A New Fractal Model of Chromosome and DNA Processes
Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes?Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sens
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Abstract Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes? Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, model, and analyze the complex forms found in nature. Fractals have also been widely not only in biology but also in medicine. To this effect, a fractal is considered an object that displays self-similarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales). It is worth noting that the problem of identifying a chromosome has become a challenge to find out which one of the models it belongs to. Nevertheless, the several different models (a hierarchical coiling, a folded fiber, and radial loop) have been proposed for mitotic chromosome but have not reached a dynamic model yet. This paper is an attempt to solve topological problems involved in the model of chromosome and DNA processes. By combining the fractal Julia process and the numerical dynamical system, we have finally found out four main points. First, we have developed not only a model of chromosome but also a model of mitosis and one of meiosis. Equally important, we have identified the centromere position through the numerical model captured below. More importantly, in this paper, we have discovered the processes of the cell divisions of both mitosis and meiosis. All in all, the results show that this work could have a strong impact on the welfare of humanity and can lead to a cure of genetic diseases.
K. Bouallegue () Computer & Embedded Systems Laboratory, University of Sfax, Tunisia High Institute of Applied Sciences and Technology of Sousse, Cit Taffala (ISSAT), 4003 Sousse Tunisie e-mail: kais [email protected] S.G. Stavrinides et al. (eds.), Chaos and Complex Systems, DOI 10.1007/978-3-642-33914-1 71, © Springer-Verlag Berlin Heidelberg 2013
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1 Introduction Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, to model and to analyze the complex forms found in nature. Fractals have found a wide application in biology and medicine. A fractal is an object that displays selfsimilarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales). Fractals have generated a great deal of interest since the advent of the computer. Lindenmayer introduced the idea of using a formal language to model the developmental processes and structures of organisms [6]. The problem of identifying a chromosome has become a challenge to find out which one of the models it belongs too [4]. Many different models have been proposed for mitotic chromosome including a hierarchical coiling model [1], a folded fiber model, a tube model [7] and radial loop model [8]. This investigation was driven by the need to solve topological problems involved in the process
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