Tryptophan side-chain structure, how should it be orientated?

Good question, this regards rotamers!

Basically, the side chain of amino acids can rotate as shown in the figure below for glutamate (Glu; E). The various option for side-chain rotation is called rotamers! Some amino-acids side chains have the potential of many rotamers (such as glutamate) while some can only adopt a few (such as tryptophan) due to steric restraints. You can read about it here on FolditWiki or in the article 'Rotamers: To be or not to be?: An Analysis of Amino Acid Side-chain Conformations in Globular Proteins'.

The set of amino acid side-chain conformations in globular proteins cannot be considered as normally distributed around some rotamer points. Outliers occur systematically. The rotamericity of an amino acid depends essentially on the different environments the amino acid meets in real protein structures. Factors such as the backbone torsion angles of the residue itself, the secondary structure and tertiary contacts influence the rotamericity. (...)

When solving a protein structure, scientists spend a lot of time on placing the amino-acid side chains into their correct rotamer position. Which rotamer a particular side chain should adapt, depend on the surrounding environments. Some amino acids side-chain are also very flexible and will move around the various rotamer position that they can adopt. In the example of glutamate (figure above), it would most likely adapt a rotamer position pointing either out towards solvents (if the the side chain is on the surface of the protein), or perhaps towards a positively charged amino acids side chain such as Arginine (R) or Lysine (K) to form salt-bridges or H-bonds.

In the case of Tryptophan (W), it is often involved in pi-stacking and would therefore be found in a rotamer position that stacks with other aromatic amino acids side chains. It is also a very bulky amino acid, and might therefore only have space in one particular conformation. Note that tryptophan (W) only has two rotamers, which are similar to the two that you drew in the updated figure, and again shown below. Note that both of these are correct, and that my hand-drawn bond angles are a bit off. These two rotamer options for tryptophan are even found in enzymes catalytic site, where the 'flipping' from one confirmation to the other is the key-mechanisms the allows substrates into or out of the active site!

These structural arrangements are a lot easier to understand in three-dimensions, if you are still struggling then it could be a good idea to use a visualisation program (e.g. PyMol or Coot) and take a look at tryptophane's and other amino acids side chains by downloading some protein structure from the PDB database.

Here are also some related questions

• Protein Structure Parameters
• How to convert PDB file of Amino Acids to rotamer tuples list of all AAs instances