Reconstructing Folding Energy Landscapes by Single-Molecule Force Spectroscopy

Woodside, Michael T.; Block, Steven M.

doi:10.1146/annurev-biophys-051013-022754

Cited by 208 publications

(197 citation statements)

References 120 publications

(187 reference statements)

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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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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 field has advanced, thanks to the development of instrumentation and the methods to analyse and interpret the data [245][246][247]. SMFS is now embedded within the scientific community and is being exploited to probe a diverse range of biological systems, including proteins, DNA, RNA and their complexes [67,81,85,157,[248][249][250][251][252].…”

Section: Discussionmentioning

confidence: 99%

The physics of pulling polyproteins: a review of single molecule force spectroscopy using the AFM to study protein unfolding

2016

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One of the most exciting developments in the field of biological physics in recent years is the ability to manipulate single molecules and probe their properties and function. Since its emergence over two decades ago, single molecule force spectroscopy has become a powerful tool to explore the response of biological molecules, including proteins, DNA, RNA and their complexes, to the application of an applied force. The force versus extension response of molecules can provide valuable insight into its mechanical stability, as well as details of the underlying energy landscape. In this review we will introduce the technique of single molecule force spectroscopy using the atomic force microscope (AFM), with particular focus on its application to study proteins. We will review the models which have been developed and employed to extract information from single molecule force spectroscopy experiments. Finally, we will end with a discussion of future directions in this field.

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“…A mixed simulation scheme was used, treating x 1 in pure Brownian fashion but evolving x 2 according to Langevin dynamics with explicit inertial terms using a modified Verlet-style algorithm (36). The density of the bead was ρ = 1.05 g/cm 3 (as for polystyrene). The system was initially thermalized in a harmonic well matching the folded or unfolded well, and tested for correct energy equipartition and velocity autocorrelation decay.…”

Section: Methodsmentioning

confidence: 99%

Reconstructing folding energy landscapes from splitting probability analysis of single-molecule trajectories

Manuel

Lambert

Woodside

2015

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

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Structural self-assembly in biopolymers, such as proteins and nucleic acids, involves a diffusive search for the minimumenergy state in a conformational free-energy landscape. The likelihood of folding proceeding to completion, as a function of the reaction coordinate used to monitor the transition, can be described by the splitting probability, p fold (x). P fold encodes information about the underlying energy landscape, and it is often used to judge the quality of the reaction coordinate. Here, we show how p fold can be used to reconstruct energy landscapes from single-molecule folding trajectories, using force spectroscopy measurements of single DNA hairpins. Calculating p fold (x) directly from trajectories of the molecular extension measured for hairpins fluctuating in equilibrium between folded and unfolded states, we inverted the result expected from diffusion over a 1D energy landscape to obtain the implied landscape profile. The results agreed well with the landscapes reconstructed by established methods, but, remarkably, without the need to deconvolve instrumental effects on the landscape, such as tether compliance. The same approach was also applied to hairpins with multistate folding pathways. The relative insensitivity of the method to the instrumental compliance was confirmed by simulations of folding measured with different tether stiffnesses. This work confirms that the molecular extension is a good reaction coordinate for these measurements, and validates a powerful yet simple method for reconstructing landscapes from single-molecule trajectories.single-molecule biophysics | force spectroscopy | nucleic acid folding | protein folding | optical tweezers S tructure formation by biological polymers like proteins and nucleic acids, an essential process linked to biological function, is typically described by energy landscape theory, in which folding is viewed as a diffusive search through the conformational space of the molecule for the minimum-energy structure (1, 2). This search takes place on an energy landscape, with the surface describing the energy of the molecule as a function of all possible conformations. Because of the many conformational degrees of freedom in even a small biopolymer, folding landscapes are inherently multidimensional, forming a hypersurface. Experimental measurements, however, typically follow some observable that is used to monitor the progress of the reaction. As a result, the full energy hypersurface is projected onto a 1D profile along the chosen reaction coordinate. There is great interest in measuring such energy landscape profiles directly, because they provide a fundamental basis for understanding folding phenomena.Recent advances in single-molecule approaches have provided powerful tools for measuring landscapes. Most notably, 1D landscape profiles can be reconstructed in several ways from force spectroscopy measurements, wherein tension is applied to a molecule and the resulting changes in the molecular extension, the reaction coordinate, are measured (3). Lands...

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Reconstructing Folding Energy Landscapes by Single-Molecule Force Spectroscopy

Cited by 208 publications

References 120 publications

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

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

The physics of pulling polyproteins: a review of single molecule force spectroscopy using the AFM to study protein unfolding

Reconstructing folding energy landscapes from splitting probability analysis of single-molecule trajectories

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