Description

Initially, Drabme uses an ensemble of boolean models and a list of drug perturbations to generate perturbed models. This means that for every combination of a boolean model generated by Gitsbe and a drug perturbation given, a new model is created by finding the targets of the perturbation’s drug(s) (see drug panel) and permanently changing their respective boolean equations to either false (when the drug is inhibiting its target - most common case scenario) or true (when the drug is causing the expression of its target).

Then, the attractors of the perturbed models are calculated and a global output response value is computed for each perturbed model using the model outputs and Equation No. (1). Thus we simulate the effect that each perturbation has on different versions of the cell network system under test (defined originally as a Gitsbe input). The perturbed models’ response values can now be used to assess which drug combinations are synergistic. Next, we focus our discussion on two-drug combinations for ease of understanding, but note that Drabme supports the synergy evaluation of higher-order drug combinations as well.

The most simple mathematical models that are used to evaluate if two drugs are synergistic or not, are the HSA (Highest Single Agent) (Gaddum 1940) and Bliss Independence (Bliss 1939) models. The simplicity of these models lies in the fact that they are effect-based (or equivalently response-based in our case)2 and do not depend on the dosages of the drugs tested (like Loewe’s model for example (Loewe 1928)). Thus, they fit perfectly with the simulation data Drabme produces - i.e. the perturbed models’ response values.

In order for these mathematical models to classify two drugs as synergistic (or not), they define an expected additive response that the combination should have if the two drugs are not interacting with each other (they are neither synergistic or antagonistic - their effects are simply added). If the (predicted or observed) combined response is lower3 than the additive one for a particular tested model/system, a synergy is called (if higher, then an antagonism). The HSA model for example, defines the additive response as the minimum of the two single-drug perturbed model responses.4 So, when the output response of the two-drug perturbed model is lower than the minimum of the two single-drug perturbed models, the two-drug combination acts synergistically upon that particular model.

The assessment of synergies in Drabme is done in two ways: model-wise and ensemble-wise (using HSA or Bliss, see configuration options). In the model-wise approach, for each drug combination, we find and compare the number of models that predicted it as synergistic vs the number of models that predicted it as antagonistic (using for example the HSA method as described in the previous paragraph). In the ensemble-wise approach, for each drug combination, we find the two average single-drug responses as well as the average response for the drug combination (from the collection of models at our disposal)5 and use the HSA (Bliss) model on these ensemble-wise values. The HSA-exceed (Bliss-exceed) value - i.e. how much lower was the average combination response value from the minimum of the two average responses of the single-drug perturbed models or from their product in the case of Bliss (per drug combination tested) - is one the main outputs of Drabme. The more negative that value is, the more synergistic the drug combination is ensemble-wise and vise-versa (the more positive, the more antagonistic).

  1. Note that the term effect is used complementary to the term response, i.e. the higher the effect of the drug, the smaller the output response or viability, which is exactly what the calculated global output responses of the perturbed models are↩︎

  2. Again, higher if we are talking about effects↩︎

  3. On the other hand, Bliss Independence defines as the additive response the product of the two single-drug perturbed model responses. So it’s a more strict model for synergies↩︎

  4. Actually, from all the models that had attractors for the specified perturbations (single or double)↩︎