Determination of Somatic and Cancer Stem Cell Self-Renewing Symmetric Division Rate Using Sphere Assays

Representing a renewable source for cell replacement, neural stem cells have received substantial attention in recent years. The neurosphere assay represents a method to detect the presence of neural stem cells, however owing to a deficiency of specific and definitive markers to identify them, their quantification and the rate they expand is still indefinite. Here we propose a mathematical interpretation of the neurosphere assay allowing actual measurement of neural stem cell symmetric division frequency. The algorithm of the modeling demonstrates a direct correlation between the overall cell fold expansion over time measured in the sphere assay and the rate stem cells expand via symmetric division. The model offers a methodology to evaluate specifically the effect of diseases and treatments on neural stem cell activity and function. Not only providing new insights in the evaluation of the kinetic features of neural stem cells, our modeling further contemplates cancer biology as cancer stem-like cells have been suggested to maintain tumor growth as somatic stem cells maintain tissue homeostasis. Indeed, tumor stem cell's resistance to therapy makes these cells a necessary target for effective treatment. The neurosphere assay mathematical model presented here allows the assessment of the rate malignant stem-like cells expand via symmetric division and the evaluation of the effects of therapeutics on the self-renewal and proliferative activity of this clinically relevant population that drive tumor growth and recurrence

On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution

Model-based prediction of progression-free survival for combination therapies in oncology

Progression-free survival (PFS) is an important clinical metric for comparing and evaluating similar treatments for the same disease within oncology. After the completion of a clinical trial, a descriptive analysis of the patients\u27 PFS is often performed post hoc using the Kaplan–Meier estimator. However, to perform predictions, more sophisticated quantitative methods are needed. Tumor growth inhibition models are commonly used to describe and predict the dynamics of preclinical and clinical tumor size data. Moreover, frameworks also exist for describing the probability of different types of events, such as tumor metastasis or patient dropout. Combining these two types of models into a so-called joint model enables model-based prediction of PFS. In this paper, we have constructed a joint model from clinical data comparing the efficacy of FOLFOX against FOLFOX + panitumumab in patients with metastatic colorectal cancer. The nonlinear mixed effects framework was used to quantify interindividual variability (IIV). The model describes tumor size and PFS data well, and showed good predictive capabilities using truncated as well as external data. A machine-learning guided analysis was performed to reduce unexplained IIV by incorporating patient covariates. The model-based approach illustrated in this paper could be useful to help design clinical trials or to determine new promising drug candidates for combination therapy trials

Novel drug candidates for the treatment of metastatic colorectal cancer through global inverse gene-expression profiling

Drug-induced gene-expression profiles that invert disease profiles have recently been illustrated to be a starting point for drug repositioning. In this study, we validate this approach and focus on prediction of novel drugs for colorectal cancer, for which there is a pressing need to find novel antimetastatic compounds. We computationally predicted three novel and still unknown compounds against colorectal cancer: citalopram (an antidepressant), troglitazone (an antidiabetic), and enilconazole (a fungicide). We verified the compounds by in vitro assays of clonogenic survival, proliferation, and migration and in a subcutaneous mouse model. We found evidence that the mode of action of these compounds may be through inhibition of TGF{beta} signaling. Furthermore, one compound, citalopram, reduced tumor size as well as the number of circulating tumor cells and metastases in an orthotopic mouse model of colorectal cancer. This study proposes citalopram as a potential therapeutic option for patients with colorectal cancer, illustrating the potential of systems pharmacology

Proteogenomic integration reveals therapeutic targets in breast cancer xenografts

Recent advances in mass spectrometry (MS) have enabled extensive analysis of cancer proteomes. Here, we employed quantitative proteomics to profile protein expression across 24 breast cancer patient-derived xenograft (PDX) models. Integrated proteogenomic analysis shows positive correlation between expression measurements from transcriptomic and proteomic analyses; further, gene expression-based intrinsic subtypes are largely re-capitulated using non-stromal protein markers. Proteogenomic analysis also validates a number of predicted genomic targets in multiple receptor tyrosine kinases. However, several protein/phosphoprotein events such as overexpression of AKT proteins and ARAF, BRAF, HSP90AB1 phosphosites are not readily explainable by genomic analysis, suggesting that druggable translational and/or post-translational regulatory events may be uniquely diagnosed by MS. Drug treatment experiments targeting HER2 and components of the PI3K pathway supported proteogenomic response predictions in seven xenograft models. Our study demonstrates that MS-based proteomics can identify therapeutic targets and highlights the potential of PDX drug response evaluation to annotate MS-based pathway activities

TRAIL-induced variation of cell signaling states provides nonheritable resistance to apoptosis.

TNFα-related apoptosis-inducing ligand (TRAIL), specifically initiates programmed cell death, but often fails to eradicate all cells, making it an ineffective therapy for cancer. This fractional killing is linked to cellular variation that bulk assays cannot capture. Here, we quantify the diversity in cellular signaling responses to TRAIL, linking it to apoptotic frequency across numerous cell systems with single-cell mass cytometry (CyTOF). Although all cells respond to TRAIL, a variable fraction persists without apoptotic progression. This cell-specific behavior is nonheritable where both the TRAIL-induced signaling responses and frequency of apoptotic resistance remain unaffected by prior exposure. The diversity of signaling states upon exposure is correlated to TRAIL resistance. Concomitantly, constricting the variation in signaling response with kinase inhibitors proportionally decreases TRAIL resistance. Simultaneously, TRAIL-induced de novo translation in resistant cells, when blocked by cycloheximide, abrogated all TRAIL resistance. This work highlights how cell signaling diversity, and subsequent translation response, relates to nonheritable fractional escape from TRAIL-induced apoptosis. This refined view of TRAIL resistance provides new avenues to study death ligands in general

A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a physical parameter $m$, which characterizes the constitutive relation between density and pressure. Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density. We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, $m \rightarrow \infty$. Since the posterior distribution across the index regime $m\in[2,\infty)$ can thus be treated in a unified manner, such theoretical results also guide the design of the numerical inference for the unknown. We propose a generic computational framework for such inverse problems, which consists of a typical sampling algorithm and an asymptotic preserving solver for the forward problem. With extensive numerical tests, we demonstrate that the proposed method achieves satisfactory accuracy in the Bayesian inference of the tumor growth models, which is uniform with respect to the constitutive relation.Comment: 29 pages, 14 figure