The role and existence of low-barrier hydrogen bonds (LBHBs) in enzymatic and protein activity has been largely debated. An interesting case is that of the photoactive yellow protein (PYP). In this protein, two short HBs adjacent to the chromophore, p-coumaric acid (pCA), have been identified by X-ray and neutron diffraction experiments. However, there is a lack of agreement on the chemical nature of these H-bond interactions. Additionally, no consensus has been reached on the presence of LBHBs in the active site of the protein, despite various experimental and theoretical studies having been carried out to investigate this issue. In this work, we perform a computational study that combines classical and density functional theory (DFT)-based quantum mechanical/molecular mechanical (QM/MM) simulations to shed light onto this controversy. Furthermore, we aim to deepen our understanding of the chemical nature and dynamics of the protons involved in the two short hydrogen bonds that, in the dark state of PYP, connect pCA with the two binding pocket residues (E46 and Y42). Our results support the existence of a strong LBHB between pCA and E46, with the H fully delocalized and shared between both the carboxylic oxygen of E46 and the phenolic oxygen of pCA. Additionally, our findings suggest that the pCA interaction with Y42 can be suitably described as a typical short ionic H-bond of moderate strength that is fully localized on the phenolic oxygen of Y42.