Basic protein structure and stability VI: Thermodynamics of protein stability

1. Basic protein structure and stability VI:Thermodynamics of protein stability Biochem 565, Fall 2008 09/10/08 Cordes

2. Native and denatured states denatured ensemble unfolded ensemble native state folded state single structure or ensemble of very similar structures; compact many different structures fluctuating; not usually very compact; disordered but not a “random coil” For some proteins, but not all, this process is readily reversible and occurs without populated intermediate forms--> “two-state” folding

3. Naive view of folding thermodynamics DGu protein becomes less stable at high temp and unfolds when TDS exceeds DH Denatured (unfolded) Native (folded) DGu = DHu - TDSu DGu DHu 0 TDSu + + favorable native state interactions broken unfolded state more disordered T

4. Less naive thermodynamics of unfolding Free energy of unfolding actually varies in a more complicated way with T. Enthalpy and entropy are both temperature dependent. Temperature dependence is described by the heat capacity DCp. DHu = DHu0+ DCp (T–T0) enthalpy and entropy not temperature independent DSu = DSu0+ DCp ln (T/ T0) DGu = DHu0– TDSu0+ DCp[T– T0–T ln (T/ T0)] figures into the total free energy as this term T0 is some arbitrary reference temperature, and DHu0and DSu0are the enthalpy and entropy at this temperature. from Becktel & Schellman, Biopolymers 26, 1859 (1987).

5. Thermodynamic breakdown of unfolding variation in enthalpy, entropy huge compared to free energy TDSu DHu slope = DCp this example: DHu, 298 = +35 kcal mol-1 DSu, 298 = +100 cal mol-1K-1 DCp = +1500 cal mol-1K-1 DGu DCp typically 10-18 cal mol-1K-1per residue (large and positive)

6. Temperature of maximal stability point of maximal stability occurs when TDS is zero (Ts) below Ts, entropy favors folding: folding less favorable as decrease temp this line represents zero above Ts, entropy disfavors folding: folding less favorable as increase temp from Becktel & Schellman, Biopolymers 26, 1859 (1987).

7. Stability curves for proteins Tc --> cold denaturation temperature--usually below freezing proteins typically not very stable: 5-20 kcal/mol at room temp proteins typically have their maximum stability near room temp Tm of a protein --> temperature at which folded/unfolded states equally populated--> DGu = 0 proteins with higher heat capacity have tighter, steeper parabolas (red curve vs. blue) A protein with a higher room temp stability could, in principle, have a lower Tm.

8. Equation for thermal denaturation DGu = DHu0– TDSu0+ DCp[T– T0–T ln (T/ T0)] assign Tm as the arbitrary reference temperature T0 DGu = DHu,Tm– TDSu,Tm + DCp[T– Tm–T ln (T/ Tm)] DGu, Tm= 0 so DHu,Tm= TmDSu,Tm DGu = DHu,Tm(1 – T/ Tm ) + DCp[T– Tm–T ln (T/ Tm)]

9. Amount of unfolded protein as function of T eqn describing DGu as function of T DGu = DHu,Tm(1 – T/ Tm ) + DCp[T– Tm–T ln (T/ Tm)] Ku = exp(-DGu/RT) = [U]/[F] fu = Ku / (1 + Ku ) Keq for unfolding reaction concentration unfolded and folded set of nested equations fraction unfolded

10. Heat denaturation curve basic sigmoidal shape of this curve derives from the “two-state” nature of the transition, but its specific shape will vary with DCp, DH so if I can somehow measure the folding transition... I can in principle extract the DCp, DH and the Tm by fitting the curve and also get DG at every temperature. Tm

11. Heat capacity and surface area from Myers et al. Protein Sci 31, 2138 (1995) Empirical studies of denaturation of proteins of known structure show that DCp of unfolding (y-axis) depends on the DASA (change in accessible surface area) upon folding (in other words the amount of surface buried). Note that proteins with disulfide (open circles) fall below the curve...why?

12. from Myers et al. Protein Sci 31, 2138 (1995) ...and as we have seen the DASA depends upon the size of the protein, in terms of the number of residues in the polypeptide chain. This means that DCp will be fairly predictable for globular proteins of a given size...on average, it’s about 14 cal/(mol-K-residue), but it can be as low as 10 or as high as 18.

13. Liquid hydrocarbon model for heat capacity • The dependence of heat capacity of unfolding upon surface area burial suggests that it might be explained simply as a function of burying the chemical groups in the protein side chains and/or main chain. • Indeed, it has been shown that a heat capacity change that parallels that observed upon protein unfolding also occurs upon dissolution of nonpolar solutes in water, so a major contributor may simply be the burial of nonpolar groups--this is called the liquid hydrocarbon model, which essentially explains the heat capacity in terms of the resemblance of a protein interior to an oil drop. • However, burial of the amide groups in the backbone also has an effect on the heat capacity, based on experiments involving dissolution of organic amides in water. It is smaller and opposite in direction to the effect of burying hydrocarbons.

14. Heat capacity and burial of surface plot showing DASAnp and DASApfor a dozen proteins of different size DCp = 0.32* DASAnp- 0.14* DASApol based on dissolution of amide compound solutes in water--note is opposite in sign. based on dissolution of hydrocarbon solutes in water The relationship above does a pretty good job of predicting heat capacities of unfolding just by treating the protein as a collection of nonpolar and polar solutes. The nonpolar surface area burial is the dominant effect and determines the sign of the heat capacity effect, both because the coefficient is larger and because more nonpolar than polar surface is buried when proteins fold. from Spolar et al. Biochemistry 31, 3947 (1992)

15. Chemical denaturants urea guanidine (guanidinium) Molecular dynamics simulations of urea denaturation suggest that it denatures proteins by several mechanisms: --competes for backbone hydrogen bonds. --some effect on solvation of hydrophobic core --affects dynamics/structure of water, altering the hydrophobic effect stronger denaturant than urea also a salt, unlike urea See Bennion & Daggett, PNAS 100, 5142 (2003).

16. Chemical denaturation curve Cm fraction unfolded in the transition zone can be translated into DGu values at each urea concentration--> see next slide

17. Linear extrapolation to zero / m value both guanidine & urea melt should extrapolate to same value of DGuH2Ohere about 4 kcal/mol DGu = DGuH2O+ m [denaturant] urea m is the slope of the DGu vs. [denaturant] curve: for urea here, it is 1.8 kcal mol-1 M-1 guanidine Data are DGu values extracted from fu in transition zone of melt

18. Stability curves determined from melts pay no attention to this scale-- 7 here is equiv. to zero. from transition zones of thermal melts from chemical denaturation at 3 different temps from Bowie & Sauer Biochemistry 1989, 28, 7139.

19. m values correlate with surface area burial, just like DCp from Myers et al. Protein Sci 31, 2138 (1995) notice how proteins with disulfide crosslinks (open circles) fall below the line...the authors corrected for this and ultimately came up with the following equation: m (urea) = 0.14 * (DASA – 995*# crosslinks)

20. Key points about protein stability • in general protein native states are weakly stable (5-20 kcal/mol) relative to unfolded states • they tend to be maximally stable around room temperature, and are subject to both cold and heat denaturation, with inversion of sign of both the enthalpy and the entropy of unfolding • large heat capacity change due partly to properties of water--large T dependence of enthalpy, entropy • much of the denaturation behavior of proteins can be understood in terms of simple burial and solvent exposure of nonpolar and polar surface area