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Using theoretical arguments and extensive Monte Carlo (MC) simulations of acoarse-grained three-dimensional off-lattice model of a \beta-hairpin, wedemonstrate that the equilibrium critical force, $F_c$, needed to unfold thebiopolymer increases non-linearly with increasing volume fraction occupied bythe spherical macromolecular crowding agent. Both scaling arguments and MCsimulations show that the critical force increases as $F_c \approx\varphi_c^{\alpha}$. The exponent $\alpha$ is linked to the Flory exponentrelating the size of the unfolded state of the biopolymer and the number ofamino acids. The predicted power law dependence is confirmed in simulations ofthe dependence of the isothermal extensibility and the fraction of nativecontacts on $\varphi_c$. We also show using MC simulations that $F_c$ islinearly dependent on the average osmotic pressure ($\mathrm{P}$) exerted bythe crowding agents on the \beta-hairpin. The highly significant linearcorrelation coefficient of 0.99657 between $F_c$ and $\mathrm{P}$ makes itstraightforward to predict the dependence of the critical force on the densityof crowders. Our predictions are amenable to experimental verification usingLaser Optical Tweezers.

Force-Induced Unzipping Transitions in an Athermal Crowded Environment