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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-1, Issue-6, December 2015

Multifratal Analysis of the Pathogenesis of Alzheimer Disease Tong-han Lan, Zi-yang Lan, Xiao Li, Hao Cai, Fei –fei Yu 

mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. The length of the coastline of Britain or the length of the perimeter of the Koch curve increases as we measure it at finer spatial resolution.The use of fractal analysis has been applied to many field[17].

The main purpose of this paper is to analyze the pathogenesis of Alzheimer Disease by means of fratal method.DNA research has previously focused on searching for low level patterns directly visible within the sequence,while ignoring high level patterns.The multifractal analysis of the pathogenesis of Alzheimer’s Disease is intended to demonstrate that a higer level of pattern information may be availible within the the pathogenesis of Alzheimer’s Disease[18].Thus the research has technically significance.

This paper is divided into four parts: the first part is the introduction of the pathogenesis of Alzheimer Disease and DNA series analysis basic state; in the second part we briefly review materials and the fratal method; the third and four part are the results and discussion.

Abstract—In this paper the fractal analysis method is introduced to characterize the self-similarity of DNA sequences.

Using this method, four whole genomes of the pathogenesis of Alzheimer’s Disease provided by NCBI are analyzed. the pathogenesis of Alzheimer’s Disease were exhibited multifractal characteristics when calculating the probability measure for four difference the pathogenesis sequences of each base indidually.From the results we find that Renyi dimension range between 0.0090 to 3.5043. the multifractal characteristic properties in the whole the pathogenesis of Alzheimer’s Disease are verified. The results of this paper suggest that the the multifractal characteristic property is one of the natural properties that DNA sequences possess, and is directly related to the structure and function of the whole DNA molecule.

Index Terms—mutilfractal,pathogenesis Disease,Renyi dimension

of

Alzheimer’s

I. INTRODUCTION Alzheimer’s disease (AD) is the most common form of dementia and the most frequent degenerative brain disorder encountered in old age, The risk of developing AD substantially increases after 65 years of age [1]. AD is quickly becoming one of the major universal healthcare problems.While the cause of this disease remains unknown, there is evidence for substantial genetic influence [1]-[5].

With the unclear pathogenesis, several hypotheses about the pathogenesis of AD, such as the Abnormal protein hypothesis, cholinergic hypothesis, oxidative stress theory and the estrogen hypothesis, etc. were proposed. Mutations in three genes, a myloid precursorprote in ( APP ), presenilin 1 and 2( PSEN1 , PSEN2 ), result in an early onset, autosomal dominant form of the disease beginning in the third or fourth decade. The ɛ4 allele of apolipoprotein E (APOE) increases the risk of both sporadic and familial AD occurring later in life around the sixth decade. Each of these genes is involved in the production or processing of the amyloid β peptide, which is deposited in the brain as dense plaques that are characteristic of the disease [3]. Today, however, there are neither precise diagnostic approaches nor effective therapeutic agents available for Alzheimer disease.

II. MATERIALS AND METHODS A. Data Resources We will use the tools of the World Wide Web to search the GenBank DNA sequence database (http://www.ncbi.nlm.nih.gov). Homo sapiens amyloid beta (A4) precursor protein (APP), RefSeqGene on chromosome 21(NCBI Reference Sequence: NG_007376.1, GI:166795291); Homo sapiens apolipoprotein E (APOE), RefSeqGene on chromosome 19(NCBI Reference Sequence: NG_007084.2, GI:163954918); Mus musculus presenilin-1 gene, alternatively spliced transcripts, complete cds,GenBank: AF007560.1, GI:2463667; Mus musculus presenilin-2 gene,strain 129X1/SvJ chromosome 12 CRA_211000022007779, whole genome shotgun sequence,GenBank: AAHY01101600.1, GI:69874353.

B. Mapping rule

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A DNA sequence i (i=1,2,…,L)of length L is comprised a series of 4 types of base as follows: adenine(A); thymine(T); guanine(G); and cytosine(C). In order to apply numerical methods to nucleotide sequence, We can also use(-2,-1,1,2) to replace {A,G,C,T},We expect it to reveal more information than one dimensional DNA walk [19].

In the past decade or so there has been a ground swell of interest in unraveling the mysteries of DNA. In order to distinguish coding regions from non-coding ones, many approaches have been proposed[6]-[11], at the same times, the nonlinear scaling method, such as complexity(12)and fractal analysis[13]−[17]were used. The word―fractal‖ was coined by Benoit Mandelbrot in the late 1970s,but objects now defined as fractal in form have been known to artists and mathematicians for centuries. Mandelbrot’s definition---―a set whose hausdorff dimension is not integer‖—is clear in

C. Fractal analysis The use of fractal analysis has been applied to many fields[Kins94],such as ion channel kinetics analysis etal, Fractals are sets which exhibit self-similar properties at different scales and are characterized by their fractal

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Multifratal Analysis of the Pathogenesis of Alzheimer Disease dimension. The word―fractal‖ was coined by Benoit Mandelbrot in the late 1970s,but objects now defined as fractal in form have been known to artists and mathematicians for centuries. Mandelbrot’s definition---―a set whose hausdorff dimension is not integer‖—is clear in mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. The length of the coastline of Britain or the length of the perimeter of the Koch curve increases as we measure it at finer spatial resolution.The use of fractal analysis has been applied to many field[19]-[21].

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D. Estimating the multifractal dimension We compute Renyi dimension for difference the pathogenesis of Alzheimer Disease of the four bases.The results were shown as Fig 4. Renyi dimension for the amyloid beta precursor protein (APP)between 0.0090 to 3.5043, Renyi dimension for apolipoprotein E between0.0023 to 1.7731, Renyi dimension for presenilin-1 gene between0.0028 to2.6578 , Renyi dimension for presenilin-2 gene between0.0217 to 3.0965.

A. The characteristic of DNA walk We find apparent patchiness in real DNA sequences—both in the noncoding and coding regions. Figure1 shows a representative DNA walk for four different of the pathogenesis of Alzheimer Disease DNA sequences. amyloid beta precursor protein

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A useful way of analyzing patchiness arising from the heterogeneous purine-pyrimidine content is DNA walk, defined as above 2.2 mapping rulers. The displacement of

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Fig1. shows a representative DNA walk for four different of the pathogenesis of Alzheimer Disease DNA sequences.

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B. The characteristic of brown noise and white noise We use simulation method and produce two series,namely brown noise and white noise , The displacement of walker after n steps y(n) is used, Fig2.shown brown noise and white noise walker.

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III. RESULTS

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C. Calculation of probabilities We can also use(-2,-1,1,2) to replace {A,G,C,T},The approach implemented is to calculate the probabilities for each individual base of the pathogenesis of Alzheimer Disease separately,Fig 3 show the pathogenesis of Alzheimer Disease difference base at window 100 condition probability distribution.The results defer guass distribution.

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D. Multifractal Dimension In practice,it is more useful to consider a signal as a multifractal, namely considering of more than one fractal.Using Renyi dimension can provide comprehension of complexity within the signal.The Renyi dimension is defined as(1)[19].Where r is the volume element size,Nr is the number of volume elements for a given volume element size,Pj is the probability of occurrence within a given volume element. The q value can be considered as a fractal dimension index.

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Fig 4.shown Renyi dimension for difference the pathogenesis of Alzheimer Disease E. After Sliding window compute multifractal dimension Multifractal characteristic of {A,G,C,T}computed over

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-1, Issue-6, December 2015 100 moving windows with a window size of 128 and offset of 1 was shown in Fig.5 for the amyloid beta precursor protein (APP), Multifractal value of A between 0.0357 to 1.0883, Multifractal value of G between 0.0345 to1.1860, Multifractal value of C between 0.0245 to 0.9557, Multifractal value of T between 0.0220 to 1.1364.The similary apolipoprotein E 、 presenilin-1 gene and presenilin-2 gene of Multifractal characteristic of {A,G,C,T} can be computed.

Multifractal characteristic of A

promote transcriptional activation, while others form the protein basis of the amyloid plaques found in the brains of patients with Alzheimer disease. Mutations in this gene have been implicated in autosomal dominant Alzheimer disease and cerebroarterial amyloidosis. Multiple transcript variants encoding several different isoforms have been found for this gene[22].Chylomicron remnants and very low density lipoprotein (VLDL) remnants are rapidly removed from the circulation by receptor-mediated endocytosis in the liver.

Apolipoprotein E, a main apoprotein of the chylomicron, binds to a specific receptor on liver cells and peripheral cells.ApoE is essential for the normal catabolism of triglyceride-rich lipoprotein constituents[23].act. these properties are considered to be related to the construction of the higher order structure of the DNA molecule.

This paper is preliminary with respect to the multifractal characteristic Exist in potential relevance to the pathogenesis of Alzheimer’s Disease. Its aim is to provide the means for the analysis of the multifractal characteristic properties of DNA sequences.although the research resuls ahown the multifractal characteristic Exist the pathogenesis of Alzheimer’s Disease, This may led to series of questions, what is the physical phenomena and possible mechanism of the pathogenesis of Alzheimer’s Disease ? How to categorize different types of the pathogenesis of Alzheimer’s Disease, how to understand the function of the pathogenesis of Alzheimer’s Disease, how to build the pathogenesis of Alzheimer’s Disease kinetics model systematically? Although the data tell us that the multifractal characteristic does exist in the pathogenesis of Alzheimer’s Disease, we will still think about the physical properties of the pathogenesis of Alzheimer’s Disease.what kind of distribution form do these the pathogenesis of Alzheimer’s Disease have? All these studies should be the future direction of research.

Multifractal characteristic of G

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IV. DISCUSSION Multifractal analysis was applied to analysize amyloid beta precursor protein 、 apolipoprotein E 、 presenilin-1 and presenilin-2 the sequences of the pathogenesis of Alzheimer’s Disease. the pathogenesis of Alzheimer’s Disease were exhibited multifractal characteristics,at the same times,it was calculated the probability measure for four difference the pathogenesis sequences of each base indidually.From the results we find that Renyi dimension range between 0.0090 to 3.5043.After Sliding window compute multifractal dimension,Multifractal characteristic of {A,G,C,T}computed over 100 moving windows with a window size of 128 and offset of 1 , for the amyloid beta precursor protein (APP), Multifractal value of {A,G,C,T} can be computed. The results were between 0.0357 to 1.0883, 0.0345 to1.1860, 0.0245 to 0.9557, 0.0220 to 1.1364 indvididly.The similary apolipoprotein E、presenilin-1 gene and presenilin-2 gene Multifractal value of {A,G,C,T}can be computed.

In this paper the multifractal characteristic properties in the whole genomes of amyloid beta (A4) precursor protein (APP) 、apolipoprotein E、presenilin-1 gene、presenilin-2 gene are verified. The results of this paper suggest that the the multifractal characteristic property is one of the natural properties that DNA sequences possess, and is directly related to the structure and function of the whole DNA molecule.There are still many discussions concerning the biological meaning and the origin of the the multifractal characteristic properties in the DNA sequences. Such as, APP gene encodes a cell surface receptor and transmembrane precursor protein that is cleaved by secretases to form a number of peptides. Some of these peptides are secreted and can bind to the acetyltransferase complex APBB1/TIP60 to

ACKNOWLEDGMENT This project was supported by China National Nature Science Foundation No:30470413, No:31160200.Hubei province Nature Science Foundation No:2004ABA220 and China Postdoctoral Science Foundation. We are also indebted to sir lan zi yang for his valuable support and helpful discussions.

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Tong-han Lan,Gongnongbin Road, Jiangan District Wuhan 430012,P R China Zi-yang Lan, Gongnongbin Road, Jiangan District Wuhan 430012,P R China Xiao Li, Gongnongbin Road, Jiangan District Wuhan 430012,P R China Hao Cai, Gongnongbin Road, Jiangan District Wuhan 430012,P R China Fei –fei Yu Gongnongbin Road, Jiangan District Wuhan 430012,P R China

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