Statistical Mechanical Models for Analyzing the Site-Specific Folding of helix-turn-helix Motifs

Abstract

Isotopically-edited IR spectroscopy can provide detailed site-specific information about the protein folding mechanism. With our equilibrium unfolding studies of two simple helix-turn-helix (hth) proteins using circular dichroism and 13C isotopically labeled infrared spectroscopy, we incorporated this experimental data into Ising-like statistical mechanical models to better understand the observed structural and energetic properties of the two proteins. Two variations of the Ising-like model were implemented: the Wato-Saito-Muñoz-Eaton (WSME) model, which can be enumerated exactly using efficient transfer matrix methods, and the Baker-Finkelstein (BF) model using a double-sequence approximation. Model parameters were optimized by simultaneously fitting the complete set of data for the whole protein as well as each helix independently to reflect what was observed through experiments. In order to give a more realistic representation of protein energy, various statistical residue-specific potential matrices were tested as the inter-residue contact energy in the model. We found that different statistical potentials varied in its success to simultaneously fit all the experimental data, however all the residue-specific matrices resulted in an improvement over considering only a single parameter for the contact energy. Both the WSME and BF models were able to reproduce the equilibrium unfolding data when analyzing the hth proteins as a whole, but the WSME model could not correctly predict the folding of only the helix when analyzed independently due to the assumptions of the model. On the other hand, the BF model was capable of reproducing the experimental data for both the whole protein and the independent helices.