Supplementary Figure 10 from Ultrasensitive Response Explains the Benefit of Combination Chemotherapy Despite Drug Antagonism

Supplemental Figure 10. Combinations of drugs with varied mechanisms applied to the linear-quadratic model. We present here a preliminary investigation of how the linear-quadratic model (LQ) could have different implications if multiple drugs exert more distinct mechanisms of killing. Different drugs may exhibit different parameter values for α and β in the LQ model, but a further complexity is whether the quadratic terms are shared or distinct, which is compared here. (A) In this article, we have modelled cyclophosphamide and doxorubicin as both causing DNA damage and jointly adding to the accumulation of damage that is represented by the ‘quadratic’ term in the LQ model. When this applies to a hypothetical combination of drugs A+B, their combined dose can reach the ultrasensitive region of response more readily. Mathematically, the sum of drugs’ effects is squared. Without formally introducing drug-drug interaction, this equation results in an isobologram plot showing drugs A+B to be additive. (B) If drugs with highly distinct mechanisms of action are combined, their forms of damage may not jointly add up in the quadratic term of the LQ model. It may instead be justified to introduce distinct quadratic terms for each drug. Interestingly, even without formally introducing drug-drug interaction, such an equation leads to an isobologram plot that exhibits antagonistic (or sub-additive) interaction, even though the effect of the drug combination has been modelled as precisely additive. This arises because a combination of two half-doses is inferior to a full-dose of either single drug, because neither single drug dose extends as far into the ‘ultrasensitive’ region of response.