PPM-Visualisations

As an example we selected two members of the insect pheromone binding protein family. The proteins in this family have a relatively simple structure - they consists of six helices, and we have conserved disulfide bridges in the family (highlighted in yellow) which help us to find the correct mapping of the helices.

The overal topology of the proteins is well conserved but all helices have slightly different orientation and position.

Based on the correct alignment of the helices guided by the conserved cysteins we calculated the superpositon, the movie shows each helix in this rigid superposition and highlights the topological mutations due to phenotypic plasticity.

The first helix is even splitted up into two smaller helices. Nevertheless they are corresponding topological elements, so we can calculate the topological mutation: this is the needed amount of rotation and translation to transform the blue structure into the red one.
The second helix shows the effect of a short insertion in the sequence: due to the longer loop preceding the red helix the helix moved and turned a little bit. Again we can calculate structural mutation due to plasticity to transform the blue structure into the red one.

The third helix is a very good example for the problems that a structure alignment program based on rigid superposition has to face. Such methods use the 3D space to find the corresponding residues, but doing so one would map not the conserved cysteins onto each other, actually one would probably introduce short gaps by "reading off" the alignment.

This is basicly also true for the remaining three helices: using the 3D distance the resulting mapping would be incorrect because of the phenotypic plasticity. With small amounts of topological mutations however we can find the conserved topology - which is highlighted in the final flexible superposition.

To determine possible core blocks we simply scan for gapless structure fragment mappings with high structural similarity. For this we calculate for every possible local structure mapping the longest possible local similar structure with a given quality.

The thick red and blue lines on the left side represent the sequence of the two proteins, diagonals represent local structure mappings for which the local superposition is shown on the right side.

To ensure that our local mappings will yield high quality we use analyze this local superposition (right side) and rather than using the RMSD as quality criteria we calculate the all 3D distances between mapped C alpha atoms(shown in this schematic example below), and enforce that all these distances are below a certain threshold. The similarity of a core block is then given by combining the block length and the rmsd.

After the detection of the core blocks we would like to combine them to mapped topologies, and calculate the topological changes.

So we basicly want to score the transformations shown in the movie. As we assume phenotypical plasticity we don't have single "right" superpositon (other than in the movie), so we calculate the topological mutation between topologies implied by block pairs:



On the left side a block pair is shown in the superposition implied by block 1, on the right side the same blocks are in the superposition of block2.

The structural mutation is given by the transformation that morphs the topology of the black structure into the topology of the blue structure. To combine the rotation and translation shown in the movie we calculate the joint superposition of the two blocks and calculate the rmsds of both blocks in this superposition independently. We calculate the rmsds of the blocks independently to avoid problems if the block lengths are very different.

The topologcial mutation cost is then given by a combination of the maximum of these rmsd values and the length of the mapping.

We can do this for all compatible core blocks (see figures below): for every compatible block pair (the left side) we calculate the joint superposition (right side), and calculate the implied topological mutation by the block pair.

This creates a graph with the core block as nodes and the topological mutation as edges. The connected subgraphs in this graph are then the matched topologies or possible alignments. So we "simply" have to calculate the similarity of these subgraphs and select the one with the highest indicated topological similarity.