Not sure I understand the question, however...
Before I started running, I could quite easily run up several flights of stairs - up to the point of being able to (just) manage 1 floor at work carrying 10 reams of paper!
Now that I'm running 10 miles a week, just walking up stairs is slightly painful - I put this down to the muscles wanting some time off to recover!
Climbing stairs is presumably an anerobic activity - more like a sprint, and I think there are two possible anerobic mechanisms that depend on the effort expended. Running probably won't make your short stair climbs much easier directly.