[The enigma of the biological interpretation of the linear-quadratic model finally resolved? A summary for non-mathematicians]

Cancer Radiother. 2016 Jun;20(4):314-21. doi: 10.1016/j.canrad.2016.02.014. Epub 2016 Jun 21.
[Article in French]


The linear-quadratic (LQ) model is the only mathematical formula linking cellular survival and radiation dose that is sufficiently consensual to help radiation oncologists and radiobiologists in describing the radiation-induced events. However, this formula proposed in the 1970s and α and β parameters on which it is based remained without relevant biological meaning. From a collection of cutaneous fibroblasts with different radiosensitivity, built over 12 years by more than 50 French radiation oncologists, we recently pointed out that the ATM protein, major actor of the radiation response, diffuses from the cytoplasm to the nucleus after irradiation. The evidence of this nuclear shuttling of ATM allowed us to provide a biological interpretation of the LQ model in its mathematical features, validated by a hundred of radiosensitive cases. A mechanistic explanation of the radiosensitivity of syndromes caused by the mutation of cytoplasmic proteins and of the hypersensitivity to low-dose phenomenon has been proposed, as well. In this review, we present our resolution of the LQ model in the most didactic way.

Keywords: ATM; DNA repair; LQ model; Modèle linéaire-quadratique; Radiosensibilité; Radiosensitivity; Réparation de l’ADN.

MeSH terms

  • Ataxia Telangiectasia Mutated Proteins / metabolism*
  • Cell Survival / physiology
  • Cell Survival / radiation effects*
  • DNA Damage / physiology
  • DNA Repair / physiology
  • DNA Repair / radiation effects
  • Dose-Response Relationship, Radiation
  • Humans
  • Linear Models*
  • Models, Biological
  • Radiation Tolerance / physiology*
  • Radiation Tolerance / radiation effects


  • Ataxia Telangiectasia Mutated Proteins