On the nature assumed

One of the tricky questions in Christology is to what extent Jesus assumed our human nature.  The problem arises when we ask, “Did Christ assume the sinful part of our nature?”  If we say yes, then it is hard to see how Christ is sinless.  If we say no, then we have to (seemingly) admit that Christ didn’t really assume all of our nature.  The answer lies along the lines that sin is accidental to our nature, not essential to it.   Therefore, Christ can essentially assume our nature without assuming the sinful part of it.