An exactly solvable, spatial model of mutation accumulation in cancer

Predictive Factors for Oligometastatic Renal Cell Carcinoma Treated with Stereotactic Radiation: A Retrospective Study

BACKGROUND AND OBJECTIVE

Stereotactic ablative radiotherapy (SAbR) has shown promise in controlling oligometastatic renal cell carcinoma (omRCC). Careful patient selection is critical, and yet the selection criteria remain unknown for patients who will not be harmed by delayed systemic therapy using SAbR. Here, we analyzed long-term follow-up of omRCC patients treated with SAbR to derive the predictors of survival benefit.

METHODS

We retrospectively reviewed patients with up to five omRCC sites treated with sequential SAbR from November 2007 to July 2022. Overall survival (OS), progression-free survival (PFS), local control (LC), and toxicity were analyzed. The predictors of PFS were analyzed using a univariate analysis and a Cox proportional hazard (CPH) model-based machine learning approach.

KEY FINDINGS AND LIMITATIONS

We analyzed 153 patients who underwent SAbR to 337 metastases with a median follow-up of 27 mo. The median OS and PFS were 61.3 and 32 mo, respectively. The rate of grade ≥3 toxicity was 1.3%, and the 3-yr rate of LC was 98%. Patients with bone and brain metastases had lower PFS on the univariate analysis. When compared with historical controls, the delayed-onset PFS with first-line systemic therapy in this cohort was not compromised. The CPH model found bone, brain, and number of metastases at diagnosis to be the predictors of PFS, with a C-index of 0.66 and 1-yr area under the curve of 0.68.

CONCLUSIONS AND CLINICAL IMPLICATIONS

For selected patients, SAbR is effective in controlling omRCC for >2 yr and can delay systemic therapy without compromising patient outcome. Bone and brain metastases, as well as an increasing number of metastases are poor predictive factors for omRCC patients treated with sequential SAbR who may benefit from upfront systemic therapy. Prospective studies are required to verify these findings.

In silico study of heterogeneous tumour-derived organoid response to CAR T-cell therapy

Chimeric antigen receptor (CAR) T-cell therapy is a promising immunotherapy for treating cancers. This method consists in modifying the patients' T-cells to directly target antigen-presenting cancer cells. One of the barriers to the development of this type of therapies, is target antigen heterogeneity. It is thought that intratumour heterogeneity is one of the leading determinants of therapeutic resistance and treatment failure. While understanding antigen heterogeneity is important for effective therapeutics, a good therapy strategy could enhance the therapy efficiency. In this work we introduce an agent-based model (ABM), built upon a previous ABM, to rationalise the outcomes of different CAR T-cells therapies strategies over heterogeneous tumour-derived organoids. We found that one dose of CAR T-cell therapy should be expected to reduce the tumour size as well as its growth rate, however it may not be enough to completely eliminate it. Moreover, the amount of free CAR T-cells (i.e. CAR T-cells that did not kill any cancer cell) increases as we increase the dosage, and so does the risk of side effects. We tested different strategies to enhance smaller dosages, such as enhancing the CAR T-cells long-term persistence and multiple dosing. For both approaches an appropriate dosimetry strategy is necessary to produce "effective yet safe" therapeutic results. Moreover, an interesting emergent phenomenon results from the simulations, namely the formation of a shield-like structure of cells with low antigen expression. This shield turns out to protect cells with high antigen expression. Finally we tested a multi-antigen recognition therapy to overcome antigen escape and heterogeneity. Our studies suggest that larger dosages can completely eliminate the organoid, however the multi-antigen recognition increases the risk of side effects. Therefore, an appropriate small dosages dosimetry strategy is necessary to improve the outcomes. Based on our results, it is clear that a proper therapeutic strategy could enhance the therapies outcomes. In that direction, our computational approach provides a framework to model treatment combinations in different scenarios and to explore the characteristics of successful and unsuccessful treatments.

Selective sweep probabilities in spatially expanding populations

Evolution during range expansions shapes biological systems from microbial communities and tumours up to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference and sweep through the population to fixation. However, most theoretical investigations of range expansions have been confined to regimes in which selective sweeps are effectively impossible, while studies of selective sweeps have either assumed constant population size or have ignored spatial structure. Here we use mathematical modelling and analysis to investigate selective sweep probabilities in the alternative yet biologically relevant scenario in which mutants can outcompete and displace a slowly spreading wildtype. Assuming constant radial expansion speed, we derive probability distributions for the arrival time and location of the first surviving mutant and hence find surprisingly simple approximate and exact expressions for selective sweep probabilities in one, two and three dimensions, which are independent of mutation rate. Namely, the selective sweep probability is approximately 1 - c w t / c m d , where c w t and c m are the wildtype and mutant radial expansion speeds, and d the spatial dimension. Using agent-based simulations, we show that our analytical results accurately predict selective sweep frequencies in the two-dimensional spatial Moran process. We further compare our results with those obtained for alternative growth laws. Parameterizing our model for human tumours, we find that selective sweeps are predicted to be rare except during very early solid tumour growth, thus providing a general, pan-cancer explanation for findings from recent sequencing studies.

SMITH: spatially constrained stochastic model for simulation of intra-tumour heterogeneity

MOTIVATION

Simulations of cancer evolution are highly useful to study the effects of selection and mutation rates on cellular fitness. However, most methods are either lattice-based and cannot simulate realistically sized tumours, or they omit spatial constraints and lack the clonal dynamics of real-world tumours.

RESULTS

Stochastic model of intra-tumour heterogeneity (SMITH) is an efficient and explainable model of cancer evolution that combines a branching process with a new confinement mechanism limiting clonal growth based on the size of the individual clones as well as the overall tumour population. We demonstrate how confinement is sufficient to induce the rich clonal dynamics observed in spatial models and cancer samples across tumour types, while allowing for a clear geometric interpretation and simulation of 1 billion cells within a few minutes on a desktop PC.

AVAILABILITY AND IMPLEMENTATION

SMITH is implemented in C# and freely available at https://bitbucket.org/schwarzlab/smith. For visualizations, we provide the accompanying Python package PyFish at https://bitbucket.org/schwarzlab/pyfish.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The 2019 mathematical oncology roadmap

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

Biodiversity in the cyclic competition system of three species according to the emergence of mutant species

Understanding mechanisms which promote or hinder existing ecosystems are important issues in ecological sciences. In addition to fundamental interactions such as competition and migration among native species, existing ecosystems can be easily disturbed by external factors, and the emergence of new species may be an example in such cases. The new species which does not exist in a current ecosystem can be regarded as either alien species entered from outside or mutant species born by mutation in existing normal species. Recently, as existing ecosystems are getting influenced by various physical/chemical external factors, mutation due to anthropogenic and environmental factors can occur more frequently and is thus attracting much attention for the maintenance of ecosystems. In this paper, we consider emergences of mutant species among self-competing three species in the cyclic dominance. By defining mutation as the birth of mutant species, we investigate how mutant species can affect biodiversity in the existing ecosystem. Through microscopic and macroscopic approaches, we have found that the society of existing normal species can be disturbed by mutant species either the society is maintained accompanying with the coexistence of all species or jeopardized by occupying of mutant species. Due to the birth of mutant species, the existing society may be more complex by constituting two different groups of normal and mutant species, and our results can be contributed to analyze complex ecosystems of many species. We hope our findings may propose a new insight on mutation in cyclic competition systems of many species.

In Silico Modeling of Immunotherapy and Stroma-Targeting Therapies in Human Colorectal Cancer

Despite the fact that the local immunological microenvironment shapes the prognosis of colorectal cancer, immunotherapy has shown no benefit for the vast majority of colorectal cancer patients. A better understanding of the complex immunological interplay within the microenvironment is required. In this study, we utilized wet lab migration experiments and quantitative histological data of human colorectal cancer tissue samples (n = 20) including tumor cells, lymphocytes, stroma, and necrosis to generate a multiagent spatial model. The resulting data accurately reflected a wide range of situations of successful and failed immune surveillance. Validation of simulated tissue outcomes on an independent set of human colorectal cancer specimens (n = 37) revealed the model recapitulated the spatial layout typically found in human tumors. Stroma slowed down tumor growth in a lymphocyte-deprived environment but promoted immune escape in a lymphocyte-enriched environment. A subgroup of tumors with less stroma and high numbers of immune cells showed high rates of tumor control. These findings were validated using data from colorectal cancer patients (n = 261). Low-density stroma and high lymphocyte levels showed increased overall survival (hazard ratio 0.322, P = 0.0219) as compared with high stroma and high lymphocyte levels. To guide immunotherapy in colorectal cancer, simulation of immunotherapy in preestablished tumors showed that a complex landscape with optimal stroma permeabilization and immune cell activation is able to markedly increase therapy response in silico These results can help guide the rational design of complex therapeutic interventions, which target the colorectal cancer microenvironment. Cancer Res; 77(22); 6442-52. ©2017 AACR.