Polycyclic nitrogen heterocyclic compounds (PANHs) can be protonated in the gas phase in mass spectrometry, in solution in acidic and biological environments, and if present, in interstellar clouds. Intrinsic molecular effects on PANH basicities can be observed by their gas phase protonation thermochemistry. We determined the gas phase basicities/proton affinities (GBs/PAs) of prototype one-nitrogen, 3-5-ring PANH compounds of increasing sizes and polarizabilities by kinetic bracketing, using proton transfer reactions to reference bases. The experimental proton affinities increase from 1-ring (pyridine, 222.2); to 2-ring (quinoline, 227.8); to 3-5-ring compounds, 227-234 kcal mol(-1). We also calculated the GB/PA values at the M06-2X/6-311+G**//B3LYP/6-31g* level. The computed PAs agree, within the experimental uncertainty, with the experimental values anchored to the upper range of the NIST GB/PA database. Specifically, the computed PAs are smaller than the experimental values by 1.4 +/- 0.9 kcal/mol for nonaromatic nitrogen reference bases and for 1-5-ring PANHs, independently of the number of rings, aromaticity, and molecular size. Therefore, a useful method to calculate proton affinities of PANH compounds can use M06-2X/6-311+G**//B3LYP/6-31g* computational PAs + 1.4 +/- 0.9 kcal mol(-1). The agreement with experiment supports the NIST database within this accuracy, in the upper range up to 235 kcal mol(-1), even though there are no direct absolute experimental anchor points in this range. For astrochemical applications, the measured PAs allow calculating the energies of the (PANH)(+center dot) + H-2 (R) (PANH)H+ + H-center dot reactions that may convert the radical ions to less reactive 11-electron ions. The reactions are endothermic or nearly thermoneutral for the 3-5-ring ions and would be very slow at low temperatures, allowing reactive (PANH)(+center dot) radical ions to persist in interstellar clouds.