### Abstract

A denaturant m-value is the magnitude of the slope of a typically linear plot of the unfolding free energy change ΔG(obs)/°vs. molar concentration (C_{3}) of denaturant. For a given protein, the guanidinium chloride (GuHCl) m-value is approximately twice as large as the urea m-value. Myers et al. (Protein Sci 1995;4:2138-2148) found that experimental m-values for protein unfolding in both urea and GuHCl are proportional to ΔASA(corr)/(max), the calculated maximum amount of protein surface exposed to water in unfolding, corrected empirically for the effects of disulfide crosslinks: (urea m-value/ΔASA(corr)/(max)) = 0.14±0.01 cal M^{-1} Å^{-2} and (GuHCl m-value/ΔASA(corr)/(max)) = 0.28±0.03 cal M^{-1} Å^{-2}. The observed linearity of plots of ΔG(obs)/°vs. C_{3} indicates that the difference in preferential interaction coefficients ΔΓ_{3} characterizing the interactions of these solutes with denatured and native protein surface is approximately proportional to denaturant concentration. The proportionality of m-values to ΔASA(corr)/(max) indicates that the corresponding ΔΓ_{3} are proportional to ΔASA(corr)/(max) at any specified solute concentration. Here we use the local-bulk domain model of solute partitioning in the protein solution (Courtenay et al., Biochemistry 2000;39:4455-4471) to obtain a novel quantitative interpretation of denaturant m-values. We deduce that the proportionality of m-value to ΔASA(corr)/(max) results from the proportionality of B_{1}/^{0} (the amount of water in the local domain surrounding the protein surface exposed upon unfolding) to ΔASA(corr)/(max). We show that both the approximate proportionality of ΔΓ_{3} to denaturant concentration and the residual dependence of ΔΓ_{3}/m_{3} (where m_{3} is molal concentration) on denaturant concentration are quantitatively predicted by the local-bulk domain model if the molal-scale solute partition coefficient K(P) and water-solute exchange stoichiometry S_{1,3} are independent of solute concentration. We obtain K(P,urea) = 1.12±0.01 and K(P,GuHCl) = 1.16±0.02 (or K(P,GuH^{+}) ≃ 1.48), values which will be useful to characterize the effect of accumulation of those solutes on all processes in which the water-accessible area of unfolded protein surface changes. We demonstrate that the local-bulk domain analysis of an m-value plot justifies the use of linear extrapolation to estimate (≤ 5% error) the stability of the native protein in the absence of denaturant (ΔG(o)/(o)), with respect to a particular unfolded state. Our surface area calculations indicate that published m-values/ΔASA ratios for unfolding of alanine-based α-helical oligopeptides by urea and GuHCl exceed the corresponding m-value/ΔASA ratios for protein unfolding by approximately fourfold. We propose that this difference originates from the approximately fourfold difference (48% vs. 13%) in the contribution of polar backbone residues to ΔASA of unfolding, a novel finding which supports the long-standing but not universally accepted hypothesis that urea and guanidinium cations interact primarily with backbone amide groups. We propose that proteins which exhibit significant deviations from the average m-value/ΔASA ratio will be found to exhibit significant deviations from the expected amount and/or average composition of the surface exposed on unfolding. (C) 2000 Wiley-Liss, Inc.

Original language | English |
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Pages (from-to) | 72-85 |

Number of pages | 14 |

Journal | Proteins: Structure, Function and Genetics |

Volume | 41 |

Issue number | SUPPL. 4 |

DOIs | |

State | Published - Oct 26 2000 |

### Keywords

- Activity coefficient
- Linear extrapolation model
- Partition coefficient
- Peptide backbone
- Protein stability

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## Cite this

*Proteins: Structure, Function and Genetics*,

*41*(SUPPL. 4), 72-85. https://doi.org/10.1002/1097-0134(2000)41:4+<72::AID-PROT70>3.0.CO;2-7