Extension-Dependent Drift Velocity and Diffusion (DrDiff) Directly Reconstructs the Folding Free Energy Landscape of Atomic Force Microscopy Experiments

Abstract

Two equilibrium force microscopy trajectories [q(t)] of high-precision single-molecule spectroscopy assays were analyzed: the pulling of an HIV RNA hairpin and of a 3-aa sequence of the bacteriorhodopsin membrane protein. Both present hundreds of two-state folding transitions, and their free-energy [F(q)] landscapes were previously obtained by deconvolving time signals with the inverse Boltzmann and p fold methods. In this letter, the two F profiles were reconstructed directly from the measured time-series by the drift-diffusion (DrDiff) framework that characterized the effective conformational drift-velocity [v(q)] and diffusion [D(q)] coefficients. The two thermodynamic F profiles reconstructed with DrDiff directly from q(t) were in good agreement with those previously obtained from the deconvolved time signals. q(t) trajectories simulated with a two-dimensional framework in which the diffusion coefficient of the pulling setup (q coordinate) differed from the molecule (x coordinate) were also analyzed by DrDiff. The performance in reconstructing F was investigated in different conditions of diffusion anisotropy in the simulated time-series using Brownian dynamics. In addition, recently developed theories were used in order to evaluate the quality of the analysis performed in the experimental time series: the memory effects and the intrinsic biomolecular dynamic properties after connecting the probe to the molecule. With the 2-dimensional diffusive models and the additional analyses, it is proposed that the different physical regimes imposed by the stiffer probes of the two biomolecules will have an impact in the measured extension-dependent D and, thus, in the reconstruction of F by DrDiff. Stiffer AFM probes may reflect the molecular behavior more faithfully and reconstruction of F might be more successful. The reported quantities extracted directly from q(t) highlights the current state of the biomolecule characterization by force spectroscopy experiments: it is still challenging despite the recent advances, yet it is very promising.

Small Neutral Crowding Solute Effects on Protein Folding Thermodynamic Stability and Kinetics

“…The code is freely available to be downloaded at . The reader is encouraged to find more details of the algorithm in other previous works. , …”

“…The reader is encouraged to find more details of the algorithm in other previous works. 47,51 Beta Tanford Value (β T ). The Beta Tanford value (β T ) is a parameter that reports on the properties of transition states, which experimentally is the ratio of equilibrium and kinetic m values 52 (10) with the subscripts U, TS, and N being the denature unfolded, transition, and native states, respectively.…”

Coordinate-Dependent Drift-Diffusion Reveals the Kinetic Intermediate Traps of Top7-Based Proteins

“…This hill-trend of D(Q) for two-state folders was also noticed by other SBM-C α 97,135 and all-atom 95,136,137 simulations and in time-series of single molecule atomic force microscopy. 138,139 D represents the mobility and the scape over a local energy barrier, and thus, it could have other trends. 81 A recent paper running alanine dipeptide recovered a D dependent on the backbone dihedral angle Ψ with oscillating downtrend and uptrend at the metastable states α and β, respectively.…”