text: user12686: What does it mean by "topology" in the case of secondary and tertiary structures of proteins?
  N.B. I am not talking about DNA/RNA/genomics. I am talking about protein folding, as it relates to protein modeling and simulation.
  
  user6322: The word topology gets used in two different contexts.
  Common case: the geometric configuration of the protein (=fold)
  In common non-computational biochemistry parlance it is just the standard English meaning of topology and just geometry, in the case of protein it means protein fold:
  https://en.wikipedia.org/wiki/Protein_fold_class
  Wiktionary (https://en.wiktionary.org/wiki/topology) say:
  
  The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing)
  
  In the of protein, unchanged by small changes in length or amino acid sequence identity —no proteases or meat-glue ligase required!
  Computational (Bio)chemistry
  Topology has a technical jargon definition in computational biochemistry and computational chemistry.
  In computational chemistry how the connections of a molecule are configured, expressed as a graph network https://en.wikipedia.org/wiki/Graph_theory, is referred to as topology. For example isopropanol and n-propanol have same number of heavy atom (nodes) and these will have the same hybridisation, but the network will have different connectivities (vertices).
  The topology definition generally runs off atom types more so than elements, these combine the element and hybridisation and other properties specific to a certain element in a molecule —e.g. amine vs. amide nitrogen vs. tryptophan ring nitrogens are different.
  The 3D embedding of said molecule is not part of its topology. Things get a bit problematic as ideal bond lengths, angles and dihedrals in dihedral space (i.e. not in cartesian space) go into the 'configuration' file (topology file) for several forcefield systems. And in others still there may be constraints or restraints specified.
  In computational biochemistry, this holds true for ligands. But with proteins there is less. The connectivity within each amino acids is preset in stone: where one to use the allo isomer of threonine as opposed to the threo one would need to define a non-canonical amino acid. So by topology of a protein it is intended the connectivity of the amino acids in chains, e.g. primary sequence devoid of cartesian coordinates.
  The word topology appears often in the context of ligands: these require custom definitions (=topologies) required to use a ligand not parameterised in the force field used, a common source of trouble.
  See also
  
  https://manual.gromacs.org/documentation/2019/reference-manual/topologies.html
  https://mdtraj.org/1.9.4/api/generated/mdtraj.Topology.html
  
  
original_text: 12686: <p>What does it mean by &quot;topology&quot; in the case of secondary and tertiary structures of proteins?</p>
  <p>N.B. I am not talking about DNA/RNA/genomics. I am talking about protein folding, as it relates to protein modeling and simulation.</p>
   6322: <p>The word topology gets used in two different contexts.</p>
  <h2>Common case: the geometric configuration of the protein (=fold)</h2>
  <p>In common non-computational biochemistry parlance it is just the standard English meaning of topology and just geometry, in the case of protein it means protein fold:</p>
  <p><a href="https://en.wikipedia.org/wiki/Protein_fold_class" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Protein_fold_class</a></p>
  <p>Wiktionary (<a href="https://en.wiktionary.org/wiki/topology" rel="nofollow noreferrer">https://en.wiktionary.org/wiki/topology</a>) say:</p>
  <blockquote>
  <p>The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing)</p>
  </blockquote>
  <p>In the of protein, unchanged by small changes in length or amino acid sequence identity —no proteases or meat-glue ligase required!</p>
  <h2>Computational (Bio)chemistry</h2>
  <p>Topology has a technical jargon definition in computational biochemistry and computational chemistry.</p>
  <p>In computational chemistry how the connections of a molecule are configured, expressed as a graph network <a href="https://en.wikipedia.org/wiki/Graph_theory" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Graph_theory</a>, is referred to as topology. For example isopropanol and n-propanol have same number of heavy atom (<em>nodes</em>) and these will have the same hybridisation, but the network will have different connectivities (<em>vertices</em>).
  The topology definition generally runs off <em>atom types</em> more so than elements, these combine the element and hybridisation and other properties specific to a certain element in a molecule —e.g. amine vs. amide nitrogen vs. tryptophan ring nitrogens are different.
  The 3D embedding of said molecule is not part of its topology. Things get a bit problematic as ideal bond lengths, angles and dihedrals in dihedral space (i.e. not in cartesian space) go into the 'configuration' file (topology file) for several forcefield systems. And in others still there may be constraints or restraints specified.</p>
  <p>In computational biochemistry, this holds true for ligands. But with proteins there is less. The connectivity within each amino acids is preset in stone: where one to use the allo isomer of threonine as opposed to the threo one would need to define a non-canonical amino acid. So by topology of a protein it is intended the connectivity of the amino acids in chains, e.g. primary sequence devoid of cartesian coordinates.
  The word topology appears often in the context of ligands: these require custom definitions (=topologies) required to use a ligand not parameterised in the force field used, a common source of trouble.</p>
  <h2>See also</h2>
  <ul>
  <li><a href="https://manual.gromacs.org/documentation/2019/reference-manual/topologies.html" rel="nofollow noreferrer">https://manual.gromacs.org/documentation/2019/reference-manual/topologies.html</a></li>
  <li><a href="https://mdtraj.org/1.9.4/api/generated/mdtraj.Topology.html" rel="nofollow noreferrer">https://mdtraj.org/1.9.4/api/generated/mdtraj.Topology.html</a></li>
  </ul>
  