One of the model systems most commonly used to study mechanical unfolding/ refolding is the 127 module from titin, a gigantic multimodular protein responsible for the so-called passive elasticity of muscle (Sect. 8.4.4, Figs. 8.2c, 8.8a, reviewed by Tskhovrebova and Trinick 2003). tte 127 module from human cardiac titin is an Ig domain from the elastic (I-band) region of the protein that was originally chosen for several reasons. Its tertiary structure was known (Fig. 8.8b), its stretching had been simulated by molecular dynamics, and it was found to be thermodynamically very stable (Table 8.1; Carrion-Vazquez et al. 1999a and references therein), ttis module, 89 amino acids long, is a ^-sandwich fold composed of seven ^-strands (AA', B, C, D, E, F, and G) that folds into two face-to-face ^-sheets through backbone hydrogen bonding and hydrophobic core interactions (Improta et al. 1996). With the exception of the parallel pair A'G, all adjacent ^-strands are antiparallel (Fig. 8.10a, left).
Simulations of 127 stretching by molecular dynamics identified its force-bearing structural components as the ^-strands A and G (proximal to the N- and C-termini of the domain, respectively), which are connected to ^-strands B and A', respectively, through two patches of backbone hydrogen bonds (Figs. 8.9, 8.10a, left; Lu et al. 1998; Klimov and ttirumalai 2000; Lu and Schulten 2000; Paci and Karplus 2000; Li and Makarov 2003). ttese two patches of hydrogen bonds are true "structural" barriers with a different mechanical resistance: a low force barrier located between P-strands A and B, which involves two hydrogen bonds between the ^-strands (outside the ^-strands there is an additional, weaker hydrogen bond), and a high-force one between ^-strands A' and G involving six hydrogen bonds. Both patches of hydrogen bonds are perpendicular to the direction of the force vector (a "shear" mechanical topology; Figs. 8.9, 8.10a, left), tte remaining hydrogen bonds in the structure are parallel to the force vector (a "zipper" mechanical topology; Figs. 8.9, 8.10a, right) and like the hydrophobic core offer low resistance to extension.
tte predictions of this model were found to be remarkably consistent with the experimental data from SMFS using polyproteins. In the length-clamp mode they revealed a series of force peaks of approximately 200 pN (at 0.6 nm ms_1), each one corresponding to the unfolding of a domain. When the overall process was modeled by the WLC equation of polymer elasticity (as a series of polymer stretching events), a stepwise increase of the polymer length (A Lc) of 28.1 nm was found, which corresponds to the length of the force-hidden region located after the A'G patch, tte hypothetical role of the A'G patch as a mechanical clamp was tested by loop insertion (Fig. 8.5d) and proline mutagenesis (Carrion-Vazquez et al. 1999b; Li et al. 2000a). In the force-clamp mode the extension-time curve revealed approximately 22-nm steps (at a constant force of 180 pN; Fig. 8.3c), corresponding to the expected increase in length due to the unfolding of a single domain. It should be noted that the 28.1-nm increase in contour length calculated from the length-clamp mode using the WLC model corresponds to the length of an unfolded module stretched at infinitely high force. At lower forces partial coiling of the amino acid chain, spontaneously driven by polymer entropic elasticity, would reduce this length (Oberhauser et al. 2001).
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Fig. 8.9. Mechanical architecture of the I27 module. Schematic representation of an I27 poly-protein.Zipper bonds in the structure are represented by dashedgreylines and shear patches (AB, A'G) by solid green lines, a Force spectrum measured by AFM (from Fisher et al. 2000). b Force spectrum predicted by steered molecular dynamics (SMD) simulations. The main stability determinants of this module are a minor mechanical barrier (A-B patch of hydrogen bonds in the polypeptide backbone) and a major one (A'G patch of hydrogen bonds in the backbone). The major resistance barrier corresponds to the force peaks in the force-exten-
tte stretching of 127 polyproteins also confirmed another prediction, of a higher resolution, made by the simulations: the existence of a weaker mechanical barrier at the AB patch, ttus, the corresponding force-extension recordings revealed a fine mechanical detail consisting of a small deviation from the pure entropic behavior described by the WLC model, which appeared as a "hump" of decreasing intensity on each of the saw teeth (Fig. 8.9). Ms deviation was interpreted as evidence for the existence of an unfolding intermediate involving the rupture of the AB patch, ttese humps are found at lower force than the unfolding peaks (approximately 100 pN, at 0.3-0.5 nm ms_1) and extend each module by approximately 7 A. Each hump represents the simultaneous rupture of the hydrogen bonds from the AB patches of all the modules that remain folded in the polyprotein stretch that has been trapped in the experiment, tte deviation is more evident in the first peak, it decreases progressively with module unfolding, and it completely disappears when all the modules of the trapped fragment have been unraveled. Hence, it appears that once a module unfolds and relaxes the force on the system, the remaining domains of the polyprotein fragment quickly refold their AB patches into their native conformation, tte existence of this unfolding intermediate in the wild-type 127 module was later confirmed by stretching mutant proteins (Marszalek et al. 1999b; Fowler et al. 2002). Moreover, it was suggested that it may play a role in the elasticity of titin beyond the normal physiological range of extensions (i.e., at high forces; Sect. 8.4.4)
In spite of the potential pitfalls of these computer simulations, they have provided a wealth of data that have deepened our understanding of how proteins respond to a mechanical force, ttus, simulations rightly predicted the experimental behavior of the 127 domain under a mechanical force. Considering, as we have seen, that simulations are often performed at pulling speeds many orders of magnitude faster than those used in experiments, in principle it is not clear that they should rightly reproduce the true process. However, the close agreement between the experiments
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