Reconstructing Folding Energy Landscape Profiles from Nonequilibrium Pulling Curves with an Inverse Weierstrass Integral Transform

Engel, Megan Clare; Ritchie, Dustin B.; Foster, Daniel A. N.; Beach, K. S. D.; Woodside, Michael T.

doi:10.1103/physrevlett.113.238104

Cited by 35 publications

(31 citation statements)

References 41 publications

(77 reference statements)

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“…The 20-30% error predicted by the theory matches well with the error found empirically in previous work by Chang et al (14). Large bead-size or linker-stiffness increases may lead to larger artifacts, however, as noted previously (15)(16)(17)(18); this is unfortunate because stiff linkers in particular allow for easier reconstruction of free-energy profiles (10,11,24,25). Optimizing assay design for one purpose (e.g., landscape reconstruction) may thus degrade its suitability for others (e.g., measuring kinetic properties).…”

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confidence: 84%

Quantifying Instrumental Artifacts in Folding Kinetics Measured by Single-Molecule Force Spectroscopy

Neupane

Woodside

2016

Biophysical Journal

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Force spectroscopy is commonly used to measure the kinetics of processes occurring in single biological molecules. These measurements involve attaching the molecule of interest to micron-sized or larger force probes via compliant linkers. Recent theoretical work has described how the properties of the probes and linkers can alter the observed kinetics from the intrinsic behavior of the molecule in isolation. We applied this theory to estimate the errors in measurements of folding made using optical tweezers. Errors in the folding rates arising from instrument artifacts were only ∼20% for constant-force measurements of DNA hairpins with typical choices of linker length and probe size. Measurements of transition paths using a constant trap position at high trap stiffness were also found to be in the low-artifact limit. These results indicate that typical optical trap measurements of kinetics reflect the dynamics of the molecule fairly well, and suggest practical limitations on experimental design to ensure reliable kinetic measurements.

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confidence: 84%

Quantifying Instrumental Artifacts in Folding Kinetics Measured by Single-Molecule Force Spectroscopy

Neupane

Woodside

2016

Biophysical Journal

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“…In this regime, as done by Woodside and coworkers (33,37), it is valid to determine the molecular diffusion coefficient D x by equating the observed rate with the Kramers rate on the deconvolved free energy profile, G M ðxÞ. This procedure is very sensitive to how accurately the molecular barrier height can be estimated.…”

Section: Resultsmentioning

confidence: 99%

On artifacts in single-molecule force spectroscopy

Cossio

Hummer

Szabó

2015

Proc. Natl. Acad. Sci. U.S.A.

102

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In typical force spectroscopy experiments, a small biomolecule is attached to a soft polymer linker that is pulled with a relatively large bead or cantilever. At constant force, the total extension stochastically changes between two (or more) values, indicating that the biomolecule undergoes transitions between two (or several) conformational states. In this paper, we consider the influence of the dynamics of the linker and mesoscopic pulling device on the force-dependent rate of the conformational transition extracted from the time dependence of the total extension, and the distribution of rupture forces in force-clamp and force-ramp experiments, respectively. For these different experiments, we derive analytic expressions for the observables that account for the mechanical response and dynamics of the pulling device and linker. Possible artifacts arise when the characteristic times of the pulling device and linker become comparable to, or slower than, the lifetimes of the metastable conformational states, and when the highly anharmonic regime of stretched linkers is probed at high forces. We also revisit the problem of relating force-clamp and force-ramp experiments, and identify a linker and loading ratedependent correction to the rates extracted from the latter. The theory provides a framework for both the design and the quantitative analysis of force spectroscopy experiments by highlighting, and correcting for, factors that complicate their interpretation.anisotropic diffusion | free energy surface | pulling device | unfolding rate T he mechanical manipulation of single molecules by laser tweezers or atomic force microscopes has led to remarkable insights into how biomolecules respond to external forces. In conceptually the simplest experiment, a single molecule is connected by a flexible polymer linker to a bead, say a micrometer in diameter, that is trapped in the focus of a laser beam. The position of this beam is adjusted so that the force on the construct is kept constant (see Fig. 1A). Suppose the molecule of interest can exist in folded and unfolded states, and that the applied force is chosen so that the populations of these states are about equal. Then the total extension hops between short (i.e., folded) and long (i.e., unfolded) values (see Fig. 1B). From such trajectories, one can extract the folding and unfolding rates. These observables are commonly analyzed using the phenomenological BellEvans model (1, 2), which ignores the possible influence of the "apparatus" that we define here as both the linker and the bead. The same is true of the simplest microscopic descriptions of force-induced transitions, where the dynamics is described as diffusion along the molecular (not total) extension, in the presence of a force-dependent free energy profile (3-7). However, such a description would be rigorously valid only when the response of the apparatus is much faster than the fluctuations of the molecular extension. In reality, this is far from being true, and, in principle, the observed transition rate...

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“…1 and 2. The barriers were reconstructed from equilibrium trajectories of the molecular extension using a method based on the committor statistics (44); as we showed previously using DNA hairpins, this method allows barrier shapes to be determined without the need to deconvolve instrumental compliance effects (24,43,(45)(46)(47). We measured the extension at F 1/2 ( Fig.…”

Section: Resultsmentioning

confidence: 99%

Direct measurement of sequence-dependent transition path times and conformational diffusion in DNA duplex formation

Neupane

Wang

Woodside

2017

Proc. Natl. Acad. Sci. U.S.A.

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The conformational diffusion coefficient, D, sets the timescale for microscopic structural changes during folding transitions in biomolecules like nucleic acids and proteins. D encodes significant information about the folding dynamics such as the roughness of the energy landscape governing the folding and the level of internal friction in the molecule, but it is challenging to measure. The most sensitive measure of D is the time required to cross the energy barrier that dominates folding kinetics, known as the transition path time. To investigate the sequence dependence of D in DNA duplex formation, we measured individual transition paths from equilibrium folding trajectories of single DNA hairpins held under tension in high-resolution optical tweezers. Studying hairpins with the same helix length but with G:C base-pair content varying from 0 to 100%, we determined both the average time to cross the transition paths, τ tp , and the distribution of individual transit times, P TP (t). We then estimated D from both τ tp and P TP (t) from theories assuming one-dimensional diffusive motion over a harmonic barrier. τ tp decreased roughly linearly with the G:C content of the hairpin helix, being 50% longer for hairpins with only A:T base pairs than for those with only G:C base pairs. Conversely, D increased linearly with helix G:C content, roughly doubling as the G:C content increased from 0 to 100%. These results reveal that G:C base pairs form faster than A:T base pairs because of faster conformational diffusion, possibly reflecting lower torsional barriers, and demonstrate the power of transition path measurements for elucidating the microscopic determinants of folding.folding | DNA hairpins | energy landscapes | optical tweezers S tructure formation in biological macromolecules like proteins and nucleic acids is a complex, dynamic process. Physically, it is described in the context of energy landscape theory as a diffusive search in conformational space for the minimumenergy structure (1-3). The speed at which this search takes place at the microscopic level is set by the conformational diffusion coefficient, D. Because D plays a key role in determining the kinetics of the folding, as encapsulated in the well-known expression for rates derived by Kramers (4), it is one of the fundamental physical determinants of folding phenomena: it connects the thermodynamics encoded in the energy landscape to the dynamics of conformational changes. The properties of D relate to such key issues as internal friction in the polymer chain (5-8), roughness in the energy landscape (9-12), projection of the full phase-space for conformational dynamics onto experimental reaction coordinates (13), and "speed limits" for folding transitions (14).Despite its importance, D remains challenging to determine experimentally. Several studies have found D from the reconfiguration times for unfolded proteins or polypeptides (15-19), using fluorescence probes to measure interactions between specific locations on the polymer chain. However, few stu...

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Reconstructing Folding Energy Landscape Profiles from Nonequilibrium Pulling Curves with an Inverse Weierstrass Integral Transform

Cited by 35 publications

References 41 publications

Quantifying Instrumental Artifacts in Folding Kinetics Measured by Single-Molecule Force Spectroscopy

Quantifying Instrumental Artifacts in Folding Kinetics Measured by Single-Molecule Force Spectroscopy

On artifacts in single-molecule force spectroscopy

Direct measurement of sequence-dependent transition path times and conformational diffusion in DNA duplex formation

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