Quantifying the Native Energetics Stabilizing Bacteriorhodopsin by Single-Molecule Force Spectroscopy

Hao Yu, David R. Jacobson, Hao Luo, and Thomas T. Perkins

Phys. Rev. Lett. 125, 068102 – Published 5 August 2020

Abstract

We quantified the equilibrium (un)folding free energy $Δ G_{0}$ of an eight-amino-acid region starting from the fully folded state of the model membrane-protein bacteriorhodopsin using single-molecule force spectroscopy. Analysis of equilibrium and nonequilibrium data yielded consistent, high-precision determinations of $Δ G_{0}$ via multiple techniques (force-dependent kinetics, Crooks fluctuation theorem, and inverse Boltzmann analysis). We also deduced the full 1D projection of the free-energy landscape in this region. Importantly, $Δ G_{0}$ was determined in bacteriorhodopsin’s native bilayer, an advance over traditional results obtained by chemical denaturation in nonphysiological detergent micelles.

Received 10 April 2020
Accepted 2 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.068102

Physics Subject Headings (PhySH)

Protein folding Protein unfolding

Proteins

Atomic force microscopy Single molecule techniques

Physics of Living Systems

Authors & Affiliations

Hao Yu ^1,†, David R. Jacobson ^2,†, Hao Luo¹, and Thomas T. Perkins ^2,3,*

¹School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
²JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309, USA
³Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, Colorado 80309, USA

^*Corresponding author. tperkins@jila.colorado.edu
^†These authors contributed equally to this work.

Correcting molecular transition rates measured by single-molecule force spectroscopy for limited temporal resolution

David R. Jacobson and Thomas T. Perkins

Phys. Rev. E 102, 022402 (2020)

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Vol. 125, Iss. 6 — 7 August 2020

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Images

Figure 1
Probing the energetics of bacteriorhodopsin (BR) starting from its fully folded state. (a) In this AFM assay, BR embedded in native membrane is unfolded from its $C$ -terminal tail into a well-defined, fully stretched state with extension $x$ . Inset: sketch of the unfolded state in a traditional chemical-denaturation experiment. Note, $\sim 60 %$ of native $α$ -helical secondary structure remains. (b) Reversible nonequilibrium force-extension curves span three structural states, separated by five and three amino acids, respectively. The graph shows one cycle of cantilever retraction (pink) and approach (blue). Segments corresponding to individual states were well fit by an elastic model (dashed lines). Insets: structures of two of the states. (c) Force- vs time record shows equilibrium transitions between the same three states (dashed lines). Data smoothed to 17 kHz.
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Figure 2
$Δ G_{0}$ determined from transition kinetics of nonequilibrium data. (a) Left: example unfolding and refolding cycle. A typical single-molecule record has $\sim 40 - 60$ such cycles. Right: enlargement showing individual transitions (colored circles). (b) Force-dependent rates for all four transitions. Error bars are standard errors of the mean from a bootstrap analysis. Lines are Bell-model fits. Line crossings reveal $F_{1 / 2}$ , the equilibrium unfolding force. Inset: illustration of how the uncorrected unfolding free energy was obtained as $Δ G_{0}^{raw} = F_{1 / 2}$ $Δ x$ , which was then corrected for work done to stretch the unfolded section of the protein. (c) Scheme of the underlying free-energy landscape. $Δ G_{0}$ denotes a change in free energy between stable states, $Δ G^{‡}$ is the height of a transition barrier, and $Δ x^{‡}$ is the distance from a stable state to that barrier.
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Figure 3
Determining $Δ G_{0}^{02}$ from the Crooks fluctuation theorem. (a) Integrating $F (Z)$ (gray) yielded the raw work $W_{raw}$ done on the entire experimental system, where $Z$ is the position of the cantilever base. (b) Histograms of work $W$ done on a particular individual protein as it was repeatedly unfolded (red, closed) and refolded (blue, open) 20 times at $v = 500 nm / s$ . $W$ was obtained from $W_{raw}$ by subtracting the work done on the cantilever and polypeptide chain [Eq. (3)]. $Δ G_{0}$ is the crossing point of the distributions (arrow).
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Figure 4
Reconstruction of the free-energy landscape of the eight-amino-acid region of interest. (a) Probability distribution of extension before (dashed cyan) and after (solid red) deconvolution. (b) Free-energy landscape before (cyan) and after (red) deconvolution. (c) Free-energy landscape at zero applied force recovered from equilibrium trajectories of an individual molecule under three different tensions (91, 93, and 96 pN in state $I_{G}^{0}$ ). For clarity, extensions are represented as contour lengths of the unfolded polypeptide chain.
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