Modeling synergistic effects by using general Hill-type response surfaces describing drug interactions

Area of Science:

• Pharmacology and Toxicology
• Mathematical Modeling
• Computational Chemistry

Background:

• Classifying mixture effects (synergistic, antagonistic, additive) relies on defining a 'null interaction' reference model.
• Current models like Additive Dose (ADM) and Multiplicative Survival (MSM) have limitations in describing complex interactions.
• A previously proposed approach used Hill-type response surfaces based on logistic differential equations for 'zero-interaction'.

Purpose of the Study:

• To extend the generalized Hill-type model to describe deviations from 'null interaction' in agent mixtures.
• To introduce parameters for drug perturbations and n-tuple interactions within mixtures.
• To identify dose combinations exhibiting maximum synergistic or antagonistic effects.

Main Methods:

• Developed a 'full-interaction' Hill response surface model incorporating interaction parameters for n-component mixtures.
• Applied the model to experimental data, fitting with maximum parameters and then reducing insignificant ones based on fit-statistics.
• Calculated 'synergy surfaces' (differences between full- and null-interaction models) to pinpoint peak interaction doses.

Main Results:

• The 'full-interaction' Hill model successfully describes mixture responses, including those with arbitrary Hill parameters and baseline effects.
• Applied to binary and ternary mixtures, the model identified dose combinations yielding maximum synergistic or antagonistic effects.
• Demonstrated that fewer parameters can often accurately describe responses, simplifying the analysis of deviations from null interaction.

Conclusions:

• The generalized Hill-type model provides a robust framework for analyzing complex mixture effects, surpassing limitations of traditional models.
• The approach effectively identifies specific dose combinations that elicit desired synergistic or antagonistic outcomes.
• Model parameter reduction facilitates focused analysis on key factors driving deviations from null interaction, enhancing understanding of mixture toxicology.