Prediction of response to anticancer treatment as simple as the resolution of ordinary differential equations?
- 1Université Paris Descartes, Sorbonne Paris Cité, Paris, France
- 2Department of Biology, Assistance Publique—Hôpitaux de Paris, European Georges Pompidou Hospital, Paris, France
- 3Department of Medicine, Institut Gustave Roussy, Villejuif, France
- Correspondence to Pr. Pierre Laurent-Puig, Bases Moléculaires de la Réponse aux Xénobiotiques INSERM UMR-S775, 45 Rue des Saints Pères, Paris 75006, France;
Contributors All the authors took part in: drafting the article or revising it critically for important intellectual content and final approval of the version to be published.
The introduction of differential equations in medicine is due to the Swiss physician mathematician, Daniel Bernoulli (1700–1782), who calculated the survival gain of the population by the generalisation of smallpox virus inoculation.1 Many models in systems biology are described as systems of ordinary differential equations, which consist of establishing series of mathematical relationships that describe the sequential changes in components of the systems over time.2 Programmed cell death, apoptosis, can be activated through two different pathways: the death receptor or extrinsic pathway, engaged by members of the tumour necrosis factor (TNF) receptor family on the cell surface; and the Bcl-2-regulated mitochondrial (B-cell lymphoma 2) or intrinsic pathway. The intrinsic pathway starts with BH3-only protein induction or post-translational activation, which results in inactivation of some BCL-2 family members. This relieves inhibition of BAX(BCL2-associated X protein) and BAK (BCL2-antagonist/killer 1) activation, which in turn promotes apoptosis through induction of permeabilisation of the outer mitochondrial membrane and subsequent release of apoptogenic molecules, such as cytochrome c and DIABLO (IAP-binding mitochondrial protein). Cytochrome c binds to APAF1 (apoptotic peptidase …