How to dock aggregated structures comprised of "elementary" protein units like LEGO pieces? There are proteins with intrinsic symmetries. For example:



I was wondering how to use transformations such as: rotations, translation, replications to construct possible structures using 2 types of proteins.

Assume I found a binding site of the 2 proteins using Molecular Dynamics simulators. 

For example the above one and this one:

 


Can I use group theory way to find possible configurations of the 2 proteins? 
How can I use the tensor product of the symmetry groups ($G_1 \times G_2$) to find possible structures?
What graphic/framework would you recommend do perform all the manipulations on the proteins? 
Is it possible to use the transfer to create some algebraic structure that will help to construct a mechanical configurations comprised of proteins? 
Is there any tool from Baker's Lab I can use for this task? 
Amy recommendation for a tool I could use to replicate, rotate and shift structure would be appreciated us well. 




TL;DR:

My goal is to use group theory or Monte Carlo simulation driven by group theory insight to create macro molecular structures using multiple (dozens) instances of the two proteins (the LEGO building blocks). 
Any idea that relates symmetry, transformations, group theory to create structures is much welcome. 



Clarification:

Given a binding point between 2 proteins, which software can I use to create the dimers into macro-structures like in LEGO namely only by replicating, translating and rotating the Lego pieces?
Try DNA origami instead 

While protein assemblies are well known, rationally using proteins to assemble larger supramolecular structures is still a difficult problem:


Predicting protein folding is an unsolved problem. Sometimes even small modifications to a sequence can change the folding propensity.
Predicting protein-protein interactions is often difficult, due to challenges in understanding protein dynamics, intermolecular interactions, and accurate predictions of protein electrostatics.


There has been some progress in terms of forcing particular protein-protein assembly through intentional side-chain modification and cross-linking, and reactive end-groups (e.g protein-based metal-organic frameworks (MOFs).

That said, use of proteins for supramolecular assemblies is far harder and less prevalent than using DNA assemblies. At the moment, DNA origami is far superior for these purposes.

Edit: If you're really looking to just copy and displace atoms, I don't think you need any particular software. I'd write a Python (or other script) that reads in the PDB files, and writes out duplicate atoms displaced in the XYZ directions as needed. Group theory can help predict the angles, but you'll still need to know the protein size to work out the geometry.