A theoretical analysis of tumour containment

To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy

Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.

Mathematical Model-Driven Deep Learning Enables Personalized Adaptive Therapy

Standard-of-care treatment regimens have long been designed for maximal cell killing, yet these strategies often fail when applied to metastatic cancers due to the emergence of drug resistance. Adaptive treatment strategies have been developed as an alternative approach, dynamically adjusting treatment to suppress the growth of treatment-resistant populations and thereby delay, or even prevent, tumor progression. Promising clinical results in prostate cancer indicate the potential to optimize adaptive treatment protocols. Here, we applied deep reinforcement learning (DRL) to guide adaptive drug scheduling and demonstrated that these treatment schedules can outperform the current adaptive protocols in a mathematical model calibrated to prostate cancer dynamics, more than doubling the time to progression. The DRL strategies were robust to patient variability, including both tumor dynamics and clinical monitoring schedules. The DRL framework could produce interpretable, adaptive strategies based on a single tumor burden threshold, replicating and informing optimal treatment strategies. The DRL framework had no knowledge of the underlying mathematical tumor model, demonstrating the capability of DRL to help develop treatment strategies in novel or complex settings. Finally, a proposed five-step pathway, which combined mechanistic modeling with the DRL framework and integrated conventional tools to improve interpretability compared with traditional "black-box" DRL models, could allow translation of this approach to the clinic. Overall, the proposed framework generated personalized treatment schedules that consistently outperformed clinical standard-of-care protocols.

SIGNIFICANCE

Generation of interpretable and personalized adaptive treatment schedules using a deep reinforcement framework that interacts with a virtual patient model overcomes the limitations of standardized strategies caused by heterogeneous treatment responses.

Tumor containment: a more general mathematical analysis

Clinical and pre-clinical data suggest that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells identified conditions under which a treatment aiming at tumor containment rather than eradication is indeed optimal. This model however neglected mutations from sensitive to resistant cells, and assumed that the growth-rate of sensitive cells is non-increasing in the size of the resistant population. The latter is not true in standard models of chemotherapy. This article shows how to dispense with this assumption and allow for mutations from sensitive to resistant cells. This is achieved by a novel mathematical analysis comparing tumor sizes across treatments not as a function of time, but as a function of the resistant population size.

Tumour Growth Mechanisms Determine Effectiveness of Adaptive Therapy in Glandular Tumours

In cancer treatment, adaptive therapy holds promise for delaying the onset of recurrence through regulating the competition between drug-sensitive and drug-resistant cells. Adaptive therapy has been studied in well-mixed models assuming free mixing of all cells and spatial models considering the interactions of single cells with their immediate adjacent cells. Both models do not reflect the spatial structure in glandular tumours where intra-gland cellular interaction is high, while inter-gland interaction is limited. Here, we use mathematical modelling to study the effects of adaptive therapy on glandular tumours that expand using either glandular fission or invasive growth. A two-dimensional, lattice-based model of sites containing sensitive and resistant cells within individual glands is developed to study the evolution of glandular tumour cells under continuous and adaptive therapies. We found that although both growth models benefit from adaptive therapy's ability to prevent recurrence, invasive growth benefits more from it than fission growth. This difference is due to the migration of daughter cells into neighboring glands that is absent in fission but present in invasive growth. The migration resulted in greater mixing of cells, enhancing competition induced by adaptive therapy. By varying the initial spatial spread and location of the resistant cells within the tumour, we found that modifying the conditions within the resistant cells containing glands affect both fission and invasive growth. However, modifying the conditions surrounding these glands affect invasive growth only. Our work reveals the interplay between growth mechanism and tumour topology in modulating the effectiveness of cancer therapy.

Convergent insights into intratumor heterogeneity

Mathematics, conventional histology, and genomics converge to confirm that highly aggressive clear cell renal cell carcinomas (CCRCCs) display low levels of intratumor heterogeneity (ITH). We hypothesize that therapeutic strategies aimed at maintaining high ITH levels would be advisable to slow down cancer evolution and to improve survival.

Adaptive therapy: a tumor therapy strategy based on Darwinian evolution theory

Cancer progression is a dynamic process of continuous evolution, in which genetic diversity and heterogeneity are generated by clonal and subclonal amplification based on random mutations. Traditional cancer treatment strategies have a great challenge, which often leads to treatment failure due to drug resistance. Integrating evolutionary dynamics into treatment regimens may be an effective way to overcome the problem of drug resistance. In particular, a potential treatment is adaptive therapy, which strategy advocates containment strategies that adjust the treatment cycles according to tumor evolution to control the growth of treatment-resistant cells. In this review, we first summarize the shortcomings of traditional tumor treatment methods in evolution and then introduce the theoretical basis and research status of adaptive therapy. By analyzing the limitations of adaptive therapy and exploring possible solutions, we can broaden people's understanding of adaptive therapy and provide new insights and strategies for tumor treatment.

A phase-field model for non-small cell lung cancer under the effects of immunotherapy

Formulating mathematical models that estimate tumor growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simplified nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. The applied immunotherapy decreases the proliferative cell concentration. Here, we model the immunotherapeutic agent concentration in the entire lung over time by an ordinary differential equation (ODE). Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to calibrate our model. Our model covers the case in which the immunotherapy is successful and limits the tumor size, as well as the case predicting a sudden relapse, leading to exponential tumor growth. Finally, we move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we demonstrate the predictive benefits that a more detailed patient-specific simulation including spatial information as a possible generalization within our framework could yield in the future.

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.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics

Adaptive therapies that alternate between drug applications and drug-free vacations can exploit competition between sensitive and resistant cells to maximize the time to progression. However, optimal dosing schedules depend on the properties of metastases, which are often not directly measurable in clinical practice. Here, we proposed a framework for estimating features of metastases through tumor response dynamics during the first adaptive therapy treatment cycle. Longitudinal prostate-specific antigen (PSA) levels in 16 patients with metastatic castration-resistant prostate cancer undergoing adaptive androgen deprivation treatment were analyzed to investigate relationships between cycle dynamics and clinical variables such as Gleason score, the change in the number of metastases over a cycle, and the total number of cycles over the course of treatment. The first cycle of adaptive therapy, which consists of a response period (applying therapy until 50% PSA reduction), and a regrowth period (removing treatment until reaching initial PSA levels), delineated several features of the computational metastatic system: larger metastases had longer cycles; a higher proportion of drug-resistant cells slowed the cycles; and a faster cell turnover rate sped up drug response time and slowed regrowth time. The number of metastases did not affect cycle times, as response dynamics were dominated by the largest tumors rather than the aggregate. In addition, systems with higher intermetastasis heterogeneity responded better to continuous therapy and correlated with dynamics from patients with high or low Gleason scores. Conversely, systems with higher intrametastasis heterogeneity responded better to adaptive therapy and correlated with dynamics from patients with intermediate Gleason scores.

SIGNIFICANCE

Multiscale mathematical modeling combined with biomarker dynamics during adaptive therapy helps identify underlying features of metastatic cancer to inform treatment decisions.

Decoding Oncofusions: Unveiling Mechanisms, Clinical Impact, and Prospects for Personalized Cancer Therapies

Cancer-associated gene fusions, also known as oncofusions, have emerged as influential drivers of oncogenesis across a diverse range of cancer types. These genetic events occur via chromosomal translocations, deletions, and inversions, leading to the fusion of previously separate genes. Due to the drastic nature of these mutations, they often result in profound alterations of cellular behavior. The identification of oncofusions has revolutionized cancer research, with advancements in sequencing technologies facilitating the discovery of novel fusion events at an accelerated pace. Oncofusions exert their effects through the manipulation of critical cellular signaling pathways that regulate processes such as proliferation, differentiation, and survival. Extensive investigations have been conducted to understand the roles of oncofusions in solid tumors, leukemias, and lymphomas. Large-scale initiatives, including the Cancer Genome Atlas, have played a pivotal role in unraveling the landscape of oncofusions by characterizing a vast number of cancer samples across different tumor types. While validating the functional relevance of oncofusions remains a challenge, even non-driver mutations can hold significance in cancer treatment. Oncofusions have demonstrated potential value in the context of immunotherapy through the production of neoantigens. Their clinical importance has been observed in both treatment and diagnostic settings, with specific fusion events serving as therapeutic targets or diagnostic markers. However, despite the progress made, there is still considerable untapped potential within the field of oncofusions. Further research and validation efforts are necessary to understand their effects on a functional basis and to exploit the new targeted treatment avenues offered by oncofusions. Through further functional and clinical studies, oncofusions will enable the advancement of precision medicine and the drive towards more effective and specific treatments for cancer patients.

Effective dose window for containing tumor burden under tolerable level

A maximum-tolerated dose (MTD) reduces the drug-sensitive cell population, though it may result in the competitive release of drug resistance. Alternative treatment strategies such as adaptive therapy (AT) or dose modulation aim to impose competitive stress on drug-resistant cell populations by maintaining a sufficient number of drug-sensitive cells. However, given the heterogeneous treatment response and tolerable tumor burden level of individual patients, determining an effective dose that can fine-tune competitive stress remains challenging. This study presents a mathematical model-driven approach that determines the plausible existence of an effective dose window (EDW) as a range of doses that conserve sufficient sensitive cells while maintaining the tumor volume below a threshold tolerable tumor volume (TTV). We use a mathematical model that explains intratumor cell competition. Analyzing the model, we derive an EDW determined by TTV and the competitive strength. By applying a fixed endpoint optimal control model, we determine the minimal dose to contain cancer at a TTV. As a proof of concept, we study the existence of EDW for a small cohort of melanoma patients by fitting the model to longitudinal tumor response data. We performed identifiability analysis, and for the patients with uniquely identifiable parameters, we deduced patient-specific EDW and minimal dose. The tumor volume for a patient could be theoretically contained at the TTV either using continuous dose or AT strategy with doses belonging to EDW. Further, we conclude that the lower bound of the EDW approximates the minimum effective dose (MED) for containing tumor volume at the TTV.

Stackelberg evolutionary game theory: how to manage evolving systems

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader's most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. We show how our results have the potential to help in fields where humans try to bring an evolutionary system into the desired outcome, such as, among others, fisheries management, pest management and cancer treatment. Finally, we discuss limitations and opportunities for applying SEGs to improve the management of evolving biological systems. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Adaptive therapy for ovarian cancer: An integrated approach to PARP inhibitor scheduling

Toxicity and emerging drug resistance are important challenges in PARP inhibitor (PARPi) treatment of ovarian cancer. Recent research has shown that evolutionary-inspired treatment algorithms which adapt treatment to the tumor's treatment response (adaptive therapy) can help to mitigate both. Here, we present a first step in developing an adaptive therapy protocol for PARPi treatment by combining mathematical modelling and wet-lab experiments to characterize the cell population dynamics under different PARPi schedules. Using data from in vitro Incucyte Zoom time-lapse microscopy experiments and a step-wise model selection process we derive a calibrated and validated ordinary differential equation model, which we then use to test different plausible adaptive treatment schedules. Our model can accurately predict the in vitro treatment dynamics, even to new schedules, and suggests that treatment modifications need to be carefully timed, or one risks losing control over tumour growth, even in the absence of any resistance. This is because our model predicts that multiple rounds of cell division are required for cells to acquire sufficient DNA damage to induce apoptosis. As a result, adaptive therapy algorithms that modulate treatment but never completely withdraw it are predicted to perform better in this setting than strategies based on treatment interruptions. Pilot experiments in vivo confirm this conclusion. Overall, this study contributes to a better understanding of the impact of scheduling on treatment outcome for PARPis and showcases some of the challenges involved in developing adaptive therapies for new treatment settings.

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.

Protein kinases: Role of their dysregulation in carcinogenesis, identification and inhibition

Protein kinases belong to the phosphor-transferases superfamily of enzymes, which "activate" enzymes via phosphorylation. The kinome of an organism is the total set of genes in the genome, which encode for all the protein kinases. Certain mutations in the kinome have been linked to dysregulation of protein kinases, which in turn can lead to several diseases and disorders including cancer. In this review, we have briefly discussed the role of protein kinases in various biochemical processes by categorizing cancer associated phenotypes and giving their protein kinase examples. Various techniques have also been discussed, which are being used to analyze the structure of protein kinases, and associate their roles in the oncogenesis. We have also discussed protein kinase inhibitors and United States Federal Drug Administration (USFDA) approved drugs, which target protein kinases and can serve as a counter to protein kinase dysregulation and mitigate the effects of oncogenesis. Overall, this review briefs about the importance of protein kinases, their roles in oncogenesis on dysregulation and how their inhibition via various drugs can be used to mitigate their effects.

Stochastic Fluctuations Drive Non-genetic Evolution of Proliferation in Clonal Cancer Cell Populations

Evolutionary dynamics allows us to understand many changes happening in a broad variety of biological systems, ranging from individuals to complete ecosystems. It is also behind a number of remarkable organizational changes that happen during the natural history of cancers. These reflect tumour heterogeneity, which is present at all cellular levels, including the genome, proteome and phenome, shaping its development and interrelation with its environment. An intriguing observation in different cohorts of oncological patients is that tumours exhibit an increased proliferation as the disease progresses, while the timescales involved are apparently too short for the fixation of sufficient driver mutations to promote explosive growth. Here, we discuss how phenotypic plasticity, emerging from a single genotype, may play a key role and provide a ground for a continuous acceleration of the proliferation rate of clonal populations with time. We address this question by combining the analysis of real-time growth of non-small-cell lung carcinoma cells (N-H460) together with stochastic and deterministic mathematical models that capture proliferation trait heterogeneity in clonal populations to elucidate the contribution of phenotypic transitions on tumour growth dynamics.

Range-Bounded Adaptive Therapy in Metastatic Prostate Cancer

Adaptive therapy with abiraterone acetate (AA), whereby treatment is cycled on and off, has been presented as an alternative to continuous therapy for metastatic castration resistant prostate cancer (mCRPC). It is hypothesized that cycling through treatment allows sensitive cells to competitively suppress resistant cells, thereby increasing the amount of time that treatment is effective. It has been proposed that there exists a subset of patients for whom this competition can be enhanced through slight modifications. Here, we investigate how adaptive AA can be modified to extend time to progression using a simple mathematical model of stem cell, non-stem cell, and prostate-specific antigen (PSA) dynamics. The model is calibrated to longitudinal PSA data from 16 mCRPC patients undergoing adaptive AA in a pilot clinical study at Moffitt Cancer Center. Model parameters are then used to simulate range-bounded adaptive therapy (RBAT) whereby treatment is modulated to maintain PSA levels between pre-determined patient-specific bounds. Model simulations of RBAT are compared to the clinically applied adaptive therapy and show that RBAT can further extend time to progression, while reducing the cumulative dose patients received in 11/16 patients. Simulations also show that the cumulative dose can be reduced by up to 40% under RBAT. Through small modifications to the conventional adaptive therapy design, our study demonstrates that RBAT offers the opportunity to improve patient care, particularly in those patients who do not respond well to conventional adaptive therapy.

Novel epigenetic therapeutic strategies and targets in cancer

The critical role of dysregulated epigenetic pathways in cancer genesis, development, and therapy has typically been established as a result of scientific and technical innovations in next generation sequencing. RNA interference, histone modification, DNA methylation and chromatin remodelling are epigenetic processes that control gene expression without causing mutations in the DNA. Although epigenetic abnormalities are thought to be a symptom of cell tumorigenesis and malignant events that impact tumor growth and drug resistance, physicians believe that related processes might be a key therapeutic target for cancer treatment and prevention due to the reversible nature of these processes. A plethora of novel strategies for addressing epigenetics in cancer therapy for immuno-oncological complications are currently available - ranging from basic treatment to epigenetic editing. - and they will be the subject of this comprehensive review. In this review, we cover most of the advancements made in the field of targeting epigenetics with special emphasis on microbiology, plasma science, biophysics, pharmacology, molecular biology, phytochemistry, and nanoscience.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Measuring competitive exclusion in non-small cell lung cancer

In this study, we experimentally measure the frequency-dependent interactions between a gefitinib-resistant non-small cell lung cancer population and its sensitive ancestor via the evolutionary game assay. We show that cost of resistance is insufficient to accurately predict competitive exclusion and that frequency-dependent growth rate measurements are required. Using frequency-dependent growth rate data, we then show that gefitinib treatment results in competitive exclusion of the ancestor, while the absence of treatment results in a likely, but not guaranteed, exclusion of the resistant strain. Then, using simulations, we demonstrate that incorporating ecological growth effects can influence the predicted extinction time. In addition, we show that higher drug concentrations may not lead to the optimal reduction in tumor burden. Together, these results highlight the potential importance of frequency-dependent growth rate data for understanding competing populations, both in the laboratory and as we translate adaptive therapy regimens to the clinic.

In Silico Investigations of Multi-Drug Adaptive Therapy Protocols

The standard of care for cancer patients aims to eradicate the tumor by killing the maximum number of cancer cells using the maximum tolerated dose (MTD) of a drug. MTD causes significant toxicity and selects for resistant cells, eventually making the tumor refractory to treatment. Adaptive therapy aims to maximize time to progression (TTP), by maintaining sensitive cells to compete with resistant cells. We explored both dose modulation (DM) protocols and fixed dose (FD) interspersed with drug holiday protocols. In contrast to previous single drug protocols, we explored the determinants of success of two-drug adaptive therapy protocols, using an agent-based model. In almost all cases, DM protocols (but not FD protocols) increased TTP relative to MTD. DM protocols worked well when there was more competition, with a higher cost of resistance, greater cell turnover, and when crowded proliferating cells could replace their neighbors. The amount that the drug dose was changed, mattered less. The more sensitive the protocol was to tumor burden changes, the better. In general, protocols that used as little drug as possible, worked best. Preclinical experiments should test these predictions, especially dose modulation protocols, with the goal of generating successful clinical trials for greater cancer control.

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

Background

Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment.

Methods

We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence.

Results

Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy.

Conclusion

Our work shows that the tumour’s spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

Cancer therapy traditionally focuses on maximising tumour cell kill with the aim of achieving a cure, but such aggressive treatment can open up space for drug-resistant cells to grow. In contrast, adaptive therapy aims to leverage competition between drug-sensitive and resistant cells by adjusting treatment to maintain the tumour at a tolerable size, whilst preserving drug-sensitive cells. This approach is being tested in trials but is not yet widely used as deeper understanding of cell-cell competition is required. Here, we used a mathematical model to investigate how strongly, and with whom, resistant cells compete during continuous and adaptive therapy, and applied our insights to hormone therapy in prostate cancer where adaptive therapy has recently been successfully trialed. Our results provide new insights into how adaptive therapy works and show that, by shaping cell competition, the tumour’s spatial architecture is important in determining therapy response.

Strobl et al. develop an agent-based spatial model of drug resistance in tumour cells under adaptive therapy. Using this model, they investigate how the tumour’s spatial architecture impacts intratumoural competitive dynamics of drug-sensitive vs. -resistant clones in response to therapy.

The impact of the spatial heterogeneity of resistant cells and fibroblasts on treatment response

A long-standing practice in the treatment of cancer is that of hitting hard with the maximum tolerated dose to eradicate tumors. This continuous therapy, however, selects for resistant cells, leading to the failure of the treatment. A different type of treatment strategy, adaptive therapy, has recently been shown to have a degree of success in both preclinical xenograft experiments and clinical trials. Adaptive therapy is used to maintain a tumor’s volume by exploiting the competition between drug-sensitive and drug-resistant cells with minimum effective drug doses or timed drug holidays. To further understand the role of competition in the outcomes of adaptive therapy, we developed a 2D on-lattice agent-based model. Our simulations show that the superiority of the adaptive strategy over continuous therapy depends on the local competition shaped by the spatial distribution of resistant cells. Intratumor competition can also be affected by fibroblasts, which produce microenvironmental factors that promote cancer cell growth. To this end, we simulated the impact of different fibroblast distributions on treatment outcomes. As a proof of principle, we focused on five types of distribution of fibroblasts characterized by different locations, shapes, and orientations of the fibroblast region with respect to the resistant cells. Our simulation shows that the spatial architecture of fibroblasts modulates tumor progression in both continuous and adaptive therapy. Finally, as a proof of concept, we simulated the outcomes of adaptive therapy of a virtual patient with four metastatic sites composed of different spatial distributions of fibroblasts and drug-resistant cell populations. Our simulation highlights the importance of undetected metastatic lesions on adaptive therapy outcomes.

Tumors are composed of different cancer cells with varying degrees of treatment resistance, which compete for a shared resource. Adaptive therapy exploits this competition. The paradigm employs patient-specific on and off treatment schedules or lower doses to permit a significant number of drug-sensitive cells to survive. The surviving sensitive cells can suppress the growth of drug-resistant cells via intratumor competition. This competition can be modulated by the spatial structure of tumors. For example, resistant cell configuration, carrying capacity, or migration rate may change local spatial competition between drug-resistant cells or between drug-sensitive and drug resistant cells. In addition, the presence of growth factors produced by stromal cells such as fibroblasts promotes the proliferation of cells, enhancing the competition. To understand the impact of forenamed factors on the outcomes of adaptive therapy, we developed a computational model, 2D on-lattice agent-based model. Our findings show that the spatial factors regulate the local competition and may hold back the benefit of adaptive therapy. Further, the impact of fibroblast depends on the respective positioning of fibroblast to the resistant cells. Finally, we simulated the outcomes of adaptive therapy on multiple metastatic lesions of mixed spatial configuration on a virtual patient. In the simulation, we highlight the importance of undetected metastatic lesions on therapy outcomes.

Spatial structure governs the mode of tumour evolution

Characterizing the mode-the way, manner or pattern-of evolution in tumours is important for clinical forecasting and optimizing cancer treatment. Sequencing studies have inferred various modes, including branching, punctuated and neutral evolution, but it is unclear why a particular pattern predominates in any given tumour. Here we propose that tumour architecture is key to explaining the variety of observed genetic patterns. We examine this hypothesis using spatially explicit population genetics models and demonstrate that, within biologically relevant parameter ranges, different spatial structures can generate four tumour evolutionary modes: rapid clonal expansion, progressive diversification, branching evolution and effectively almost neutral evolution. Quantitative indices for describing and classifying these evolutionary modes are presented. Using these indices, we show that our model predictions are consistent with empirical observations for cancer types with corresponding spatial structures. The manner of cell dispersal and the range of cell-cell interactions are found to be essential factors in accurately characterizing, forecasting and controlling tumour evolution.

Precision sampling fuels precision oncology: an evolutionary perspective

Intratumor heterogeneity (ITH) develops in malignant tumors. Precision sampling that captures this tumor variability is essential for the implementation of precision oncology. We highlight the necessity to update current sampling protocols and implement a strategy to ensure ITH detection and characterization. A cost-effective strategy for such sampling has been modeled in clear cell renal cell carcinoma (CCRCC).

Darwinian Approaches for Cancer Treatment: Benefits of Mathematical Modeling

One of the major problems of traditional anti-cancer treatments is that they lead to the emergence of treatment-resistant cells, which results in treatment failure. To avoid or delay this phenomenon, it is relevant to take into account the eco-evolutionary dynamics of tumors. Designing evolution-based treatment strategies may help overcoming the problem of drug resistance. In particular, a promising candidate is adaptive therapy, a containment strategy which adjusts treatment cycles to the evolution of the tumors in order to keep the population of treatment-resistant cells under control. Mathematical modeling is a crucial tool to understand the dynamics of cancer in response to treatments, and to make predictions about the outcomes of these treatments. In this review, we highlight the benefits of in silico modeling to design adaptive therapy strategies, and to assess whether they could effectively improve treatment outcomes. Specifically, we review how two main types of models (i.e., mathematical models based on Lotka-Volterra equations and agent-based models) have been used to model tumor dynamics in response to adaptive therapy. We give examples of the advances they permitted in the field of adaptive therapy and discuss about how these models can be integrated in experimental approaches and clinical trial design.

Gene Duplication and Gene Fusion Are Important Drivers of Tumourigenesis during Cancer Evolution

Chromosomal rearrangement and genome instability are common features of cancer cells in human. Consequently, gene duplication and gene fusion events are frequently observed in human malignancies and many of the products of these events are pathogenic, representing significant drivers of tumourigenesis and cancer evolution. In certain subsets of cancers duplicated and fused genes appear to be essential for initiation of tumour formation, and some even have the capability of transforming normal cells, highlighting the importance of understanding the events that result in their formation. The mechanisms that drive gene duplication and fusion are unregulated in cancer and they facilitate rapid evolution by selective forces akin to Darwinian survival of the fittest on a cellular level. In this review, we examine current knowledge of the landscape and prevalence of gene duplication and gene fusion in human cancers.

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one's fitness not only depends on one's own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer's eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.

Evolutionary Dynamics of Treatment-Induced Resistance in Cancer Informs Understanding of Rapid Evolution in Natural Systems

Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and evolution in human dominated landscapes - in recognizing the need for evolutionarily informed management strategies. The speed of evolution matters. Here, we employ game-theoretic modeling to compare time to progression with continuous maximum tolerable dose to that of adaptive therapy where treatment is discontinued when the population of cancer cells gets below half of its initial size and re-administered when the cancer cells recover, forming cycles with and without treatment. We show that the success of adaptive therapy relative to continuous maximum tolerable dose therapy is much higher if the population of cancer cells is defined by two cell types (sensitive vs. resistant in a polymorphic population). Additionally, the relative increase in time to progression increases with the speed of evolution. These results hold with and without a cost of resistance in cancer cells. On the other hand, treatment-induced resistance can be modeled as a quantitative trait in a monomorphic population of cancer cells. In that case, when evolution is rapid, there is no advantage to adaptive therapy. Initial responses to therapy are blunted by the cancer cells evolving too quickly. Our study emphasizes how cancer provides a unique system for studying rapid evolutionary changes within tumor ecosystems in response to human interventions; and allows us to contrast and compare this system to other human managed or dominated systems in nature.

Paracrine Behaviors Arbitrate Parasite-Like Interactions Between Tumor Subclones

Explaining the emergence and maintenance of intratumor heterogeneity is an important question in cancer biology. Tumor cells can generate considerable subclonal diversity, which influences tumor growth rate, treatment resistance, and metastasis, yet we know remarkably little about how cells from different subclones interact. Here, we confronted two murine mammary cancer cell lines to determine both the nature and mechanisms of subclonal cellular interactions in vitro. Surprisingly, we found that, compared to monoculture, growth of the “winner” was enhanced by the presence of the “loser” cell line, whereas growth of the latter was reduced. Mathematical modeling and laboratory assays indicated that these interactions are mediated by the production of paracrine metabolites resulting in the winner subclone effectively “farming” the loser. Our findings add a new level of complexity to the mechanisms underlying subclonal growth dynamics.

Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives

When eradication is impossible, cancer treatment aims to delay the emergence of resistance while minimizing cancer burden and treatment. Adaptive therapies may achieve these aims, with success based on three assumptions: resistance is costly, sensitive cells compete with resistant cells, and therapy reduces the population of sensitive cells. We use a range of mathematical models and treatment strategies to investigate the tradeoff between controlling cell populations and delaying the emergence of resistance. These models extend game theoretic and competition models with four additional components: 1) an Allee effect where cell populations grow more slowly at low population sizes, 2) healthy cells that compete with cancer cells, 3) immune cells that suppress cancer cells, and 4) resource competition for a growth factor like androgen. In comparing maximum tolerable dose, intermittent treatment, and adaptive therapy strategies, no therapeutic choice robustly breaks the three-way tradeoff among the three therapeutic aims. Almost all models show a tight tradeoff between time to emergence of resistant cells and cancer cell burden, with intermittent and adaptive therapies following identical curves. For most models, some adaptive therapies delay overall tumor growth more than intermittent therapies, but at the cost of higher cell populations. The Allee effect breaks these relationships, with some adaptive therapies performing poorly due to their failure to treat sufficiently to drive populations below the threshold. When eradication is impossible, no treatment can simultaneously delay emergence of resistance, limit total cancer cell numbers, and minimize treatment. Simple mathematical models can play a role in designing the next generation of therapies that balance these competing objectives.