Optimising the non-bonded interactions independently of, and after, the bonded interactions as we have done can potentially perturb the bonded distributions so that they no longer match the corresponding AA distributions. We verified that this was not the case by comparing the AA bonded distributions to those obtained from a 100 ns simulation of the CG model with the parameterised bonded and non-bonded interactions (ESI Section S3.3). Good agreement between the AA and CG distributions was still found in all cases. The final bonded and non-bonded parameters are given in the ESI in Section S14.