An Effective Solvent Theory Connecting the Underlying Mechanisms of Osmolytes and Denaturants for Protein Stability  Apichart Linhananta, Shirin Hadizadeh, Steven Samuel Plotkin  Biophysical Journal  Volume 100, Issue 2, Pages 459-468 (January 2011) DOI: 10.1016/j.bpj.2010.11.087 Copyright © 2011 Biophysical Society Terms and Conditions

Figure 1 (A) Reduced heat capacity (C∗ = CV/kB) versus reduced temperature T∗ of Trp-cage Gō model with implicit solvent. The plot is obtained by using the multiple-histogram method. The data points and error bars are averages taken from five independent runs at each temperature. (Inset, dashed curve) Pair potential for the native contact C(12)-N(46). (Inset, solid curve) Transfer PMF superposed on the pair potential in a neutral solvent, obtained by averaging the change in PMF over several native contacts upon transfer to the neutral solvent (see the Supporting Material for further description). (B) Probability distributions of energy for protein-protein plus protein-solvent interactions, obtained by the histogram method, for several solvents at their respective folding temperatures (implicit solvent, T∗f = 4.05; neutral solvent with ɛ∗ps = 0, T∗f = 4.55; protective osmolyte solvent with ɛ∗ps = 0.4, T∗f = 5.08; and denaturing osmolyte solvent with ɛ∗ps = −0.4, T∗f = 3.91). For explicit solvents, the energy generally includes protein-solvent interaction energy; however, for the implicit and neutral hard-sphere solvent, this contribution to the energy is zero. Protective osmolytes shift to higher energies and show less cooperative transition, whereas denaturing osmolytes shift to lower energies and show more cooperative transition. Comparing the neutral and implicit solvent histograms, the native ensemble shifts to higher energy because it has less overall native structure due to the less cooperative folding transition. The unfolded ensemble also shifts to the right because even though there is a tendency to have more native long-range contacts (with |i – j| ≥ 4), there are fewer local contacts. Biophysical Journal 2011 100, 459-468DOI: (10.1016/j.bpj.2010.11.087) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 2 (a) C∗versus T∗ of Trp-cage in solvent for protein-solvent contact energy ɛ∗ps = 0 (solid line); ɛ∗ps = 0.2, 0.4, 0.6, and 0.8 (dashed lines); and ɛ∗ps = −0.2, −0.4, and −0.6 (dotted lines). ɛ∗ss = −1 for all solvents. (b) C∗ versus T∗ of plots Trp-cage for several solvent models. In implicit solvent (thick solid line), in 1000 spherical reference solvent molecules with ɛ∗ss = −1, ɛ∗ps = 0 (thin solid line, this curve is identical to the ɛ∗ps = 0 curve in panel a); in 1000 pure hard-sphere spherical solvents with ɛ∗ss = 0, ɛ∗ps = 0 (dashed line); in 1500 pure hard-sphere spherical solvents ɛ∗ss = 0, ɛ∗ps = 0 (dashed-dotted line); and in 1000 urealike spherical solvents with ɛ∗ss = −1, ɛ∗ps = −0.3 (dotted line). Biophysical Journal 2011 100, 459-468DOI: (10.1016/j.bpj.2010.11.087) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 3 (a) Radius of gyration of the unfolded states with Q < 0.2 taken at the temperatures of the heat capacity peaks in Fig. 2, plotted as a function of the protein-solvent interaction energy ɛ∗ps. The unfolded states progressively become more collapsed as the solvent moves from that containing denaturant to one containing osmolyte. (Insets) Snapshots of representative unfolded states for ɛ∗ps = −0.6 and ɛ∗ps = +0.8. These snapshots are obtained by taking the first sampled conformation that had a RGY within 2% of the average value given by the plotted data point. (b) Cooperativity of the folding transition, defined by the ratio of the van' t Hoff enthalpy over calorimetric enthalpy, as a function of ɛ∗ps. The transition becomes more cooperative for denaturant-containing solvents, and less cooperative for osmolyte-containing solvents. (Insets) Histograms of the values of Q at the midpoints of the transition (at the respective heat capacity peak temperatures) for ɛ∗ps = −0.6 and ɛ∗ps = +0.8, which are strongly bimodal for a denaturant-containing solvent, and unimodal (for the Trp cage model) for a strong osmolyte-containing solvent. Biophysical Journal 2011 100, 459-468DOI: (10.1016/j.bpj.2010.11.087) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 4 (a) Free energy versus protein native fraction (Q) at T∗ = 4.8 for ɛ∗ps = 0 (solid line), ɛ∗ps = 0.4 (dashed line), and ɛ∗ps = −0.2 (dotted line), with solvent-solvent contact energy fixed at ɛ∗ss = −1. (b) Total energy 〈E〉 versus Q. (c) Entropy(S) versus Q. (d) Changes in enthalpy between osmolyte and neutral solvent ΔE = E(ɛ∗ps = 0.4) – E (ɛ∗ps = 0) (dashed line), and between denaturant solvent and neutral solvent ΔE = E(ɛ∗ps = −0.2) – E (ɛ∗ps = 0) (dotted line). (e) Change in entropy (ΔS) versus Q, for osmolyte solvent (ɛ∗ps = 0.4) compared to neutral solvent (ɛ∗ps = 0), i.e., ΔS = S(ɛ∗ps = 0.4) – S (ɛ∗ps = 0) (dashed line), and for denaturant (ɛ∗ps = −0.2) solvent compared to neutral (ɛ∗ps = 0) solvent ΔS = S(ɛ∗ps = −0.2) – S (ɛ∗ps = 0). (f) Comparison between weak and strong denaturants, by plotting E(ɛ∗ps = −0.2) – E (ɛ∗ps = 0) (dash-dotted, and shifted by −270ɛ to appear on the same scale) and E(ɛ∗ps = −0.6) – E (ɛ∗ps = 0) (solid) versus Q. Strong denaturants enthalpically stabilize the unfolded state relative to the folded state, whereas weak denaturants mildly stabilize the folded state (but entropically destabilize it). Biophysical Journal 2011 100, 459-468DOI: (10.1016/j.bpj.2010.11.087) Copyright © 2011 Biophysical Society Terms and Conditions