A hetero dimeric system

Small peptides such as Aβ16-22 or Ac-PHF6 are unstructured in isolation and simulation of aggregation of such small peptides does not involve the complication of formation of structure of a single poly-peptide chain. A large number of proteins however exist in oligomeric complexes, with a non-trivial native conformation for each member of a complex. One rather difficult challenge would be to simulate a system of many chains, starting with a random conformation for each chain, and showing that the physics based simulations lead to the correct oligomeric state with correctly folded chains assembled properly. There is at least one example where this can be done with ProFASi.

This system is a designed hetero dimeric leucine zipper, called AB zipper, PDB id 1U2U. Each chain is 30 residues in size. In the native state, both chains are folded into simple helices, and are bound to each other by hydrophobic interactions. Unbiased parallel tempering MC simulations with ProFASi, just like those described here for small helical or β-sheet peptides, produce a minimum energy state with both chains folded and joined together in the proper arrangement. But for such systems, the probabilities of folded/unfolded monomeric/dimeric states depend on concentration (related to the size of the periodic box).

Progress of RMSD of chain A (RMSD-1), chain B(RMSD-2), temperature and total energy in MC time. The apparent folding and unfolding of the two chains in unison is a meaningless correlation (see text below). The left and right plots are from two different replicas.

A cursory glance at run time history traces of this system might suggest that the two proteins fold cooperatively, as in the figures above. The chains seem to be either both folded or both unfolded. But there is a completely different explanation for this apparent correlation. It turns out that in the model, both chains fold into their native states independently. In the two chain simulations, there are lots of examples of two folded chains with no interaction between them. Separate simulations of the two chains in isolation confirms this. The temperature dependence of helix content for the two chains is also very similar.

The apparent "synchronous" folding and unfolding of the chains has more to do with the parallel tempering algorithm than with the two poly-peptide chains. As the temperature of one replica rises and falls, both chains experience the same temperature changes. Since their thermal properties in the model are similar, both unfold when the temperature rises and both fold when the temperature falls below their nearly identical melting temperatures (312 and 313 K). This gives the appearance that the folding of one chain has something to do with the folding of the other. In reality, most of the times the chains are too far apart in the simulation box to affect the folding behaviour of one another.

Our interpretation of the data is that in the model the two chains fold independently, and then, sometimes, join together to form the dimer. The dimer formation probability is a function of the concentration. The mean energy of the dimer is about 20 kcal/mol lower than two folded monomers as seen in the figure below. The folded dimer structure is also very close to the PDB structure.

Left: The minimum energy structure (coloured) of the two chain system superimposed on the PDB structure (gray) of the dimer. Right: The mean energy for all states with both chains folded, as a function of pRMSD, the RMSD calculated over the backbone atoms of both chains, minimised with respect to the periodic box.