The many dimensions of combination therapy: How to combine antibiotics to limit resistance evolution

In combination therapy, bacteria are challenged with two or more antibiotics simultaneously. Ideally, separate mutations are required to adapt to each of them, which is a priori expected to hinder the evolution of full resistance. Yet, the success of this strategy ultimately depends on how well the combination controls the growth of bacteria with and without resistance mutations. To design a combination treatment, we need to choose drugs and their doses and decide how many drugs get mixed. Which combinations are good? To answer this question, we set up a stochastic pharmacodynamic model and determine the probability to successfully eradicate a bacterial population. We consider bacteriostatic and two types of bactericidal drugs -- those that kill independent of replication and those that kill during replication. To establish results for a null model, we consider non-interacting drugs and implement the two most common models for drug independence -- Loewe additivity and Bliss independence. Our results show that combination therapy is almost always better in limiting the evolution of resistance than administering just one drug, even though we keep the total drug dose constant for a 'fair' comparison. Yet, exceptions exist for drugs with steep dose-response curves. Combining a bacteriostatic and a bactericidal drug which can kill non-replicating cells is particularly beneficial. Our results suggest that a 50:50 drug ratio -- even if not always optimal -- is usually a good and safe choice. Applying three or four drugs is beneficial for treatment of strains with large mutation rates but adding more drugs otherwise only provides a marginal benefit or even a disadvantage. By systematically addressing key elements of treatment design, our study provides a basis for future models which take further factors into account. It also highlights conceptual challenges with translating the traditional concepts of drug independence to the single-cell level. ### Competing Interest Statement The authors have declared no competing interest.