Final answer:
The gut and LES are innervated by both intrinsic (enteric nervous system) and extrinsic (autonomic nervous system) components, involving interaction among myenteric and submucosal plexuses, celiac ganglion, inferior mesenteric ganglion, and intramural ganglia.
Step-by-step explanation:
The innervation of the gut and the lower esophageal sphincter (LES) involves both intrinsic and extrinsic components. The intrinsic innervation is mainly provided by the enteric nervous system which houses two plexuses, the myenteric plexus responsible for motility and the submucosal plexus for regulating digestive secretions. In contrast, the extrinsic innervation involves the autonomic nervous system, comprising sympathetic and parasympathetic fibers.
Specifically, the greater splanchnic nerve, containing fibers from central sympathetic neurons, projects onto the celiac ganglion. The lesser splanchnic nerve similarly contains fibers that bypass the chain ganglia to synapse at the inferior mesenteric ganglion. These ganglia are part of the collateral, or prevertebral, ganglia which also interact with the enteric nervous system to regulate functions of the abdominal organs including the gut.
It is worth noting that the parasympathetic nervous system's involvement is through intramural ganglia found within the walls of the alimentary canal, which enhance gastrointestinal secretion and motility when stimulated. This occurs during the rest-and-digest response, complementing the role of the enteric system.