Discuss the relationship between Shylock and Antonio and explain how this relationship affects the plot
Short answer: The relationship between the Venetian moneylender Antonio and the Jewish usurer Shylock is one of animosity and mistrust. With such conditions in their relationship, Shylock's loaning of money to Antonio takes on extraordinary conditions that affect other characters as well, such as Portia, who comes to Antonio's defense in the end.
The history of Venice is one of many conquests and advancements, as well as conflicts with those who were not Venetian. Among those held in disdain were the Jewish merchants who had come to this wealthy city of commerce. Before the time of Shakespeare's writing The Merchant of Venice, Jews were confined to the Ghetto Nuova, a small, dirty island, and there were only certain hours that that they were allowed out. In addition, there were other restrictions placed upon them, such as having to wear a yellow hat or a yellow badge. Later, at the time of Shakespeare's play, Jews were allowed in Venice, but confined to a ghetto designated for them.
Antonio is a typical Venetian moneylender who has disdain for the Jew Shylock because of his usury; that is, because he charges exorbitant rates of interest on the money that he lends.
I hate him for he is a Christian;
But more for that in low simplicity
He lends out money gratis, and brings down
The rate of usance here with us in Venice. (1.3)
This disdain that Antonio possesses sets the tone for the plot of Shylock's strangely conditional lending money to Antonio
Signior Antonio, many a time and oft
In the Rialto you have rated me
About my moneys and my usances;
Still have I borne it with a patient shrug,
For suff'rance is the badge of all our tribe (2.7)
Likewise, it also opens the way for the subplot of Launcelot's departure from the service of Shylock, Jessica's renouncing her faith and leaving home to be with Lorenzo, a Christian. And, most of all, it opens the way for Antonio, in the main subplot, to have enough money to help his friend Bassanio, who wants to marry Portia, along with driving this subplot to its conclusion as Portia saves Antonio from losing a pound of flesh. Certainly the antipathy between Antonio and Shylock helps to develop the dimensions of friendship, brotherly love, and male/female love.