Convergence of the FWLC-predicted extension to the classic WLC prediction for large L. The predicted fractional extension x/L is shown as a function of the contour length L (at fixed applied force). The different curves correspond to different theoretical assumptions: 1), the classic WLC solution, calculated using the method of Marko and Siggia (4); 2), the FWLC with unconstrained boundary conditions at both ends of the chain; 3), the FWLC with half-constrained boundary conditions at both ends of the chain; and 4), the FWLC with perpendicular boundary conditions at both ends of the chain (see Fig. 4). The different panels show different applied forces: (A) 0.1 pN, (B) 1 pN. The polymer persistence length is p = 50 nm. Note that the WLC prediction is independent of contour length, and the FWLC predictions converge to the WLC prediction as L increases. The convergence occurs more quickly for higher applied force (note different y axis scales for different panels). For low applied force, the more constrained boundary conditions lead to a larger predicted fractional extension (see text).