Dependence ofthe Force Fu on the Loading Rate r

tte force at which an unfolding event occurs depends on the loading rate used during extension of the protein:

where v is the pulling speed. As we have seen, different pulling speeds simply reflect different time windows during which the mechanical force is acting (i.e., time exposure), ttus, in forced unfolding experiments a protein domain unfolds driven by two competing forces: thermal and mechanical. Since the former has less time to act at high pulling speeds, the unfolding force and hence the mechanical stability depend on the rate of extension, tte faster the pulling speed, the higher the force required to cause the unfolding of the domain, tte speed-dependence of a typical protein system can be seen in Fig. 8.6b (i.e,. titin 127 domain; Sect. 8.4.1).

tte range of pulling speeds of a typical AFM is limited to 3 orders of magnitude, between approximately 0.01 and 10 nm ms_1 (Fig. 8.1d). tte lower limit of the pulling speed is due to the large mechanical loop of a standard AFM apparatus, which makes thermal drift the limiting factor. At very high pulling speeds the viscous drag of the solvent and the cantilever response are the factors that introduce errors. Nevertheless, as we will see in Sect. 8.6.1 the use of a short, low-noise cantilever can reduce this effect (Viani et al. 1999).

In cases where the physiological range of speeds are lower that the AFM ones (Fig. 8.1d), can we extrapolate the behavior of the system to the lower range? Put in other words, is this dependence linear? Recent data from both the direct measurement of intermolecular interactions using the biomembrane force probe (Sect. 8.6.2; Merkel et al. 1999) and the analysis of protein mutations on a titin Ig domain using the AFM (Sect. 8.4.1; Williams et al. 2003) suggest that this may not be the case.

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