Suicide is painless, it brings on many changes...

Cell suicide does indeed bring on many changes, but it's far from painless, or at least modelling it is. To get an example of just what's involved, I'd recommend having a look at the wonderfully well written paper by Cho et al. The authors use first order ordinary differential equations (ODEs) to show how the protein TNFa (Tumour Necrosis Factor-alpha) triggers a sequence of protein interactions that lead to the release of NFkb (Nuclear Factor-kappa-beta), a bound group of proteins heavily involved the response of the immune system. NFkb activity is closely associated, for example, with inflammation and cell termination (known as apoptosis).

The pathway is written as a series of chemical reactions where each reaction is catalysed by an enzyme. These reactions can be described using the law of mass action, which says that the rate of a reaction is proportional to the product of the concentration of the reactants. In a chain of reactions, the products of each reaction combine with other reactants to fuel further reactions and the behaviour of the whole chain is heavily dependent on the reaction rate constants. If they're too mismatched the pathway can swell with proteins in the middle or be starved of fuel. This picture is complicated by the recycling of the enzymes and the reverse reactions which accompany only part of the catalysis process.

What makes this sort of modelling challenging is that so few of the rate constants are known. To quote Cho et al., "The exact value of parameters, such as the concentration of each signaling protein, the rate constants for the generation and degradation, etc., are difficult to obtain because their numerical values not only depends on the species and tissue, but also on the physiological state of the cells/organism." So the rate constants used are just educated guesses. Nonetheless, Cho et al. show that by adding a dollop of TNFa to the pathway, it leads to a surge in the amount of NFKB produced.

The two plots shown are taken from their paper. The first shows the dose of TNFa (pure dashed line) at time zero and the second shows the NFKB response (pure solid line), which gets into its stride at about 50 seconds. It is clear from their results that TNFa plays an powerful role in triggering the immune response.

Reference
Cho, K. (2003). Investigations Into the Analysis and Modeling of the TNFÂ -Mediated NF-Â B-Signaling Pathway. Genome Research, 13(11), 2413-2422. DOI: 10.1101/gr.1195703