Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2011-12-26
Nonlinear Sciences
Pattern Formation and Solitons
Submitted to Phys. Rev. E, 13 figures
Scientific paper
A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and an harmonic second-neighbor coupling. Under an external stretching applied t o the chain ends, the intersite Morse-like potential results in the appearance of a double-well potential within each chain monomer, whereas the interaction between the second neighbors provide s a homogeneous bistable (degenerate) ground state, at least within a certain part of the chain. As a result, different conformational changes occur in the chain under the external forcing. The transition regions between these conformations are described as topological solitons. With a strong second-neighbor interaction, the solitons describe the transition between the bistable ground states. However, the key point of the model is the appearance of a heterogenous structure, when the second-neighbor coupling is sufficiently weak. In this case, a part of the chain has short bonds with a single-well potential, whereas the complementary part admits strongly stretched bonds with a double-well potential. This case allows us to explain the existence of a plateau in the force-stretching diagram for DNA and alpha-helix protein. Finally, the soliton dynamics are studied in detail.
Christiansen Peter L.
Savin Alexander V.
Zolotaryuk A. V.
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