Bring a pot of water to a boil for the pasta.
In a pot large enough to accommodate the mussels, heat 2 tablespoons of the butter and gently cook shallots, celery and 2 tablespoons parsley for about 5 minutes. Add the wine and bring to a boil. Add the mussels and raise the heat. When the steam starts to escape, shake the pot, keeping the cover tightly on to rotate mussels inside. Let them cook for 5 to 7 minutes or until the mussels open.
Meanwhile, place the pasta in the boiling water and cook for 3 to 5 minutes or until tender. Drain and portion out. Discard mussels that remain closed. Set the open mussels, in their shells, over pasta. Pour the mussel cooking liquid through a fine strainer into a saucepan. Reduce quickly and slightly. Whisk in remaining two tablespoons of butter and parsley. Season to taste with salt and pepper and pour over mussels and pasta.