Yes, you can remap a PDB entry to a gene.

Remember:

• Gene > transcription>Transcript >translation> Protein
• Protein data is rendered as sequence (primary structure), predicted structure (secondary structure) and 3D structure using X-ray/NMR crystallography (these data sets are in PDB, but it's a central repository of structural data)
• PDB files are structural data of proteins
• The blueprint is your genes, but the transcript has to goes through processing steps before protein synthesis.
• Splicing, exon structure, RNA editing and other post-translational modifications are critical steps, etc.
• You will have a representative protein structure. Don't expect the mapping to be a direct 3:1 (codon: amino acid ratio).

RCSB (the site you referred in your answer) or Uniprot ID mapping is the best way to do this mapping.

PS. RTWP on Protein Structure

Hey, UniProtID mapping another way to go. http://www.uniprot.org/uploadlists/

DAVID can also be used for this purpose. https://david.ncifcrf.gov/summary.jsp

Just to complement ahmedakhokhar's useful answer:

You can upload your list of genes to the UniProt ID mapping (http://www.uniprot.org/uploadlists) and map them to UniProtKB. Once you have your result, you can add additional criteria, e.g. "AND database:(type:pdb)" and customize your output by adding or removing columns (cf http://www.uniprot.org/help/customize or

Then click on "Download" and select tab-delimited format. You may use the "preview first 10" option to double-check what your download will look like before you proceed to the full download.

Yes, you can map gene symbols to PDB IDs. Try Biomart. If you know R, use biomaRt in bioconductor or try to convert HGNC ID to PDBe IDs using the web interface of BioMart.