Systematic development of coarse-grained polymer models Patrick ...

3.10 Comparison of the fractional extension with its high ν asymptotic expansion for the
MarkoandSiggiapotential................................. 37
3.11 Comparison of the zero-force slope with its high ν asymptotic expansion for the
MarkoandSiggiapotential................................. 39
3.12 Calculation of the relative error of the mean fractional extension for a bead-spring
model as the level of coarse-graining changes with the FENE potential. . . . . . . . 43
3.13 Calculation of λ for the three different criteria at different levels of coarse-graining
fortheFENEpotential. .................................. 44
3.14 Calculation of the relative error of the mean fractional extension for a bead-spring
model for different best fit criteria with the FENE potential. . . . . . . . . . . . . . 45
3.15 Calculation of the longitudinal root-mean-squared fluctuations at different levels of
coarse-grainingwiththeFENEpotential. ........................ 46
3.16 Calculation of the transverse root-mean-squared fluctuations at different levels of
coarse-grainingwiththeFENEpotential. ........................ 47
4.1 Multiplepathstobuildabead-springmodel. ...................... 52
4.2 Physical interpretation of Polymer Ensemble Transformation (PET) method. . . . . 53
4.3 The physical justification for the PET method is based on sorting all configurations
ofthepolymerintocategories. .............................. 54
4.4 Comparison of the spring force law chosen from the Random Walk Spring (RWS)
model and the inverse Langevin function. . ....................... 57
4.5 Progression from the constant extension partition function to the spring force in the
Random Walk Spring model for ν =3........................... 58
4.6 Series of spring forces necessary to model chains with m rods of length A and m rods
of length 5A for m =1, 2, 3, 4, 5, 6, with the arrow denoting increasing m. . . . . . . 61
4.7 Series of spring forces necessary to model chains with m rods of length A and m rods
of length pA for m =1, 2, 3, 4, 5, 6, with the arrow denoting increasing m. . . . . . . 62
4.8 This shows the convergence of a BD simulation for a spring force law that models
two rods of a freely jointed chain. . . ........................... 63
4.9 This shows the convergence of a BD simulation for a spring force law that models
three rods of a freely jointed chain. . ........................... 64
4.10 Relative error in the equilibrium moments of the spring length between an approximate
spring force law compared with an equal rod freely jointed chain. . . . . . . . . 68
4.11 Relative error in the average fractional extension between an approximate spring
force law compared with an equal rod freely jointed chain. ............... 69
4.12 Relative error in the equilibrium moments of the spring length between an approximate
spring force law compared with a unequal rod freely jointed chain. . . . . . . . 70
4.13SpringforcelawforadumbbellmodelofF-actin..................... 71
4.14 Restricting the configurations within a category eliminates the coupling in a multispringworm-likechainmodel................................
72
4.15 Illustration of a worm-like chain with vectors connecting positions on the chain. . . . 74
4.16 Sketch of the average fractional extension as a function of the applied force for a
continuousworm-likechainmodel. ............................ 75
4.17 Relative error in the fractional extension versus force for the Marko-Siggia spring
usingthelow-forcecriterionfortheeffectivepersistencelength............. 78