Measuring the Folding Landscape of a Harmonically Constrained Biopolymer

Abstract

Pioneering studies have shown that the probability distribution of opening length for a DNA hairpin, recorded under constant force using an optical trap, can be used to reconstruct the energy landscape of the transition. However, measurements made under constant force are subject to some limitations. Under constant force a system with a sufficiently high energy barrier spends most of its time in the closed or open conformation, with relatively few statistics collected in the transition state region. We describe a measurement scheme in which the system is driven progressively through the transition by an optical trap and an algorithm is used to extract the energy landscape of the transition from the fluctuations recorded during this process. We illustrate this technique in simulations and demonstrate its effectiveness in experiments on a DNA hairpin. We find that the combination of this technique with the use of short DNA handles facilitates a high-resolution measurement of the hairpin's folding landscape with a very short measurement time.

Nonlinear irreversible thermodynamics of single-molecule experiments

“…Many mesoscopic systems of great interest ranging from biology, such as proteins, RNA or DNA molecules [1][2][3][4][5][6][7][8][9][10], to nano-engeneering, like rotaxanes and catenanes [11][12][13], have similar dynamic behaviors due to their intrinsic properties and structure, as well as to their strong coupling with the surroundings. In particular, when they are subject to stressing conditions, like stretching forces or radiative interaction, the dynamics of these systems may present critical oscillations and stochastic resonance phenomena.…”

“…In order to highlight the ideas and simplify the presentation, we apply our formalism to analyze single RNA macromolecule stretching experiments which provide information on its energy landscape [2][3][4][5][6][7][8][9]16]. Specifically, the existence of a loop in the force-extension curve (FEC) implies that there is a range of tensions for which two stable configurations of the system are possible.…”

Optimal reconstruction of the folding landscape using differential energy surface analysis

“…By determining the distance between the micro-sphere and the sample chamber boundary and subtracting off the instantaneous extension of the double-stranded DNA handles (estimated using a worm-like chain model of DNA elasticity) the extension of the hairpin itself is determined [16]. The apparatus and experimental procedure has been described elsewhere [8]. and for folding of the hairpin in Fig.…”

“…By selecting an appropriate value of α and varying x 0 , the system can be forced to visit various regions of the reaction coordinate, allowing more uniform convergence of statistics. This technique, often referred to as umbrella sampling [6], is widely used in simulations [7], and has been applied to single molecule experiments [8].…”

The molecular yo-yo method: Live jump detection improves throughput of single-molecule force spectroscopy for out-of-equilibrium transitions

“…Single-molecule force spectroscopy (SMFS), in particular, has proven a powerful method by which to study the mechanochemistry of molecular motors, including kinesins [1][2][3] , myosins [4][5][6] , polymerases [7][8][9][10][11] , helicases [12][13][14] , chromatin remodellers [15][16][17] , and the ribosome 18,19 . SMFS has also transformed our understanding of nucleic acid [20][21][22][23] and protein folding [24][25][26][27][28][29][30][31][32][33] , and biological assembly processes, such as chromatin compaction [34][35][36][37][38][39][40][41][42][43][44][45][46] . In all of these cases, the key questions are: What microscopic states are populated at a given force?…”