Quantifying protein folding transition States with φ(t)

Protein Folding Stability and Kinetics in Alginate Hydrogels

Proteins are commonly encapsulated in alginate gels for drug delivery and tissue-engineering applications. However, there is limited knowledge of how encapsulation impacts intrinsic protein properties such as folding stability or unfolding kinetics. Here, we use fast relaxation imaging (FReI) to image protein unfolding in situ in alginate hydrogels after applying a temperature jump. Based on changes in the Förster resonance energy transfer (FRET) response of FRET-labeled phosphoglycerate kinase (PGK), we report the quantitative impact of multiple alginate hydrogel concentrations on protein stability and folding dynamics. The gels stabilize PGK by increasing its melting temperature up to 18.4 °C, and the stabilization follows a nonmonotonic dependence on the alginate density. In situ kinetic measurements also reveal that PGK deviates more from two-state folding behavior in denser gels and that the gel decreases the unfolding rate and accelerates the folding rate of PGK, compared to buffer. Phi-value analysis suggests that the folding transition state of an encapsulated protein is structurally similar to that of folded protein. This work reveals both beneficial and negative impacts of gel encapsulation on protein folding, as well as potential mechanisms contributing to altered stability.

High-Resolution Mapping of the Folding Transition State of a WW Domain

Fast-folding WW domains are among the best-characterized systems for comparing experiments and simulations of protein folding. Recent microsecond-resolution experiments and long duration (totaling milliseconds) single-trajectory modeling have shown that even mechanistic changes in folding kinetics due to mutation can now be analyzed. Thus, a comprehensive set of experimental data would be helpful to benchmark the predictions made by simulations. Here, we use T-jump relaxation in conjunction with protein engineering and report mutational Φ-values (Φ(M)) as indicators for folding transition-state structure of 65 side chain, 7 backbone hydrogen bond, and 6 deletion and /or insertion mutants within loop 1 of the 34-residue hPin1 WW domain. Forty-five cross-validated consensus mutants could be identified that provide structural constraints for transition-state structure within all substructures of the WW domain fold (hydrophobic core, loop 1, loop 2, β-sheet). We probe the robustness of the two hydrophobic clusters in the folding transition state, discuss how local backbone disorder in the native-state can lead to non-classical Φ(M)-values (Φ(M) > 1) in the rate-determining loop 1 substructure, and conclusively identify mutations and positions along the sequence that perturb the folding mechanism from loop 1-limited toward loop 2-limited folding.

Temperature-dependent downhill unfolding of ubiquitin. I. Nanosecond-to-millisecond resolved nonlinear infrared spectroscopy

Transient thermal unfolding of ubiquitin is investigated using nonlinear infrared spectroscopy after a nanosecond laser temperature jump (T-jump). The abrupt change in the unfolding free energy surface and the ns time resolution allow us to observe a fast response on ns to micros time-scales, which we attribute to downhill unfolding, before a cross-over to ms kinetics. The downhill unfolding by a sub-population of folded proteins is induced through a shift of the barrier toward the native state. By adjusting the T-jump width, the effect of the initial (T(i)) and final (T(f)) temperature on the unfolding dynamics can be separated. From the amplitude of the fast downhill unfolding, the fractional population prepared at the unfolding transition state is obtained. This population increases with both T(i) and with T(f). A two-state kinetic analysis of the ms refolding provides thermodynamic information about the barrier height. By a combination of the fast and slow unfolding and folding parameters, a quasi-two-state kinetic analysis is performed to calculate the time-dependent population changes of the folded state. This calculation coincides with the experimentally obtained population changes at low temperature but deviations are found in the T-jump from 67 to 78 degrees C. Using temperature-dependent barrier height changes, a temperature Phi value analysis is performed. The result shows a decreasing trend of Phi(T) with temperature, which indicates an increase of the heterogeneity of the transition state. We conclude that ubiquitin unfolds along a well-defined pathway at low temperature which expands with increasing temperature to include multiple routes.

Parallel folding pathways in the SH3 domain protein

The transition-state ensemble (TSE) is the set of protein conformations with an equal probability to fold or unfold. Its characterization is crucial for an understanding of the folding process. We determined the TSE of the src-SH3 domain protein by using extensive molecular dynamics simulations of the Go model and computing the folding probability of a generated set of TSE candidate conformations. We found that the TSE possesses a well-defined hydrophobic core with variable enveloping structures resulting from the superposition of three parallel folding pathways. The most preferred pathway agrees with the experimentally determined TSE, while the two least preferred pathways differ significantly. The knowledge of the different pathways allows us to design the interactions between amino acids that guide the protein to fold through the least preferred pathway. This particular design is akin to a circular permutation of the protein. The finding motivates the hypothesis that the different experimentally observed TSEs in homologous proteins and circular permutants may represent potentially available pathways to the wild-type protein.

Rate-temperature relationships in lambda-repressor fragment lambda 6-85 folding

Two classes of lambda(6-85) mutants (those richer in alanine, and those richer in glycine) have very similar slopes in an Arrhenius plot of the unfolding rates but very different temperature dependencies of the folding rates. Temperature-dependent interactions (e.g., hydrophobicity) play a large role in the initial stages of folding but not in the initial stages of unfolding of lambda(6-85). Placement of the transition state in terms of its surface exposure and entropy shows that at least two reaction coordinates are required to describe folding of all mutants over the full temperature range. The unusual Arrhenius plots of the very fastest mutant provide an additional kinetic signature for downhill folding.

The effects of nonnative interactions on protein folding rates: theory and simulation

Proteins are minimally frustrated polymers. However, for realistic protein models, nonnative interactions must be taken into account. In this paper, we analyze the effect of nonnative interactions on the folding rate and on the folding free energy barrier. We present an analytic theory to account for the modification on the free energy landscape upon introduction of nonnative contacts, added as a perturbation to the strong native interactions driving folding. Our theory predicts a rate-enhancement regime at fixed temperature, under the introduction of weak, nonnative interactions. We have thoroughly tested this theoretical prediction with simulations of a coarse-grained protein model, by using an off-lattice C(alpha)model of the src-SH3 domain. The strong agreement between results from simulations and theory confirm the nontrivial result that a relatively small amount of nonnative interaction energy can actually assist the folding to the native structure.

On the extended beta-conformation propensity of polypeptides at high temperature

At room temperature, natural polypeptides exposed to high concentrations of a strong denaturant nearly attain the circular dichroism spectra characteristic of random coils. As temperature is increased, the spectra begin to show the signature of a substantial fraction of extended chain, the structure common in beta-sheets. This structural propensity at high temperature is not altered by concentration changes over a greater than 1000-fold range, so it is not caused by aggregation. Four proteins with different folds and varying amounts of alpha-helical and beta-sheet secondary structure, in the presence or absence of denaturant, all were subject to extended chain formation upon heating. This effect arises naturally from the steric constraints associated with polypeptides and is probably counteracted, not enhanced, by hydrophobic interactions. Molecular dynamics simulations in the 298-1000 K range reveal an attractive potential of mean force in the extended chain region of the Ramachandran diagram, which broadens as the temperature is raised. We also demonstrate a direct correlation between extended structure content and the rate of aggregation kinetics. Thus pre-existing extended structure could funnel proteins into aggregates.