Can energy landscape roughness of proteins and RNA be measured by using mechanical unfolding experiments?

Hyeon, Changbong; Thirumalai, D.

doi:10.1073/pnas.1833310100

Cited by 160 publications

(144 citation statements)

References 21 publications

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“…Nonnative attractions are expected to affect the roughness of the energy landscape (53)(54)(55)(56). To explore the effects of nonnative attractive interactions on the folding dynamics, we add recently published amino acid pair potentials developed for proteinprotein interactions (57) on top of the original Gō-like model for native interactions (see SI Text).…”

Section: Resultsmentioning

confidence: 99%

Coordinate-dependent diffusion in protein folding

Best

Hummer

2009

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

276

312

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Diffusion on a low-dimensional free-energy surface is a remarkably successful model for the folding dynamics of small single-domain proteins. Complicating the interpretation of both simulations and experiments is the expectation that the effective diffusion coefficient D will in general depend on the position along the folding coordinate, and this dependence may vary for different coordinates. Here we explore the position dependence of D, its connection to protein internal friction, and the consequences for the interpretation of single-molecule experiments. We find a large decrease in D from unfolded to folded, for reaction coordinates that directly measure fluctuations in Cartesian configuration space, including those probed in single-molecule experiments. In contrast, D is almost independent of Q, the fraction of native amino acid contacts: Near the folded state, small fluctuations in position cause large fluctuations in Q, and vice versa for the unfolded state. In general, position-dependent free energies and diffusion coefficients for any two good reaction coordinates that separate reactant, product, and transition states, are related by a simple transformation, as we demonstrate. With this transformation, we obtain reaction coordinates with position-invariant D. The corresponding free-energy surfaces allow us to justify the assumptions used in estimating the speed limit for protein folding from experimental measurements of the reconfiguration time in the unfolded state, and also reveal intermediates hidden in the original free-energy projection. Lastly, we comment on the design of future single-molecule experiments that probe the position dependence of D directly.O ne of the remarkable consequences of the energy landscape theory of protein folding is that folding can be effectively modeled as diffusion along a one-dimensional reaction coordinate (1-5). In such a diffusion model, the rate of folding is determined by the height of the free-energy barrier and a kinetic prefactor that depends on the diffusion coefficient along the reaction coordinate. For proteins with high free-energy barriers separating the folded and unfolded states, only the diffusion coefficient at the barrier top contributes to the rate. For ultrafast folding proteins, where the barrier heights can be quite small or vanish completely, the diffusion coefficient along the entire reaction coordinate contributes to the rate (6-11). The prefactor therefore also approximates the "speed limit" for protein folding, analogous to the diffusion-limited rate for bimolecular reactions (7,8,12,13). A number of groups have investigated the prefactor experimentally by varying solvent viscosity (14-18). However, viscogens tend to affect the rate not only by increasing the solvent friction, but also by changing the free-energy barrier height and curvature, requiring measurements at viscogen concentrations that alter neither the stability nor the viscosity-corrected activation energy (11,19).A more direct method of obtaining diffusion coefficients for foldi...

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Section: Resultsmentioning

confidence: 99%

Coordinate-dependent diffusion in protein folding

Best

Hummer

2009

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

276

312

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“…This value contrasts with the much higher value ‡ ϭ 4 ϫ 10 9 s Ϫ1 that we obtained in the mechanical experiments. The lower values obtained in classical biochemistry assays have often been explained in terms of Kramers' theory (58 -60), which relates the rate at which the protein diffuses to the transition state (52,(61)(62)(63) under high friction conditions. Both the TST and the Kramers' formalisms share the Arrhenius exponential term.…”

Section: Discussionmentioning

confidence: 99%

Direct Quantification of the Attempt Frequency Determining the Mechanical Unfolding of Ubiquitin Protein

Popa

Fernández

Garcia-Manyes

2011

Journal of Biological Chemistry

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Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. A deep understanding of protein dynamics relies on the accurate determination of the free energy surface that governs the (un)folding reaction. In the case of small proteins, the (un)folding process is generally described by a two-state scenario, whereby the native and unfolded states are separated by a prominent energy barrier (1). The conversion between these two states has been traditionally given the treatment of a firstorder chemical reaction, where the concentration of the reactant species, the native state of the protein, decreases exponentially with time (2). Such a simplified kinetic analysis provides the framework to study the (un)folding reaction in terms of the Eyring transition state theory (TST), 3 which allows quantification of the rate constant for a given chemical reaction as a function of temperature (3, 4)where ‡ is the prefactor, k B is the Boltzmann constant, T is the absolute temperature, and ⌬G ‡ is the activation energy. In this simplified equation,where C°is the standard state concentration, h is the Planck's constant, and n is the order of the reaction. The factor (k B T/h) is a frequency factor, equal to 6 ps Ϫ1 at 300 K, for the crossing of the transition state. The generalized transmission coefficient, ␥(T), relates the actual rate of the reaction to that obtained from the simple transition state theory, in which ␥(T) ϭ 1. Over the last two decades, a great number of studies have reported the effect of temperature on the (un)folding kinetics of a plethora of distinct proteins using different biochemistry bulk techniques. With a few exceptions (5), the apparent consensus (6) is that although protein unfolding usually follows simple Arrhenius kinetics, the folding kinetics exhibit more complex dependences with temperature, resulting in curvature in the ln k f versus 1/T plots (7-12). The origin of such non-Arrhenius behavior during the folding reaction can be generically explained either in terms of the rate of escape from different minima along a rough energy landscape, thus yielding super-Arrhenius kinetics, or most likely, based on the hydrophobic effect, involving a large change in heat capacity during the folding process (13-15), with the heat capacity of the transition state placed somewhere in between the folded and unfolded states (16).Single molecule force spectroscopy has provided a new vista on the molecular mechanisms underlying protein (un)folding at the subnanometer scale (17). In stark contrast with protein unfolding experiments conducted using traditional bulk experiments, where the radius of g...

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“…Recently, single-molecule techniques have been used to probe features of the energy landscape of proteins and RNA that are not easily accessible in ensemble experiments (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18). It is possible to construct the shape of the energy landscape, including the energy scales of ruggedness (19,20), by using dynamical trajectories that are generated by applying a constant force ( f ) to the ends of proteins and RNA (14,15,21,22). If the observation time is long enough for the molecule to sample the accessible conformational space, then the time average of an observable X recorded for the ␣th molecule [͗X͘ ϭ t3ϱ lim ( 1 t )͐ 0 t d X ␣ ( )] should equal the ensemble average (͗X͘ ϭ t3ϱ…”

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confidence: 99%

Force-dependent hopping rates of RNA hairpins can be estimated from accurate measurement of the folding landscapes

Hyeon

Morrison²,

Thirumalai

2008

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

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The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated by using single-molecule force-clamp experiments by attaching semiflexible polymers to the ends of hairpins, have been used to infer their folding landscapes. Using simulations and theory, we study the effect of the dynamics of the attached handles on the handle-free RNA free-energy profile F eq o (zm), where zm is the molecular extension of the hairpin. A molecular understanding of how proteins and RNA fold is needed to describe the functions of enzymes (1) and ribozymes (2), interactions between biomolecules, and the origins of misfolding that is linked to a number of diseases (3). The energy-landscape perspective has provided a conceptual framework for describing the mechanisms by which unfolded molecules navigate the large conformational space in search of the native state (4-6). Recently, single-molecule techniques have been used to probe features of the energy landscape of proteins and RNA that are not easily accessible in ensemble experiments (7-18). It is possible to construct the shape of the energy landscape, including the energy scales of ruggedness (19,20), by using dynamical trajectories that are generated by applying a constant force ( f ) to the ends of proteins and RNA (14,15,21,22). If the observation time is long enough for the molecule to sample the accessible conformational space, then the time average of an observable X recorded for the ␣th molecule [͗X͘ ϭ t3ϱ, and the distribution P(X) should converge to the equilibrium distribution function P eq (X). By using this strategy, laser optical tweezer (LOT) experiments have been used to obtain the sequence-dependent folding landscape of a number of RNA and DNA hairpins (8,14,15,23), by using X ϭ R m , the end-to-end distance of the hairpin that is conjugate to f, as a natural reaction coordinate. In LOT experiments, the hairpin is held between two long handles [DNA (15) or DNA/RNA hybrids (8)], whose ends are attached to polystyrene beads (Fig. 1a). The equilibrium free-energy profile ␤F eq (R m ) ϭ ϪlogP eq (R m ) (␤ ϵ 1/k B T, k B is the Boltzmann constant, and T is the absolute temperature) may be useful in describing the dynamics of the molecule, provided R m is an appropriate reaction coordinate.The dynamics of the RNA extension in the presence of f (z m ϭ z 3Ј Ϫ z 5Ј Ϸ R m , provided transverse fluctuations are small) is indirectly obtained in an LOT experiment by monitoring the distance between the attached polystyrene beads (z sys ϭ z p Ϫ z o ), one of which is optically trapped at the center of the laser focus (Fig. 1a). The goal of these experiments is to extract the folding landscape [␤F eq o (z m )] and the dynamics of the hairpin in the absence of handles by using the f-dependent trajectories z sys (t). To achieve these goals, the fluctuations in the handles should minimally perturb the dynamics of the hairpin to probe the true dynamics of a molecule of interest. However, dependi...

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Can energy landscape roughness of proteins and RNA be measured by using mechanical unfolding experiments?

Cited by 160 publications

References 21 publications

Coordinate-dependent diffusion in protein folding

Coordinate-dependent diffusion in protein folding

Direct Quantification of the Attempt Frequency Determining the Mechanical Unfolding of Ubiquitin Protein

Force-dependent hopping rates of RNA hairpins can be estimated from accurate measurement of the folding landscapes

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