Hypothesis\n\nWe hypothesize that combining galactooligosaccharides (GOS) supplementation with regular aerobic exercise produces a greater increase in hippocampal brain‑derived neurotrophic factor (BDNF) and a larger reduction in anxiety scores than either intervention alone, but only in participants whose baseline stool shows high relative abundance of Faecalibacterium prausnitzii.\n\n## Rationale\n\nPrebiotic fibers such as GOS raise colonic butyrate production [2], and butyrate crosses the blood‑brain barrier to inhibit histone deacetylases, thereby promoting BDNF transcription [4]. Aerobic exercise independently elevates circulating BDNF via muscle‑derived signals [6]. When both pathways are active, we expect additive or synergistic HDAC inhibition and neurotrophic signaling. F. prausnitzii is a major butyrate producer; individuals already rich in this taxon may generate more butyrate from a given GOS dose, amplifying the central effect [5]. In contrast, low F. prausnitzii may limit butyrate yield, blunting the synergy.\n\n## Testable Predictions\n\n1. In a randomized controlled trial, the GOS + exercise group will show a significantly larger increase in serum BDNF (proxy for central BDNF) after 8 weeks than the GOS‑only, exercise‑only, and placebo groups only among participants with baseline F. prausnitzii above the median.\n2. The same subgroup will exhibit a greater reduction in validated anxiety scales (e.g., GAD‑7) compared with other groups.\n3. Mediation analysis will reveal that change in fecal butyrate concentration accounts for a significant portion of the BDNF increase and anxiety improvement in the synergistic subgroup.\n4. Participants with low baseline F. prausnitzii will not differ significantly between intervention arms, indicating a microbiota‑dependent interaction.\n\n## Proposed Study Design\n\n- Population: Adults aged 18‑45 with mild‑to‑moderate anxiety (GAD‑7 8‑14), no antidepressant use.\n- Stratification: Screen stool via 16S rRNA sequencing; allocate to high vs low F. prausnitzii strata.\n- Interventions (2 × 2 factorial within each stratum):\n - GOS 5 g/day vs maltodextrin placebo\n - Supervised aerobic exercise 30 min, 3×/week at 65 % VO₂max vs stretching control\n- Duration: 8 weeks.\n- Outcomes: Serum BDNF (ELISA), fecal butyrate (GC‑MS), GAD‑7, and optional hippocampal volume via MRI.\n- Analysis: Mixed‑effects model testing interaction between GOS, exercise, and F. prausnitzii stratum; mediation via bootstrapped indirect effects.\n\nIf the hypothesis holds, it would justify microbiome‑guided prescribing of prebiotic‑exercise combos for anxiety, moving beyond the modest, inconsistent effects seen when prebiotics are used alone [1,3] and provide a mechanistic bridge between microbial metabolism and neurotrophic signaling.