An unstructured synthetic peptide linker is stretched in an optical trap at

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch The elastic polymer: DNA from random walk to worm-like chain

Problem

An unstructured synthetic peptide linker is stretched in an optical trap at 298 K298\,\mathrm{K}. In the low-force entropic regime a single data point is read off the trace: at a force f=0.50 pNf = 0.50\,\mathrm{pN} the fractional extension is z/L=0.050z/L = 0.050. Treat the linker as a worm-like chain and use the low-force (Gaussian-spring) limit z/L=2ξpf/(3kBT)z/L = 2\xi_p f/(3k_BT). ((a)) Find the persistence length ξp\xi_p of the linker from this one point. ((b)) Convert ξp\xi_p into a bending rigidity κ=ξpkBT\kappa = \xi_p k_BT, quoted in J m\mathrm{J\,m}. ((c)) A folded domain elsewhere in the same construct has n=64n = 64 residues and, unfolded, adds contour length at 0.38 nm0.38\,\mathrm{nm} per residue; the folded domain itself already spans 4.0 nm4.0\,\mathrm{nm} end to end. Predict the contour-length increment ΔL\Delta L that appears in an unfolding trace when this domain opens.

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