How is the theme of friendship and sacrifice expressed in "The Last Leaf" by O. Henry?

Friendship and sacrifice meet in O. Henry's story about two friends and a cranky old man who dwell in "quaint old Greenwich Village."

Sue from Maine and Joanna from California move together into "a joint studio" at the top of a three-story brick dwelling. When Joanna, called "Johnsy" by her friend Sue, becomes gravely ill, the doctor estimates her chances of survival are one in ten. "And that chance is for her to want to live," he tells Sue. Before he departs, he urges Sue to find someone or something to motivate Johnsy to survive.

Afraid for Johnsy, her loving friend tries to stir the weakened young woman's desire to live. However, as Sue later sits at her drawing board working on a magazine illustration, she hears Johnsy counting. When she asks her friend what she is counting, Johnsy replies that she has been counting the ivy leaves outside on a building as they fall off their vine in the bitter cold.

"When the last one goes, I must go, too. I've known that for three days. Didn't the doctor tell you?"

Sue tries to encourage her friend by saying,

"What have old ivy leaves to do with your getting well? ...Why, the doctor told me this morning that your chances for getting well real soon were...ten to one!"

A determined Johnsy insists that she will watch the last leaf fall before it grows dark. Then she will "turn loose" her hold on life and fall too.

Sue orders Johnsy to remain in bed while she descends to the ground floor to find Behrman, the old man who (she claims) she wants to use as a model for an old miner. 

...[Behrman] was a fierce little old man, who scoffed terribly at softness in any one, and who regarded himself as especial mastiff-in-waiting to protect the two young artists in the studio above.

When Sue informs Behrman of Johnsy's declaration that she will die when the last ivy leaf falls, he becomes angry and ridicules such an idea. He accompanies Sue upstairs, where they find Johnsy asleep. Sue pulls down the window shade, and they move to another room in order to peer out its window. For a grim, meaningful instant, Sue and Behrman look at each other.

Throughout the night Sue keeps watch over her friend. When she awakens from only an hour's sleep, she finds Johnsy staring at the green shade. Johnsy insists that Sue pull up the shade so that she can see; with dread Sue does so. On the brick wall is one ivy leaf, hanging "bravely" despite its yellow serrated edges. When it is still there the next day, the leaf's stubborn clinging to the wall moves the ailing Johnsy to feel guilty for wanting to die. With a will to live now, she asks Sue for some broth.

The next day the doctor declares Johnsy out of danger. That afternoon a saddened Sue informs Johnsy that the janitor found Behrman helpless with pain the day after the older man visited them. He was taken to the hospital, where he later died. Sue tells Johnsy that the last leaf, which still has not moved, was painted onto the wall by Mr. Behrman. "It's Behrman's masterpiece--he painted it there the night that the last leaf fell."

Sue's friendship provides Johnsy loving care through her illness. It is also Sue's love for her friend that takes her downstairs to solicit the sympathy of Behrman. His loving, sacrificial act provides Johnsy the motivation to live.