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Long noncoding RNA (lncRNA) within mRNA sequences of Alzheimer’s disease genes, namely, APP, APOE, PSEN1, and PSEN2, has been analyzed using fractal dimension (FD) computation and correlation analysis. We examined lncRNA by comparing mRNA FD to corresponding coding DNA sequences (CDSs) FD. APP, APOE, and PSEN1 CDSs select slightly higher FDs compared to the mRNA, while PSEN2 CDSs FDs are lower. The correlation coefficient for these sequences is 0.969. A comparative study of differentially expressed MAPK signaling pathway lncRNAs in pancreatic cancer cells shows a correlation of 0.771. Selection of higher FD CDSs could indicate interaction of Alzheimer’s gene products APP, APOE, and PSEN1. Including hypocretin sequences (where all CDSs have higher fractal dimensions than mRNA) in the APP, APOE, and PSEN1 sequence analyses improves correlation, but the inclusion of erythropoietin (where all CDSs have higher FD than mRNA) would suppress correlation, suggesting that HCRT, a hypothalamus neurotransmitter related to the wake/sleep cycle, might be better when compared to EPO, a glycoprotein hormone, for targeting Alzheimer’s disease drug development. Fractal dimension and entropy correlation have provided supporting evidence, consistent with evolutionary studies, for using a zebrafish model together with a mouse model, in HCRT drug development.

The instructions of a genetic sequence are carried by the fluctuations or variations in the nucleotide bases along the sequence. The bioinformatics of a sequence can be studied if the sequence is modeled as a series based on the nucleotide atomic number of the nucleotides A, T, C, and G. A recent study on such fluctuation in the FOXP2 gene pathway has been reported [

This project focuses on the study of disease related genetic sequences. The lncRNAs within the mRNA sequences in Alzheimer’s disease genes, namely, APP or AD1, APOE or AD2, PSEN1 or AD3, and PSEN2 or AD4, have been analyzed in terms of fractal dimension computation and correlation analysis. The exploratory hypothesis that the lncRNA sequences embedded in a transcribed mRNA sequence would exhibit correlation in Alzheimer’s disease genes has been studied in a comparative fractal dimension model of mRNA sequences versus coding DNA sequences (CDSs), which do not include the lncRNA sequences.

The data used in this study was downloaded from GenBank according to the following Gen-ID numbers. The studied human genes are APP-Gen-ID-351 containing 10 mRNA variants, APOE-Gen-ID-348, PSEN1-Gen-ID-5663 having 2 mRNA variants, PSEN2-Gen-ID-5664 having two mRNA variants, HCRT-Gen-ID-3060, HCRTR1-Gen-ID-3061 (HCRT Receptor-1), HCRTR2-Gen-ID-3062 (HCRT Receptor-2), EPO-Gen-ID-2056, and EPOR-Gen-ID-2057. The MAPK signaling pathway gene accession numbers have been listed in the report of differential expression of long non-coding intronic RNAs in pancreatic cancer cells [

A sequence with a relatively low nucleotide variety would have low Shannon’s entropy (more constraints) in terms of the set of 16 possible dinucleotide pairs. A sequence’s entropy can be computed as the sum of ^{4}). For mono-nucleotide consideration, the maximum entropy is two bits per mononucleotide with four possibilities (2^{2}). In general, the monoentropy is proportional to di-nucleotide entropy with

Roughly speaking, fractal dimension measures the complexity of a self-similar sequence. For a 1D sequence such as a DNA sequence, a fractal dimension near 2 indicates great complexity, while one closer to 1 would indicate little complexity, variety, or information. Among the various fractal dimension methods, the Higuchi fractal method is well suited for studying signal fluctuation [

Consider

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data2 = circshift(data,

data2 = abs(data2 − data);

data2 (1 :

end

% calculate slopes (FDs)

slope = zeros(1, width);

for

temp = 1 : 1 :

End

The ratio of CDS length to mRNA length ranges from 0.23 to 0.78 in the studied Alzheimer’s disease sequences. A negative correlation with

The fractal dimension correlation of the CDSs versus mRNAs in Alzheimer’s disease is displayed in Figure

The fractal dimension correlation of the APP, APOE, PSEN1, and PSEN2 CDSs versus mRNAs in Alzheimer’s disease is displayed with

The fractal dimension correlation of the differentially expressed MAPK signaling pathway long noncoding intronic RNA in pancreatic cancer cells with a correlation of

The systematic selection of higher fractal dimension CDSs could be indicative of certain characteristic interaction of the Alzheimer’s gene products APP, APOE, and PSEN1 where a correlation with

The fractal dimension correlation of the APP, APOE, PSEN1, HCRT, HCRT-R1, and HCRT-R2 CDSs versus mRNAs in Alzheimer’s disease is displayed with

The regression intercepts in Figures

The correlation results suggest a hypothesis where HCRT, a neurotransmitter only produced in the hypothalamus and related to the wake/sleep cycle, could be a relatively more important candidate as a blocker or promoter when compared to EPO, a glycoprotein hormone produced by kidney and liver, for targeting drug development with application to Alzheimer’s disease clinical trials. The HCRT hypothesis would be consistent with MRI brain scans (168 regions) containing microarray array expression level data from the Allen Brain Atlas database. The brain scan data analysis has showed higher Skewness value in HCRT Receptor-2 expression level distribution (Figure

HCRT Receptor-2 expression level distribution in the brain regions (168 regions for each patient) using the 4-patient data from Allen Brain Atlas. The expression level

EPO Receptor expression level distribution in the brain regions (168 regions for each patient) using the 4-patient data from Allen Brain Atlas. The expression level

HCRT expression level distribution in the brain regions (168 regions for each patient) using the 4-patient data from Allen Brain Atlas. The expression level

EPO expression level distribution in the brain regions (168 regions for each patient) using the 4-patient data from Allen Brain Atlas. The expression level

Mouse model has become a popular choice in drug development since evolution has been a corner stone for the understanding of biology. A plot of fractal dimension versus entropy for HCRT CDSs in human, mouse, and zebrafish is displayed in Figure

A plot of fractal dimension versus entropy for HCRT CDSs in human, mouse, and zebrafish is displayed with

A plot of fractal dimension versus entropy for HCRT-R2 CDSs in human, mouse, and zebrafish is displayed with

Recently the R47H variant of TREM2 was reported to be associated with Late-onset Alzheimer’s disease (LOAD) [

The fractal dimension correlation of the TYROBP-Variants 1–4 and TREM2 CDSs versus mRNAs involved in Late-onset Alzheimer’s disease.

Fractal dimension versus entropy for TYROBP-Variant 1, TYROBP-Variant 2, TYROBP-Variant 3, TYROBP-Variant 4, and TREM2 CDSs involved in Late-onset Alzheimer’s disease in human. The fractal dimension is represented on the

As [

High correlation results are also observed in two other neurodegenerative disease involving TYROBP. The Nasu-Hakola disease, a disorder affecting both brain and bone, is known to be related to the malfunctioning of TREM2 or TYROBP [

The long noncoding RNAs (lncRNAs) within the mRNA sequences in Alzheimer’s disease genes, namely, APP, APOE, PSEN1, and PSEN2, have been analyzed in terms of fractal dimension computation and correlation analysis. The results show that APP, APOE, and PSEN1 CDSs select slightly higher fractal dimensions as compared to the mRNA sequences with a pattern evidenced by correlation coefficient of

The project was partially supported by CUNY research Grant J. Ye thanks the NSF-REU program for student support. E. Cheung and S. Dehipawala thank QCC Physics Department for the hospitality. The authors thank Dr. N. Le of Thomas Jefferson Medical School Pathology Department, 1020 Locust Street, Philadelphia, PA 19107, USA for discussion. The authors, thank the research groups cited in the paper for posting their data and software in the public domain.