In school we are told that in 1453 the Ottoman turks took the city of Constantinople from the dying Byzantine Empire, preventing Europe from trading throuh the Silk Road and thus causing Cristopher Columbus to persuade the kings of Castille to fund an expedition to reach the Far East through the Atlantic Ocean.

However, was the taking of Constantinople really important to kickstart the Age of Discovery, especially considering Portugal had already begun circumnavigating around Africa? Moreover, how was Constantinople important at all if by 1453 the Turks already controlled plenty of territory around it, in the Balkans and Anatolia? And even if the city was important at all, why would the Turks prevent Europe from trading through their lands, considering how immensely lucrative that would have been for them?

So this is my question: was the fall of Constantinople relevant in any way to the discovery of America?