Fractal behavior of poly(GC) and poly(TA) DNA segments arranged in quasiperiodic Fibonacci sequence

Abstract

We used the atomistic molecular mechanics method with a well-known universal force field (UFF), as implemented in forcite module, to investigate the fractal properties of the poly GC and poly TA base pairs diluted in solvent, grown in conformity with the quasiperiodic Fibonacci sequence. It was obtained through simulations, and demonstrated that solvent-accessible surface area and volume of these molecules follow power-law behavior that depends on the chain length with exponent near 1 for the volume, and for the surface. The exponents calculated presented a dependence on the solvent probe radius. It was demonstrated that only in a rigid simple model these exponents converge to unity as the chain length increases to infinity. However the reason for fractionary exponents found here could be just attributed to finite size effect, but in fact, the flexibility plays a central rule in a real molecular system, and could explain the fractionary exponents obtained here. Both classes of macromolecules analyzed present a self-similar characteristic that could assist for understanding of several biological properties, and result in a variety of potential applications.