Order Statistics Theory of Unfolding of Multimeric Proteins

Dynamic force spectroscopy has become indispensable for the exploration of the mechanical properties of proteins. In force-ramp experiments, performed by utilizing a time-dependent pulling force, the peak forces for unfolding transitions in a multimeric protein (D)_N are used to map the free energy landscape for unfolding for a protein domain D. We show that theoretical modeling of unfolding transitions based on combining the observed first (f₁), second (f₂), …, N^th (f_N) unfolding forces for a protein tandem of fixed length N, and pooling the force data for tandems of different length, n₁ < n₂ < … < N, leads to an inaccurate estimation of the distribution of unfolding forces for the protein D, ψ_D(f). This problem can be overcome by using Order statistics theory, which, in conjunction with analytically tractable models, can be used to resolve the molecular characteristics that determine the unfolding micromechanics. We present a simple method of estimation of the parent distribution, ψ_D(f), based on analyzing the force data for a tandem (D)_n of arbitrary length n. Order statistics theory is exemplified through a detailed analysis and modeling of the unfolding forces obtained from pulling simulations of the monomer and oligomers of the all-β-sheet WW domain.