Modelling bistable tumour population dynamics to design effective treatment strategies

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.

Characterization of gene cluster heterogeneity in single-cell transcriptomic data within and across cancer types

Despite the remarkable progress in probing tumor transcriptomic heterogeneity by single-cell RNA sequencing (sc-RNAseq) data, several gaps exist in prior studies. Tumor heterogeneity is frequently mentioned but not quantified. Clustering analyses typically target cells rather than genes, and differential levels of transcriptomic heterogeneity of gene clusters are not characterized. Relations between gene clusters inferred from multiple datasets remain less explored. We provided a series of quantitative methods to analyze cancer sc-RNAseq data. First, we proposed two quantitative measures to assess intra-tumoral heterogeneity/homogeneity. Second, we established a hierarchy of gene clusters from sc-RNAseq data, devised an algorithm to reduce the gene cluster hierarchy to a compact structure, and characterized the gene clusters with functional enrichment and heterogeneity. Third, we developed an algorithm to align the gene cluster hierarchies from multiple datasets to a small number of meta gene clusters. By applying these methods to nine cancer sc-RNAseq datasets, we discovered that cancer cell transcriptomes were more homogeneous within tumors than the accompanying normal cells. Furthermore, many gene clusters from the nine datasets were aligned to two large meta gene clusters, which had high and low heterogeneity and were enriched with distinct functions. Finally, we found the homogeneous meta gene cluster retained stronger expression coherence and associations with survival times in bulk level RNAseq data than the heterogeneous meta gene cluster, yet the combinatorial expression patterns of breast cancer subtypes in bulk level data were not preserved in single-cell data. The inference outcomes derived from nine cancer sc-RNAseq datasets provide insights about the contributing factors for transcriptomic heterogeneity of cancer cells and complex relations between bulk level and single-cell RNAseq data. They demonstrate the utility of our methods to enable a comprehensive characterization of co-expressed gene clusters in a wide range of sc-RNAseq data in cancers and beyond.

Summary: We propose quantitative methods to analyze cancer sc-RNAseq data: measures of intra-tumoral heterogeneity, characterization of a hierarchy of gene clusters, and alignment of gene cluster hierarchies from multiple datasets.

Optimal Strategy and Benefit of Pulsed Therapy Depend On Tumor Heterogeneity and Aggressiveness at Time of Treatment Initiation

Therapeutic resistance is a fundamental obstacle in cancer treatment. Tumors that initially respond to treatment may have a preexisting resistant subclone or acquire resistance during treatment, making relapse theoretically inevitable. Here, we investigate treatment strategies that may delay relapse using mathematical modeling. We find that for a single-drug therapy, pulse treatment-short, elevated doses followed by a complete break from treatment-delays relapse compared with continuous treatment with the same total dose over a length of time. For tumors treated with more than one drug, continuous combination treatment is only sometimes better than sequential treatment, while pulsed combination treatment or simply alternating between the two therapies at defined intervals delays relapse the longest. These results are independent of the fitness cost or benefit of resistance, and are robust to noise. Machine-learning analysis of simulations shows that the initial tumor response and heterogeneity at the start of treatment suffice to determine the benefit of pulsed or alternating treatment strategies over continuous treatment. Analysis of eight tumor burden trajectories of breast cancer patients treated at Memorial Sloan Kettering Cancer Center shows the model can predict time to resistance using initial responses to treatment and estimated preexisting resistant populations. The model calculated that pulse treatment would delay relapse in all eight cases. Overall, our results support that pulsed treatments optimized by mathematical models could delay therapeutic resistance.

Predator-Prey in Tumor-Immune Interactions: A Wrong Model or Just an Incomplete One?

Tumor-immune interactions are often framed as predator-prey. This imperfect analogy describes how immune cells (the predators) hunt and kill immunogenic tumor cells (the prey). It allows for evaluation of tumor cell populations that change over time during immunoediting and it also considers how the immune system changes in response to these alterations. However, two aspects of predator-prey type models are not typically observed in immuno-oncology. The first concerns the conversion of prey killed into predator biomass. In standard predator-prey models, the predator relies on the prey for nutrients, while in the tumor microenvironment the predator and prey compete for resources (e.g. glucose). The second concerns oscillatory dynamics. Standard predator-prey models can show a perpetual cycling in both prey and predator population sizes, while in oncology we see increases in tumor volume and decreases in infiltrating immune cell populations. Here we discuss the applicability of predator-prey models in the context of cancer immunology and evaluate possible causes for discrepancies. Key processes include "safety in numbers", resource availability, time delays, interference competition, and immunoediting. Finally, we propose a way forward to reconcile differences between model predictions and empirical observations. The immune system is not just predator-prey. Like natural food webs, the immune-tumor community of cell types forms an immune-web of different and identifiable interactions.

How Should Cancer Models Be Constructed?

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

Establishing patient-tailored variability-based paradigms for anti-cancer therapy: Using the inherent trajectories which underlie cancer for overcoming drug resistance

Drug resistance is a major obstacle for successful therapy of many malignancies and is affecting the loss of response to chemotherapy and immunotherapy. Tumor-related compensatory adaptation mechanisms contribute to the development of drug resistance. Variability is inherent to biological systems and altered patterns of variability are associated with disease conditions. The marked intra and inter patient tumor heterogeneity, and the diverse mechanism contributing to drug resistance in different subjects, which may change over time even in the same patient, necessitate the development of personalized dynamic approaches for overcoming drug resistance. Altered dosing regimens, the potential role of chronotherapy, and drug holidays are effective in cancer therapy and immunotherapy. In the present review we describe the difficulty of overcoming drug resistance in a dynamic system and present the use of the inherent trajectories which underlie cancer development for building therapeutic regimens which can overcome resistance. The establishment of a platform wherein patient-tailored variability signatures are used for overcoming resistance for ensuing long term sustainable improved responses is presented.

Executable cancer models: successes and challenges

Making decisions on how best to treat cancer patients requires the integration of different data sets, including genomic profiles, tumour histopathology, radiological images, proteomic analysis and more. This wealth of biological information calls for novel strategies to integrate such information in a meaningful, predictive and experimentally verifiable way. In this Perspective we explain how executable computational models meet this need. Such models provide a means for comprehensive data integration, can be experimentally validated, are readily interpreted both biologically and clinically, and have the potential to predict effective therapies for different cancer types and subtypes. We explain what executable models are and how they can be used to represent the dynamic biological behaviours inherent in cancer, and demonstrate how such models, when coupled with automated reasoning, facilitate our understanding of the mechanisms by which oncogenic signalling pathways regulate tumours. We explore how executable models have impacted the field of cancer research and argue that extending them to represent a tumour in a specific patient (that is, an avatar) will pave the way for improved personalized treatments and precision medicine. Finally, we highlight some of the ongoing challenges in developing executable models and stress that effective cross-disciplinary efforts are key to forward progress in the field.