PubMed · 8416167
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A Messori, G Scroccaro, N Martini. 1993-01-01. Calculation errors in meta-analysis.. https://doi.org/10.7326/0003-4819-118-1-199301010-00022
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In order to calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has the essential features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we demonstrate a method for accurately recovering the given contact potential from only a knowledge of which sequences fold to which structures and what the non-native structures are. Second, we show how to derive from the same information more general potential functions having much better positive correlations between potential function value and conformational deviation from the native. These functions consequently permit faster and more reliable searches for the native conformation, given the native sequence. Furthermore, the method for finding such potentials is easily applied to more realistic protein models.
Recent computational studies of simple models of protein folding have concluded that a pronounced energy minimum (i.e. large gap in energy between low-energy states of the model) is a necessary and sufficient condition to ensure folding of a sequence to its lowest-energy conformation. Here, we show that this conclusion strongly depends on the particular temperature scheme selected to govern the simulations. On the other hand, we show that there is a dominant factor determining if a sequence is foldable. That is, the strength of possible interactions between residues close in the sequence. We show that sequences with many possible strong local interactions (either favorable or, more surprisingly, a mixture of strong favorable and unfavorable ones) are easy to fold. Progressively increasing the strength of such local interactions makes sequences easier and easier to fold. These results support the idea that initial formation of local substructures is important to the foldability of real proteins.
Given a probability distribution from which the energy spectrum of a random peptide is to be sampled, we derive a general expression for the probability that such a peptide will fold to a unique native state and for the probability distribution of the native energy. This latter result allows us to localize the energy of folding based on model parameters and is one advantage of our formulation. Evidence from both the lattice theory of proteins and protein threading experiments suggest that the energy spectrum for the compact states of a peptide chain is Gaussian in form. For this reason we have derived from the more general framework the specific formulas that apply in the Gaussian case, where one requires only the number of states and the variance of the Gaussian distribution in order to apply the theory. This simplicity allows us to perform calculations that we compare with calculations previously made by others based on statistical thermodynamics. We find qualitative agreement, but a significant correction to prior estimates of folding probability derived from the Gaussian assumption is necessary.