Quantification of interactions between solutes and small model compounds
The preferential interaction (µ23) is dissected into contributions (α values) from each type of atom on the model compound, as described by the following equation:
Where µ23 quantifies the interaction between solute 2 (often a biopolymer or model compound) and solute 3 (often an osmolyte, denaturant, or Hofmeister salt), relative to their interactions with solvent water. μ23 can be thought of as the free energy of transfer of the model compound (species 2) from water to a solution that is 1 molal in the solute (species 3). Subscript i refers to each atom type on solute 2. The α value quantifies the strength of the interaction potential of solute 3 with 1 Å2 of ASA (water-accessible surface area) of each atom type i on solute 2. Software for measuring ASA can be found here.
The value of µ23 can also be interpreted in terms of the solute partitioning model (SPM) as in this equation:
Where Kp is the ratio of local to bulk concentration of solute 3, b1ASA is the number of waters of hydration in two layers of water at the surface area of interest, and 55.5 is the molality of pure water.
The same equation can be rewritten to solve for the α value in terms of the partition coefficient Kp:
Quantifying Interactions of Nucleobase Atoms with Model Compounds for the Peptide Backbone and Glutamine and Asparagine Side Chains in Water [PubMed]
α-values (cal mol−1 molal−1 Å−2)
| Nucleobase Surface Type | Urea | Methylurea | Ethylurea | 1,1-dimethylurea | 1,3-dimethylurea | 1,1-diethylurea |
|---|---|---|---|---|---|---|
| Carbonyl sp2 O | −0.80 ± 0.05 | −0.23 ± 0.06 | −0.12 ± 0.06 | 0.06 ± 0.09 | 0.45 ± 0.05 | 0.71 ± 0.12 |
| Amino sp3 N | −0.29 ± 0.04 | −0.46 ± 0.05 | −0.81 ± 0.05 | −1.23 ± 0.07 | −1.07 ± 0.05 | −1.64 ± 0.1 |
| Ring sp2 N | −0.70 ± 0.04 | −1.15 ± 0.08 | −1.36 ± 0.07 | −1.70 ± 0.10 | −1.13 ± 0.07 | −2.01 ± 0.13 |
| Methyl sp3 C | −0.57 ± 0.03 | −0.80 ± 0.04 | −1.01 ± 0.05 | −1.07 ± 0.06 | −1.33 ± 0.03 | −1.26 ± 0.08 |
| Ring sp2 C | −0.57 ± 0.02 | −1.3 ± 0.07 | −1.57 ± 0.07 | −2.02 ± 0.07 | −1.92 ± 0.04 | −2.70 ± 0.10 |
µ23 values (cal mol-1 molal-1)
| Model Compound | Urea | Methylurea | Ethylurea | 1,1-dimethylurea | 1,3-dimethylurea | 1,1-diethylurea |
|---|---|---|---|---|---|---|
| Naphthalene | -166 ± 5.9 | -361 ± 15 | -390 ± 15 | -554 ± 33 | -568 ± 9.4 | -749 ± 14 |
| Anthracene | -195 ± 5.9 | -475 ± 43 | -588 ± 40 | -697 ± 33 | -639 ± 24 | -914 ± 57 |
| 3-methylindole | -156 ± 13 | -267 ± 12 | -367 ± 20 | -526 ± 27 | -436 ± 8.7 | --- |
| Caffeine | -249 ± 11 | -308 ± 9.3 | -362 ± 17 | -375 ± 20 | -397 ± 7 | -462 ± 29 |
| Theophylline | -211 ± 3.7 | -306 ± 10 | -379 ± 14 | -375 ± 30 | -387 ± 12 | -376 ± 18 |
| Theobromine | -220 ± 14 | -290 ± 8.2 | -302 ± 14 | -398 ± 12 | -373 ± 15 | -460 ± 16 |
| Hypoxanthine | -175 ± 8.1 | -224 ± 14 | -332 ± 11 | -397 ± 16 | -296 ± 12 | --- |
| Adenine | -151 ± 3.9 | -317 ± 9.7 | -339 ± 7.8 | -437 ± 14 | -374 ± 9.1 | -597 ± 12 |
| 2,6-diamino Purine | -171 ± 6 | -282 ± 9.6 | -390 ± 7.9 | -542 ± 17 | -424 ± 9.4 | -667 ± 18 |
| Uric Acid | -236 ± 12 | -279 ± 14 | -283 ± 14 | -327 ± 16 | --- | --- |
| 1,3-dimethyl-6-amino Uracil | -141 ± 6.5 | -213 ± 7.5 | -294 ± 7.1 | -324 ± 9.5 | -287 ± 7.9 | -341 ± 15 |
| Thymine | -188 ± 2.4 | -196 ± 8.1 | -206 ± 13 | -273 ± 10.5 | -238 ± 3.7 | -290 ± 16 |
| Uracil | -171 ± 16 | -163 ± 4.7 | -185 ± 7.9 | -190 ± 9.4 | -147 ± 3.1 | -267 ± 11 |
| Cytosine | -143 ± 8 | -168 ± 6.7 | -193 ± 9.1 | -211 ± 4.9 | -200 ± 4.6 | -247 ± 15 |
| 5-amino Uracil | -151 ± 9.1 | -133 ± 7.1 | -184 ± 9.8 | -206 ± 6.6 | -156 ± 7.9 | -251 ± 24 |
| 6-amino Uracil | -159 ± 4.9 | -183 ± 7.5 | -249 ± 11 | -378 ± 21 | -257 ± 8.3 | -415 ± 19 |
Water accessible surface area (ASA) (Å2)
| Model Compound | Amide sp2 O | Amide sp2 N | Aliphatic sp3 C | Amide sp2 C |
|---|---|---|---|---|
| Urea | 47.9 | 130.2 | 0 | 7.2 |
| Methylurea | 38.3 | 87.5 | 88.4 | 6.5 |
| Ethylurea | 38.3 | 82 | 124.6 | 6.5 |
| 1,1-dimethylurea | 38.3 | 54.5 | 148.7 | 6.2 |
| 1,3-dimethylurea | 28.7 | 44.9 | 176.7 | 5.8 |
| 1,1-diethylurea | 35.7 | 50 | 208.9 | 3.7 |
Experimental Atom-by-Atom Dissection of Amide-Amide and Amide-Hydrocarbon Interactions in H2O [PubMed]
α-values (cal mol−1 molal−1 Å−2)
| Amide O | Amide N | Aliphatic sp3 C | Amide sp2 C | Aromatic sp2 C | |
|---|---|---|---|---|---|
| Urea | -0.52 ± 0.04 | -0.09 ± 0.02 | -0.07 ± 0.01 | -0.69 ± 0.06 | -0.59 ± 0.01 |
| Methylurea | 0.52 ± 0.08 | -0.44 ± 0.03 | -0.31 ± 0.01 | -0.99 ± 0.07 | -1.36 ± 0.08 |
| Ethylurea | 0.79 ± 0.06 | -0.55 ± 0.02 | -0.43 ± 0.01 | -1.2 ± 0.05 | -1.61 ± 0.07 |
| 1,1-dimethylurea | 1.09 ± 0.07 | -0.61 ± 0.03 | -0.35 ± 0.01 | -1.53 ± 0.05 | -2.04 ± 0.08 |
| 1,3-dimethylurea | 1.68 ± 0.09 | -0.77 ± 0.03 | -0.56 ± 0.01 | -1.87 ± 0.06 | -1.95 ± 0.04 |
| 1,1-diethylurea | 1.73 ± 0.09 | -0.84 ± 0.03 | -0.64 ± 0.01 | -1.88 ± 0.07 | -2.7 ± 0.1 |
| 1,3-diethylurea | 2.35 ± 0.09 | -1.01 ± 0.04 | -0.76 ± 0.01 | -2.28 ± 0.07 | -2.97 ± 0.13 |
| Naphthalene | -4.44 ± 0.8 | 0.85 ± 0.29 | -2.71 ± 0.07 | -2.88 ± 0.83 | --- |
Values of µ23 (or self-interaction µ22ex/2) in (cal mol-1 molal-1)
| Urea | Methylurea | Ethylurea | 1,1-dimethylurea | 1,3-dimethylurea | |
|---|---|---|---|---|---|
| Urea | (-42.4 ± 4.3) | -37.8 ± 1.9 | -43.8 ± 2.3 | -35.7 ± 2.1 | -30.2 ± 1.1 |
| Methylurea | -37.8 ± 1.9 | (-38.6 ± 3.9) | -59.4 ± 2.3 | -46.8 ± 2.1 | -59.1 ± 2.8 |
| Ethylurea | -43.8 ± 2.3 | -59.4 ± 2.3 | (-75.6 ± 7.6) | -69.2 ± 2.7 | -83.1 ± 2.9 |
| 1,1-dimethylurea | -35.7 ± 2.1 | -46.8 ± 2.1 | -69.2 ± 2.7 | (-28.8 ± 2.9) | -61.6 ± 1.9 |
| 1,3-dimethylurea | -30.2 ± 1.1 | -59.1 ± 2.8 | -83.1 ± 2.9 | -61.6 ± 1.9 | (-66.6 ± 6.7) |
| 1,1-diethylurea | -39.7 ± 1.2 | -78.3 ± 1.9 | -96.2 ± 2.7 | -77.7 ± 2.7 | -114 ± 3.6 |
| 1,3-diethylurea | -40.3 ± 2.5 | -87.8 ± 3.3 | -102.7 ± 1.9 | -79.8 ± 2.8 | -125 ± 3.5 |
| 1,1-diethylurea | 1,3-diethylurea | Malonamide | Propionamide | Methylacetamide | |
| Urea | -39.7 ± 1.2 | -40.3 ± 2.5 | -54.9 ± 2.5 | -36.8 ± 2 | -36.3 ± 1.7 |
| Methylurea | -78.3 ± 1.9 | -87.8 ± 3.3 | -43.8 ± 1.4 | -62.3 ± 1.7 | -49.7 ± 1.8 |
| Ethylurea | -96.2 ± 2.7 | -91.7 ± 2.7 | -48.5 ± 2.4 | -67.6 ± 1.7 | -72.2 ± 1.5 |
| 1,1-dimethylurea | -77.7 ± 2.7 | -79.8 ± 2.8 | -30.6 ± 1.8 | -53.5 ± 2.3 | -42.2 ± 1.7 |
| 1,3-dimethylurea | -114 ± 3.6 | -125 ± 3.5 | -27.3 ± 2.4 | -68.5 ± 1.9 | -66.2 ± 2.8 |
| 1,1-diethylurea | (-115 ± 12) | -146 ± 4.5 | -34.6 ± 1.3 | -78.2 ± 1.5 | -89 ± 1.9 |
| 1,3-diethylurea | -146 ± 4.5 | (-133 ± 13) | -21.7 ± 1.2 | -72.7 ± 2.5 | -87.1 ± 2.2 |
| AAMA | Formamide | Methylformamide | Anthracene | Naphthalene | |
| Urea | -52.4 ± 5.9 | -62.9 ± 2.2 | -56.1 ± 2.9 | -194 ± 5.9 | -165 ± 5.9 |
| Methylurea | -61.3 ± 3.3 | -48.8 ± 3 | -53.7 ± 1.7 | -472 ± 43 | -359 ± 15 |
| Ethylurea | -70.6 ± 1.7 | -39.2 ± 1.1 | -74.9 ± 1.9 | -584 ± 40 | -387 ± 15 |
| 1,1-dimethylurea | -39.8 ± 2.3 | -51.6 ± 1.7 | -60.2 ± 1.7 | -693 ± 33 | -551 ± 32 |
| 1,3-dimethylurea | -60.9 ± 2.6 | -52.6 ± 1.6 | -66.7 ± 1.9 | -635 ± 24 | -565 ± 9.4 |
| 1,1-diethylurea | -78.3 ± 3.1 | -51.4 ± 1.7 | -77.5 ± 2.3 | -907 ± 56 | -691 ± 9.1 |
| 1,3-diethylurea | -80.3 ± 2.9 | -48.9 ± 1.3 | -81.6 ± 2.5 | -1064 ± 74 | -738 ± 16 |
Water accessible surface area (ASA) (Å2)
| Amide sp2 O | Amide sp2 N | Aliphatic sp3 C | Amide / Aromatic sp2 C | |
|---|---|---|---|---|
| Urea | 47.9 | 130.2 | 0 | 7.2 |
| Methylurea | 38.3 | 87.5 | 88.4 | 6.5 |
| Ethylurea | 38.3 | 82 | 124.6 | 6.5 |
| 1,1-dimethylurea | 38.3 | 54.5 | 148.7 | 6.2 |
| 1,3-dimethylurea | 28.7 | 44.9 | 176.7 | 5.8 |
| 1,1-diethylurea | 35.7 | 50 | 208.9 | 3.7 |
| 1,3-diethylurea | 28.7 | 33.8 | 249.2 | 5.8 |
| Malonamide | 65.7 | 123.2 | 48.5 | 8.5 |
| Propionamide | 36.8 | 61.6 | 124.5 | 4.3 |
| Methylacetamide | 35.3 | 19 | 178 | 3.5 |
| AAMA | 62.5 | 21.1 | 257.7 | 4.3 |
| Formamide | 51.3 | 70.8 | 0 | 40.2 |
| Methylformamide | 41.7 | 27.7 | 88.4 | 39.5 |
| Dimethylformamide | 41.7 | 0.8 | 157.7 | 30.7 |
| Ethyleneurea | 49 | 57.1 | 113.6 | 7 |
| Dimethylacetamide | 35.3 | 0.8 | 220.1 | 3.6 |
| Tetramethylurea | 29.9 | 0.8 | 266.4 | 3.3 |
| Naphthalene | 0 | 0 | 0 | 273 |
| Anthracene | 0 | 0 | 0 | 338 |
Composite amide, hydrocarbon, and amide-hydrocarbon α-values to predict solute effects on protein folding
α-values (cal mol−1 molal−1 Å−2)
| Amide | Hydrocarbon | Combined | |
|---|---|---|---|
| Urea | -0.39 ± 0.03 | -0.12 ± 0.01 | -0.18 ± 0.01 |
| Methylurea | 0.24 ± 0.06 | -0.42 ± 0.01 | -0.27 ± 0.02 |
| Ethylurea | 0.46 ± 0.12 | -0.55 ± 0.02 | -0.33 ± 0.03 |
| Butyl urea | 0.86 ± 0.04 | -0.82 ± 0.04 | -0.45 ± 0.03 |
| 1,1-dimethylurea | 0.59 ± 0.05 | -0.5 ± 0.01 | -0.26 ± 0.01 |
| 1,3-dimethylurea | 0.87 ± 0.08 | -0.67 ± 0.02 | -0.33 ± 0.02 |
| 1,1-diethylurea | 1.06 ± 0.10 | -0.87 ± 0.03 | -0.45 ± 0.03 |
| 1,3-diethylurea | 1.31 ± 0.18 | -0.96 ± 0.05 | -0.46 ± 0.05 |
Basis of protein stabilization by K Glutamate: unfavorable interactions with carbon, oxygen groups. [PubMed]
Values of µ23 for Interactions of KGlu with Model Compounds (cal mol-1 m-1)
| Model Compound | Experimental µ23 | Model Compound | Experimental µ23 | |
|---|---|---|---|---|
| Acetyl-ala-methylamide | 406 ± 6 | Proline | 161 ± 4 | |
| 1,3-diethylurea | 348 ± 7 | Valine | 117 ± 5 | |
| Naphthalene | 322 ± 14 | Methylurea | 111 ± 6 | |
| Glycine betaine | 292 ± 4 | Malonamide | 48 ± 2 | |
| Benzene | 291 ± 11 | Alanine | 29 ± 2 | |
| 1,1-diethylurea | 284 ± 4 | Urea | 31 ± 2 | |
| 1,3-dimethylurea | 249 ± 5 | Glycine | -50 ± 4 | |
| Propionamide | 174 ± 6 |
KGlu-Group Interaction Potentials (α-values) and Corresponding Local-Bulk KGlu Partition Coefficients (Kp)
| Surface Type | α (cal mol-1 m-1 Å2) | SPM Kp |
|---|---|---|
| Aliphatic sp3 C | 1.34 ± 0.02 | 0.63 ± 0.01 |
| sp2 C | 1.25 ± 0.04 | 0.65 ± 0.01 |
| Amide O | 0.76 ± 0.15 | 0.79 ± 0.02 |
| Carboxylate O | 0.37 ± 0.07 | 0.9 ± 0.01 |
| Amide N | -0.39 ± 0.07 | 1.11 ± 0.01 |
| Cationic N | -1.87 ± 0.07 | 1.52 ± 0.01 |