Effects of different perturbations on the energy spectrum of the native state and the ensemble of non-native conformations. The effects of four different extreme cases of perturbations are depicted. In case (i), a native contact with a contact-frequency of 1/|Z| (|Z| is the ensemble size) is eliminated, thereby causing the energy of the native state, En, to increase to E'n but not affecting the energies of the non-native states. The gap between the energy of the native state and the energies of all the non-native states is, therefore, reduced by E'n-En. In case (ii), a native contact with a contact-frequency value that approaches one is eliminated, thereby causing the energies of the native state and most of the non-native states to increase by E'n-En without changing the energy gap. In case (iii), a non-native contact with a contact frequency of 1/|Z| is eliminated without changing the energy gap as there is no change in the energies of the native state and most of the non-native states. In case (iv), a non-native contact with a contact-frequency value that approaches one is eliminated, thereby increasing the energies of most of the non-native states and also the gap in energy between these states and the native state.