It is well known that a DNA macromolecule is a most important complex biological system for the simple reason that it is the repertory of the genetic codes of a descent. Thus, the behavioral study of its functioning is the center of interest of several researchers. For instance, understanding the mechanisms of transcription and replication in the DNA double-helix are some of essential problems of DNA physics and molecular biology. Complete solution of the problem has not been attained because of insufficient knowledge of the DNA helix transformation mechanisms and the complex structure of the macromolecule. It had been found that due to the presence of phosphate groups along the DNA’s strands, the long-range interactions (LRI) exists in that macromolecule and allows to take into account the screening of the interactions or an indirect coupling between base pairs via water filaments. Furthermore, the DNA and RNAP are constituted by specific sites such as promoter, coding, or terminator, which has a specific sequence of bases and peptides, and this makes the strands site dependent or inhomogeneous. Many qualitative discrepancies have been discovered and shared by theoretical findings so that the real long-range force to be adopted for DNA dynamics remains unclear. To contribute to these behavioral analysis of the DNA’s molecule while studying the influence of LRI on its dynamics, we have considered spin model of that molecule (a form of modeling among several DNA’s models which exist because of enormous degrees of freedom in dynamics of a DNA macromolecule) in which we introduce the intra-strand LRI when an inhomogeneous RNAP molecule comes to bind on an inhomogeneous DNA molecule at the biological temperature. It comes out from our results that the breather-like solitons, solitary waves which govern the transport of bubbles during the transcription, are deeply influenced by the LRI. Indeed, we find that the energy of the bubble (or bubble height) decreases with the decreasing of the LRI’s parameter (the dimensionless inverse radius of interaction) and if a base pair interacts with many other pairs which form the bubble (the width of bubble increases while its height decreases). The results also show that inhomogeneities introduce some fluctuations in the localized region of the breather. This dynamical behavior may act as energetic activators of the enzyme transport during the process of transcription in DNA and reinforces the efficiency and sturdiness of energy localization within transcription phenomenon.