Experimental test of ensemble inequivalence and the fluctuation theorem in the force ensemble in DNA pulling experiments

Abstract

We experimentally test the validity of the Crooks fluctuation theorem (CFT) in the force ensemble by pulling DNA hairpins, first with magnetic tweezers, next with optical tweezers using force feedback. The CFT holds when using the definition of work W f = − xdf , where x is the molecular extension and f is the force. In contrast, it does not hold when using the usual definition, appropriate for the constant extension ensemble, W x = f dx, showing the importance of the contribution of boundary terms to the full entropy production in a clear example of statistical ensemble inequivalence in small systems. We also evaluate the differences in the average dissipated work in the force ensemble as compared to the extension ensemble, highlighting ensemble inequivalence also at the level of molecular kinetics.

DNA polymerase Gp90 activities and regulations on strand displacement DNA synthesis revealed at single‐molecule level

“…To study the effects of GC content on SDDS by gp90 exo ‐ , we employed 50%‐GC hairpins. The unzipping force of 50%‐GC hairpin is 14.7 ± 1.6 pN (mean ± SD, N = 184) (Figure S1I,J), which is a little higher than that of 11%‐GC hairpin and is consistent with other studies 24,41,42 . Interestingly, the 50%‐GC DNA hairpin is repeatable in stretching cycles in the presence of 100 or 500 μM dNTPs, and neither SDDS nor PE occurs on DNA hairpins (Figure 2H, Figure S1K,L).…”

“…The unzipping force of 50%-GC hairpin is 14.7 ± 1.6 pN (mean ± SD, N = 184) (Figure S1I,J), which is a little higher than that of 11%-GC hairpin and is consistent with other studies. 24,41,42 Interestingly, the 50%-GC DNA hairpin is repeatable in stretching cycles in the presence of 100 or 500 μM dNTPs, and neither SDDS nor PE occurs on DNA hairpins (Figure 2H, Figure S1K,L). The unzipping force of 50%-GC DNA hairpin in the presence of gp90 exoand dNTPs is 18.5 ± 3.7 pN (mean ± SD, N = 32) at 100 μM and 19.7 ± 3.5 pN (mean ± SD, N = 55) at 500 μM dNTPs (Figure S1J), both of which are significantly higher than that of 50%-GC hairpin alone, indicating that gp90 exobinds to the DNA hairpin and enhances its stability.…”

Jarzynski on work and free energy relations: The case of variable volume

“…As numerous experiments have nevertheless verified the JE, 23,24,27 further analysis seems to be necessary. Below we consider a simple, but paradigmatic example, in which the JE as developed above does not seem to hold.…”

“…Improving our understanding of these facts may help better define the range of applicability of the JE, and to interpret experiments 18,23,24 . Therefore, in this paper, we discuss some of the issues raised by the JE formalism, investigating the simple, but also paradigmatic example of an object with a variable volume.…”

Dependence of Work on the Pulling Speed in Mechanical Ligand Unbinding

“…The dependence of the average dissipated work on the displacement in the DNA hairpin pulling experiment was obtained numerically, but the analytical formula was missing. 17 This prompted us to develop a theory by exactly solving a one-dimensional problem, which shows that at sufficiently low pulling speeds, the dependence of W on V is determined using the quadratic function of ln( V ). We also performed all-atom simulations of protein–ligand complexes in explicit water, which confirmed our theory.…”