Can I describe in my own word few experiments from some academic papers to write a popular science book? My book is about a theory that is based upon existing theories and recent experiments in biology. Since biology is not my main field, and since my theory is interesting to the general public, I self-published my book.

The response to my book has been good.

But now I am afraid because I have described several mainstream biological experiments in my book, which although I accessed through my institution, and are not in the public domain. I was careful to cite the original research and describe results in a short, non technical way, in my own words. I also included several graphs in my book that I drew myself in a qualitative way, based upon the diagrams of the research papers. 

So, can there be any legal issues with my book? A friend of mine is suggesting that I need to get permission from publishers of the research papers before describing the content of their papers, because I used their material for commercial purpose (to write my book).

I must clarify that the experiments that I have described are only a part of my book, about 20%, and the rest of the book uses the experiments to develop a semi-original biological theory of my own. I needed to describe the experiments to let the readers know the basis of my arguments.
In general, copyright protects words, sounds, images, and similar artifacts.  Copyright does not, however, protect ideas or knowledge.  The use of ideas and knowledge can be protected by a patent.  No intellectual property right, however, can be used to prevent a person from describing a published piece of information in their own words.

In your case, it sounds as though you are taking what you have learned by reading about this scientific work and presenting it with your own original words and images.  As such, I think that you have nothing to fear, as long as you are certain to give appropriate references and credit to the original authors whose work you are describing.  In a popular science publication, such citations might be more informal than in a peer-reviewed scientific paper, but as long as they are clear to the reader, what you describe doing appears to be entirely ethical and appropriate.