I am designing a cloning experiment to remove a domain of the protein my lab studies using gibson assembly. It seems to me that the overhangs I design into primers targeting the two sides of the domain (essentially bridging the gap between the two ends, beginning just before the domain and continuing just after it ends) will likely anneal to both sides nonspecifically, resulting in a mixture of products, some that contain the domain I am trying to remove, some that don't.
Are there any measures I can take to prevent nonspecific annealing such as digesting the protein beforehand or manipulating the Tm values of each 'segment' of the primers? Is there a better technique that I can use to eliminate the domain?
Thanks!