In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encoding thousands of large noncoding RNAs (lncRNAs), interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. It is a challenge target using higher dimensional tools to organize various complex interactive properties as visual maps. In this paper, a Pseudo DNA Variant MapPDVM is proposed following Cellular Automata to represent multiple maps that use four Meta symbols as well as DNA or RNA representations. The system architecture of key components and the core mechanism on the PDVM are described. Key modules, equations and their I/O parameters are discussed. Applying the PDVM, two sets of real DNA sequences from both the sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with two sets of pseudo DNA sequences generated by a stream cipher HC-256 under different modes to show their intrinsic properties in higher levels of similar relationships among relevant DNA sequences on 2D maps. Sample 2D maps are listed and their characteristics are illustrated under a controllable environment. Various distributions can be observed on both noncoding and coding conditions from their symmetric properties on 2D maps.
Finding a proper generation mechanism for specific functional DNA sequences is a challenge task in the modern bioinformatics. DNA sequences are composed of four meta symbols on {A,C,T,G}. From an algebraic viewpoint, it is feasible to transfer any 0 - 1 sequence under Cellular Automata following a 2 bits transforming table to generate pseudo DNA sequences. Considering different configurations, there is 24 = 4! possible rules in transformation. Considering generations of 0 - 1 sequences, pseudo random number generation mechanism [1,2] takes the central position in modern cryptography [3-6]. Associated with advanced development of bioinformatics, advanced DNA sequencing and analyzing techniques [7-24] have significantly progressed over the past decade.
In DNA analysis, visualization methods play a key role in the Human Genome Project (HGP) [
In 2012, ENCODE released a coordinated set of 37 papers published in key Journals of Nature, Science, Genome Biology and Genome Research. These publications show that approximately 20% of non-coding DNA in the human genome is functional while an additional 60% is transcribed with no known function [
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 previously believed [
DNA analysis plays a key role in modern genomic application [
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 to explore complex interactive properties [8-18].
In current situation, it is necessary for advanced researchers to shift focus in computational cell biology from directly sequencing data to making higher-level interpretation and exploring efficient content-based retrieval mechanism for genomes.
DNA cryptography makes joined research in the field of DNA computing and cryptography. Different results are published such as simulating DNA evolution [
In typical results of DNA cryptography on encryption, different coding schemes could be randomly selected. E.g. the algorithm in paper [
Stream ciphers are an important class of encryption algorithms. A stream cipher is a symmetric cipher which operates with a time-varying transformation on individual plaintext digits. HC-256 is a stream cipher designed to provide bulk encryption in software at high speeds while permitting strong confidence in security. A 128-bit variant was submitted in 2004 as an eSTREAM cipher candidate; it has been selected as one of the four final contestants in the software profile [
Variant construction is a new structure on Cellular Automata 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 [25,26], 2D maps [27,28], variant pseudo-random number generator [29-31], DNA maps [32,33] and dynamic properties on variant phase spaces [
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 various polarized distributions and further symmetric properties are visualized.
This paper establishes a Pseudo DNA Variant Map (PDVM) following Cellular Automata. The PDVMis a unified framework to analyze complex DNA interactions for both artificial and natural DNA sequences. This paper provides an extending version on [
In this section, system architecture and their core components are discussed with the use of diagrams. The refined definitions and equations of this system are described in the next section—Pseudo DNA Variant Map.
Specific symbols for groups are listed as follows:
V A symbol is selected from four DNA symbols
∀t All DNA sequences are selected,
The four components of a PDVM are the Binary To DNA (BTD), the Binary Probability Measurement (BPM), the Mapping Position (MP), and the Visual Map (VM) as shown in
The architecture is shown in
In the first part of the system, the t-th sequence
Using this unified DNA sequence, four vectors of probability measurements are created from the t-th selected DNA sequence with
With eight parameters in an input group, there are three sets of parameters in the intermediate group and one set of parameters in the output group.
The three groups of parameters are listed as follows.
The BTD component shown in
If mode = 2 condition, double number of 0 - 1 elements are required to generate a given length pseudo DNA sequence than mode = 1 condition. The BTD component uses an input vector on either binary or DNA format as input, under a set of input parameters to process transformation. The output of the BTD component is composed of a unified vector of DNA format in a given set of conditions.
The BPM component shown in
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.
The MP component shown in
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
The VM component shown in
The VM component processes all selected DNA sequences as input to generate paired values for each sequence. The output of the VM component is composed of four 2D maps to show the final visual distribution for the system.
In this section, definitions and equations are provided to describe the PDVM. In addition to the initial preparation, seven core modules are involved in the BTD, BM, PM, HIS, NH, PP and VM components respectively.
Let
Let
Let X denote a DNA sequence with N elements, D denote a symbol set with four elements i.e.
From this input and associated parameters, following operations are performed.
If mode = 0, for all I,
If mode = 1, for all pairs of I and
Under this condition, a 0 - 1 sequence with N elements can generate a pseudo DNA sequence with the same elements.
If mode = 2, only half pairs of I
Under this condition, a 0 - 1 sequence with N element can generate a pseudo DNA sequence with
In both conditions,
e.g. Let a binary sequence
Selecting a certain
Normal rules of DNA cryptography [21,22] take only r = 1 and mode = 2 conditions for transformations. For mode = 1 situations, normal rules cannot be covered.
From a Cellular Automata viewpoint, this type of transformation plays a key role in the PDVM. This is a significantly distinguishable condition to check whether generated pseudo DNA sequences with/without non-coding properties.
For a given I-th element, four projective operators can be defined and denoted as
Applying the four operators to all elements, the DNA sequence X can be reorganized into the four binary sequences of 0 - 1 values. i.e.
e.g. Let a DNA sequence
It is interesting to notice that the basic relationship between a DNA sequence X and its four
The projection
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
Under this construction, four sets of probability measurements established.
The probability operator
Since the BPM generates four sets of probability measurement, it is necessary to perform further operations in the MP component shown in
In the HIS component as the first module in
Let
Collecting all possible values, a histogram distribution can be established,
The histogram
Under this construction, a normalized histogram can be defined as
After the NH component processed, its output provides the PP component for further operations as the third module in
Relevant probability vectors have (n + 1) distinguished values; four sets of normalized vectors can be organized as a linear order as follows,
Under this condition, four linear sets of probability vectors are established,
For four vectors, their components can be normalized respectively,
Four sets of probability vectors are composed of a complete partition on their measurements.
Using this set of measurements, two mapping functions can be established to calculate a pair of values to map analyzed DNA sequence into a 2D map as follows.
Let
In the PP component, four paired values are generated and each pair indicates a specific position on a 2D map for the selected DNA sequence. The core operations of three key components: BTD, BPM and MP for a selected sequence are performed in Figures 2(b)-(d).
Since only one point of a 2D map is determined for a selected DNA sequence, it is essential to apply relativelarger number of DNA sequences as inputs to generate visible distributions. This type of operations will be performed in the VM component shown in
In a general condition, the VM component processes a selected data set
Each sequence can be processed to apply the same procedures of the BTD, 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
A sample 2D map of VM is shown in
Under this construction, a total number of 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.
Two types of data sets are selected for comparison. The first type of data sets is real DNA data sequences collected from both human and plan genomes to illustrate their differences on 2D maps. The second type of data set is collected from the Stream Cipher HC-256 to generate a pseudo random binary sequence under a certain condition.
It is important to use some real DNA sequences to illustrate various test results of the PDVM. Two sets of DNA sequences are selected and relevant resource features are 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 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 one file right.
The second DNA data set are selected from some plant gene database for comparison. One set of DNA sequences of Corn genomes are stored in file 201 - 500 that contains 2700 DNA sequences and each sequence has around 200 - 600 elements. It may be ordinary single sequences without complex secondary structures.
The Stream Cipher HC-256 has being used to generate a binary sequence on a total length of
Using the PDVM in various parameters, six sets of pseudo DNA sequences are generated and their 2D maps are illustrated, analyzed and compared in following subsections.
Using the two files of DNA sequences and two pseudo binary sequences in three parameters, relevant 2D maps are listed in Figures 4-7 under different conditions to illustrate their spatial distributions using the PDVM in a controllable environment.
In
In
In
In
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
Using a set of selected parameters, two groups of eight 2D maps are compared in
potentially contained in DNA sequences. Selected parameters are in the range of
In convenient description, let ~ be a similar operator, for groups (a) & (b), four pairs of {(a1) ~ (a2), (a3) ~ (a4), (b1) ~ (b2) ~ (b3) ~ (b4)} maps i.e. (right-A ~ right-T, right-C ~ right-G, 201-500-A ~ 201-500-T ~ 201-500-C ~ 201-500-C). Two sets of maps have a stronger similar distribution among their projections. From a symmetric viewpoint, three clustering classes could be identified as {(a1) ~ (a2), (a3) ~ (a4), (b1) ~ (b2) ~ (b3) ~ (b4)} respectively. This type of similar clustering distributions may strongly indicate eight maps with intrinsically higher levels of DNA sequences with clear A-T & G-C pairs of symmetric relationships on right for noncoding sequences. And another set of four maps may have similar distributions for coding sequences.
Using a set of selected parameters, six groups of twenty four 2D maps are listed in
In a convenient comparison, using a set of selected parameters, six groups of twenty four 2D maps are compared in
Using a similar operator
In general, this set of map results illustrates directly visual comparisons with similarity between real DNA and pseudo DNA sequences on PDVM maps, their similarly clustering distributions may indicate those simulation results with comparable mechanism to analogy complex behaviors of real DNA sequences with extra A-T & G-C pairs of symmetric relationships or A-T-G-C equal distributions in their higher levels of relationships applying the Stream Cipher mechanism.
This paper proposes the architecture to support the Pseudo DNA Variant Map on Cellular Automata. Using a binary random sequence as input, a set of special pseudo DNA sequences can be generated. Under 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 the PDVM architecture description in diagrams, main components, modules, expressions and important equations for the PDVM. Core models and diagrams, sample results are illustrated to apply two types of data sets selected from real DNA sequences and two types of controllable modes to generate relevant pseudo random sequences from the Stream Cipher HC-256 for comparison under the PDVM testing. After the proper set of parameters selected, suitable visual distributions could be observed using the PDVM. Results in Figures 4-7 provide useful evidences systematically to support proposed PDVM useful in checking higher levels of symmetric/similar properties among complex DNA sequences in both natural and the artificial environment.
This construction could provide useful insights to simulate spatial information on complex DNA expressions especially on both large non-coding and coding RNA/DNA construction via 2D maps to explore higher levels of complex interactive environments using Cellular Automata schemes in near future.
Thanks to Weiqiong Zhang for generating maps, Ruoyu Shen for generating HC-256 pseudo DNA sequences, to the school of software Yunnan University, the key laboratory of Yunnan software engineering and the key laboratory for Conservation and Utilization of Bio-resource for excellent working environment, to the Yunnan Advanced Overseas Scholar Project (W8110305), the Key R&D project of Yunnan Higher Education Bureau (K1059178) and National Science Foundation of China (61362014) for financial supports to this project.
Project supported by NSF of China (61362014), the Key R&D project of Yunnan Higher Education Bureau (K1059178) and Yunnan Advanced Overseas Scholar Project (W8110305).