It is very difficult to answer your question. It is depend on different parameters: Which kind of proteins? In which status should this interaction measured (e.g. in vivo or ex-vivo or in vitro)? How is NPs functionalised?
The surface coverage will depend on the radius of the NPs as well as its charge. The surface charge density will depend on the ionic strength and the pH of the solution. But basically all protein will adsorb to gold, the time of residence is just not the same. If your protein has a cystein group , you can expect a stronger affinity via covalent bond ( thiol bonding). DNA is the most charged polymer in nature so you can expect strong electrostatic interaction with the DNA lying down onto the NPs surface
i am agree with your comment but if there is no functionalization on the nanoparticles and size will be comparable to the molecules size. (Lets example protein will be rhodopsin or bacteriorhodopsin and rest nanoparticles will be same as said above) then is there any way to find out interaction behaviour.....
As far as I know, their interactions are multifaceted. To be simple, the charged interactions exist forming a corona around nano particles. The cellular uptake is vastly influenced by this protein corona. If you want to find what type of about the interactions occur in your research, I think spectroscopic techniques will be best choice.