Please add <code> tags around your data, you had to go through a preview page to post this and so you should have noticed it was badly formed.

As to your problem:

• open file one
• while there are records in the file
  • if the line contains a string followed by one of your required strings
    • add the initial string to a hash of acceptable gene strings.
• open file 2
• while there are records in the file
  • if the line begins with a > and the rest of the line exists in your hash
    • write this line to a temp file
    • read the next line and add it to the temp file also (I think, not sure of what you have specified)
• rename the temp file to file2 if you wish to overwrite the original version.

Code that up and come back with any specific issues you are having.