The gut microbiome plays a crucial role in human health, and its dysbiosis is implicated in various diseases, including IBS. However, manipulating the microbiome effectively is challenging due to its inherent dynamism and complexity. Microbiome-targeted interventions, such as probiotic use in IBS, often yield inconsistent results. Optimal dosage, treatment duration, and strain combinations remain largely undetermined. This study hypothesizes that mathematical modeling can optimize IBS treatment by predicting the microbiome's response to interventions. While existing models like the generalized Lotka-Volterra (gLV) model have been applied to ecosystems, they are not ideally suited for the human gut due to the unique factors of defecation and the presence of multiple microbial niches. Therefore, a novel model is needed to better capture the gut microbiome's dynamic behavior.

Existing research highlights the complexity and dynamic nature of the gut microbiome's response to external interventions. Studies on probiotic efficacy in IBS have shown heterogeneous responses, emphasizing the need for personalized approaches. Previous work suggested that the microbiome's initial composition influences its response to interventions, such as low FODMAP diets. Mathematical modeling has been employed to study ecological systems, but applying it to the human gut presents unique challenges. Models like the gLV model have limitations in representing the defecation process and the diverse niches within the gut.

This study developed a novel NEDN model, adapting the gLV model to account for defecation and non-extinction of gut microbes. The model incorporates daily biological growth and defecation steps, ensuring that all microbial genera remain present, reflecting the existence of diverse niches. The model's parameters (inherent growth rates and interaction matrix) were fitted using published dense time-series data from a single individual. The NEDN model was compared to the gLV model based on cumulative deviation and prediction accuracy for microbiome composition over time. In silico simulations were conducted using the NEDN model to investigate the microbiome's response to two types of perturbation: probiotic-like intervention (addition of *Clostridium* cluster XIVa) and laxative-like treatment (reduction of total microbial population). Different doses and frequencies of probiotic intervention were tested. A three-arm, randomized, open-label clinical trial was conducted to compare three CB regimens in 56 IBS patients: 1) LP (laxative immediately followed by CB for 2 weeks); 2) L2P (laxative followed by a 2-week interval before CB for 2 weeks); and 3) P (CB alone for 2 weeks). Patients were assessed using a Likert-7 symptom score system and IBS-QoL questionnaires at baseline, week 2, and week 4. Faecal samples were collected and analyzed using 16S rRNA gene sequencing. Alpha and beta diversities were calculated and compared across groups and with a healthy control group. Taxonomic composition was analyzed at the phylum and genus levels.

The NEDN model demonstrated a superior fit to the time-series data compared to the gLV model, exhibiting lower cumulative deviation and stable error over time. In silico simulations revealed that the gut microbiome tends towards a few stable states and that it is resilient to single-dose probiotic interventions. However, repeated probiotic administration was more effective at shifting the microbiome composition. Importantly, simulations suggested that a laxative-like treatment, by reducing the overall microbial population, creates a more favorable environment for probiotic intervention, thus requiring a lower probiotic dose to achieve a similar effect. The clinical trial showed that the LP regimen (laxative followed by CB) resulted in the most pronounced relief of IBS symptoms (abdominal pain, discomfort, bloating, urgency) during the 2-week CB treatment period. The LP group also showed significant improvement in the summed symptom score compared to the L2P and P groups. While there was some reduction in symptoms in all groups, the effect was most significant in the LP group. Analysis of the gut microbiome revealed that the LP group, but not the L2P group, achieved alpha diversity comparable to the healthy control group after 2 weeks of CB treatment. The LP group also showed a decrease in beta diversity, indicating a more homogeneous microbiome similar to the healthy control group after 2 weeks of treatment. These findings align with the in silico simulations, suggesting that the sequential laxative-probiotic approach is most effective in restoring a healthier gut microbiome composition and alleviating IBS symptoms. The abundance of Proteobacteria was lower in IBS patients than healthy individuals at baseline, while Bifidobacterium was overrepresented. These were not significantly altered by treatment.

This study's findings demonstrate that integrating mathematical modeling and clinical trials offers a powerful approach to optimizing microbiome-targeted therapies for IBS. The NEDN model successfully captured the gut microbiome's dynamics and provided valuable insights into the optimal timing and dose of probiotic intervention. The clinical trial results validate the model's prediction that a sequential laxative-probiotic approach is more effective than probiotic monotherapy in relieving IBS symptoms. The observed improvement in microbiome composition in the LP group supports the hypothesis that laxative bowel cleaning prepares the gut for more effective probiotic intervention. The study's success in improving symptoms and microbiome composition in IBS patients using a relatively simple, low-cost intervention has significant clinical implications. Further research is needed to confirm the findings and to explore the applicability of this approach to other probiotics and IBS subtypes. Future work will benefit from improvements to the NEDN model for complex interventions and from clinical trials with placebo control and larger sample sizes.

This study demonstrates the efficacy of a novel sequential laxative-*C. butyricum* regimen in reducing IBS symptoms and modulating the gut microbiome. The integration of mathematical modeling and clinical trials proved invaluable in identifying this optimal approach. Future research should focus on validating these findings in larger, placebo-controlled trials and exploring the effects of other probiotics and their optimal combinations.

This study has several limitations. The clinical trial was an open-label study without a placebo control group, which might introduce bias. The sample size of the clinical trial was relatively small and the patients were recruited from a single center. The 4-week follow-up period was short, and long-term effects are unknown. The NEDN model's performance might be improved by incorporating more microbial genera and more precise laxative treatment parameters. The strength of laxative treatment was estimated rather than measured.