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Force-extension formula for the worm-like chain model from a variational principle.
Yue Chan1, Richard G Haverkamp, James M Hill
1Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia.
Journal of Theoretical Biology
|October 20, 2009
Summary
We developed a new analytical formula for stiff polymers, like DNA, using a variational principle. This formula reveals phase transitions and predicts molecular fracture, improving our understanding of polymer elasticity.
Area of Science:
- Polymer Physics
- Statistical Mechanics
- Biophysics
Background:
- Stiff polymers (DNA, RNA, cellulose) are modeled as chains of rigid subunits.
- Existing models like the freely jointed chain and worm-like chain have limitations.
- Current force-extension formulas for worm-like chains rely on interpolation and numerical solutions.
Purpose of the Study:
- To derive an analytical force-extension formula for the worm-like chain model.
- To incorporate monomer orientation and thermal equilibrium into polymer elasticity.
- To identify new physical phenomena in stretched polymers.
Main Methods:
- Application of a variational principle to find minimum energy configurations.
- Analytical derivation of the force-extension formula.
- Incorporation of thermal equilibrium and monomer orientations.
Main Results:
- A new analytical force-extension formula for the worm-like chain model.
- Identification of terms for free energy and cut-off force, indicating entropic-enthalpic transition and fracture.
- Prediction of two phase changes: super-helix to soliton, then soliton to twisted line.
Conclusions:
- The new formula accurately describes polymer stretching, including phase transitions.
- Molecules undergo at least one phase change before reaching full contour length.
- The formula shows good agreement with experimental data and statistical approaches.
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