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Measurement of work in single-molecule pulling experiments
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10.1063/1.3155084
/content/aip/journal/jcp/130/23/10.1063/1.3155084
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/23/10.1063/1.3155084

Figures

Image of FIG. 1.
FIG. 1.

Schematic definition of the model under study. The pipette is at rest with respect to the thermal bath, while the trap is moving with velocity . The trap and the system are approximated by two harmonic potentials with stiffness and , respectively. The rest length of the trap spring is 0, while the rest length of the molecule spring is if the hairpin is closed and if it is open .

Image of FIG. 2.
FIG. 2.

(a) A typical FDC obtained by numerical simulation of Eq. (9). The shaded area is equivalent to the accumulated work [see Eq. (11)]. (b) The FEC associated to the pulling experiment represented in (a). The shaded area is equivalent to the transferred work [see Eq. (12)].

Image of FIG. 3.
FIG. 3.

Dependence on the sample size of the mode of (i.e., the maximum of the distribution for , see Appendix B). The dimensionless variable is , where and are the mean and standard deviations of the normally distributed transferred work . The represented curve is the numerical solution to Eq. (B9).

Image of FIG. 4.
FIG. 4.

Numerical test of Eq. (25). The theoretical prediction is compared to the results of numerical simulations of Eq. (9). In abscissa, is the standard deviation of the transferred work values ; different values of are obtained by varying the filter applied to the data. In ordinate, we represent the error (due to the erroneous use of in the Jarzynski estimator) (in units) on the determination of the free energy of formation of the hairpin. Each point represents the result of the analysis of trajectories.

Image of FIG. 5.
FIG. 5.

Experimental test of Eq. (25). In abscissa, is the standard deviation of the transferred work values ; different values of are obtained by varying the stiffness of the trap and the bandwidth. In ordinate, we represent the error (due to the erroneous use of in the Jarzynski estimator) on the determination of the hairpin energy levels. See Table I for further details about the data.

Image of FIG. 6.
FIG. 6.

(a) An experimental FDC observed with a high-frequency (20 kHz) and a low-frequency (1 kHz) data acquisition system. The area under the curve, which is a measure of the accumulated work , practically does not change. (b) The FEC associated to the pulling experiment represented in (a). The area under the curve, which represents the transferred work , depends on the frequency of the data acquisition system because of the large fluctuations of the integration extrema. Insets: magnified views of the region around the maximum of the force.

Image of FIG. 7.
FIG. 7.

Graph of using high- and low-frequency data, accumulated and transferred work. Data have been shifted along the horizontal axis to be easily compared. Data for the accumulated work (circles and squares) fall into a (bandwidth-independent) straight line of slope 1.00(8) in quantitative agreement with the prediction by the fluctuation relation Eq. (26). However data for the transferred work (triangles and rhombs) exhibit bandwidth-dependent very small slopes (around 0.03) that exclude the validity of an equivalent relation to Eq. (26) for the transferred work.

Image of FIG. 8.
FIG. 8.

Comparison between the histogram of the transferred work in one of the experiments reported in Table I and the normal distribution that better approximates it.

Image of FIG. 9.
FIG. 9.

Comparison between the histogram of the accumulated work in one of the experiments reported in Table I and the Gumbel distribution that better approximates it.

Tables

Generic image for table
Table I.

Experimental results: Comparison between the experimental (also shown in Fig. 5) and the theoretical [based on Eq. (25)] values of . The data sets labeled “1 kHz” and “20 kHz” refer to the same experiment, with the standard (low-frequency) and the new (high-frequency) data acquisition system. The stiffness of the trap is measured in , while is the number of trajectories.

Generic image for table
Table II.

Experimental results. The data sets labeled “1 kHz” and “20 kHz” refer to the same experiment, with the standard (low-frequency) and the new (high-frequency) data acquisition system. The data sets labeled “ave ” are obtained from 20 kHz data by averaging over points.

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/content/aip/journal/jcp/130/23/10.1063/1.3155084
2009-06-19
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Measurement of work in single-molecule pulling experiments
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/23/10.1063/1.3155084
10.1063/1.3155084
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