Modeling Double DNA Helix Main Chains of the Free and Forced Fractional Order Vibrations

Abstract

DNA transcription process is well described at biochemical level. During transcription, double DNA interacts with transcription proteins; a part of double DNA is unzipped, and only one chain helix is used as a matrix for transcription. Different models oftwo coupled homogeneous DNAchain vibrations are proposed in the literature. To better understand the DNA transcription process and its behavior through biomechanical point of view, we consider double DNA (dDNA) as an oscillatory system that oscillates in forced regimes. When data from dDNA molecule are not transcripted, we consider that dDNA molecule oscillates in a manner of free fractional order vibrations.On the basis of previous results (DNA mathematical models published by N.Kovaleva, L. Manevich in 2005 and 2007, and multi-pendulum models by Hedrih (Stevanović) and Hedrih) we obtain a corresponding pair of main chain subsystems of the double DNA helix. Analytical expressions of the eigen circular frequencies and eigen fractional order characteristic numbers for the homogeneous model of the double DNA fractional order chain helix are obtained. Also, the corresponding eigen free and forced fractional order vibration modes and possibilities of the appearance of resonant regimes, as well as dynamical absorption under the external forced excitations are considered. Two sets of eigen normal coordinates of the double DNA chain helix for separation of the system into two uncoupled main eigen chains are identified. On the basis of the derived analytical expressions, a transfer of external excitation forced signals is analyzed. There are different cases of the resonant state in one of the main chains, and there are no interactions between main chains for special cases of the external one frequency forced excitation. This may correspond to the base pair order in complementary chains of DNA double helix in a living cell.