Adaptation in CRISPR-Cas systems enables the generation of an immunological memory to defend against invading viruses. This process is driven by foreign DNA spacer (termed protospacer) selection and integration mediated by Cas1-Cas2 protein. Recently, different states of Cas1-Cas2, in its free form and in complex with protospacer DNAs, were solved by X-ray crystallography. In this paper, molecular dynamics (MD) simulations are employed to study crystal structures of one free and two protospacer-bound Cas1-Cas2 complexes. The simulated results indicate that the protospacer binding markedly increases the system stability, in particular when the protospacer containing the PAM-complementary sequence. The hydrogen bond and binding free energy calculations explain that PAM recognition introduces more specific interactions to increase the cleavage activity of Cas1. By using principal component analysis (PCA) and intramolecular angle calculation, this study observes two dominant slow motions associated with the binding of Ca1-Cas2 to the protospacer and potential target DNAs respectively. The comparison of DNA structural deformation further implies a cooperative conformational change of Cas1-Cas2 and protospacer for the target DNA capture. We propose that this cooperativity is the intrinsic requirement of the CRISPR integration complex formation. This study provides some new insights into the understanding of CRISPR-Cas adaptation.