Analysis of a Mathematical Model of Apoptosis: Individual Differences and Malfunction in Programmed Cell Death

TL;DR

This study uses a mathematical model to analyze apoptosis, identifying key parameters influencing cell survival and testing potential treatments, highlighting individual variability in treatment responses.

Contribution

It performs sensitivity analysis on an apoptosis model and simulates treatment effects, emphasizing the importance of molecular heterogeneity in personalized therapy.

Findings

Proteasome inhibitors are most effective but may have side effects.

Treatment efficacy varies with individual proapoptotic protein levels.

Bcl-2 inhibitors activate caspase-3 only in Bax-deficient cells.

Abstract

Apoptosis is an important area of research because of its role in keeping a mature multicellular organism's number of cells constant hence, ensuring that the organism does not have cell accumulation that may transform into cancer with additional hallmarks. Firstly, we have carried out sensitivity analysis on an existing mitochondria-dependent mathematical apoptosis model to find out which parameters have a role in causing monostable cell survival i.e., malfunction in apoptosis. We have then generated three healthy cell models by changing these sensitive parameters while preserving bistability i.e., healthy functioning. For each healthy cell, we varied the proapoptotic production rates, which were found to be among the most sensitive parameters, to yield cells that have malfunctioning apoptosis. We simulated caspase-3 activation, by numerically integrating the governing ordinary differential equations of a mitochondria-dependent apoptosis model, in a hypothetical malfunctioning cell which is treated by four potential treatments, namely: (i) proteasome inhibitor treatment, (ii) Bcl-2 inhibitor treatment, (iii) IAP inhibitor treatment, (iv) Bid-like synthetic peptides treatment. The simulations of the present model suggest that proteasome inhibitor treatment is the most effective treatment though it may have severe side effects. For this treatment, we observed that the amount of proteasome inhibitor needed for caspase-3 activation may be different for cells in individuals with a different proapoptotic protein deficiency. We also observed that caspase-3 can be activated by Bcl-2 inhibitor treatment only in those hypothetical malfunctioning cells with Bax deficiency but not in others. These support the view that molecular heterogeneity in individuals may be an important factor in determining the individuals' positive or negative responses to treatments.