Gene Roddenberry and Isaac Asimov had some communication after Asimov wrote some disparaging comments about the scientific accuracy of Star Trek. They eventually became firm friends and Roddenberry turned to him for advice on how to better portray the character of Kirk who was supposed to be the centre of the show but was being overshadowed by the characters of Spock and McCoy.
Then, too, it might be well to unify the team of Kirk and Spock a bit, by having them actively meet various menaces together with one saving the life of the other on occasion. The idea of this would be to get people to think of Kirk when they think of Spock.
To which Roddenberry replies
Your comments on Shatner and Spock were most interesting and I have passed them on to Gene Coon and others. We've followed one idea immediately, that of having Spock save his Captain's life, in an up-coming show.
Which episode is Gene Roddenberry referring to in this letter?
The full correspondence can be found here