A resonant enhancement of the water-1H relaxation rate at three distinct frequencies in the range 0.5-3 MHz has been observed in a variety of aqueous biological systems. These so-called quadrupole (Q) peaks have been linked to a dipolar flip-flop polarization transfer from 1H nuclei to rapidly relaxing amide 14N nuclei in rotationally immobilized proteins. While the Q-peak frequencies conform to the known amide 14N quadrupole coupling parameters, a molecular model that accounts for the intensity and shape of the Q peaks has not been available. Here, we present such a model and test it against an extensive set of Q-peak data from two fully hydrated crosslinked proteins under conditions of variable temperature, pH and H/D isotope composition. We propose that polarization transfer from bulk water to amide 14N occurs in three steps: from bulk water to a so-called intermediary proton via material diffusion/exchange, from intermediary to amide proton by cross-relaxation driven by exchange-mediated orientational randomization of their mutual dipole coupling, and from amide proton to 14N by resonant dipolar relaxation 'of the second kind', driven by 14N spin fluctuations, which, in turn, are induced by restricted rigid-body motions of the protein. An essentially equivalent description of the last step can be formulated in terms of coherent 1H-->14N polarization transfer followed by fast 14N relaxation. Using independent structural and kinetic information, we show that the Q peaks from these two proteins involve approximately 7 intermediary protons in internal water molecules and side-chain hydroxyl groups with residence times of order 10(-5) s. The model not only accounts quantitatively for the extensive data set, but also explains why Q peaks are hardly observed from gelatin gels.