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We first compare the geometric frameworks behind the Uhlmann andBerry phases in a fiber-bundle language and then evaluate the Uhlmannphases of bosonic and fermionic coherent states. The Uhlmann phases ofboth coherent states are shown to carry geometric information anddecrease smoothly with temperature. Importantly, the Uhlmann phasesapproach the corresponding Berry phases as temperature decreases.Together with previous examples in the literature, we propose acorrespondence between the Uhlmann and Berry phases in thezero-temperature limit as a general property except some special casesand present a conditional proof of the correspondence. 

ABSTRACT Microbial diversity is reduced in the gut microbiota of animals and humans treated with selective serotonin reuptake inhibitors (SSRIs) and tricyclic antidepressants (TCAs). The mechanisms driving the changes in microbial composition, while largely unknown, is critical to understand considering that the gut microbiota plays important roles in drug metabolism and brain function. Using Escherichia coli , we show that the SSRI fluoxetine and the TCA amitriptyline exert strong selection pressure for enhanced efflux activity of the AcrAB-TolC pump, a member of the resistance-nodulation-cell division (RND) superfamily of transporters. Sequencing spontaneous fluoxetine- and amitriptyline-resistant mutants revealed mutations in marR and lon, negative regulators of AcrAB-TolC expression. In line with the broad specificity of AcrAB-TolC pumps these mutants conferred resistance to several classes of antibiotics. We show that the converse also occurs, as spontaneous chloramphenicol-resistant mutants displayed cross-resistance to SSRIs and TCAs. Chemical-genomic screens identified deletions in marR and lon, confirming the results observed for the spontaneous resistant mutants. In addition, deletions in 35 genes with no known role in drug resistance were identified that conferred cross-resistance to antibiotics and several displayed enhanced efflux activities. These results indicate that combinations of specific antidepressants and antibiotics may have important effects when both are used simultaneously or successively as they can impose selection for common mechanisms of resistance. Our work suggests that selection for enhanced efflux activities is an important factor to consider in understanding the microbial diversity changes associated with antidepressant treatments. IMPORTANCE Antidepressants are prescribed broadly for psychiatric conditions to alter neuronal levels of synaptic neurotransmitters such as serotonin and norepinephrine. Two categories of antidepressants are selective serotonin reuptake inhibitors (SSRIs) and tricyclic antidepressants (TCAs); both are among the most prescribed drugs in the United States. While it is well-established that antidepressants inhibit reuptake of neurotransmitters there is evidence that they also impact microbial diversity in the gastrointestinal tract. However, the mechanisms and therefore biological and clinical effects remain obscure. We demonstrate antidepressants may influence microbial diversity through strong selection for mutant bacteria with increased AcrAB-TolC activity, an efflux pump that removes antibiotics from cells. Furthermore, we identify a new group of genes that contribute to cross-resistance between antidepressants and antibiotics, several act by regulating efflux activity, underscoring overlapping mechanisms. Overall, this work provides new insights into bacterial responses to antidepressants important for understanding antidepressant treatment effects.