Barrier Heights and Diffusion Coefficients in Protein Folding
Naganathan, Athi Narayanan
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A widely held view with respect to the folding of single-domain proteins is that they are two-state. In other words, it is seemingly sufficient to invoke just two thermodynamic macrostates - folded and unfolded - to explain the experimental data with a transition-state like picture. Unfortunately, a chemical two-state model and the resulting conventional analyses do not estimate the barrier height which is essential in determining whether protein folding can be approximated as a two-state, all-or-none transition. However, the energy landscape theory of protein folding predicts small and even zero folding free energy barriers (downhill folding) because of partial or complete compensation between large enthalpic and entropic terms as folding proceeds. They have been recently validated by the thorough experimental characterization of proteins that fold globally downhill (BBL) and those that fold over marginal free energy barriers. In light of these findings, the question of whether this observation is an exception or merely the tip of the iceberg assumes primary importance. Analyzing the experimental data on previously characterized proteins with statistical mechanical models, it is shown here that the barrier to folding are indeed small and the folding phase space can be quantitatively classified into four regimes - global downhill, marginal barrier, twilight-zone and two-state like. The average effective diffusion coefficient to folding (D<sub>eff</sub>) is predicted to be strongly temperature dependent changing from 1/(20-25 microseconds) at 298 K to 1/(2 microseconds) at ~330-340 K. The activation term on the D<sub>eff</sub> is found to scale linearly with the protein size while the folding rates themselves scale inversely with the square root of protein length. This work further highlights the importance of baselines and proposes additional thermodynamic and kinetic signatures of downhill folding. A comprehensive experimental and theoretical characterization of PDD, a structural and functional homolog of BBL is also presented. The results indicate that PDD folds downhill at 298 K while crossing a marginal barrier at the apparent T<sub>m</sub>. The evolutionary conservation of downhill folding indirectly suggests that this folding behavior has a functional consequence. In short, this work underlines the need for a fundamental shift towards physical models in characterizing protein folding processes.