Coiled-coil polyhedra.html

Modelling

Topology of two-dimensional lattice made of single type of polypeptide chain

Our goal was to investigate the possible topologies that can lead to 2D or 3D assemblies consisting of three coiled-coil forming segments as the simplest building block. We also restricted the analysis in the first stage to the assemblies composed of one single type of polypeptide.

Legend:
a and a’ – parallel heterodimer and its pair
A and A’ – antiparallel heterodimer and its pair
A – antiparallel homodimer (pairs with itself)
a – parallel homodimer (pairs with itself)

Two-dimensional lattice can form through many different ways as well it can be assembled from different primitive cells.
Let us first consider only options using only one type of polypeptide chain comprising three coiled-coil segments, which is the simplest type of building block.
It turns out that trigonal lattice is geometrically easily obtainable as seen in the example below, where we use three segments of different antiparallel homodimers.

Figure 1

Figure 2

Creating three-dimensional polygons from a single type of polypeptide chain

Note: here we show all possible assemblies, again restrict our discussion only to cases with one-type-three-element chains.

The simplest polyhedron that we can form is tetrahedron or triangular pyramid (a polyhedron composed of four triangular faces, three of which meet at each vertex). Tetrahedron is formed from four polypeptide chains. It can be assembled using any of the polypeptide chains with structures a-B-a’, A-B-C or a-B-a as seen on the animation below:

ANIMATION!!!!!!!!


It should be noted that all of the cyclic permutations are also possible to form this type of polyhedra.

The next structure that can be obtained is n-sided prism, where the n depends on the polypeptide concentration, temperature and length of the linker (among other parameters). Some types of chains (combinations of coiled-coil-forming segments) even pre-define whether n can be even or odd (i.e. a-b-a’ forms prisms with even number of sides, contrary to a-B-a’ where there are no limitations on the accessible number of sides). This assembly is possible to obtain from different ways – below is presented example a-b-a’, which can form a box (parallelepiped) as the smallest polyhedron of this type of polypeptide chain:

Figure 4

Enumeration of all possible combinations for the assembly of structures made of single polypeptide chain and three coiled-coil forming segments

Figure 5

Extension to self-assemblies made of several different polypeptide chains

Here is where real diversity begins. Let us loot at some examples:

Example A

Example B

Example C

Example D

Figure 6

Figure 8: Example A and B

Figure 9: Example C and D

Figure 10: Cube