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Non-linear Hamiltonian models for DNA

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Abstract

Nucleic acids’ physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse-grained models, e.g., the worm-like-chain, taken from polymer physics. In this review article, I discuss an intermediate (mesoscopic) approach and show how to build a three-dimensional Hamiltonian model which accounts for the main interactions responsible for the stability of the helical molecules. While the 3D mesoscopic model yields a sufficiently detailed description of the helix at the level of the base pair, it also allows one to predict the thermodynamical and structural properties of molecules in solution. Relying on the idea that the base pair fluctuations can be conceived as trajectories, I have built over the past years a computational method based on the time-dependent path integral formalism to derive the partition function. While the main features of the method are presented, I focus here in particular on a newly developed statistical method to set the maximum amplitude of the base pair fluctuations, a key parameter of the theory. Some applications to the calculation of DNA flexibility properties are discussed together with the available experimental data.

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Notes

  1. The PB model is usually represented by a ladder as in Fig. 2 of ref. Peyrard et al. (2008) where the bases are depicted as extended objects. In fact, the Hamiltonian assumes a point-like description for the bases as in Fig. 1.

  2. The coefficients \(a_m\) should not be confused with the inverse length \(\bar{a}_n\) of the site-dependent Morse potential.

  3. In principle, the Fourier coefficients in Eq. (11) are integrated on an even domain. However, too negative \(a_m\)’s are discarded due to the physical condition associated to the hard core of the one-particle potential. The latter is tuned by the parameter which regulates the range of the Morse potential (see Section 2). The asymmetry in the choice of \(a_m\)’s included in the computation explains why \(P_j(R_0,\, 0)\) may get slightly larger than 1/2. Hence, the approximation sign is used in the text.

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  1. School of Science and Technology, University of Camerino, 62032, Camerino, Italy

    Marco Zoli

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Zoli, M. Non-linear Hamiltonian models for DNA. Eur Biophys J 51, 431–447 (2022). https://doi.org/10.1007/s00249-022-01614-z

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