title: Antimicrobial combinations: Bliss independence and Loewe additivity derived from mechanistic multi-hit models.
abstract: Antimicrobial peptides (AMPs) and antibiotics reduce the net growth rate of bacterial populations they target. It is relevant to understand if effects of multiple antimicrobials are synergistic or antagonistic, in particular for AMP responses, because naturally occurring responses involve multiple AMPs. There are several competing proposals describing how multiple types of antimicrobials add up when applied in combination, such as Loewe additivity or Bliss independence. These additivity terms are defined ad hoc from abstract principles explaining the supposed interaction between the antimicrobials. Here, we link these ad hoc combination terms to a mathematical model that represents the dynamics of antimicrobial molecules hitting targets on bacterial cells. In this multi-hit model, bacteria are killed when a certain number of targets are hit by antimicrobials. Using this bottom-up approach reveals that Bliss independence should be the model of choice if no interaction between antimicrobial molecules is expected. Loewe additivity, on the other hand, describes scenarios in which antimicrobials affect the same components of the cell, i.e. are not acting independently. While our approach idealizes the dynamics of antimicrobials, it provides a conceptual underpinning of the additivity terms. The choice of the additivity term is essential to determine synergy or antagonism of antimicrobials.This article is part of the themed issue 'Evolutionary ecology of arthropod antimicrobial peptides'.
authors.affiliation: Institute of Integrative Biology, ETH Zurich, Universitätsstrße 16, 8092 Zurich, Switzerland desiree.baeder@env.ethz.ch.
authors.forename: Desiree Y
authors.identifier: 0000-0002-5585-6143
authors.initials: DY
authors.lastname: Baeder
authors.affiliation: Evolutionary Biology, Institut für Biologie, Freie Universität Berlin, Königin-Luise-Straße 1-3, 14195 Berlin, Germany.
authors.forename: Guozhi
authors.initials: G
authors.lastname: Yu
authors.affiliation: Institute of Integrative Biology, ETH Zurich, Universitätsstrße 16, 8092 Zurich, Switzerland.
authors.forename: Nathanaël
authors.initials: N
authors.lastname: Hozé
authors.affiliation: Evolutionary Biology, Institut für Biologie, Freie Universität Berlin, Königin-Luise-Straße 1-3, 14195 Berlin, Germany Berlin-Brandenburg Institute of Advanced Biodiversity Research (BBIB), Altensteinstraße 6, 14195, Berlin, Germany.
authors.forename: Jens
authors.initials: J
authors.lastname: Rolff
authors.affiliation: Institute of Integrative Biology, ETH Zurich, Universitätsstrße 16, 8092 Zurich, Switzerland roland.regoes@env.ethz.ch.
authors.forename: Roland R
authors.identifier: 0000-0001-8319-5293
authors.initials: RR
authors.lastname: Regoes
mesh_terms: D000818:Animals; D000890:Anti-Infective Agents / Q000494:pharmacology*; D023181:Antimicrobial Cationic Peptides / Q000494:pharmacology*; D001419:Bacteria / Q000187:drug effects*; D019476:Insect Proteins / Q000494:pharmacology*; D007313:Insecta / Q000382:microbiology*; D008954:Models, Biological
chemical_list: D000890:Anti-Infective Agents; D023181:Antimicrobial Cationic Peptides; D019476:Insect Proteins
keywords: antagonism; antibiotics; antimicrobial peptide responses; mathematical modelling; pharmacodynamic function; synergy