The immune and enteric systems have been implicated in psychopathology, including depressive disorders. However, the precise neurocognitive mechanisms remain unclear. The present study uses Brain-Inspired Spiking Neural Network (SNN) technique to model electroencephalographic (EEG) data as a function of gut-microbiota, inflammation, and depressive symptoms. Forty-two participants (nonclinical cohort) were assessed for Bacteroides-Prevotella (BAC) colonization in faecal samples, Interleukin 6 (IL-6) in peripheral blood, depressive symptoms (self-report of cognitive and non-cognitive symptoms) and brain function (resting state EEG). SNN models were applied to EEG data to generate connection weight values across scalp regions. Connection weights were visualized as a function of 1) depression; 2) inflammation; 3) gut microbiome. Lower depression and higher BAC were associated with higher frontal connection weights (cognitive depression = bilateral, non-cognitive and BAC = left hemisphere only). Lower cognitive depression and lower IL-6 were associated with higher posterior connection weights. The SNN models achieved higher accuracy for theta and alpha EEG sub-bands, highlighting their relevance in differentiating between groups. These findings emphasize the potential of SNNs in predicting parameters from brain functional connectivity data and developing targeted diagnostic and intervention strategies.