where U n (x) is the potential at iteration n as a function of the variable x, 0 ≤ a n ≤ 1 is a parameter that controls how much the potential changes between iterations, P target (x) is the target AA distribution, and P n (x) is the CG distribution at iteration n. For non-bonded interactions, P(x) is the radial distribution function (RDF) g(r). For bonded interactions it takes the forms P bond (l)/l 2 , P angle (θ )/ sin(θ ), P dihed (φ ), and P improp (ψ) for the bond length, angle, dihedral, and improper dihedral distributions, respectively, where l is the bond length, θ the bond angle, and φ and ψ proper and improper dihedral angles, respectively. In all cases, the resulting potentials were fit to analytical functions defined in ESI Section S3.1, giving good agreement between the CG and AA distributions, as shown in ESI Section S3.3. The fit of the analytical CG potential functions to the Boltzmann inversion of the target distributions was used as the initial guess for all parameters, with the value of the LJ energy parameter ε LJ for each of the non-bonded interactions constrained to be initially 0.1 ≤ ε LJ < 1 in order to prevent extensive aggregation. The constraint on ε LJ was removed for the iterative procedure. Bonded interactions were optimised first, by comparing the target distributions from the AA trimer simulations with distributions from an equivalent CG system. The non-bonded parameters were then optimised by comparing the target distributions from the AA monomer simulations with distributions from an equivalent an equivalent CG system. The volume of the CG system was fixed at approximately the average volume of the equilibrated AA system in each case. Further details of the coarse-graining procedure are given in the ESI, Section S3.