Worm-like Ising model for protein mechanical unfolding under the effect of osmolytes

Abstract

We show via single-molecule mechanical unfolding experiments that the osmolyte glycerol stabilizes the native state of the human cardiac I27 titin module against unfolding without shifting its unfolding transition state on the mechanical reaction coordinate. Taken together with similar findings on the immunoglobulin-binding domain of streptococcal protein G (GB1), these experimental results suggest that osmolytes act on proteins through a common mechanism that does not entail a shift of their unfolding transition state. We investigate the above common mechanism via an Ising-like model for protein mechanical unfolding that adds worm-like-chain behavior to a recent generalization of the Wako-Saitô-Muñoz-Eaton model with support for group-transfer free energies. The thermodynamics of the model are exactly solvable, while protein kinetics under mechanical tension can be simulated via Monte Carlo algorithms. Notably, our force-clamp and velocity-clamp simulations exhibit no shift in the position of the unfolding transition state of GB1 and I27 under the effect of various osmolytes. The excellent agreement between experiment and simulation strongly suggests that osmolytes do not assume a structural role at the mechanical unfolding transition state of proteins, acting instead by adjusting the solvent quality for the protein chain analyte.

Figure 1

(A) Native structure of GB1 (PDB code 1PGA). (B) The native structure of I27(PDB code 1TIT) showing the A, A′, and G strands.

Figure 2

Average unfolding force of I27 at various pulling speeds increases in the presence of glycerol 30% v/v, and increases again slightly when adjusting for the viscous drag-force on the cantilever. As a guide to the eye, we fitted a dashed line to the average unfolding forces in each condition with a fixed slope of k_BT/(Δx_u log₁₀ (e)), where e is Euler's constant and Δx_u = 0.25 nm. The formula for the eye-guide fixed slope has been inspired from the so-called standard method of kinetic parameter estimation, and it was not used for the statistical estimation of the kinetic parameters that we report, which was performed instead via maximum-likelihood estimation (see Section S2.9 in the Supporting Material).

Figure 3

(Color online) Logarithm of the unfolding rate of GB1 as a function of the stretching force in two solvent conditions, namely the most destabilizing one and the most stabilizing one, selected such as to reduce visual clutter. (Points) Inverse of the average unfolding time from at least 125 trajectories. (Lines) Fit of Bell's model via Eq. S17 in the Supporting Material.

Figure 4

(Color online) Logarithm of the unfolding rate of I27 as a function of the stretching force in two different solvent conditions. Each point represents the inverse of the average unfolding time from at least 125 trajectories. (Lines) Fit of Bell's model via Eq. S17 in the Supporting Material over two different linear regimes, selected for each solvent condition so as to minimize the total squared error. In the absence of osmolytes, the crossing point was found to be 80 pN, whereas in the presence of glycerol 30% v/v the crossing point was found to be 85 pN.

Figure 5

Simulated velocity-clamp curve of (GB1)₈. The velocity was 969 nm/s, the cantilever spring constant was 0.06 N/m, and the solvent had a GndCl concentration of 2.25 M.

Figure 6

(Color online) Average unfolding force versus pulling velocity in different solvent conditions for protein (GB1)₈. (Points) Average unfolding force from at least 125 trajectories.

Figure 7

Simulated velocity-clamp curve of I27. The velocity was 50.1 nm/s, the cantilever spring constant was 0.06 N/m, and the solvent was free of osmolytes.

Figure 8

Average unfolding force versus pulling velocity in different solvent conditions for protein I27. (Points) Average unfolding force from at least 1000 trajectories.