A Novel Mathematical Approach for Analysis of Integrated Cell-Patient Data Uncovers a 6-Gene Signature Linked to Endocrine Therapy Resistance.

A significant number of breast cancers develop resistance to hormone therapy. This progression, while posing a major clinical challenge, is difficult to predict. Despite important contributions made by cell models and clinical studies to tackle this problem, both present limitations when taken individually. Experiments with cell models are highly reproducible but do not reflect the indubitable heterogenous landscape of breast cancer. On the other hand, clinical studies account for this complexity but introduce uncontrolled noise due to external factors. Here, we propose a new approach for biomarker discovery that is based on a combined analysis of sequencing data from controlled MCF7 cell experiments and heterogenous clinical samples that include clinical and sequencing information from The Cancer Genome Atlas. Using data from differential gene expression analysis and a Bayesian logistic regression model coupled with an original simulated annealing-type algorithm, we discovered a novel 6-gene signature for stratifying patient response to hormone therapy. The experimental observations and computational analysis built on independent cohorts indicated the superior predictive performance of this gene set over previously known signatures of similar scope. Together, these findings revealed a new gene signature to identify patients with breast cancer with an increased risk of developing resistance to endocrine therapy.

Classification of tolerable/intolerable mucosal toxicity of head-and-neck radiotherapy schedules with a biomathematical model of cell dynamics.

PURPOSE: The purpose of this study is to present a biomathematical model based on the dynamics of cell populations to predict the tolerability/intolerability of mucosal toxicity in head-and-neck radiotherapy. METHODS AND MATERIALS: Our model is based on the dynamics of proliferative and functional cell populations in irradiated mucosa, and incorporates the three As: Accelerated proliferation, loss of Asymmetric proliferation, and Abortive divisions. The model consists of a set of delay differential equations, and tolerability is based on the depletion of functional cells during treatment. We calculate the sensitivity (sen) and specificity (spe) of the model in a dataset of 108 radiotherapy schedules, and compare the results with those obtained with three phenomenological classification models, two based on a biologically effective dose (BED) function describing the tolerability boundary (Fowler and Fenwick) and one based on an equivalent dose in 2 Gy fractions (EQD2 ) boundary (Strigari). We also perform a machine learning-like cross-validation of all the models, splitting the database in two, one for training and one for validation. RESULTS: When fitting our model to the whole dataset, we obtain predictive values (sen + spe) up to 1.824. The predictive value of our model is very similar to that of the phenomenological models of Fowler (1.785), Fenwick (1.806), and Strigari (1.774). When performing a k = 2 cross-validation, the specificity and sensitivity in the validation dataset decrease for all models, from ˜1.82 to Ëœ1.55-1.63. For Fowler, the worsening is higher, down to 1.49. CONCLUSIONS: Our model has proved useful to predict the tolerability/intolerability of a dataset of 108 schedules. As the model is more mechanistic than other available models, it could prove helpful when designing unconventional dose fractionations, schedules not covered by datasets to which phenomenological models of toxicity have been fitted.

A mathematical model of dynamics of cell populations in squamous epithelium after irradiation.

PURPOSE: To develop multi-compartment mechanistic models of dynamics of stem and functional cell populations in epithelium after irradiation. Methods and materials: We present two models, with three (3C) and four (4C) compartments respectively. We use delay differential equations, and include accelerated proliferation, loss of division asymmetry, progressive death of abortive stem cells, and turnover of functional cells. The models are used to fit experimental data on the variations of the number of cells in mice mucosa after irradiation with 13 Gy and 20 Gy. Akaike information criteria (AIC) was used to evaluate the performance of each model. RESULTS: Both 3C and 4C models provide good fits to experimental data for 13 Gy. Fits for 20 Gy are slightly poorer and may be affected by larger uncertainties and fluctuations of experimental data. Best fits are obtained by imposing constraints on the fitting parameters, so to have values that are within experimental ranges. There is some degeneration in the fits, as different sets of parameters provide similarly good fits. CONCLUSIONS: The models provide good fits to experimental data. Mechanistic approaches like this can facilitate the development of mucositis response models to nonstandard schedules/treatment combinations not covered by datasets to which phenomenological models have been fitted. Studying the dynamics of cell populations in multifraction treatments, and finding links with induced toxicity, is the next step of this work.