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

Native and denatured states native state folded state denatured ensemble unfolded ensemble 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

Naive view of folding thermodynamics Native (folded) Denatured (unfolded) GuGu  G u =  H u - T  S u ++ unfolded state more disordered favorable native state interactions broken GuGu T HuHu TSuTSu protein becomes less stable at high temp and unfolds when T  S exceeds  H 0

Less naive thermodynamics of unfolding  H u =  H u 0 +  C p (T–T 0 )  S u =  S u 0 +  C p ln (T/ T 0 )  G u =  H u 0 – T  S u 0 +  C p [T– T 0 –T ln (T/ T 0 )] T 0 is some arbitrary reference temperature, and  H u 0 and  S u 0 are the enthalpy and entropy at this temperature. enthalpy and entropy not temperature independent 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  C p. figures into the total free energy as this term from Becktel & Schellman, Biopolymers 26, 1859 (1987).

GuGu TSuTSu HuHu slope =  C p this example:  H u, 298 = +35 kcal mol -1  S u, 298 = +100 cal mol -1 K -1  C p = cal mol -1 K -1  C p typically cal mol -1 K -1 per residue (large and positive) Thermodynamic breakdown of unfolding variation in enthalpy, entropy huge compared to free energy

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

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

Equation for thermal denaturation  G u =  H u 0 – T  S u 0 +  C p [T– T 0 –T ln (T/ T 0 )]  G u =  H u,Tm – T  S u,Tm +  C p [T– T m –T ln (T/ T m )]  H u,Tm = T m  S u,Tm  G u, Tm = 0 so  G u =  H u,Tm (1 – T/ T m ) +  C p [T– T m –T ln (T/ T m )] assign T m as the arbitrary reference temperature T 0

Amount of unfolded protein as function of T  G u =  H u,Tm (1 – T/ T m ) +  C p [T– T m –T ln (T/ T m )] K u = exp(  G u /RT) = [U]/[F] f u = K u / (1 + K u ) fraction unfolded concentration unfolded and folded K eq for unfolding reaction eqn describing  G u as function of T set of nested equations

Heat denaturation curve TmTm so if I can somehow measure the folding transition... I can in principle extract the  Cp,  H and the T m by fitting the curve and also get  G at every temperature. basic sigmoidal shape of this curve derives from the “two-state” nature of the transition, but its specific shape will vary with  Cp,  H

Heat capacity and surface area Empirical studies of denaturation of proteins of known structure show that  Cp of unfolding (y-axis) depends on the  ASA (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? from Myers et al. Protein Sci 31, 2138 (1995)

...and as we have seen the  ASA depends upon the size of the protein, in terms of the number of residues in the polypeptide chain. This means that  Cp 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. from Myers et al. Protein Sci 31, 2138 (1995)

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.

Heat capacity and burial of surface  C p = 0.32*  ASA np *  ASA pol based on dissolution of amide compound solutes in water--note is opposite in sign. based on dissolution of hydrocarbon solutes in water from Spolar et al. Biochemistry 31, 3947 (1992) 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. plot showing  ASA np and  ASA p for a dozen proteins of different size

Chemical denaturants urea guanidine (guanidinium) stronger denaturant than urea also a salt, unlike urea 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 See Bennion & Daggett, PNAS 100, 5142 (2003).

Chemical denaturation curve CmCm fraction unfolded in the transition zone can be translated into  G u values at each urea concentration--> see next slide

Linear extrapolation to zero / m value urea m is the slope of the  G u vs. [denaturant] curve: for urea here, it is 1.8 kcal mol -1 M -1  G u =  G u H2O + m [denaturant] both guanidine & urea melt should extrapolate to same value of  G u H2O here about 4 kcal/mol guanidine Data are  G u values extracted from f u in transition zone of melt

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

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 * (  ASA – 995*# crosslinks) m values correlate with surface area burial, just like  C p

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