Answer: Our paper's science writer, whose column I read every week, recently reported on exoplanets.
Explanation: There are three ideas here.
1. Our paper's science writer
2. They recently reported on exoplanets
3. How I read their column every week.
Two of the ideas are included in the sentence (1 and 2), and the last simply needs to be modified.
"Whose" is a determiner and associates things with other things. In the last idea, we associate their column to them: whose column... Then, we add how I read it every week and say, "...whose column I read every week."
