'Filter rows of file based on match in a second file

I have two files with a list of genes (and some other information) and want to report a third file that contains genes from file 1 that are not found in file 2.

Here is the first file:

A01 23915164    23915314    Bra040361   AT3G07100   18.59019807
A02 1595601 1595688 Bra028560   AT5G10870   28.48729677
A02 20515443    20516351    Bra029367   AT5G23340   16.06774844
A03 14688282    14689512    Bra001273   AT3G07870   13.93575203
A06 472776  473620  Bra039661   AT1G53210   52.96447989
A08 2624078 2634861 Bra014189   AT1G49450   22.62572775
A09 30817052    30819592    Bra031704   AT1G10170   14.95032844
A10 532340  532466  Bra033282   AT1G01140   10.5095903

And here are the first 5 lines of the second file:

A01 3710694 3710789 Bra011117   11.85222101
A01 9480352 9483285 Bra026368   11.96344966
A01 23915165    23915314    Bra040361   18.59019807
A02 1595602 1595688 Bra028560   28.48729677
A02 1674981 1675077 Bra023317   17.90385707

For both files, the gene names are in column 4. I thought this would be pretty easy to do with something like awk, but am having trouble. Any suggestions for how I can achieve my desired filtering filtering?

shell


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