Denaturation of proteins: electrostatic effects vs. hydration

Abstract

The unfolding transition of proteins in aqueous solution containing various salts or uncharged solutes is a classical subject of biophysics. In many cases, this transition is a well-defined two-stage equilibrium process which can be described by a free energy of transition ΔG _u and a transition temperature T _m. For a long time, it has been known that solutes can change T _m profoundly. Here we present a phenomenological model that describes the change of T _m with the solute concentration c _s in terms of two effects: (i) the change of the number of correlated counterions Δn _ci and (ii) the change of hydration expressed through the parameter Δw and its dependence on temperature expressed through the parameter dΔc _p/dc _s. Proteins always carry charges and Δn _ci describes the uptake or release of counterions during the transition. Likewise, the parameter Δw measures the uptake or release of water during the transition. The transition takes place in a reservoir with a given salt concentration c _s that defines also the activity of water. The parameter Δn _ci is a measure for the gain or loss of free energy because of the release or uptake of ions and is related to purely entropic effects that scale with ln c _s. Δw describes the effect on ΔG _u through the loss or uptake of water molecules and contains enthalpic as well as entropic effects that scale with c _s. It is related to the enthalpy of transition ΔH _u through a Maxwell relation: the dependence of ΔH _u on c _s is proportional to the dependence of Δw on temperature. While ionic effects embodied in Δn _ci are independent of the kind of salt, the hydration effects described through Δw are directly related to Hofmeister effects of the various salt ions. A comparison with literature data underscores the general validity of the model.

Fig. 1. Evaluation of the measured transition enthalpy ΔH_u by eqn (8). (a) ΔH_u as the function of salt concentration c_s. The marks show the experimental data for the unfolding of ribonuclease in presence of the salts indicated in the graph. These data have been taken from Table 1 of Francisco et al. (b) ΔH_u as the function of ΔT_m = T_m − T⁰_m. The solid lines indicate the fit of eqn (8) whereas the green dashed line indicates the transition enthalpy calculated by eqn (8) with the average value Δc_p,0 ≅ 4.6 kJ (K⁻¹ mol⁻¹) and dΔc_p/dc_s = 0. See text for further explanation.

Fig. 2. Comparison of theory and experimental data taken from the denaturation of RNase A for the 3 kosmotropic salt NaCl, NH₄Cl, LiCl and for the chaotropic salt NaSCN. The points show the transition temperatures taken in presence of different salts as indicated in the graph (see Table 1 of ref. 18). The solid lines mark the calculated transition temperatures T_m calculated from the fit parameters Δn_ci and Δw(T⁰_m) (cf.Table 1). See text for further explanation.

Fig. 3. Reversal of T_m through a competition of counterion release and preferential hydration. The data marked by red points have been measured by Senske et al. for the unfolding of RNase A at pH = 5 in presence of an increasing concentration of NaCl. The solid line marks the fit by theory with the parameters Δn_ci = −0.60 and Δw = −31.7 (eqn (23), the term quadratic in ΔT has been neglected). The green dashed line marks the temperature T⁰_m. See text for further explanation.