In a previous question I asked about a simple case, I'm now trying to write equations for proteins that bind multivalently. In the simplest case proteins $A_1$ and $A_2$ can bind to up to two $L$ proteins. This gives a massive chemical equation:
`enter image description here

where $(AL_1AL_2)_r$ is a tetramer where $A_1$ and $A_2$ are both bound to both of the $A$ proteins in a ringlike structure. But this diagram misses out one possible state, $A_1LA_2$ which is connected in this way:

enter image description here.

I can't see a way of joining this extra state to the above chemical equation without arrows crossing each other.

What is the best way of formatting these kinds of complex protein reaction equations?

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    $\begingroup$ Anyway, this is a question for TeX.SE. Or maybe even for math.SE (these things look mighty reminiscent of so-called commutative diagrams), just remove everything chemical before asking it there. $\endgroup$ – Ivan Neretin Feb 9 '18 at 13:18
  • $\begingroup$ Agreed that it is a maths problem first, then a TeX one. Frankly, if the diagram is going to be too complex to layout, then it will be too complex to read. Several different diagrams (as you show here) will be more understandable, $\endgroup$ – gilleain Feb 9 '18 at 14:34
  • $\begingroup$ How would you divide it in to several different diagrams? $\endgroup$ – Abijah Feb 9 '18 at 15:20
  • $\begingroup$ @IvanNeretin i've corrected it $\endgroup$ – Abijah Feb 9 '18 at 15:26
  • $\begingroup$ This isn't a Tex problem, I can use xypics fine to generate the above, what I'm interested in is how protein chemists format these kinds of equations (even if it means splitting them up). My external examiner has insisted on chemical equations for every system I investigate in my thesis, so I have to include no matter how ugly it is. There are well studied systems dramatically more complex than this (like microtubules ), so clearly there must be a standard notation used by protein chemists. $\endgroup$ – Abijah Feb 9 '18 at 15:44

Generally speaking, for these sorts of complex reactions, you want to go to more than two dimensions. (At least for the initial bit.)

For each potential binding reaction you have a different dimension. That is, for $L$ binding to $A_1$ on site 1, you go horizontally. For $L$ binding to $A_2$ on site 1, you go vertically. For $L$ binding to $A_1$ on site 2, you go in the Z dimension, and then for $L$ binding to $A_2$ on site 2, you go in the 4th dimension.

Obviously, you can't put an actual 4D representation on paper. In fact, you can't put a 3D representation on paper. But if you're lucky, you can do a bit of topological rearrangement of the network and then do a projection of your network onto a 2D plane.

For example, if you have three potential binding interactions, each independent, then your system can be represented as the corners and edges of a cube. You can then represent this system by any of the standard projections of a 3D cube into 2D space.

For four potential binding interactions, it's the the corners and edges of a tesseract. Projecting a tesseract onto 2D space is much harder, in that there's no way to do it without lines crossing. But depending on what you want to represent, you might be able to adequately mark the crossings, or add "jumps" between two sub-graphs. (That is, have two more sub-graphs and have a systematic way of going from nodes on one graph to the node on the other graph with implicit reaction edges.)

For an arbitrary reaction graph, there's no guarantee that the crossing number of the graph is going to be zero -- that is, there's no guarantee that you'll be able to represent the network on a 2D page without crossings or jumps. Often the best you can do is attempt to be systematic about things, and then add crossings/jumps as appropriate.


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