## 1 Introduction  
Autism spectrum disorder (ASD) is a complex heterogeneous neurodevelopmental condition characterized by varying degrees of challenges in social communication and interactions, often coupled with repetitive behaviors, as well as an impaired ability to learn and behave [1, 2]. While causes for ASD remain unknown, several twin studies suggest a high degree of genetic heritability, with correlations among monozygotic twins being significantly higher than those for dizygotic twins on multiple ASD measures [3, 4]. Furthermore, ASD is often associated with a high prevalence of gastrointestinal (GI) issues [5], and it has been suggested that serotonin (5-hydroxytryptamine, or 5-HT) may be a factor that affects both sides of this equation [6]. In fact, elevated serotonin levels in the blood were one of the first biomarkers correlated with autism, with a quarter to a third of individuals with ASD exhibiting hyperserotonemia [7, 8]. Over 95% of serotonin is synthesized in the gut [9]; blood serotonin is found in platelets [10], which do not synthesize it but utilize a 5-HT transporter SERT to take it up as they circulate through the gut [11, 12]. Hyperactivity of SERT, which is encoded by a variant of the SIC64a gene, has been associated with both ASD and, interestingly, obsessive-compulsive disorder (OCD).  
A possible mechanistic link between serotonin specifically in the gut and ASD has been studied in an intriguing experiment by [PERSON] et al. [13]. In the gut, serotonin functions not only as a neurotransmitter but also as a growth factor [14, 15] by promoting neurogenesis of the enteric (gut) nervous system (ENS). In [13], the authors evaluated the hypothesis that SERT hyperactivity in a mouse model can drive structural and functional GI deficits due to altered serotonin signaling in the gut. The authors compared the impact of SERT signaling on ENS size for mice with hyperactive SERT (Ala56 mice) who exhibit whole blood hyperserotonemia, as well as brain and behavioral abnormalities, with wild type mice and with SERT receptor knock out mice (SERTKO). The authors show that due to the increased activity of SERT in Ala56 mice, the size of the ENS can be up to 60% smaller at 6-8 weeks compared to WT mice, since increased clearance of serotonin from the gut due to SERT hyperactivity prevents serotonin from acting as a growth factor on the ENS (in the experiment, the authors used 10 mice per group, and the reported results were statistically significant). These animals tended to exhibit repetitive behaviors, delayed communication, and deficits in social interactions. Furthermore, the authors showed that the deficits could be reversed by administering a highly selective 5-HT4 agonist, prucalopride, during critical periods of neurodevelop, which normalized enteric neuronal numbers in the SERT Ala56 mice and alleviated some of the social deficits.  
The goal of this work is to explore more deeply the possible factors that connect gut concentration of serotonin, SERT expression, and ENS size. This is achieved through a mathematical model aimed at reproducing key features of the experiment conducted by [13]. The model is used to identify three key factors that can affect the relationship between serotonin and the ENS. A possible scaling of these results from mice to humans is proposed, followed by simulations that take into account changes in serotonin production that have been observed in neurotypical children compared to children with ASD. A discussion of possible connections between hypoplastic ENS and its impact on the brain, as well as possible implications of this hypothesis, concludes this work.