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. 2020 Apr 28;53(8):3021-3029.
doi: 10.1021/acs.macromol.0c00278. Epub 2020 Apr 14.

Interplay between Viscoelasticity and Force Rate Affects Sequential Unfolding in Polyproteins Pulled at Constant Velocity

Moran Elias-Mordechai  1 , Einat Chetrit  1 , Ronen Berkovich  1   2
Affiliations

Interplay between Viscoelasticity and Force Rate Affects Sequential Unfolding in Polyproteins Pulled at Constant Velocity

Moran Elias-Mordechai et al. Macromolecules. .

Abstract

Polyproteins are unique constructs, comprised of folded protein domains in tandem and polymeric linkers. These macromolecules perform under biological stresses by modulating their response through partial unfolding and extending. Although these unfolding events are considered independent, a history dependence of forced unfolding within polyproteins was reported. Here we measure the unfolding of single poly(I91) octamers, complemented with Brownian dynamics simulations, displaying increasing hierarchy in unfolding-foces, accompanied by a decrease in the effective stiffness. This counters the existing understanding that relates stiffness with variations in domain size and probe stiffness, which is expected to reduce the unfolding forces with every consecutive unfolding event. We utilize a simple mechanistic viscoelastic model to show that two effects are combined within a sequential forced unfolding process: the viscoelastic properties of the growing linker chain lead to a hierarchy of the unfolding events, and force-rate application governs the unfolding kinetics.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
FX measurements of poly(I91) unfolding at three representative pulling velocities, V = 50 (red), 100 (blue), and 1000 (green) nm/s. (A) Three exemplary FX unfolding traces. (B) Mean unfolding forces (obtained from the maximal forces at each unfolding event) as a function of unfolding event (domain) number, N. (C) Mean chain stiffness, measured by the slope of the linear regime prior to each unfolding event (dF/dx), at each unfolding event (filled symbols), and the effective stiffness (Keff), estimated with eq 2 and eq 3 (open symbols), showing a softening of the chain with the increase of its polymeric (linker) element after each unfolding event.
Figure 2
Figure 2
Force-rate variations with the domain number. (A) Unfolding forces (maximal forces, Fmax, collected from the FX unfolding traces measured at V = 1000 nm/s) plotted against the time they took place on (green triangles, with increasing shade for each consecutive unfolding event). The slopes of the linear fits (solid black lines) estimate the local, event dependent, unfolding rate, dF/dt. (B) Force-rates from experimental data measured at V = 50 (red), 100 (blue), and 1000 (green) nm/s. dF/dt obtained from the slopes of the maximal unfolding forces with time (as in A) are marked by solid symbols, while rates estimated by ⟨dF/dx⟩N × V are marked by blank, line connected small symbols. (C) Estimation of dF/dt from the maximal unfolding forces from BD simulations at V = 4000 nm/s. (D) Force-rates calculated from BD simulations at V = 40 (light blue), 400 (purple), and 4000 (black) nm/s.
Figure 3
Figure 3
Effect of the pulling velocity on force-rates and chain stiffness. (A) Poly(I91) N-averaged force-rates ⟨dF/dt⟩ (solid turquoise diamonds) and ⟨⟨dF/dx⟩⟩ × V (small open turquoise diamonds) as a function of the pulling velocity. (B) BD N-averaged force-rates ⟨dF/dt⟩ (solid black diamonds) and ⟨⟨dF/dx⟩⟩ × V (small open diamonds) as a function of the pulling velocity. (C) N-averaged stiffness, ⟨⟨dF/dx⟩⟩, as a function of the pulling velocity for poly(I91) (solid tangerine diamonds), and BD simulations (open diamonds).
Figure 4
Figure 4
Viscoelastic response of the extending linker with unfolding events and pulling velocity. (A) Adaptation of the constitutive Zener model to a linker (characterized with a stiffness Kl and internal friction μ), in series with the stiffness of the probe (KS). μ calculated with eq 5, with the experimental parameters as a function of chain length (B) and pulling velocity for three extensions (C), and with the BD parameters (D, E) respectively.
Figure 5
Figure 5
Measured unfolding forces as a function of their corresponding local stiffness. (A) Maximal unfolding forces vs mean chain stiffness from poly(I91) FX measurements, both as a function of domain number (chain length), at V = const. (B) Maximal unfolding forces vs mean chain stiffness from poly(I91) FX measurements, both as a function of pulling velocity, at N = const. Respectively corresponding to (A) and (B), maximal unfolding forces vs mean chain stiffness from BD simulations for V = const. (C), and N = const. (D).
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