We had a paper accepted in one of the top biology journals (IF=15). It is a work in which I participated in the part of computational biology, and was submitted by a colleague, she being the corresponding author since she is an expert on the field. We had a major revision and I had to do an outstanding work and a lot of calculations in order to have the paper accepted. I even developed a new approach. So now that we are at the proof stage, I would like to request her to appear in the paper as co-corresponding author since this is very important in my country. I do not know exactly how to do it. I will tell her to add me as co-corresponding with the text “to which all computational biology based correspondence should be addressed” since she is wet lab biologist. But I do not think this will be enough argument for her, i guess she will say initial ideas came from her side. What do you suggest for my “cover letter” to her?
While I don't really understand the value of this to you, not being in your immediate culture, the solution is clear as it is in most similar situations.
If you want something, just ask for it. Give her your reasons why it is important to you and why you need this at this time. If you ask it as a favor and not as a demand you might be more likely to prevail.
You may not be successful, but nothing you do can guarantee success. Asking keeps it collegial and preserves your relationship for the future.
Yes, you contributed, but so did she, I assume. In most places corresponding author is just a task, not an honor.
I'll suggest that whatever happens in the handling of a single publication it is unlikely to have much of an effect on your career. Working for long-term relationships is, to me, much more important than any check mark on a box or minor point on a CV.
What you write to your colleague is very similar to what you're writing here. You've strongly contributed to the computational side of this paper, and those computations form a substantial part of the paper. You feel that sharing corresponding authorship would accurately reflect both of your contributions. That's basically it.
You could also ask for a shared last authorship, and you should definitely consider asking for a shared first for your student who's done the computations.
Congratulations on the paper!