In this paper, the non-catalytic interaction between soot and nitric oxide (NO) for their simultaneous reduction is studied on different types of reactive sites that can be present on soot. The reaction mechanism proposed in our previous work [Sander et al., Carbon, 47:866-875, 2009] has been extended by including seven newly proposed reaction pathways. The energetics and the kinetics of the new reactions are studied using density functional theory (DFT) and transition state theory, respectively, and their evaluated rates are presented. Due to a discrepancy in the rate for CO removal from soot surface in the literature, a new rate for it is suggested. A Polycyclic Aromatic Hydrocarbon (PAH) model, referred to as the kinetic Monte Carlo-Aromatic Site (KMC-ARS) model is used to simulate the reaction between NO and soot to form CO, N2 and N2O. The simulation results are compared to the experimental findings both qualitatively and quantitatively. A satisfactory agreement between them is obtained with the newly proposed rate for CO removal. The reaction between NO and soot is found to depend strongly on the type of sites present on soot, and the reaction temperature. For a set of temperatures, computed structures of PAHs are analysed to determine the functional groups present on PAHs, which are responsible for the decrease in soot reactivity towards NO with increasing reaction time. The interaction between NO and soot in isothermal conditions reveals that with increasing temperature, the number of O atoms remaining on soot surface decreases, and the number of N atoms increases for a given reaction time.