Pulling experiment

Hummer, G. Szabo, A., Free energy reconstruction from nonequilibrium singlemolecule pulling experiments, Proc. Natl Acad. Sci. USA 2001, 98, 3658-3661... 

The above derivation shows that Jarzynski s identity is an immediate consequence of the Feynman-Kac theorem. This connection has not only theoretical value, but is also useful in practice. First, it forms the basis for an equilibrium thermodynamic analysis of nonequilibrium pulling experiments [3, 15]. Second, it helps in deriving a Jarzynski identity for dynamics using thermostats. Moreover, this derivation clarifies an important aspect trajectories can be thought of as mapping initial conditions (I = 0) to trajectory endpoints, and the Boltzmann factor of the accumulated work reweights that map to give the desired Boltzmann distribution. Finally, it can be easily extended to transformations between steady states [17] in which non-Boltzmann distributions are stationary. 

With Jarzynski s identity in the form of (8.46), we can apply to it the skewed momenta method simply by setting A[r(f)] = exp(— /3Wt). However, we anticipate that the method will be most useful in the particular case of calculating free energy profiles from pulling experiments, for which Hummer and Szabo have provided a modified form of Jarzynski s expression [106]. 

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). 

Fig.13 Schematic view of a typical setup of single molecule pulling experiments and an illustration of the generic free energy potential G(z) [87]. The x-position denominates the cantilever and the z-position denominates the cantilever tip to which one end of DNA molecule is attached. Reprinted with permission...

Hummer G, Szabo A. Kinetics from nonequilibrium single-molecule pulling experiments. Biophys J 2003 85 5-15. 

In this section we analyze in detail two cases where analytical calculations are available and FTs have been experimentally tested one extracted from physics, the other from biology. We first analyze the bead in a trap and later consider single molecule pulling experiments. These examples show that there are lots of interesting observations that can be made by comparing theory and nonequilibrium experiments in simple systems. 

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.)...

Fig. 10.13 Melting of low density polyethylene (LDPE) (Equistar NA 204-000) in a starve-fed, fully intermeshing, counterrotating Leistritz LMS 30.34 at 200 rpm and 10 kg/h. (a) The screw element sequence used (h) schematic representation of the melting mechanism involving pellet compressive deformation in the calender gap (c) the carcass from screw-pulling experiments. [Reprinted by permission from S. Lim and J. L. White, Flow Mechanisms, Material Distribution and Phase Morphology Development in Modular Intermeshing counterrotating TSE, Int. Polym. Process., 9, 33 (1994).]...

Two push-pull experiments consisted of pumping water from B-5 into B-3 followed by recovery of the injected water. The pH of the injected water was adjusted between 5.1 and 6.4 through the addition of HCL Recovery and field-testing of water from B-3 indicated minimal or no removal of arsenic. The results are consistent with the laboratory experiments, which indicated that the basalt has limited capacity for arsenic adsorption. A similar experiment consisted of adding of FeClj to inaease the adsorption capacity of the aquifer and to deaease the pH. Arsenic concentrations were significantly lower in the recovered water. 

The second push-pull experiment pushed about 610 L from well B-5 at a rate of about 8.3 L/min into well B-3 with the addition of about 55 g of Fe in the form FeCls. After about one hour, well B-3 was pumped until more than twice the injected volume was recovered. The low pH in the water during the beginning of the recovery period was caused by precipitation of iron oxide, as described by the reaction Fe + 2 H O = FeOOH + 3H. Field colorimetric analysis of arsenic indicated that arsenic was removed... 

Figure 5. Arsenic removal during push-pull experiment. Pumping rate was 2.5 L/min for the first 130 L and 7.2 L/min therectfter.

Dudko, O. K., Hummer, G., and Szabo, A. 2006. Intrinsic rates and activation free energies from single-molecule pulling experiments, Phys Rev Lett 96,108101. 

Eom, K., Makarov, D. E., and Rodin, G. J. 2005. Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single-molecule pulling experiments, Phys Rev E Stat Nonlin Soft Matter Phys 71,021904. 

Basic model of solute diffusion in Y123 crystal pulling experiments... 

This is the nonequilibrium work theorem, which remains valid no matter how gently or violently we force the piston in changing the volume from to Vg. This result has been derived using various theoretical approaches (Crooks, 1998, 1999 Hummer and Szabo, 2001 Jarzynski, 1997a,b) and confirmed by the Berkeley RNA-pulling experiment discussed above (Liphardt et al., 2002). 

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