The three states of globular proteins: Acid denaturation

Abstract

We describe statistical mechanical theory that aims to predict protein stabilities as a function of temperature, pH, and salt concentration, from the physical properties of the constituent amino acids: (1) the number of nonpolar groups, (2) the chain length, (3) the temperature-dependent free energy of transfer, (4) the pKa's (including those in the native state) and their temperature dependencies. We calculate here the phase diagrams for apomyoglobin and hypothetical variant proteins. The theory captures essential features of protein stability including myoglobin's Tm vs pH as measured by P. L. Privalov [(1979) Advances in Protein Chemistry, Vol. 33, pp. 167-241] and its ionic strength vs pH phase diagram as measured by Y. Goto and A. L. Fink [(1990) Journal of Molecular Biology, Vol. 214, pp. 803-805]. The main predictions here are the following: (1) There are three stable states, corresponding to native (N), compact denatured (C), and highly unfolded (U), with transitions between them. (2) In agreement with experiments, the compact denatured state is predicted to have enthalpy closer to U than N because even though there is considerable hydrophobic "clustering" in C, this nevertheless represents a major loss of hydrophobic contacts relative to configurations (N) that have a hydrophobic "core." (3) C becomes more prominent in the phase diagram with increasing nonpolar content or decreasing chain length, perhaps thus accounting for (a) why lysozyme and alpha-lactalbumin differ in their denatured states, and (b) why shortened Staph nuclease molecules are compact. (4) Of major importance for protein calorimetry is Privalov's observation that the enthalpy of folding, delta H (T, pH) is independent of pH. The theory accounts for this through the prediction that the main electrostatic contribution to stability is not enthalpic; the main contribution is the entropy, mainly due to the different distributions of protons and small ions in the native and denatured states.

Single-molecule spectroscopy of the unexpected collapse of an unfolded protein at low pH

“…2): unfolded CspTm at pH 2.9 exhibits R G values surprisingly close to those found at pH 7. Two types of theories, 30,32,33 a polyampholyte theory and an ion-cloud model, both of which have previously been used successfully to describe electrostatic interactions in unfolded proteins, 4,33,59 fail to correctly predict the dimensions of unfolded CspTm at low pH and indicate the presence of additional intra-chain interactions at pH 2.9. The only chemical difference between unfolded CspTm at pH 2.9 and pH 7 is the protonation of 12 acidic groups (8 Glu, 3 Asp, C-terminus).…”

“…Once the electrostatic potential ψ is known, all other quantities such as the free energy of electrostatic repulsion (g rep ), the chemical free energy due to the preferential enrichment of counterions inside the volume of the chain (g chem ), and the entropy of distributing the protons to the ionizable groups (g α ) can be computed. 33,59,60 It should be noted that the ion-cloud model deviates from other polyelectrolyte models by its explicit incorporation of the chemical potential difference (g chem ) resulting from the preferential enrichment of counterions arround the potential iso-surface defined by the volume average of the electrostatic potential, ψ . The free energy of the electrical double layer resulting from protein charges and counterions is given by the repulsive electrostatic contribution of the protein charges (g rep ) and the chemical free energy of the counterion accumulation (g chem ).…”

“…The free energy of the electrical double layer resulting from protein charges and counterions is given by the repulsive electrostatic contribution of the protein charges (g rep ) and the chemical free energy of the counterion accumulation (g chem ). According to Alonso,Stigter and Dill,33,59 the total electrostatic free energy of the chain (g el ) additionally includes an entropic contribution resulting from the protonation equilibria of the ionizable amino acids in the chain (g α ), and is given by…”

“…In order to estimate the effect of g el (r G ) on the dimensions of unfolded CspTm, we follow the work of Alonso, Stigter, and Dill, 59 and add g el (r G ) to the potential of mean force of the chain as given by the theory of Sanchez, 18 leading to a modification of Eq. (1):…”

Single‐Molecule Fluorescence Studies of Protein Folding and Conformational Dynamics

“…There are cases where additional intermediate structures are involved and phase diagrams can be constructed that delineate their existence as a function of external conditions. [47][48][49][50] In some proteins, these intermediates are populated transiently in kinetic experiments under nonequilibrium conditions, 51-54 but it is not always clear whether these intermediates are productive on-pathway intermediate or simply off-pathway traps, 55 as suggested by the energy landscape theory.…”