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

[![amino acids, their protonated and deprotonated forms and pKa-values](https://i.stack.imgur.com/FFOeJ.png)](https://i.stack.imgur.com/FFOeJ.png) 

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):

[![Hydrogen bonding between lysine and glutamate](https://i.stack.imgur.com/9Lxh6.png)](https://i.stack.imgur.com/9Lxh6.png)  

source of picture: [Wikipedia](https://upload.wikimedia.org/wikipedia/commons/b/b4/Next_Revisit_Glutamic_Acid_Lysine_salt_bridge.png)