Résumé : Persistence is a phenotypic phenomenon occurring at a very low frequency in bacterial populations, enabling individual bacteria to tolerate antibiotic exposure. In the first part of this thesis, the role of Envelope Stress Responses (ESRs) of E. coli in persistence to antibiotics of the β-lactam class was investigated. Results show that ESRs do not contribute to survival, and only the σE response is induced by β-lactams but σE activity does not predict survival. The second part is dedicated to the development of a microfluidic sorting device in collaboration with Guillaume De Timàry, Ph.D. student in the Benoit Scheid team at the TIPs laboratory (ULB). The device is based on the Pinched Flow Fractionation method, allowing separation of cells of different sizes, which can ultimately be used to separate filamentous persister cells to the fluoroquinolone ofloxacin from the short dead cells.