Cas1 and Cas2 are highly conserved proteins across clustered-regularly-interspaced-short-palindromic-repeat-Cas systems and play a significant role in protospacer acquisition. Based on crystal structure of twofold symmetric Cas1-Cas2 in complex with dual-forked protospacer DNA (psDNA), we conducted all-atom molecular dynamics simulations to study the psDNA binding, recognition, and response to cleavage on the protospacer-adjacent-motif complementary sequence, or PAMc, of Cas1-Cas2. In the simulation, we noticed that two active sites of Cas1 and Cas1' bind asymmetrically to two identical PAMc on the psDNA captured from the crystal structure. For the modified psDNA containing only one PAMc, as that to be recognized by Cas1-Cas2 in general, our simulations show that the non-PAMc association site of Cas1-Cas2 remains destabilized until after the stably bound PAMc being cleaved at the corresponding association site. Thus, long-range correlation appears to exist upon the PAMc cleavage between the two active sites ($10 nm apart) on Cas1-Cas2, which can be allosterically mediated by psDNA and Cas2 and Cas2' in bridging. To substantiate such findings, we conducted repeated runs and further simulated Cas1-Cas2 in complex with synthesized psDNA sequences psL and psH, which have been measured with low and high frequency in acquisition, respectively. Notably, such intersite correlation becomes even more pronounced for the Cas1-Cas2 in complex with psH but remains low for the Cas1-Cas2 in complex with psL. Hence, our studies demonstrate that PAMc recognition and cleavage at one active site of Cas1-Cas2 may allosterically regulate non-PAMc association or even cleavage at the other site, and such regulation can be mediated by noncatalytic Cas2 and DNA protospacer to possibly support the ensued psDNA acquisition.