## 4 Impact of Individual Mechanisms on the ENS  
It can be seen from the model, and predicted intuitively, that in addition to serotonin production (here captured by parameter \(a\) in Equations (A1) and (A2) in the Appendix A) there are two other key components that could qualitatively affect ENS size: firstly, serotonin clearance through activity of SERT, drugs, or any other receptor that is involved in the clearance of serotonin from the gut, preventing it from acting as a growth factor (here captured as parameter _sett_); and secondly, the rate of ENS growth as a function of serotonin (here captured by parameter \(\mathsf{k_{n}}\) in Equation (A1) in the Appendix A). In Figure 4, all three factors are varied to assess their relative impact on ENS size relative to the norm (blue, solid) by time = 5 years, including the dynamic human serotonin production function from Figure 3.  
As one can see in Figure 4, while all three of these factors can affect the size of the ENS by t = 5 years, and while each of them can certainly contribute to the deviation of ENS size from 100%, neither in this range can solely drive the ENS into the 60% range, which would have corresponded to ENS size for the ASD phenotype in the work of [PERSON] et al. [13]. Given the complexity of this condition and its heterogeneity, even for this subset of phenotypes, it is most likely that it is a combination of these factors that would result in the critical phenotype. That is, it is most likely that that there is intrinsic population variability with respect to each of these parameters, and it is a combination of the three rather than a single one that translates into ENS hypoplasia of sufficient severity to manifest in an ASD-like phenotype. Figure 3: Differences in serotonin synthesis capacity (K complex, mL/g/min) over time for ASD and non-ASD children as reported by [PERSON] et al. [17] and captured by the model. The published data from [17] were digitized using WebPlotDigitizer. To assess the impact of the combination of these factors, we carried out a parameter sweep over these three properties--_sert_ (rate of SERT-mediated serotonin uptake in the gut), \(k_{n}\) (rate of serotonin-mediated ENS growth), and \(a\) (rate of serotonin production over time in the gut)--and recorded the corresponding size of the ENS relative to the norm at t = 5 years (Figure 5). Figure 4: Model-based assessment of the impact of varying the three main factors that functionally connect levels of serotonin in the gut and ENS size. Solid blue line represents the norm (\(k_{n}\) = 10.1; \(sert\) = 0.4; \(a\) = 0.0006); dot-dashed red and dashed green lines represent the impact of deviation of the norm. (**a**) The rate of serotonin clearance (\(sert\) = 0.4) and rate ENS growth as a function of serotonin concentration (\(k_{n}\) = 10.1) are fixed; rate of serotonin production over time \(a\) is varied. (**b**) Rate of serotonin production over time (parameter \(a\)) and serotonin-mediated ENS growth (\(k_{n}\)) are fixed; rate of SERT-mediated serotonin clearance from the gut is varied. (**c**) Varying rate of serotonin-mediated ENS growth (\(k_{n}\)), while keeping the other two factors fixed. As can be seen in Figure 5, a confluence of factors can indeed significantly affect the size of the ENS (here collected at t = 5 years old), more so than each individual factor by itself. As can be seen in Figure 5a, even when serotonin production (parameter \(a\)) is fixed, a low rate of serotonin-mediated ENS growth (parameter \(k_{n}\)) or high rate of SERT activity (_sert_) can result in significantly lower ENS size. In Figure 5b, one can see that when \(\text{k}_{\text{n}}\) is fixed, it is the rate of serotonin production rather than SERT expression that determines ENS size. In Figure 5c, fixing _sert_ shows that \(k_{n}\) is more important when \(a\) is high to ensure normal ENS size but is less impactful for low values of \(a\).