Abstract
Immunoglobulin A is a class of antibodies produced by the adaptive immune system and secreted into the gut lumen to fight pathogenic bacteria. We recently demonstrated that the main physical effect of these antibodies is to enchain daughter bacteria, i.e. to cross-link bacteria into clusters as they divide, preventing them from interacting with epithelial cells. These links between bacteria may break over time. Using analytical and numerical calculations on several models to check the results robustness, we study the rate of increase in the number of free bacteria as a function of the replication rate of bacteria, and the resulting distribution of chain sizes. At higher replication rates, the bacteria replicate before the link between daughter bacteria breaks, leading to growing cluster sizes. However at low growth rates two daughter cells have a high probability to break apart. Thus the gut could produce IgA against all the bacteria it has encountered, but the most affected bacteria would be the fast replicating ones, which could destabilize the microbiota.
