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Force-Induced Unzipping Transitions in an Athermal Crowded Environment

Using theoretical arguments and extensive Monte Carlo (MC) simulations of a coarse-grained three-dimensional off-lattice model of a β-hairpin, we demonstrate that the equilibrium critical force, $F_c$, needed to unfold the biopolymer increases non-linearly with increasing volume fraction occupied by the spherical macromolecular crowding agent. Both scaling arguments and MC simulations show that the critical force increases as $F_c \approx φ_c^α$. The exponent $α$ is linked to the Flory exponent relating the size of the unfolded state of the biopolymer and the number of amino acids. The predicted power law dependence is confirmed in simulations of the dependence of the isothermal extensibility and the fraction of native contacts on $φ_c$. We also show using MC simulations that $F_c$ is linearly dependent on the average osmotic pressure ($\mathrm{P}$) exerted by the crowding agents on the β-hairpin. The highly significant linear correlation coefficient of 0.99657 between $F_c$ and $\mathrm{P}$ makes it straightforward to predict the dependence of the critical force on the density of crowders. Our predictions are amenable to experimental verification using Laser Optical Tweezers.