However, any other line or curve fails the test, including, for example, a straight line with an x-axis intercept greater than zero (e.g., Figure 1C, where a dose of 4 would give an effect of 15). As shown in the example in Figure 1B, a line with zero intercepts passes the Sham Combination test the predicted additive effect for (2,2) is 10 + 10 = 20, which matches the actual effect for the dose of 4. Thus, the effect of the dosing pair (a,b) = (2,2) is known-it will be the effect for a dose of 4. In the hypothetical situation of the test, the two drugs A and B have identical dosing curves. However, this method, Response Additivity, only works under highly specific conditions, as illustrated by the Sham Combination test ( Figures 1B,C): when the dosing curves are linear with zero intercepts. A common approach to determine the predicted additive effect of a combination treatment of drug A and drug B for a particular dosing pair (a,b) is to add the individual effects ( Figure 1A). While determining a predicted additive effect at first appears to be a straightforward task, decades of intense discussion in the field show otherwise. Then, if that predicted additive effect is different than the actual effect of the combination treatment, by definition the drugs interact. To assess whether any two drugs interact, either with synergism or antagonism, the central objective is to determine the predicted additive effect of the combination treatment (i.e., the effect if there is zero interaction between the drugs). Currently, the field lacks a method to assess interactions for compounds with dosing curves that are not easily fit to a Hill-slope equation. For over 35 years the field has actively formulated and evaluated various methodologies to assess synergism and its counterpart, antagonism, and numerous reviews discuss the appropriate use of these methods.
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The central question is whether two drugs interact synergistically-that is, if their combined effect is greater than what is predicted based on their individual effects-and this seemingly simple question has been challenging to address. This approach has been successfully adopted in diverse areas including chemotherapy ( Mokhtari et al., 2017), malaria ( Fidock et al., 2004), and HIV ( Arts and Hazuda, 2012). Combining two or more drugs in a single treatment has significant promise for pharmacological intervention, due primarily to better efficacy, less toxicity, and fewer side effects ( Lehàr et al., 2009). The field of drug discovery is looking beyond the traditional one-target, one-drug paradigm ( Keith et al., 2005). DE/ZI eliminates the need to determine the best fit equation for a given data set and values experimentally-derived results over formulated fits. For the assessed Nrf2 activators, sulforaphane and di- tert-butylhydroquinone, this approach revealed synergistic interactions at higher dosing concentrations consistently across data sets and potential antagonistic interactions at lower concentrations. Using a Monte-Carlo method, DE/ZI generates a measure of synergy or antagonism for each dosing pair with an associated error and p-value, resulting in a 3D response surface. This method, termed Dose-Equivalence/Zero Interaction (DE/ZI), can be used with traditional Hill-slope response curves, and it also can assess interactions for compounds with non-traditional curves, using a nearest-neighbor approach.
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We introduce a method based on the principles of Loewe Additivity to assess synergism and antagonism for two compounds in combination. Nrf2 activators generally have non-traditional dose response curves that are hormetic, or U-shaped. For example, sulforaphane sourced from broccoli sprouts is the subject of over 70 clinical trials. Known as Nrf2 activators, this class of compounds upregulates a battery of cytoprotective genes and shows significant promise for prevention of numerous chronic diseases.
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![how to use calcusyn how to use calcusyn](https://europepmc.org/articles/PMC3809771/bin/JCI64210.t1.jpg)
Specifically, our goal was to assess small-molecule modulators of antioxidant response element (ARE)-driven gene expression, which is largely regulated by the Nrf2 transcription factor. However, the field lacks methodology to assess synergistic or antagonistic interactions for drugs with non-traditional dose response curves. Multi-drug combination therapy carries significant promise for pharmacological intervention, primarily better efficacy with less toxicity and fewer side effects. Department of Chemistry, Villanova University, Villanova, PA, United States.