Trade-off between positive and negative design of protein stability: from lattice models to real proteins

Abstract

Two different strategies for stabilizing proteins are (i) positive design in which the native state is stabilized and (ii) negative design in which competing non-native conformations are destabilized. Here, the circumstances under which one strategy might be favored over the other are explored in the case of lattice models of proteins and then generalized and discussed with regard to real proteins. The balance between positive and negative design of proteins is found to be determined by their average "contact-frequency", a property that corresponds to the fraction of states in the conformational ensemble of the sequence in which a pair of residues is in contact. Lattice model proteins with a high average contact-frequency are found to use negative design more than model proteins with a low average contact-frequency. A mathematical derivation of this result indicates that it is general and likely to hold also for real proteins. Comparison of the results of correlated mutation analysis for real proteins with typical contact-frequencies to those of proteins likely to have high contact-frequencies (such as disordered proteins and proteins that are dependent on chaperonins for their folding) indicates that the latter tend to have stronger interactions between residues that are not in contact in their native conformation. Hence, our work indicates that negative design is employed when insufficient stabilization is achieved via positive design owing to high contact-frequencies.

Figure 1. Relationship between the impact of positive design on the stability of different lattice folds and their respective average contact-frequencies.

The values of a measure of the effect of positive design of stability, (i,j)>_short, for the 1081 different folds of 25 residue-long sequences on a 5×5 lattice are plotted against their respective average contact-frequencies, . A linear correlation is observed with r = −0.6082 and a P-value<0.0001.

Figure 2. Relationship between the impact of negative design on the stability of different lattice folds and their respective average contact-frequencies.

The values of a measure of the effect of negative design of stability, (i,j)>_long, for the 1081 different folds of 25 residue-long sequences on a 5×5 lattice are plotted against their respective average contact-frequencies, . A linear correlation is observed with r = 0.6390 and a P-value<0.0001.

Figure 3. Trade-off between the effects of positive and negative design on the stabilities of different lattice folds.

The values of a measure of the effect of negative design of stability, (i,j)>_long, for the 1081 different folds of 25 residue-long sequences on a 5×5 lattice are plotted against their respective values of a measure of the effect of positive design of stability, <D^(i,j)>_short. A linear correlation is observed with r = −0.96 and a P-value<0.0001.

Figure 4. Distributions of densities of correlated mutations at positions involved in long-range interactions for different classes of lattice folds with increasing values of average contact-frequency.

The 1081 different folds of 25 residue-long sequences on a 5×5 lattice were ordered according to their average contact frequency, (), and then divided into three equal-sized groups comprising the folds with the lowest (A), in between (B) and highest (C) values of , respectively. It can be seen that the density of correlated mutations tends to increase as the average contact-frequency of the fold increases.

Figure 5. Distributions of correlated mutation densities in the case of the five different sets of real proteins examined in this study.

The densities of correlated mutations were calculated for the sets of control proteins (A), classes I (B), II (C) and III (D) of the GroEL-interacting proteins and the intrinsically unstructured proteins (E). It can be seen that the density of correlated mutations of these sets increases with the increasing likelihood that their average ‘contact-frequency’ has increased.