Towards a structural biology of the hydrophobic effect in protein folding

The hydrophobic effect is a major driving force in protein folding. A complete understanding of this effect requires the description of the conformational states of water and protein molecules at different temperatures. Towards this goal, we characterise the cold and hot denatured states of a protein by modelling NMR chemical shifts using restrained molecular dynamics simulations. A detailed analysis of the resulting structures reveals that water molecules in the bulk and at the protein interface form on average the same number of hydrogen bonds. Thus, even if proteins are ‘large’ particles (in terms of the hydrophobic effect, i.e. larger than 1 nm), because of the presence of complex surface patterns of polar and non-polar residues their behaviour can be compared to that of ‘small’ particles (i.e. smaller than 1 nm). We thus find that the hot denatured state is more compact and richer in secondary structure than the cold denatured state, since water at lower temperatures can form more hydrogen bonds than at high temperatures. Then, using Φ-value analysis we show that the structural differences between the hot and cold denatured states result in two alternative folding mechanisms. These findings thus illustrate how the analysis of water-protein hydrogen bonds can reveal the molecular origins of protein behaviours associated with the hydrophobic effect.

the mutation on the folding kinetics and native state stability, it is possible to map one by one interaction patterns in the transition states. The relative formation of the contact is commonly called the Φ value and, as detailed below, can be also used as a restrain for molecular dynamics simulations to determine the structures of the transition state ensembles at nearly atomic resolution 5 .
Because our aim was to compare the hot and cold denaturation pathways of frataxin, we analyzed the folding equilibrium and kinetics of frataxin as a function of temperature, and then compared it with different site-directed mutants (Table S1 and Figure S3). All the site directed variants, as well as wild-type frataxin, were subjected to thermal induced denaturation equilibria, monitored by CD spectroscopy, and temperature jump relaxation kinetics, in analogy to what recently reported 6 .
The analysis of the kinetic folding mechanism of frataxin as a function of temperature requires a deconvolution of the folding and unfolding components from the observed rate constants. Thus, given that the observed rate constant is governed by the sum of the rate constants for the forward and reverse reactions, we calculated the folding (k F ) and unfolding (k U ) rate constants by using the thermodynamic parameters obtained from equilibrium thermal denaturation experiments (see above). The following equations were employed where K D-N represents the equilibrium constant, obtained from equilibrium thermal denaturation experiments.
The dependence of the activation free energy on temperature can be described following the transition state theory as 4 where ΔH TS is the activation enthalpy, T is the absolute temperature in Kelvin, T 0 is a temperature of reference, ΔS TS is the activation entropy and Δc p TS is the change in heat capacity. Then, by fitting Eyring's equation 4 to the folding and unfolding rate constants the following equations may be derived The observed relaxation rate constants, together with the deconvoluted folding and unfolding components, for wild type frataxin and its site directed mutants are reported in Figure S10. In order to ensure sample conductivity, all experiments (including equilibrium) were carried out in the presence of 50 mM sodium sulfate. The calculated changes in free energies for the transition and native states upon mutation and their associated Φ value are reported in Table   S1. Because of the complexity of the analysis, we chose to focus our calculations at experimental conditions that could be directly explored by T-jump, avoiding extrapolation at higher or lower temperatures, and obtained for each mutant two sets of Φ values, referring to the transition states at high (323 K) and low (287 K) temperature. As detailed below, the experimentally determined Φ values were used as restrained in molecular dynamics simulations, to determine the ensemble structure of the hot and cold transition states for folding.
Thermal denaturation was followed on a JASCO circular dichroism (CD) spectropolarimeter (JASCO, Inc., Easton, MD), in a 1-mm quartz cuvette at 222 nm. Protein concentration was typically 10-20 µM. The relaxation kinetics were measured by using a Hi-Tech PTJ-64 capacitor-discharge T-jump apparatus (Hi-Tech, Salisbury, UK). Temperature was rapidly changed with discharge of about 35 kV on the solution, corresponding to a jump-size of 9 K.
Usually 10-20 individual traces were averaged. The fluorescence change of Nacetyltryptophanamide (NATA) was used in control measurements. Degassed and filtered samples were slowly pumped through the 0.5 x 2 mm quartz flow cell before data acquisition.
The excitation wavelength was 296 nm and the fluorescence emission was measured using a 320 nm cut-off glass filter. Protein concentration was typically 10-20 µM. The buffer used in both equilibrium and kinetic experiments was 20 mM Hepes at pH 7.0 in the presence of 50 mM sodium sulfate and 2 mM DTT. The mutants I68A, I79V and L111A expressed poorly and were denatured at the investigated experimental conditions. a These mutants display thermodynamic stabilities too similar to wild-type frataxin (ΔΔGeq <0.4 kcal mol−1), which prevents accurate calculation of Φ-values 7 . b These mutants display non standard Φ-values (Φ-values higher than 1 or less than 0) and therefore were not used in restrained molecular dynamics simulations. The presence of unusual Φ-values in frataxin has been previously described, on the light of the high level of frustration of this protein 8 .     0  10  20  30  40  50  60  70  80  90  100  110 also Table S1). Figure S11. Free energy profiles for the CDS (black) and the HDS (green) as a function of the fraction of native-contacts (Q). The two profiles show that the HDS exhibits more native contacts than the CDS, but also that the free energy barrier for folding is steeper for the HDS than the CDS.