Force-extension

The SMD simulations were based on an NMR structure of the Ig domain 127 of the cardiac titin I-band (Improta et ah, 1996). The Ig domains consist of two /9-sheets packed against each other, with each sheet containing four strands, as shown in Fig. 8b. After 127 was solvated and equilibrated, SMD simulations were carried out by fixing one terminus of the domain and applying a force to the other in the direction from the fixed terminus to the other terminus. Simulations were performed as described by Eq. (1) with V = 0.5 A/ps and if = 10 ksT/A 414 pN/A. The force-extension profile from the SMD trajectory showed a single force peak as presented in Fig. 8a. This feature agrees well with the sawtooth-shaped force profile exhibited in AFM experiments. 

FIGURE 9.18 Elastic properties of cross-linked recombinant resilin. (a) A single force-extension curve recorded for a sample of cross-linked recombinant resilin (approach curve solid, retract curve dotted). 

FIGURE 21.3 Concept of nanofishing, (a) Schematic drawing and (b) force-extension (stress-strain) curve. 

In addition to the use of cyclohexane, dimethylformamide (DMF) was used as a good solvent. So as to pick up the thiol-modified terminal, gold-coated cantilevers were used. The nominal values of their spring constant ki were 30 or 110 pN nm . A typical force-extension curve measured in cyclohexane is shown in Figure 21.4. The solvent temperature was kept at about 35°C, which corresponded to its temperature for PS chains. Thus, a chain should behave as an ideal chain. The slope at the lowest extension limit (dashed line in Figure 21.4) was 1.20 X lO" N m . ... 

In a poor solvent (cyclohexane at 5°C), a polymer chain takes on a condensed globular state because constituent molecules are repulsed by the solvent molecules. Nanofishing of this chain revealed a perfectly different force-extension curve, as shown in Figure 21.5. It was observed that constant force continued from about 30 to 130 nm after nonspecific adsorption between a... 

Fig. 8. (a) Schematic of the AFM pulling experiments and expected unraveling of an individual nucleosome as a result of pulling on the DNA. (b) Example force-extension curves on isolated chicken erythrocyte chromatin fibers redrawn from Ref [69]. (c) Idealized schematic of a typical force-extension curve obtained on pulling single titin moleeules, as in the experiments of Rief et al. [71]. (d) Explanation of the titin force curve by successive unfolding of individual protein domains (see text). 

Earlier attempts to use the AFM for mechanically stretching chromatin fibers have run into a rather unexpected artifact. Long native chromatin fibers isolated from chicken erythrocytes, or fibers assembled in vitro from purified histones and relatively short, tandemly repeated DNA sequences were deposited on mica or glass surfaces and pulled with the AFM tip [69,70]. In such stretching experiments the scanning of the sample in the x- and y-direction used for imaging was disabled, and the cantilever-mounted tip was allowed to move only in the z-direction, i.e., upwards and downwards, away and towards the surface. When the AFM tip is pushed into the sample, it may attach to the sample by non-specific adsorption upon retraction it stretches the sample and force-extension curves are recorded (see Fig. lb for an explanation of a typical force curve). 

While structural transitions at the level of nucleosomes are still outside the scope of current models, applying a constant force to both ends of the liber allows to simulate the low end of the force-extension curve. First results from our own work (Aumann, Caudron, Wedemann, and Langowski, manuscript in preparation) are shown in Fig. 5. In this particular example, a nucleosome repeat of 200 bp and a linker DNA length of 11 bp was used. 

To measure the force-extension law of a small biomolecule, these authors employed a two-step strategy. First, the background repulsive force-distance profile, in the absence of biomolecules, Fbg(h), is measured, h being the interparticle spacing. Then, once the biocomplexes have been properly attached within each interval between colloids, the same measurement is repeated, allowing determination of the force-distance profile of this irreversible assembly The force / >(/t)... 

C. Bouchiat, M.D. Wang, J.-F. Allemand, T. Strick, S.M. Block, and V. Croquette Estimating the Persistence Length of a Worm-Like Chain Molecule from Force-Extension Measurements. Biophys. J. 76, 409 (1999). 

Figure 10.2 Single molecule force-extension curve of three different types of molecules (a) a short chain or rigid tod molecule (b) a long chain polymer with multiple domains, such as titin, where bi-b represents the unfolding of individual domains and (c) a tegular random coil long chain. Adapted from Smith et al. (1999). Copyright 1999 Nature Publishing Group.

The single chain force-extension curves for both the control polymer (9) and the modular polymer (8) are shown in Figure 10.3 (Guan et al. 2004). For control... 

Figure 10.3 AFM single chain force-extension data, (a) An overlay of representative force-extension curves for modular polymer 8. Sawtooth patterned curves were consistently obtained, (b) One representative single chain force-extension curve for control polymer 9, in which only one peak was observed, (c) A single chain force-extension curve for modular polymer 8 shows the characteristic sawtooth pattern with three peaks. In Figure 10.2b and c, all scattered dots represent experimental data and the solid lines are results from WLC fitting. Adapted from Guan et al. (2004). Copyright 2004 American Chemical Society.

Figure 10.6 (a) A molecular model for one double-closed loop (DCL) module used in the stody. (b) An AFM single molecule force-extension curve for the DCL modular... 

Figure 7. Mechanical unfolding of RNA molecules (a, b) and proteins (c, d) using optical tweezers, (a) Experimental setup in RNA pulling experiments, (b) Pulling cycles in the homologous hairpin and force rip distributions during the unfolding and refolding at three pulling speeds. (C) Equivalent setup in proteins, (d) Force extension curve when pulUng the protein RNAseH. Panel (b) is from Ref. 86. Panels (a) and (d) are a courtesy from C. Cecconi [84]. (See color insert.)...

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