particular mutations can change with age and advantageous mutations can become deleterious or vice versa. This perspective can explain unique properties of childhood disorders, for example, the frequently observed phenomenon of a self-limiting leukemia in newborns with trisomy 21, but also explains other puzzling observations such as the increased risk of leukemia in patients with bone marrow failure or chemotherapy induced myelodysplasia.

Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions.

We investigate the in vivo patterns of stem cell divisions in the human hematopoietic system throughout life. In particular, we analyze the shape of telomere length distributions underlying stem cell behavior within individuals. Our mathematical model shows that these distributions contain a fingerprint of the progressive telomere loss and the fraction of symmetric cell proliferations. Our predictions are tested against measured telomere length distributions in humans across all ages, collected from lymphocyte and granulocyte sorted telomere length data of 356 healthy individuals, including 47 cord blood and 28 bone marrow samples. We find an increasing stem cell pool during childhood and adolescence and an approximately maintained stem cell population in adults. Furthermore, our method is able to detect individual differences from a single tissue sample, i.e. a single snapshot. Prospectively, this allows us to compare cell proliferation between individuals and identify abnormal stem cell dynamics, which affects the risk of stem cell related diseases.

Sequential karyotyping in Burkitt lymphoma reveals a linear clonal evolution with increase in karyotype complexity and a high frequency of recurrent secondary aberrations.

Typical Burkitt lymphoma is characterized by an IG-MYC translocation and overall low genomic complexity. Clinically, Burkitt lymphoma has a favourable prognosis with very few relapses. However, the few patients experiencing disease progression and/or relapse have a dismal outcome. Here we report cytogenetic findings of seven cases of Burkitt lymphoma in which sequential karyotyping was performed at time of diagnosis and/or disease progression/relapse(s). After case selection, karyotype re-review and additional molecular analyses were performed in six paediatric cases, treated in Berlin-Frankfurt-Münster-Non-Hodgkin lymphoma study group trials, and one additional adult patient. Moreover, we analysed 18 cases of Burkitt lymphoma from the Mitelman database in which sequential karyotyping was performed. Our findings show secondary karyotypes to have a significant increase in load of cytogenetic aberrations with a mean number of 2, 5 and 8 aberrations for primary, secondary and third investigations. Importantly, this increase in karyotype complexity seemed to result from recurrent secondary chromosomal changes involving mainly trisomy 21, gains of 1q and 7q, losses of 6q, 11q, 13q, and 17p. In addition, our findings indicate a linear clonal evolution to be the predominant manner of cytogenetic evolution. Our data may provide a biological framework for the dismal outcome of progressive and relapsing Burkitt lymphoma.

Dynamics of leukemia stem-like cell extinction in acute promyelocytic leukemia.

Many tumors are believed to be maintained by a small number of cancer stem-like cells, where cure is thought to require eradication of this cell population. In this study, we investigated the dynamics of acute promyelocytic leukemia (APL) before and during therapy with regard to disease initiation, progression, and therapeutic response. This investigation used a mathematical model of hematopoiesis and a dataset derived from the North American Intergroup Study INT0129. The known phenotypic constraints of APL could be explained by a combination of differentiation blockade of PML-RARα-positive cells and suppression of normal hematopoiesis. All-trans retinoic acid (ATRA) neutralizes the differentiation block and decreases the proliferation rate of leukemic stem cells in vivo. Prolonged ATRA treatment after chemotherapy can cure patients with APL by eliminating the stem-like cell population over the course of approximately one year. To our knowledge, this study offers the first estimate of the average duration of therapy that is required to eliminate stem-like cancer cells from a human tumor, with the potential for the refinement of treatment strategies to better manage human malignancy.

Cancer initiation with epistatic interactions between driver and passenger mutations.

We investigate the dynamics of cancer initiation in a mathematical model with one driver mutation and several passenger mutations. Our analysis is based on a multi-type branching process: we model individual cells which can either divide or undergo apoptosis. In the case of a cell division, the two daughter cells can mutate, which potentially confers a change in fitness to the cell. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic context of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. While our model is not designed as a specific model for a particular cancer, the underlying idea is motivated by clinical and experimental observations in Burkitt Lymphoma. In this tumor, the hallmark mutation leads to deregulation of the MYC oncogene which increases the rate of apoptosis, but also the proliferation rate of cells. This increase in the rate of apoptosis hence needs to be overcome by mutations affecting apoptotic pathways, naturally leading to an epistatic fitness landscape. This model shows a very interesting dynamical behavior which is distinct from the dynamics of cancer initiation in the absence of epistasis. Since the driver mutation is deleterious to a cell with only a few passenger mutations, there is a period of stasis in the number of cells until a clone of cells with enough passenger mutations emerges. Only when the driver mutation occurs in one of those cells, the cell population starts to grow rapidly.