Statistical analyses of protein folding rates from the view of quantum transition

Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism.Especially,the temperature dependence of the folding rate remains unsolved in the literature.Starting from the assumption that protein folding is an event of quantum transition between molecular conformations,we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies.The non-Arrhenius temperature relation for 16 proteins,whose experimental data had previously been available,was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation.A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory.The statistical comparisons of the folding rates for 65 two-state proteins were carried out,and the theoretical vs.experimental correlation coefficient was 0.73.Moreover,the maximum and the minimum folding rates given by the theory were consistent with the experimental results.     

Thermodynamic characterisation of two transition states along parallel protein folding pathways

Recent work has shown that a β-sandwich domain from the human muscle protein titin (TI I27) unfolds via more than one pathway, providing experimental evidence for a long-standing theoretical prediction in protein folding. Here we present a thermodynamic analysis of two transition states along different folding pathways for this protein. The unusual upwards curvature previously observed in the denaturant-dependent unfolding kinetics is increased at both high and low temperatures, indicating that the high denaturant pathway is becoming more accessible. The transition states in each pathway are structurally distinct and have very different heat capacities. Interestingly the nucleation-condensation pathway is dominant at all physiologically relevant temperatures, supporting the suggestion that pathways with diffuse rather than localised transition states have been selected for by evolution to prevent misfolding.     

Evidence for sequential barriers and obligatory intermediates in apparent two-state protein folding

Many small proteins fold fast and without detectable intermediates. This is frequently taken as evidence against the importance of partially folded states, which often transiently accumulate during folding of larger proteins. To get insight into the properties of free energy barriers in protein folding we analyzed experimental data from 23 proteins that were reported to show non-linear activation free-energy relationships. These non-linearities are generally interpreted in terms of broad transition barrier regions with a large number of energetically similar states. Our results argue against the presence of a single broad barrier region. They rather indicate that the non-linearities are caused by sequential folding pathways with consecutive distinct barriers and a few obligatory high-energy intermediates. In contrast to a broad barrier model the sequential model gives a consistent picture of the folding barriers for different variants of the same protein and when folding of a single protein is analyzed under different solvent conditions. The sequential model is also able to explain changes from linear to non-linear free energy relationships and from apparent two-state folding to folding through populated intermediates upon single point mutations or changes in the experimental conditions. These results suggest that the apparent discrepancy between two-state and multi-state folding originates in the relative stability of the intermediates, which argues for the importance of partially folded states in protein folding.     

Free energy landscapes of RNA/RNA complexes: with applications to snRNA complexes in spliceosomes

We develop a statistical mechanical model for RNA/RNA complexes with both intramolecular and intermolecular interactions. As an application of the model, we compute the free energy landscapes, which give the full distribution for all the possible conformations, for U4/U6 and U2/U6 in major spliceosome and U4atac/U6atac and U12/U6atac in minor spliceosome. Different snRNA experiments found contrasting structures, our free energy landscape theory shows why these structures emerge and how they compete with each other. For yeast U2/U6, the model predicts that the two distinct experimental structures, the four-helix junction structure and the helix Ib-containing structure, can actually coexist and specifically compete with each other. In addition, the energy landscapes suggest possible mechanisms for the conformational switches in splicing. For instance, our calculation shows that coaxial stacking is essential for stabilizing the four-helix junction in yeast U2/U6. Therefore, inhibition of the coaxial stacking possibly by protein-binding may activate the conformational switch from the four-helix junction to the helix Ib-containing structure. Moreover, the change of the energy landscape shape gives information about the conformational changes. We find multiple (native-like and misfolded) intermediates formed through base-pairing rearrangements in snRNA complexes. For example, the unfolding of the U2/U6 undergoes a transition to a misfolded state which is functional, while in the unfolding of U12/U6atac, the functional helix Ib is found to be the last one to unfold and is thus the most stable structural component. Furthermore, the energy landscape gives the stabilities of all the possible (functional) intermediates and such information is directly related to splicing efficiency.     

Sequence of events in folding mechanism: beyond the Gō model

Simplified Gō models, where only native contacts interact favorably, have proven useful to characterize some aspects of the folding of small proteins. The success of these models is limited by the fact that all residues interact in the same way so that the folding features of a protein are determined only by the geometry of its native conformation. We present an extended version of a Calpha-based Gō model where different residues interact with different energies. The model is used to calculate the thermodynamics of three small proteins (Protein G, Src-SH3, and CI2) and the effect of mutations (DeltaDeltaGU-N, DeltaDeltaGdouble dagger-N, DeltaDeltaGdouble dagger-U, and phi-values) on the wild-type sequence. The model allows us to investigate some of the most controversial areas in protein folding, such as its earliest stages and the nature of the unfolded state, subjects that have lately received particular attention.