Can glutamic acid and arginine form H-bond at physiological pH? I was wondering if, say, glutamic acid and arginine can form H-bonds at physiological pH?

 

According to the figure arginine has a $\ce{NH3+}$ group and glutamic acid a $\ce{COO-}$ group at physiological pH.
I know hydrogen bonding is possible amongst $\ce{NH2}$, $\ce{HF}$ and $\ce{OH}$. But $\ce{-NH2}$ is in the protonated form and the $\ce{-COOH}$ in the deprotonated form.

What will happen: 


Will $\ce{-NH3+}$ donate its $\ce{H+}$ to $\ce{-COO^-}$ to form $\ce{-NH2}$ and $\ce{-COOH}$ and then form hydrogen bonds?
Will they attract each other because of the opposite charge, with resulting H-bonding
No H-bonding will occur.


(maybe the first and second option are combined, I didn't really know how to formulate it)

UPDATE
How is the H-bond possible in the following figure (I would think this is just an electrostatic interaction, this figure suggest it would a combination of both):


source of picture: Wikipedia
Yes, glutamate and arginine can form a hydrogen bond at physiological pH. Remember of course, that as soon as you enter aquaeous media, everything will be saturated by hydrogen bonds from the surrounding water molecules. But inside a protein an arginine—glutamate hydrogen bond is perfectly viable. Arginine will donate the hydrogen bond using an $\ce{N-H}$ bond and glutamate will receive towards a carboxylate.

Note, by the way, that your picture gives a wrong structure of protonated arginine. The correct protonation of the guanidine group is given in the image below (taken from Wikipedia).