Transition States in Protein Folding Kinetics: The Structural Interpretation of Phi-values

Phi-values are experimental measures of the effects of mutations on the folding kinetics of a protein. A central question is which structural information Phi-values contain about the transition state of folding. Traditionally, a Phi-value is interpreted as the 'nativeness' of a mutated residue in the transition state. However, this interpretation is often problematic because it assumes a linear relation between the nativeness of the residue and its free-energy contribution. We present here a better structural interpretation of Phi-values for mutations within a given helix. Our interpretation is based on a simple physical model that distinguishes between secondary and tertiary free-energy contributions of helical residues. From a linear fit of our model to the experimental data, we obtain two structural parameters: the extent of helix formation in the transition state, and the nativeness of tertiary interactions in the transition state. We apply our model to all proteins with well-characterized helices for which more than 10 Phi-values are available: protein A, CI2, and protein L. The model captures nonclassical Phi-values 1 in these helices, and explains how different mutations at a given site can lead to different Phi-values.Comment: 26 pages, 7 figures, 5 table

Electrical measurements on fused quartz under shock compression

The resistivities of specimens of SiO_2 (fused quartz) singly and doubly shocked in the 10–45 and 27–90 GPa ranges, respectively, demonstrate a marked decrease from values of ∼10–0.1 Ω⋅m at a single‐shock pressure of ∼40 and a double‐shock pressure of ∼74 GPa. These states correspond to calculated shock temperatures of ∼3300 and ∼3600 K, respectively. At shock pressures below 36 GPa the measured resistivity versus calculated shock temperature agrees closely with ambient‐pressure and high‐temperature resistivity data. This suggests that the ionic conduction mechanisms inferred to control electrical properties at ambient pressure also act under shock‐induced high temperatures in quartz and the presumed high‐pressure phase, stishovite into which fused quartz appears to transform above 20 GPa. At 36–40 GPa the rapid decrease in resistivity by a factor of 10^2 suggests a further transformation to an unknown phase which may correspond to the onset of melting. The existing pressure‐density Hugoniot data do not demonstrate any anomalous density change associated with this phase change

Shock-induced radiation spectra of fused quartz

An optical multichannel analyzer is applied to observe shock-induced radiation spectra of fused quartz in the 23–31 GPa shock-pressure range. Characteristics of sample-driver interface strongly influence both intensity and profile of the observed spectra. Brightness and color temperature are determined by an integration of spectral radiance and a fit to the greybody radiation spectrum, respectively. The resultant brightness and color temperature are lower and considerably higher than those estimated by the theoretical calculation, respectively. Some broad but strong line spectra are, however, superimposed onto the continuous greybody radiation spectrum even though the influences of the interface are reduced as much as possible. The line spectra are probably caused by electroluminescence and/or triboluminescence

Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.Comment: 9 pages, 6 figures, 1 tabl

K_6 minors in 6-connected graphs of bounded tree-width

We prove that every sufficiently big 6-connected graph of bounded tree-width either has a K_6 minor, or has a vertex whose deletion makes the graph planar. This is a step toward proving that the same conclusion holds for all sufficiently big 6-connected graphs. Jorgensen conjectured that it holds for all 6-connected graphs.Comment: 33 pages, 8 figure