Sk. Sarif Hassan

Underlying mathematics in diversification of human olfactory receptors in different loci

As per conservative estimate, approximately 51–105 Olfactory Receptors (ORs) loci are present in human genome occurring in clusters. These clusters are apparently unevenly spread as mosaics over 21 pairs of human chromosomes. Olfactory Receptor (OR) gene families which are thought to have expanded for the need to provide recognition capability for a huge number of pure and complex odorants, form the largest known multigene family in the human genome. Recent studies have shown that 388 full length and 414 OR pseudo-genes are present in these OR genomic clusters. In this paper, the authors report a classification method for all human ORs based on their sequential quantitative information like presence of poly strings of nucleotides bases, long range correlation and so on. An L-System generated sequence has been taken as an input into a star-model of specific subfamily members and resultant sequence has been mapped to a specific OR based on the classification scheme using fractal parameters like Hurst exponent and fractal dimensions.

DNA sequence evolution through Integral Value Transformations.

In deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) plays a significant role. DNA can be thought as a one-dimensional multi-state CA, more precisely four states of CA namely A, T, C, and G which can be taken as numerals 0, 1, 2 and 3. Earlier, Sirakoulis et al. (2003) reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of the DNA evolutions with the help of only four linear CA rules. The DNA sequences which are produced through the CA evolutions, however, are seen by us not to exist in the established databases of various genomes although the initial seed (initial global state of CA) was taken from the database. This problem motivated us to study the DNA evolutions from more fundamental point of view. Parallel to CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT). Interestingly, on applying the IVT systematically, we have been able to show that each of the DNA sequence at various discrete time instances in IVT evolutions can be directly mapped to a specific DNA sequence existing in the database. This has been possible through our efforts of getting quantitative mathematical parameters of the DNA sequences involving fractals. Thus we have at our disposal some transformational mechanism between one DNA to another.

Quantitative Description of Genomic Evolution of Olfactory Receptors

We investigate how the evolutionary network is associated among Human, Chimpanzee and Mouse with regards to their genomic information. We provide a quantitative description of genomic evolution through indexes based on fractals and mathematical morphology. These indexes are carefully chosen and reveal quantitatively the similarity or differences among the structure of the concerned sequences. They also reveal how the sequences have evolved over the course of time. We have considered olfactory receptors (ORs) as our case study. These ORs do function in different species with the subtle differences in between the structures of DNA sequences. Such differences are quantified in this paper.

Designing exons for human olfactory receptor gene subfamilies using a mathematical paradigm

Ligands for only two human olfactory receptors are known. One of them, OR1D2, binds to Bourgeonal, a volatile chemical constituent of the fragrance of the mythical flower, Lily of the valley or Our Lady’s tears, Convallaria majalis (also the national flower of Finland). OR1D2, OR1D4 and OR1D5 are three full-length olfactory receptors present in an olfactory locus in the human genome. These receptors are more than 80% identical in DNA sequences and have 108 base pair mismatches among them. Apparently, these mismatch positions show no striking pattern using computer pattern recognition tools. In an attempt to find a mathematical rule in those mismatches, we find that an L-system generated sequence can be inserted into the OR1D2 subfamily-specific star model and novel full-length olfactory receptors can be generated. This remarkable mathematical principle could be utilized for making new subfamily olfactory receptor members from any olfactory receptor subfamily. The aroma and electronic nose industry might utilize this rule in future.

L-Systems: a mathematical paradigm for designing full length human genes and genomes

We have shown how L-Systems can generate both an exon (human OR) and a system containing both exons and introns (human mitochondria). Ligands for only two human olfactory (OR) receptors are known. One of them, OR1D2, binds to Bourgeonal, a volatile chemical constituent of the fragrance Lily of the valley (Convallaria majalis). OR1D2, OR1D4 and OR1D5 are three full- length olfactory receptors present in an olfactory locus in human genome. These receptors are more than 80% identical in DNA sequences and have 108 base pair mismatches among them. We have used L-system mathematics to show a closely related subfamily of OR1D2, OR1D4 and OR1D5. Craig Venters group reported experimental construction of long DNA molecules adopting several working hypotheses. A mathematical rule for generating such long sequences would shed light on several fundamental problems in various areas of biology, for example evolution of long DNA chains in chromosomes, the reasons for existence of long stretches of non-coding regions, as well as usher in automated methods for the preparation of long DNA chains to enable chromosome engineering. However, this mathematical principle must have room for editing/correcting DNA sequences locally in the areas of genomes where mutation and/or DNA polymerase has introduced errors over millions of years of evolution. Here we present the whole mitochondrial genome (exons and introns) generated by the L-Systems.

Fractal and mathematical morphology in intricate comparison between tertiary protein structures

Intricate comparison between two given tertiary structures of proteins is as important as the comparison of their functions. In literature, several algorithms have been devised to compute the simil...

Quantification of miRNAs and Their Networks in the light of Integral Value Transformations

Abstract MicroRNAs (miRNAs) which are on average only 21-25 nucleotides long are key post-transcriptional regulators of gene expression in metazoans and plants. A proper quantitative understanding of miRNAs is required to comprehend their structures, functions, evolutions etc. In this paper, the nucleotide strings of miRNAs of three organisms namely Homo sapiens (hsa), Macaca mulatta (mml) and Pan troglodytes (ptr) have been quantified and classified based on some characterizing features. A network has been built up among the miRNAs for these three organisms through a class of discrete transformations namely Integral Value Transformations (IVTs), proposed by Sk. S. Hassan et al [1, 2]. Through this study we have been able to nullify or justify one given nucleotide string as a miRNA. This study will help us to recognize a given nucleotide string as a probable miRNA, without the requirement of any conventional biological experiment. This method can be amalgamated with the existing analysis pipelines, for small RNA sequencing data (designed for finding novel miRNA). This method would provide more confidence and would make the current analysis pipeline more efficient in predicting the probable candidates of miRNA for biological validation and filter out the improbable candidates.

The variations of human miRNAs and Ising like base pairing models

miRNAs are small about 22-base pair long, RNA molecules are of extreme biological importance. Like other longer RNA molecules, messages in miRNAs are encoded by the permutations of only four nucleotide bases represented by A, U, C and G. However, just like words in any language, not all combination of these alphabets make a meaningful word. In fact, we find that the distributions of nucleotides bases in human miRNAs show significant deviation from randomness. First, a miRNA sequence containing four bases are mapped into a binary string with three kinds of classifications according to their chemical properties. Then, we propose a simple nearest neighbor model (Ising model) to understand the statistical variations in human miRNAs.

Analysis of Purines and Pyrimidines distribution over miRNAs of Human, Gorilla, Chimpanzee, Mouse and Rat

Meaningful words in English need vowels to break up the sounds that consonants make. The Nature has encoded her messages in RNA molecules using only four alphabets A, U, C and G in which the nine member double-ring bases (adenine (A) and Guanine (G)) are purines, while the six member single-ring bases (cytosine (C) and uracil (U)) are pyrimidines. Four bases A, U, C and G of RNA sequences are divided into three kinds of classifications according to their chemical properties. One of the three classifications, the purine-pyrimidine class is important. In understanding the distribution (organization) of purines and pyrimidines over some of the non-coding RNAs, all miRNAs of the three species (human, gorilla and chimpanzee) of Hominidae family and two species (mouse and rat) from of Muridae family are considered. The distribution of purines and pyrimidines over miRNA shows deviation from randomness. Based on the quantitative metrics (fractal dimension, Hurst exponent, Hamming distance, distance pattern of purine-pyrimidine, density distribution of purine-pyrimidine and Shannon entropy) five different clusters have been made for the five species. We have observed some couple of results including the closeness of different clusters among the five species.

Steganography Technique to Prevent Data Loss by Using Boolean Functions

Steganalysis technique embedded the secret message, so we have to conceal the very important data. Our main objective is undetectability, robustness and capacity of the hidden data. Existing image steganography techniques used various methods to hide data in a perfect manner. We used many Boolean functions to achieve a data (image)-hiding method or image steganography without loss of any information. Also, the data can be hidden and unhidden efficiently through the Boolean functions. Our experiments and corresponding outcome deliver that it is more secured than the existing approaches of steganography.