Modular model of TNFalpha cytotoxicity

Bistability regulates TNFR2-mediated survival and death of T-regulatory cells

A subgroup of T cells called T-regulatory cells (Tregs) regulates the body's immune responses to maintain homeostasis and self-tolerance. Tregs are crucial for preventing illnesses like cancer and autoimmunity. However, contrasting patterns of Treg frequency are observed in different autoimmune diseases. The commonality of tumour necrosis factor receptor 2 (TNFR2) defects and decrease in Treg frequency on the onset of autoimmunity demands an in-depth study of the TNFR2 pathway. To unravel this mystery, we need to study the mechanism of cell survival and death in Tregs. Here, we construct an ordinary differential equation (ODE)-based model to capture the mechanism of cell survival and apoptosis in Treg cells via TNFR2 signalling. The sensitivity analysis reveals that the input stimulus, the concentration of tumour necrosis factor (TNF), is the most sensitive parameter for the model system. The model shows that the cell goes into survival or apoptosis via bistable switching. Through hysteretic switching, the system tries to cope with the changing stimuli. In order to understand how stimulus strength and feedback strength influence cell survival and death, we compute bifurcation diagrams and obtain cell fate maps. Our results indicate that the elevated TNF concentration and increased c-Jun N-terminal kinase (JNK) phosphorylation are the major contributors to the death of T-regulatory cells. Biological evidence cements our hypothesis and can be controlled by reducing the TNF concentration. Finally, the system was studied under stochastic perturbation to see the effect of noise on the system's dynamics. We observed that introducing random perturbations disrupts the bistability, reducing the system's bistable region, which can affect the system's normal functioning.

Mathematical models of cytotoxic effects in endpoint tumor cell line assays: critical assessment of the application of a single parametric value as a standard criterion to quantify the dose-response effects and new unexplored proposal formats

The development of convenient tools for describing and quantifying the effects of standard and novel therapeutic agents is essential for the research community, to perform more precise evaluations. Although mathematical models and quantification criteria have been exchanged in the last decade between different fields of study, there are relevant methodologies that lack proper mathematical descriptions and standard criteria to quantify their responses. Therefore, part of the relevant information that can be drawn from the experimental results obtained and the quantification of its statistical reliability are lost. Despite its relevance, there is not a standard form for the in vitro endpoint tumor cell lines' assays (TCLA) that enables the evaluation of the cytotoxic dose-response effects of anti-tumor drugs. The analysis of all the specific problems associated with the diverse nature of the available TCLA used is unfeasible. However, since most TCLA share the main objectives and similar operative requirements, we have chosen the sulforhodamine B (SRB) colorimetric assay for cytotoxicity screening of tumor cell lines as an experimental case study. In this work, the common biological and practical non-linear dose-response mathematical models are tested against experimental data and, following several statistical analyses, the model based on the Weibull distribution was confirmed as the convenient approximation to test the cytotoxic effectiveness of anti-tumor compounds. Then, the advantages and disadvantages of all the different parametric criteria derived from the model, which enable the quantification of the dose-response drug-effects, are extensively discussed. Therefore, model and standard criteria for easily performing the comparisons between different compounds are established. The advantages include a simple application, provision of parametric estimations that characterize the response as standard criteria, economization of experimental effort and enabling rigorous comparisons among the effects of different compounds and experimental approaches. In all experimental data fitted, the calculated parameters were always statistically significant, the equations proved to be consistent and the correlation coefficient of determination was, in most of the cases, higher than 0.98.

Computer-aided biophysical modeling: a quantitative approach to complex biological systems

When dealing with the biophysics of tumors, analytical and numerical modeling tools have long been regarded as potentially useful but practically immature tools. Further developments could not just overturn this predicament, but lead to completely new perspectives in biology. Here, we give an account of our own computational tool and how we have put it to good use, and we discuss a paradigmatic example to outline a path to making cell biology more quantitative and predictive.