## 3 Results
### Stratification Meta-Analysis of MIC Values of Each Hop Compound
Meta-Analysis of MIC Values of Hop Compounds and Extracts Stratified According to Gram +/- and Oxygen-Requirement Microorganisms  
Gram classification profoundly shapes intrinsic drug susceptibility: the thick, accessible peptidoglycan of Gram-positive cells contrasts with the lipopolysaccharide-rich outer membrane and efflux machinery that shield Gram-negative bacteria, creating distinct permeability barriers and resistance phenotypes [57; 58; 59; 60]. Because hop prenylated flavonoids and bitter acids are relatively hydrophobic, their ability to traverse or destabilize these radically different envelope architectures is expected to diverge, making a Gram-based stratification essential for interpreting the true spectrum of activity. Accordingly, we conducted subgroup meta-analyses for Gram-positive and Gram-negative strains (Supplementary Table S2). As shown in Figure 10A and Table 6, MIC values for Gram-positive bacteria are lower than those of Gram-negative suggesting that thicker peptidoglycan walls of Gram-positive are more permeable to hops compounds compared to the outer lipopolysaccharide-saccharides membrane of Gram-negative. These results indicate that the hydrophobic prenylated flavonoids and bitter acids freely penetrate the porous peptidoglycan of Gram-positive bacteria, whereas the LPS outer membrane of Gram-negative species restricts their uptake, leading to higher MIC values in the latter group. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Compound** & **Time (h)** & **Gram** & **MIC** & **95\% CI** & **Number of Studies** & **Publication Bias (\(p\)-Value)** \\ \hline
**Flavonoids** & 24 & Positive & 22.64 & 12.42–32.85 & 39 & 0.667 \\ \cline{2-6}  & 48 & Positive & 182.91 & 52.78–313.0 & 63 & 0.00 \\  & & Negative & 427.6 & 70.30–784.9 & 10 & 0.840 \\ \hline
**Bitter acids** & 24 & Positive & 57.97 & 4.19–111.8 & 62 & 0.206 \\ \cline{2-6}  & 48 & Positive & 432.95 & 333.4–532.5 & 74 & 0.492 \\  & & Negative & 512.86 & 287.9–37.8 & 14 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Meta-analysis of MIC values of hop compounds and extracts stratified according to Gram-positive or Gram-negative microorganisms. Figure 9: Meta-analysis of MIC values for classes of hop compounds and extracts against probiotic and non- probiotic microorganisms at different incubation time points. Oxygen phenotype intrinsically shapes a bacterium's bioenergetics and redox balance: obligate aerobes derive ATP via ROS-producing oxidative phosphorylation, strict anaer \begin{table}
\begin{tabular}{l l l l l l l} \hline
**Compound** & **Time (h)** & **Gram** & **MIC** & **95\% CI** & **Number of Studies** & **Publication Bias (p-Value)** \\ \hline
**CO\({}_{2}\)-extract** & 24 & Positive & 341.13 & 73.5–608.8 & 24 & 0.365 \\ \cline{2-7}  & 48 & Positive & 870.01 & 393.2–1347 & 39 & 0.360 \\ \hline
**Hydralcoholic extract** & 24 & Positive & 143.55 & 61.69–225.4 & 22 & 0.330 \\  & & Negative & 625.0 & 624.4–625.6 & 4 & N/A \\ \cline{2-7}  & 48 & Positive & 136.8 & 101.2–172.4 & 40 & 0.00 \\  & & Negative & 270.8 & 174.3–367.3 & 13 & 0.00 \\ \hline
**Hydroacetonic extract** & 24 & Positive & 55.66 & 12.15–99.16 & 14 & 0.026 \\ \cline{2-7}  & 48 & Positive & 92.26 & 71.86–112.7 & 14 & 0.00 \\ \hline \end{tabular} \(\mathrm{N/A:}\) not applicable.  
\end{table} 
Table 6: _Cont._  
Figure 10: Meta-analysis of MIC values for classes of hop compounds extracts against Gram-positive and Gram-negative bacteria at different incubation time points (**A**) and against aerobic, anaerobic, and facultative anaerobic microorganisms at different incubation time points (**B**). obes rely on fermentation or non-oxygen electron acceptors, while facultative anaerobes can toggle between these pathways depending on environmental O\({}_{2}\)[61; 62; 63].