Their not related by blood, Mikasa was adopted by Eren's family. Mikasa basically fell in love with Eren before she was adopted, because he helped her get the strength to fight in a very tough situation.
She becomes very protective of Eren because he is always jumping head first into situations like fights even though he's outmatched, but she's there to back him up and she's actually an amazing fighter.
So Eren gets a little jealous and envious of Mikasa because she would always bail him out, and because she's an amazing fighter.
So basically the dynamic is Mikasa loves Eren, and we've seen Eren have moments of at least caring about her.
Won't go into current storylines lol.