Variant Map Construction to Detect Symmetric Properties of Genomes on 2D Distributions

Visualization Methods have played a key role in the Human Genome Project. After further development in other international projects such as ENCODE, larger numbers of Genome Databases are established and mass Genomewide gene expression measurements are developed. In current situation, it is necessary to shift targets in computational cell biology from collecting sequential data to making higher-level interpretation and exploring efficient content-based retrieval mechanism for genomes. Mammalian genomes encode thousands of large non-coding RNAs (lncRNAs), many of which regulate gene expression, interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. Using higher dimensional visualization tools, their complex interactive properties could be organized as different visual maps. The Variant Map Construction VMC as an emerging scheme is systematically proposed in this paper to apply multiple maps that uses four Meta symbols as same as DNA or RNA representations. System architecture of key components and core mechanism on the VMC are described. Key modules, relevant equations and their I/O parameters are discussed. Using the VMC system, two DNA data sets of multiple real sequences are tested to show their visible properties in higher levels of intrinsic relationships among relevant DNA sequences in 2D maps. Visual results are briefly analyzed to explore their intrinsic properties and symmetric characteristics on relevant genome sequences under 2D maps of the Variant Map Construction. A set of sample 2D maps are included and their characteristics are illustrated under various controllable environment. Journal of Data Mining in Genomics & Proteomics J o u r n a l of D ata Mi ning in Gmics & rot e o m i c s ISSN: 2153-0602 Citation: Zheng J, Zhang W, Luo J, Zhou W, Liesaputra V (2014) Variant Map Construction to Detect Symmetric Properties of Genomes on 2D Distributions. J Data Mining Genomics Proteomics 5: 150. doi:10.4172/2153-0602.1000150


Introduction
Visualization Methods have played a key role in the Human Genome Project (HGP) [1,2]. After HGP completed successfully, a public research consortium-the Encyclopedia of DNA Elements (ENCODE) were launched by the National Human Genome Research Institute (NHGRI) in 2003 to find all functional elements in the human genome as one of the most critical projects by NHGRI to explore genomes after HGP.
In 2012, ENCODE released a coordinated set of 30 papers published in key Journals of Nature, Genome Biology and Genome Research. These publications show that approximately 20% of noncoding DNA in the human genome is functional while an additional 60% is transcribed with no known function [3]. Much of this functional non-coding DNA is involved in the regulation of the expression of coding genes [4]. Furthermore the expression of each coding gene is controlled by multiple regulatory sites located both near and distant from the gene. These results demonstrate that gene regulation is far more complex than was previously believed [5]. Mammalian genomes encode thousands of large non-coding RNAs (lncRNAs), many of which regulate gene expression, interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome [6]. Associated with different international projects, larger numbers of Genome Databases are established and mass Genome-wide gene expression measurements are developed. Due to huge amount of DNA sample collections and extremely difficulties to determine their variation properties in wider applications [7], it is essential for us to extend advanced DNA analysis models, methods and tools in further extensions to explore emerging models and concepts to interpret complex interactions among complicated sets of DNA sequences in real environments.
In current situation, it is necessary for advanced researchers to shift targets in computational cell biology from directly collecting sequential data to making higher-level interpretation and exploring efficient content-based retrieval mechanism for genomes. Using higher dimensional visualization tools, their complex interactive properties could be organized as different visual maps systematically.

DNA Analysis
DNA analysis plays a key role in modern genomic application [2]. The HGP is heavily relevant to advanced DNA sequencing and analysis techniques. DNA sequences are composed of four Meta symbols on {A, T, G, C} as basic structure. Classical DNA double helix structure makes the first level of pair construction of DNA sequences with A & T and G & C complementary structures as the first level of symmetric relationships. A typical DNA sequencing result is shown in Figure 1a. Four Meta symbols could be separated as four projective sequences.
In ENCODE, recent Genomic analysis results are indicated that encoded sequences have only 20 percent in human genomes and around 80 percent genomes look like useless sequences. Under further assumptions, it seems that additional symmetric properties are required to satisfy the second, third and higher levels of structural constructions

Variant Construction and DNA
Variant construction is a new structure composed of logic, measurement and visualization models to analyze 0-1 sequences under variant conditions. The further details of this construction can be checked on variant logic [13,14], 2D maps [15,16] and variant phase spaces [17]. Since the variant system uses another set of four Meta symbols { , , , } ⊥ + − Τ to describe system, this typical correspondence shown in Figure 1b may provides a natural mapping between DNA and variant data sequences.
Since DNA sequences are played an essential role to explore different symmetric properties based on analysis approaches, in this paper, measurement and visual models are proposed systematically to use a fixed segment structure to measure four meta symbols distributions in their spectrum construction. Under this construction, refined symmetric features can be identified from their polarized distributions and further symmetric properties are visualized.

Target of this Paper
The target of this paper is to establish the Variant Map Construction (VMC) as an emerging scheme systematically based on variant logic schemes [13][14][15][16][17] to apply multiple maps that uses four Meta symbols as same as DNA or RNA representations. System architecture of key components and core mechanism on the VMC are described. Key modules, relevant equations and their I/O parameters are discussed. Applying the VMC system, two DNA data sets of multiple real sequences are collected to show their intrinsic properties in higher levels of intrinsic relationships among relevant DNA sequences on various 2D maps. Further detailed descriptions and discussions are contained.

System Architecture
In this section, system architecture and their core components are briefly discussed with the use of diagrams. The refined definitions and equations of this system are described in the next section-Variant Map Construction.

Architecture
The three components of a variant map construction are the Binary Probability Measurement (BPM), Mapping Position (MP), and Visual Map (VM) as shown in Figure 2. The architecture is shown in Figure  2a with the key modules of the three core components being shown in (Figures 2b-2d) respectively.
In the first part of the system, four vectors of probability measurements are created from the t-th selected DNA sequence with N t elements as an input. Multiple segments are partitioned by a fixed number of n elements for each segment; at least m t segments can be identified by the BPM component.

Output group:
{Map v } Four 2D maps for distributions, V∈D

BPM-Binary probability measurement
The BPM component as shown in Figure   The BPM component transforms a selected DNA sequence to generate four 0-1 vectors by BM module for the input DNA sequence. Then four probability vectors are generated by the PM module as the output of the BPM under a fixed length of segment condition.

MP-Mapping position
The MP component as shown in Figure 2c The MP component uses probability measurements as input, under a given k condition to generate each relevant histogram and its normalized distribution. The output of the MP component is composed of four paired values controlled in a given condition

VM-Visual map
The VM component shown in Figure 2d is composed of one module: VM Visual Map. Three parameters are input signals. Collected all selected DNA sequences, four 2D maps are generated by the VM component as the output result.
Inputgroup: ∀t all possible DNA sequences are selected, 0 t < T ≤ X t An input DNA vector with N t elements, Four paired values for the t-th DNA sequence,

Variant Map Construction
In this section, brief definitions and equations are provided to describe the proposed VMP system. In addition to the initial preparation, six core modules are involved in the BM, PM, HIS, NH, PP and VM components respectively.

Initial preparation
Let X denotes a DNA sequence with N elements, D denotes a symbol set with four elements i.e. D={A,G,T,C}. This type of a DNA sequence can be described as a four valued vector follows: X=(X(0),…,X(I),…,X(N-1)), Applying the four operators to all elements, the DNA sequence X can be reorganized as four binary sequences in 0-1 values. i.e.
E.g. Let a DNA sequence X=CTGATTAGCCAT, N = 12, its four binary sequences can be represented as follows. X=CTGATTAGCCAT It is interesting to notice that the basic relationship between a DNA sequence X and its four M V sequences are exactly same as in a modern DNA sequencing procedure to separate a selected DNA sequence into the four Meta symbol sequences shown in Figure 1a. This correspondence could be the key feature to apply the proposed scheme naturally in simulating complex behaviors for any DNA sequence. The projection M V provides the required operation in the BM component as the first module shown in Figure 2b.

PM module
For this set of the four binary sequences, it is convenient to partition them into m segments and each segment contained a fixed number of n elements. For the l-th segment, let 0 ≤ l<m, 0 ≤ j<n, the I-th position will be I=1*n+J, four probability measurements { , , , ,} T A G C ρ ρ ρ ρ can be defined. The probability operator ρ V generates four probability measurement vectors in the PM component as the second module shown in Figure  2b. After the BM and PM processes, the whole procedure of the BPM component is complete in Figure 2b.

HIS module
Since the BPM generates four sets of probability measurement, it is necessary to perform further operations in the MP component shown in Figure 2c as follows.
In the HIS component as the first module in Figure 2c

NH module
Under this construction, a normalized histogram can be defined as In the PP component, four paired values are generated and each pair indicates a specific position on a 2D map relevant to the selected DNA sequence. The core operations of two key components: BPM and MP for a selected DNA sequence are performed in Figures 2b and 2c.

VM module
Since only one point of a 2D map is determined for a selected DNA sequence, it is essential to apply larger number of DNA sequences as inputs to generate visible distributions. This type of operations will be performed in the VM component shown in Figure 2d.
In a general condition, the VM component processes a selected DNA set t T-1 t=0 {X } composed of T sequences, the t-th sequence with N t elements can be expressed by t N t t t t t t X =(X (0),...,X (I),...,X (N -1),X D ∈ each sequence can be processed to apply the same procedures of the BPM and MP components. Since for each segment, its length n will be fixed for all selected sequences, it is essential to make number of segments be [ ] N n in convention to match each sequence. Under this expression, the last module VM collects all T pairs of positions on relevant 2D visual maps as follows, A sample 2D map of VM is shown in Figure 3; this provides an assistant illustration for this type of visual maps on a case of multiple sequences.
Under this construction, T DNA sequences are transformed as T visual points on four 2D visual maps that would be help analyzers to explore their intrinsic symmetry properties among four binary sequences.

Data resources
It is important to use some real DNA sequences to illustrate various test results of the VMC system. Two sets of DNA sequences are selected and relevant resource features are briefly described as follows.
The first data set originally comes from the human genome assembly version 37 and was taken from the reference sequences of 13 anonymous volunteers from Buffalo, New York. Hi-C technology [1] used to analyze chromatin interaction role in genome. From a genomic analysis viewpoint, this set of data may contain more complex secondary or higher level structures. A special structure nearly the GRCh37 DNA sequence has been identified to explore their spatial characteristics. After positive and negative sequencing, each data file contain 2700 DNA sequences and each sequence has around 500 elements stored in two files left and right respectively.
The second data set are selected from some plant gene database for comparison. Two DNA sequence sets are stored in file201-500 and random_201-500. Each data file contains 2700 DNA sequences and each sequence has around 200-600 elements. Both of them may be ordinary single sequences without complex secondary structures.

Sample results
Using the two sets of DNA sequences, four groups of 2D maps are listed in Figures 4-7 under different conditions to illustrate their spatial distributions using Variant Map Construction in a controllable environment. In Figure 4, two groups of ten 2D maps are shown in the range of n=3, k=7, N 200 600, T=2700 ≅  for comparison; (a1- (d)  10) ten Map A maps for the file Right; (b1-10) ten Map G maps for the file 201-500 respectively. In Figure 5, four groups of sixteen 2D maps are listed in the range of n=15, k={2,3,4,7}, N 500, T=2700; (a) group (a1-a4) four Map A maps; (b) group (b1-b4) four Map T maps; (c) group (c1-c4) four Ma pG maps; (d) group (d1-d4) four Map C maps for the file right. In Figure 6

Symmetric Analysis Based on 2D Maps
Four groups of 2D maps contain different information, it is necessary to make a brief discussion on their important issues as follows. The first group of results shown in Figure 4 presents two sets of ten 2D maps from two data files: right and 201-500 undertaken various lengths of basic segment from 3-90 to illustrate their variations respectively. Ten 2D maps of Figure 4 (a1-a10) for the file right show significant trace on their visual distributions; the numbers of main visible clusters identified are decreased when the length of segment has being increased e.g. (a3-a10). However lesser length of segment does not provide refined visual distinctions with larger region in fuzzy areas e.g. (a1-a2). From a structural viewpoint, middle ranged numbers of length provide better clustering results e.g. (a3-a5) for further analysis targets. To check another ten 2D maps of Figure 4 (b1-b10) for the file 201-500, different visual distributions are observed; the numbers of main visible clusters identified are decreased when the length of segment has being increased less significantly e.g. (b4-b10). However lesser length of segment does not provide refined visual distinctions with wider regions in fuzzy areas e.g. (b1-b3). In general, middle ranged numbers of length still provide better clustering effects e.g. (b4-b7) for further analysis purpose. It is interesting to observe different maps when control parameter k changed. Four groups of sixteen 2D maps for the file right are shown in Figure 5 on the range of n=15,k={2,3,4,7},N 200 600,T=2700 ≅  ; four groups in (a)-(d) provide four maps to share the same other parameters with different k values. Checking visible clusters in different maps, it is important to notice nearly same numbers of clusters identified in the same group, but different groups may contain significantly different numbers. Lesser k value (e.g. k=2) makes a tighter distribution and larger k value (e.g. k=7) takes better separation on the maps. Through k=7 maps provide better separation effects, it is easy to observe their y axis values already in 10 8 range. Four groups of sixteen 2D maps for the file 201-500 are shown in Figure 6 in the range of n=15,k={2,3,4,7},N 200 600,T=2700 ≅  . This group of 2D maps can be compared with 2D maps in Figure 5. Under the same parameters, similar visible effects and feature clustering properties could be observed if various k values are selected. Using a set of selected parameters, four groups of sixteen 2D maps are compared in Figure 7 for four files: left, right, 201-500 and random_201-500 to explore higher levels of symmetric properties for secondary or higher levels of structures potentially contained in DNA sequences.

Conclusion
This paper proposes architecture to support the Variant Map Construction. Using a DNA sequence, variant measures, probability measurement and normalized histogram, a pair of values can be determined by a series of controlled parameters. Collecting relevant pairs on multiple DNA sequences, four 2D maps can be generated. The main results of this paper provide a brief architecture description in diagrams, core components, modules, expressions and important equations for the construction.
In addition to core models and diagrams, sample results are illustrated to apply two sets of selected DNA sequences for testing. After proper set of parameters selected, suitable visual distributions could be observed using the VMC system. Results in Figures 4-7 provide useful evidences systematically to support proposed VMC system useful in checking higher levels of symmetric properties among complex DNA sequences. This construction could provide useful spatial information on complex DNA sequences via 2D maps to explore higher dimensional environments in near future.