Control and conquer" -this is the philosophy behind adaptive therapy, which seeks to exploit intra-tumoural competition to avoid, or at least, delay the emergence of therapy resistance in cancer. Motivated by promising results from theoretical, experimental and, most recently, a clinical study in prostate cancer, there is an increasing interest in extending this approach to other cancers. As such, it is urgent to understand the characteristics of a cancer which determine whether it will respond well to adaptive therapy, or not. A plausible candidate for such a selection criterion is the fitness cost of resistance. In this 1 .

Control and conquer" -this is the philosophy behind adaptive therapy, which seeks to exploit intra-tumoural competition to avoid, or at least, delay the emergence of therapy resistance in cancer. Motivated by promising results from theoretical, experimental and, most recently, a clinical study in prostate cancer, there is an increasing interest in extending this approach to other cancers. As such, it is urgent to understand the characteristics of a cancer which determine whether it will respond well to adaptive therapy, or not. A plausible candidate for such a selection criterion is the fitness cost of resistance. In this 1 paper, we study a simple competition model between sensitive & resistant cell populations to investigate whether the presence of a cost is a necessary condition for adaptive therapy to extend the time to progression beyond that of a standard-of-care continuous therapy. We find that for tumours close to their environmental carrying capacity such a cost of resistance is not required. However, for tumours growing far from carrying capacity, a cost may be required to see meaningful gains. Notably, we show that in such cases it is important to consider the cell turnover in the tumour and we discuss its role in modulating the impact of a cost of resistance. Overall, our work helps to clarify under which circumstances adaptive therapy may be beneficial, and suggests that turnover may play an unexpectedly important role in the decision making process.

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.

(1) Background: Adaptive therapy aims to tackle cancer drug resistance by leveraging intra-tumoural competition between drug-sensitive and resistant cells. Motivated by promising results in prostate cancer there is growing interest in extending this approach to other cancers. Here we present a theoretical study of intra-tumoural competition during adaptive therapy, to identify under which circumstances it will be superior to aggressive treatment, and how it can be improved through combination treatment; (2) Methods: We study a 2-D, on-lattice, agent-based tumour model. We examine the impact of different micro-environmental factors on the comparison between continuous drug administration and the adaptive schedule pioneered in the first-in-human clinical trial. (3) Results: We show that the degree of crowding, the initial resistance fraction, the presence of possible resistance costs, and the rate of tumour cell turnover are key determinants of the benefit of adaptive therapy. Subsequently, we investigate whether combination with treatments which amplify proliferation or which target cell turnover can prolong tumour control. While the former increases competition, we find that only the latter can robustly improve time to progression; (4) Conclusion: Our work helps to identify selection factors for adaptive therapy and provides stepping stones towards the rational design of multi-drug adaptive regimens.

The evolutionary dynamics of tumor initiation remain undetermined, and the interplay between neoplastic cells and the immune system is hypothesized to be critical in transformation. Colorectal cancer (CRC) presents a unique opportunity to study the transition to malignancy as pre-cancers (adenomas) and early-stage cancers are frequently resected. Here, we examine tumor-immune eco-evolutionary dynamics from pre-cancer to carcinoma using a computational model, ecological analysis of digital pathology data, and neoantigen prediction in 62 patient samples. Modeling predicted recruitment of immunosuppressive cells would be the most common driver of transformation. As predicted, ecological analysis reveals that progressed adenomas co-localized with immunosuppressive cells and cytokines, while benign adenomas co-localized with a mixed immune response. Carcinomas converge to a common immune “cold” ecology, relaxing selection against immunogenicity and high neoantigen burdens, with little evidence for PD-L1 overexpression driving tumor initiation. These findings suggest re-engineering the immunosuppressive niche may prove an effective immunotherapy in CRC.

Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno-and phenotypic intratumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

Immune therapies have shown promise in a number of cancers, and clinical trials using the anti-PD-L1/PD-1 checkpoint inhibitor in lung cancer have been successful for a number of patients. However, some patients either do not respond to the treatment or have cancer recurrence after an initial response. It is not clear which patients might fall into these categories or what mechanisms are responsible for treatment failure. To explore the different underlying biological mechanisms of resistance, we created a spatially explicit mathematical model with a modular framework. This construction enables different potential mechanisms to be turned on and off in order to adjust specific tumor and tissue interactions to match a specific patient's disease. In parallel, we developed a software suite to identify significant computed tomography (CT) imaging features correlated with outcome using data from an anti-PDL-1 checkpoint inhibitor clinical trial for lung cancer and a tool that extracts these features from both patient CT images and “virtual CT” images created from the cellular density profile of the model. The combination of our two toolkits provides a framework that feeds patient data through an iterative pipeline to identify predictive imaging features associated with outcome, whilst at the same time proposing hypotheses about the underlying resistance mechanisms.

Evolutionary therapies, such as adaptive therapy, have shown promise in delaying treatment resistance in late-stage cancers. By alternating between drug applications and drug-free vacations, competition between sensitive and resistant cells can be exploited to maximize the time to progression. However, the optimal schedule of this dosing regimen depends on the properties of the tumor, which often are not directly measurable in clinical practice. In this work, we propose that the initial cycle of adaptive therapy can be used as a tool to probe the relevant tumor properties. We present a framework for estimating individual and collective components of a metastatic system through tumor response dynamics, which uses a system of off-lattice agent-based models to represent individual metastatic lesions within independent domains, all of which are subject to the same systemic therapy. We find that the first cycle of adaptive therapy delineates several features of the computational metastatic system: larger metastases have longer cycles; a higher proportion of drug resistant cells slows the cycles; and a faster cell turnover rate speeds up drug response time and slows the regrowth time. The number of metastases does not affect cycle times, as response dynamics are dominated by the largest tumors rather than the aggregate. In addition, the heterogeneity of the system is also a guide for therapeutic approaches: generally, systems with more between-tumor (intertumor) heterogeneity had better success with continuous therapy, while systems with more within-tumor (intratumor) heterogeneity responded better to adaptive therapy. Intertumor heterogeneity was found to correlate more with dynamics from patients with high and low Gleason scores while intratumor heterogeneity was correlated with dynamics from patients with intermediate Gleason scores.