SMFS experiments have shown that (1) the mechanical stability, given by the most probable unfolding force (Fu), is not correlated with thermodynamic stability (AG) or with melting temperature (Tm=AG/AS; Table 8.1, reviewed by Carrion-Vazquez et al. 2000), (2) chemical and mechanical unfolding follow different pathways (Best et al. 2001; Fowler et al. 2002) and have different unfolding barriers (Best et al. 2001; Brockwell et al. 2002), (3) the mechanical stability and the mechanical unfolding pathway depend on the pulling geometry and the application points of the force such that proteins present mechanically weak spots (Brockwell et al. 2003; Carrion-Vazquez et al. 2003), and (4) mechanical stability can be modulated by ligand binding (Ainavarapu et al. 2005).
SMFS experiments do not provide direct structural information on the dynamics of unfolding but they do provide many parameters that are sensitive to the structure of the protein under study (Table 8.1; Li et al. 2000a). We have seen that proteins show abroad range of responses to mechanical stress, which cannot easily be rationalized in terms of predictors of mechanical resistance (Table 8.1). However, to date only a few proteins have been analyzed, each with a varying degree of detail (19 different ones in this survey; Table 8.1). ttus, although the molecular basis underlying the mechanical resistance of proteins is still unclear, we have seen that several determinants can be identified through these studies: amino acid sequence, mechanical topology, unloaded unfolding rate constant, and pulling geometry.
tte force equation for the unfolding process (Eq. 8) predicts that the mechanical stability (Fu) depends on the unfolding distance, Axu (i.e., the location of the transi tion state along the mechanical reaction coordinate), the height of the barrier (AG^ which depends on fc°), and the loading rate (r). tte effect of a force is stronger the further from the native state it acts (Bustamante et al. 2004). For instance, to overcome a 12-fceT barrier (7.2 kcal moL1) would require an unfolding force of 200 pN for a protein that has an unfolding distance of 0.25 nm, while for a different protein, a similar barrier would require only 100 pN if it were located at an unfolding distance of 0.50 nm (at the same loading rate).
tte molecular structure of a protein poses constraints on the location of the transition state in mechanical unfolding. It has been suggested that tertiary interactions have shorter distances to their transition states than secondary structures, and they tend to be brittler than secondary interactions (i.e., they break at high forces and after small deformations), which are more compliant (breaking at low forces and after large deformations). Furthermore, tertiary interactions may require more time to equilibrate than secondary ones and, therefore, they often present hysteresis in the pulling-relaxation cycle (reviewed by Bustamante et al. 2004). Mechanical proteins tend to be assortments of modules, often mostly of the same type (e.g., Ig, fibronectin), although they frequently display distinct mechanical stabilities. Low forces would stretch the more compliant domains (with longer distances to their transition states, e.g., 10FNfnIII domain; Table 8.1) while the brittle domains (with shorter distances to their transition states, e.g., 127 domain) would maintain their structure at higher applied forces, requiring extreme forces to unfold them.
Most proteins show a high degree of connectivity and as a result their unfolding seems to be highly cooperative with the stability of secondary structures depending on their tertiary context and often presenting no intermediates. Still, owing to the local action of the applied force, their mechanical stability tends to be related to highly localized molecular structures near the mechanical "breakpoint" rather than to the global structure. For instance, the mechanical stability of titin 127 has been found to depend exclusively on a specific, highly localized clamp of six backbone hydrogen bonds, the A'G patch (reviewed by Carrion-Vazquez et al. 2000), and the associated side-chain packing (i.e., hydrophobic) interactions between the A' and G strands, tte hydrophobic core of this structure plays no role in resisting force (Best et al. 2003b). As we have seen (Sect. 8.4.2, Table 8.1) and as predicted by simulations (Lu and Schulten 1999), ^-strand proteins tend to unfold at higher unfolding forces and to be brittler than a-helical ones. Furthermore, ^-strand proteins with a shear mechanical topology are mechanically more stable than zipper ^-strand proteins, ttis seems to derive from two effects: the higher energy barrier necessary for breaking many bonds in parallel (vs. breaking individual bonds in series) and the greater stiffness of this link (compared with the stiffness of a single bond or several bonds in series). As a result, the distance to the transition state is shorter owing to a deep well in the potential energy (Bustamante et al. 2004).
In contrast to the findings on the 127 domain, recent experiments combining SMFS, molecular dynamics simulations, and $-value analysis have revealed that the barrier to mechanical unfolding in the TNfnIII-3 domain involves only a few hydrogen bonds but significant side-chain packing (i.e., hydrophobic) interactions of the amino acid residues from both the peripheral ^-strands and the core (Ng et al. 2005). ttus, while it remains to be explored whether other fnlll domains share this mechanism, it seems clear now that the highly localized hydrogen-bonding and associated packing interactions (as found in 127) may not be the dominant determinant of mechanical stability for other groups of protein structures.
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