(717f) Thermodynamic Perturbation Theory and Property Network for Coarse Grain DNA Model

A coarse grain model of a deoxyribonucleic acid (DNA) single strand is proposed by considering each nucleotide to consist of a trimer of tangent homonuclear hard-sphere segments (phosphate, sugar and base) with added attractive interactions. The entire strand (oligonucleotide) is constructed by forming covalent bonds between the sugar (articulation) segment and the phosphate segment on a neighboring nucleotide. Each of two popular covalent bonding platforms for branched hard-sphere chains [1, 2] is used with a recently proposed hard-sphere equation of state [3] to obtain the athermal free energy component, and dispersion forces are incorporated at a van der Waals mean field level. The model is further refined by adding a term for type I hydrogen bonding within the statistical associating fluid theory (SAFT) framework for Watson-Crick (base-pair) association to form DNA double-strands (dimers) (see Figure 1 for a depiction of double-stranded DNA model). Hydrogen bonding sites are also added to the phosphate, sugar and base segments for cross-association with the solvent water. Finally, phosphate segments are negatively charged and sodium (or potassium) cations are represented by positively charged hard-spheres (same diameter as solvent water and all DNA segments in original version of model).

The residual Helmholtz free energy of the resulting aqueous DNA system including counterions is derived, and used to obtain expressions for a variety of properties including osmotic coefficient and viscosity of the solution and diffusivity of DNA in water as functions of DNA fragment length. Several illustrations are given to highlight key points, and suggestions are made on how the model can be improved by considering heteronuclear segments and bond angle dependence

REFERENCES

[1] Marshall, B. and W. G. Chapman, Three Branched Chain Equations of State Based on Wertheimâ??s Perturbation Theory, J. Chem. Phys. 138, 174109 (2013).

[2] Blas, F. J. and L. F. Vega, Thermodynamic Properties and Phase Equilibria of Branched Chain Fluids Using First- and Second-Order Wertheimâ??s Thermodynamic Perturbation Theory, J. Chem. Phys. 115, 3906-3915 (2001).

[3] Gow, A. S. and R. B. Kelly, Twenty-One New Theoretically Based Cubic Equations of State for Athermal Hard-Sphere Chain Pure Fluids and Mixtures, AIChE Journal 61, 1677-1690 (2015).

Figure 1. Homonuclear hard-sphere branched chain coarse grained model of DNA including dispersion, electrostatic interactions and hydrogen bonding.