## 3 Results
### Stratification Meta-Analysis of MIC Values of Each Hop Compound
Prenylated flavonoids and bitter acids from hops collapse the proton-motive force and inhibit redox-sensitive dehydrogenases--targets that are most abundant in aerobic and facultative respiratory chains but largely absent in strict anaerobes [64; 65; 66; 67]; so, their efficacy is expected to vary across these metabolic guilds. Therefore, stratifying our meta-analysis by aerobic, anaerobic, and facultative anaerobic groups (Supplementary Table S2) provides mechanistic context for any differential MIC patterns and clarifies where hop-derived compounds may be most therapeutically or industrially applicable. Accordingly, we carried out oxygen-based subgroup analyses (Supplementary Table S2). Our results (Figure 10B and Table 7) reveal that hop compounds exhibit higher MIC values for aerobic bacteria compared to anaerobic or facultative anaerobic ones. Finally, publication bias was more prominent for studies performed for 48 h of incubation (Tables 6 and 7). Taken together, the higher MICs against aerobic species suggest that hop compounds act most efficiently in low-oxygen or anaerobic niches--information that can guide their deployment in food packaging, gut-targeted formulations and products, or fermentation systems where anaerobic bacteria dominate. As natural, plant-based antimicrobials, hop compounds could meet the growing demand for clean-label solutions and may also support antibiotic use by reducing the needed dose and slowing resistance development. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Compound** & **Time (h)** & **Probiotic** & **MIC** & **95\% CI** & **Number of Studies** & **Publication Bias (p-Value)** \\ \hline
**Flavonoids** & 24 & \begin{tabular}{c} Facultative \\ anaerobic \\ Aerobic \\ \end{tabular} & 23.94 & 12.20–35.68 & 36 & 0.006 \\  & 48 & \begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 287.2 & 48.54–525.88 & 16 & 0.807 \\  & & \
\begin{tabular}{c} Aerobic \\ Anaerobic \\ \end{tabular} & 642.9 & 273.8–1012 & 13 & 0.059 \\  & &
\begin{tabular}{c} Anaerobic \\ \end{tabular} & 59.23 & 45.99–58.46 & 43 & 0.749 \\ \hline
**Bitter acids** & 24 & \
\begin{tabular}{c} Facultative \\ anaerobic \\ anaerobic \\ \end{tabular} & 50.22 & 28.04–72.40 & 50 & 0.473 \\  & &
\begin{tabular}{c} Aerobic \\ Anaerobic \\ \end{tabular} & 90.25 & 0–255.5 & 12 & 0.587 \\ \hline
**48** & \begin{tabular}{c} Facultative \\ anaerobic \\ anaerobic \\ \end{tabular} & 375 & 130.0–620.0 & 2 & N/A \\  & & \
\begin{tabular}{c} Anaerobic \\ Aerobic \\ \end{tabular} & 438.5 & 343.7–533.4 & 82 & 0.00 \\  & &
\begin{tabular}{c} Aerobic \\ \end{tabular} & 627.5 & 214.3–1040 & 4 & N/A \\ \hline
**CO\({}_{2}\)-extract** & 24 & \
\begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 408.7 & 98.99–718.3 & 20 & 0.272 \\  & &
\begin{tabular}{c} Anaerobic \\ \end{tabular} & 3.49 & 2.73–4.25 & 4 & N/A \\ \hline
**48** & \begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 44.09 & 7.92–80.25 & 19 & 0.278 \\  & & \
\begin{tabular}{c} Aerobic \\ \end{tabular} & 2.19 & 1197–3173 & 15 & 0.022 \\  & &
\begin{tabular}{c} Anaerobic \\ \end{tabular} & 62.5 & 0–162.2 & 5 & \\ \hline
**Hydalcoholic-extract** & 24 & \
\begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 190.0 & 94.481–285.4 & 23 & 0.196 \\  & &
\begin{tabular}{c} Aerobic \\ \end{tabular} & 429.7 & 46.820–812.5 & 3 & N/A \\ \hline
**48** & \
\begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 142.3 & 89.950–194.7 & 29 & 0.00 \\  & &
\begin{tabular}{c} Anaerobic \\ \end{tabular} & 202.7 & 147.354–257.9 & 24 & 0.00 \\ \hline
**Hydroacetonic-extract** & 24 &
\begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 55.66 & 12.15–99.16 & 14 & 0.026 \\ \hline
**48** &
\begin{tabular}{c} Facultative \\ anaerobic \\ \end{tabular} & 92.26 & 71.86–112.66 & 14 & 0.00 \\ \hline \hline \end{tabular}  
N/A: not applicable.  
\end{table} 
Table 7: Meta-analysis of MIC values of hop compounds and extracts stratified according to oxygen tolerance activity microorganisms.