Coarse grained modeling of self assembled DNA 3D structure using pragmatic soft ellipsoid contact potential

TL;DR

This work extends a coarse-grained ellipsoid contact potential (ECP) to DNA by introducing six interacting terms, including base pairing via $V_{ECP}$ and implicit solvent $V_{solv}$, enabling efficient sampling of renaturation and melting. The model includes backbone bending ($V_{bend}$) and dihedral ($V_{dihedral}$) terms, constrained bonds via the RATTLE algorithm, and long-range electrostatics via Debye-Hückel ($V_{el}$), within an $NVT$ Langevin framework. Phase behavior is captured as a first-order-like transition at $T^* = 0.483 \epsilon_0 /(N k_B)$ with a peak in $C_V$, and the melting curve derived from the pairing fraction $\Phi$ agrees with experimental data. Structural metrics yield a helix diameter near 20 Å, a rise per base pair of about 3.677 Å, and bend/dihedral angles around $99^\circ$ and $17^\circ$, supporting the realism of the coarse-grained description and its potential for DNA–lipid or DNA–protein contexts.

Abstract

In this paper, we present a coarse-grained model of DNA based on the soft ellipsoid contact potential (ECP) to evaluate the base pairing interaction properly. We extend the ellipsoid contact like potential model (ECP), suitably modified and used previously by our group to model lipid bilayer phases with considerable success. This potential is used for base-base interactions, along with other potentials to capture bending, dihedral and solvent effects. The model shows a phase transition during hybridization and is able to reproduce the experimental melting curves with sufficient adequacy. Thermodynamical, along with conformational characteristics and structural properties of our model are studied in detail.

Figures (5)

• Figure 1: Potential energy profiles for the flat bottom implicit solvent potential for side-side $\theta = 90^\circ$ and end-end configurations $\theta=0^\circ$.
• Figure 2: Phase transition curves obtained from simulation. (A) Variation of the potential of mean force (PMF) with temperature. The jump at $T^\ast = 0.48$ indicates a phase change where ssDNA hybridizes into dsDNA. (B) Variation of specific heat capacity obtained from fluctuations in total energy $\langle \Delta E\rangle^2/T^{\ast2}$. Fluctuations are significantly higher around $T^\ast = 0.48$ where transition occurs in Fig A. (C) Melting curve obtained by fitting the sigmoid function given in Equation \ref{['eq:1']} over the pairing fraction $\Phi$ for each temperature. The crosses $(\times)$ are actual data from simulation over which the sigmoid function is fitted. The dotted curve denotes a reference experimental curve taken from Ref Owczarzy2004 as mentioned in Section III C.
• Figure 3: (A) Bending angle distribution. (B) Dihedral angle distribution. Both distributions settle at equilibrium value with peaks at $99^\circ$ and $17^\circ$ respectively as the system cools towards hybridized state.
• Figure 4: (A) Estimate of the helix diameter from model simulation. (B) Average rise per base pair obtained by calculating the local helical axis using the scheme described in Section III B. The local helical axis is given by the principal component of the covariance matrix formed from the base centers around the bases being probed. Estimated value from graph is around 3.677 Å
• Figure 5: Snapshots from the simulation. The particle sizes are slightly reduced to enhance visual clarity. (A) Initially the two chains are separate from each other. The system is heated well to ensure a random starting configuration of position and orientation. (B) As the system is cooled beyond the transition point, the bases begin binding with their complementary counterparts. Here the first binding event occurs between the bases on opposite strands. As can be seen, hybridization starts at one end and moves forward from there. (C) The strands slide forward along the bases of its complementary strand. This is feasible since in our model, base pairing lowers free energy. (D) Finally, as all bases pair successfully, the strands hybridize into a double helix structure.