Convergence of effective potentials for side chains, panel (a), and ACE and side chains, panel (b), to the limiting, density-independent shape in the limit of long-range contacts. Quantities dU1−i and dU0−i measure how much two potentials with contact numbers i + 1 and i differ. Arrows indicate where the dependence drops almost to zero. Multiple simulations and iterations are shown. The difference for the two shortest contacts, 1–2 and 1–3, for side chains and 0–1 and 0–2 for ACE group, is too large to be shown on the given scale.