Gerund question

"We could not explain John's designating the area around the water cooler for "working" employees."

I thought an 'of' was needed after 'designating' as in the following sentence which is of my making:
"We could not explain John's designating of the area around the water cooler for "working" employees."

These are the usual forms:

1. To designate X as Y
2. His designating (of) X as Y
3. The designating of X as Y
4. The designation of X as Y

The verb takes a direct object, as does the gerund; but the verbal noun in #3 and the deverbal noun in #4 require an "of". (This is a common pattern.)

Best wishes,

MrP