Mathematical Blockchain Modeling of Peer-to-Peer Networks for Gene Expression in Cell Population

The study presents a mathematical modeling for supporting the premise that our body is composed of blockchain systems. A cell population is considered a space with peer-to-peer communication networks for applying blockchain protocol. Transaction is defined as gene expression that constantly occurs for protein synthesis in each cell. The transaction process proceeds according to the blockchain protocol with sharing and recording the data on the blockchain ledger. The premise comes from the clues of the previous research such that the cell population is a complex structured network system having cell-to-cell connections. Although individual cells exhibit stochastic nonlinear dynamic behavior, cell population shows consensus behavior that reaches to ensemble through interaction among cells. It is inferred that gene expression is not regulated by the corresponding cell only nor determined by external intelligence such as the brain. This is achieved through a consensus through stochastic interactions between cells over the whole cell population. These findings imply that mathematical blockchain modeling is a suitable for gene expression process. The original contribution of the study is a methodology for applying mathematically the blockchain protocol to the real biological gene expression process. In other words, the DNA sequence is converted into a numeral bit sequence that makes it possible to implement the blockchain protocol. A new DNA sequence scheme is proposed with adding methylated cytosine and adenine as the 5th and 6th bases for including epigenetic information which has profound effect on gene expression and regulation. The methodology was applied to the real biological synthesis process of protein samples. The protein is composed of amino acids that are encoded by triplet codons of 216 kinds with 6 base RNA sequence. The gene expression information is traced backward from a synthesized protein sample, amino acids of codons, RNA transcript up to DNA sequence. One of the results is a numeric value in the form of a bit sequence with which mathematical blockchain modeling is applicable. The cryptographic authentication and the consensus process are mathematically proven to work properly by the blockchain protocol. It implies that the same protein is synthesized, but with different epigenetic data, then protein's latent material properties will certainly be different. Although the result has not been justified by the biologic experiment yet, it is sure that the biological hidden algorithm inside DNA sequence will be revealed by the binary bit-logic with physical on/off states which is mathematically proven. The research will greatly contribute to disease treatment and medicine development as well as epigenetics in the future.


(Title)
Mathematical Blockchain Modeling of Peer-to-Peer networks for Gene Expression in Cell Population

(Abstract)
The study presents a mathematical modeling for supporting the premise that our body is composed of blockchain systems. A cell population is considered a space with peer-to-peer communication networks for applying blockchain protocol. Transaction is defined as gene expression that constantly occurs for protein synthesis in each cell.
The transaction process proceeds according to the blockchain protocol with sharing and recording the data on the blockchain ledger. The premise comes from the clues of the previous research such that the cell population is a complex structured network system having cell-tocell connections. Although individual cells exhibit stochastic nonlinear dynamic behavior, cell population shows consensus behavior that reaches to ensemble through interaction among cells. It is inferred that gene expression is not regulated by the corresponding cell only nor determined by external intelligence such as the brain. This is achieved through a consensus through stochastic interactions between cells over the whole cell population. These findings imply that mathematical blockchain modeling is a suitable for gene expression process.
The original contribution of the study is a methodology for applying mathematically the blockchain protocol to the real biological gene expression process. In other words, the DNA sequence is converted

I. Introduction
In the case of multicellular eukaryotic organisms such as humans, as one cell continues to divide into the same cell, it becomes a living  [1,2,3] In this study, it is assumed that gene expressions in cell population are shared by data, regulated by consensus and stored in the form of a blockchain with cryptographic security over peer-to-peer (P2P) networks. [4,5] This proposal is supported by some clues from previous studies as follows.
The first clue from previous research is that gene expression shows the nature of complex networks in the cell population. The basic research issue is to unravel the structure and dynamics of the networks. Some  [12,13,14] In summary, this study attempts to explain the principle of gene expression in organisms by adopting blockchain concepts such as secure P2P networks, the cryptographic hash algorithm and the consensus algorithm in the cell population.

II. Mathematical Blockchain Modeling
The original contribution of the study is a methodology for applying mathematically the blockchain protocol to the real biological gene expression process. In other words, the DNA sequence is converted into a numeral bit sequence that makes it possible to implement the blockchain protocol.

II.1 Cellular Blockchain Concept
Blockchain began with the motivation of collective governance of a group of nodes with a decentralized P2P network system. This technology ensures transparency and reliability by data sharing and consensus with security.
As an example, blockchain shows the possibility of replacing the legacy TTP (Trusted Third Party), a central bank, with cryptocurrency such as Bitcoin [15,16,17]. A cellular blockchain concept is motivated by the collective governance of gene expression in the cell population. In other words, a local organ is autonomously coordinating gene expression by a blockchain process rather than by a centralized intelligence, such as the brain. Figure 1 shows the similarity between the digital blockchain formed in the internet space and the cellular blockchain formed in our body. It is assumed that the digital node corresponds to a cell and the CPU corresponds to DNA in the cellular blockchain.

II.2 Cellular Blockchain Cryptograph
A purpose of blockchain is to provide the cell population with security over the cell-to-cell communication network by using cryptography, which is the process of encrypting and decrypting cellular data. The cellular public and private key pair is a crucial element of cryptography.
This is how private and public keys work together. The private key is used to encrypt cellular block data and the public key is used to decrypt it to execute transactions such as gene expression. A single cell on the blockchain network in the cell population has its own private and public key pair and cellular address, which may be assigned in the stage of cell formation. Figure 3 presents a real biophysical situation with a virtual scenario.
Step 1: The blockchain system generates and assigns a unique random number to the cell by the binary system of on/off status in the hidden virtual level. The binary number is converted into a 12-digit hexadecimal numeral value of private key (4ef17e7cab3e) through the hashing algorithm, which is described in further detail in the next section. The numeral private key is converted into a quaternary numeral system, and then mapped to the corresponding nucleobase AGCT to be biophysically observable in the DNA. Thus, each cell has its own cellular private key in a real 18-digit DNA sequence (CTGGTCATTGATAGAACC).
Step 2: The cellular private key in Step 1 creates its pairing public key by using complex functioning defined in the hidden virtual level. The resulting binary number is converted into a 12-digit hexadecimal numeral hash value (633f01ec34cc) for the public key. The public key in the quaternary system is mapped to a real 18-digit DNA sequence (GCAGACTCGGATACAACA) for the cellular public key in the observable biophysical layer. Thus, a cell can go through authentication for the blockchain network with its own private and public key pair.

Figure 3 Blockchain Security over Cell-to-Cell Communication Network
Step 3: The cellular address is an identification number of the cell for the blockchain network. The address is derived by using the hashing process twice with a public key. The cellular address is designated to a 12-digit hexadecimal number (1e4e18fde20b) in a hidden virtual level and is observable with quaternary mapping to a real 18-digit DNA sequence (GGGCCCTCATAATCTGCG) in the biophysical layer. The receiver cell can obtain the sender's address from the public key.
DNA in a cell is programmed in the nucleobase sequence for gene

II.3 Cellular Secure Hash Algorithm
The cellular hash algorithm is the process of taking the input nucleobase sequence of any length and turning it into a cryptographic nucleobase sequence output of the fixed length. It is a one-way irreversible encryption. A cryptographic hash algorithm needs to have several crucial qualities to be considered useful: Every hash is different from another. The same hash will always be generated for the same data. It is impossible to infer input data based on the hash output value.
Even with a small change to the input, the whole hash will be changed.  For the other table of DNA sequence (II), which is slightly changed by the methylation of cytosine and adenine, the outcome of CSHA18 is That is,

III. Methodology
In this study, a methodology for applying the blockchain protocol to the cell population has been illustrated by the process of transaction for gene expression.

III.1 Cellular Blockchain Transaction Process
In Figure   In this way, a current block is formed and connected to the previous block. The number of blocks in connection is continuously increased over time to form a cellular blockchain. The blockchain is finally confirmed through the consensus process in the cell population for the final security stage. The details of this are described in the next section.

III.2 Cellular Blockchain Consensus Algorithm
This section describes the consensus algorithm for the cellular As an example shown in Figure 6, a sequence of gene expression is booked for cell 4, followed by the sequence of cells 9, cell 1, cell 2, cell 8 and cell 3. A transaction ledger of sequences is created in this way.
The current block includes not only the transaction data but also the cellular hash value of the previous block and the arbitrary nonce matrix.
The consensus algorithm is based on a game rule in which the player

IV. Application
The blockchain methodology has been applied to the real biological

V. Results
The study has presented the results of application to the real biological synthesis process of protein sample.
As shown in Figure  blockchain protocol.

VI. Further Discussion
A new triple codon scheme, which has been used in the results, is to be discussed furthermore. In addition, a cryptocurrency concept, which is the core application in the digital blockchain, is to be discussed for cellular blockchain ecosystem.

VI.1 Triplet Codons Scheme
The 9-digit DNA sequence is transcribed into 3 triplet RNA codons. In conventional biology [27,28], the possible case is 64 kinds of codons from the AGCU quaternary nucleobase RNA system. However, these codons do not distinguish the methylated nucleobase components. In this study, by adding 2 more methylated RNA nucleobases, the 6 kinds of RNA nucleobase form the 216 kinds of triplet codon. In the previous result, Cell #4 is going to the gene expression process with a 9-digit nucleobase DNA sequence. It is transcribed to the RNA sequence, which is composed of 3 triplet codons. is Double methylated Leucine; is Cytosine methylated Isoleucine, and is Adenine methylated Threonine. These codons include information on epigenetic effects on the amino acids and proteins.
Thus far, it is understood that if the nucleobase sequences of the genetic layer are the same, the results of protein synthesis are the same.
However, if the data of the epigenetic layer are different, the results must be different. The role of epigenetic data has not yet been identified in the process of protein synthesis. In this study, it is postulated that the epigenetic data may be used for the regulation of gene expression and for the sustainable cellular blockchain ecosystem with cryptocurrency.

VI.2 Cryptocurrency Concept for Cellular Blockchain Ecosystem
To maintain the blockchain ecosystem continuously, digital cryptocurrency is introduced. [29,30] Then, what is the concept of cryptocurrency in the cellular blockchain?
Cryptocurrency should be able to exchange and store some measurable As a result, 1 CC is reduced in the balance. Alternatively, in the 2 nd cell, the methylation is 1 CC and the demethylation is 2 CC, so the balance is increased by 1 CC.
What is the biomaterial that embodies biophysically cellular cryptocurrency? In this study, it is assumed that one of the biomaterials is a DNMT (DNA methyltransferase) [31] that activates methylation.
Once the amount of DNMT corresponding to 1 CC is determined, the amount of DNMT accumulated in the cell can be converted into CC, which will be the current balance in CC. As such, the balance of cryptocurrency is booked in the blockchain ledger as a result of the transaction of gene expression. The balance represents epigenetic plasticity that can be inherited by future generations. [32] In more detail, in order to activate competition to reach consensus, more cells should participate in the game, depleting ATP (adenosine triphosphate) in the mitochondria. [33] If so, what is the motivation of the cell to induce it? It may be a selfish characteristic of cells. [34,35] In other words, it may be such a cloning instinct that accumulates the effects of gene expression occurring in the cell population through epigenetic plasticity to strengthen its inherent empirical traits and transmit it to the next generation.
Such transactions with cellular cryptocurrency are used to sustain the blockchain ecosystem. In addition to transactions, a cell can earn the cryptocurrency by the consensus game. The cell that has won a consensus game is granted a certain amount of cryptocurrency as a reward. Instead, the cell must consume much energy in the mitochondria with ATP during the game for mining process. To compensate for ATP depletion, the cells buy ATP from the others in CC.
Therefore, in the blockchain ecosystem, it is necessary to regulate and maintain the exchange rate between the appropriate ATP and CC within the cell group for sustainability. In the actual biophysical layer, DNMT and ATP are exchanged.

VII. Conclusion
The conclusion of this study is such a premise that our body is a blockchain system. This means that all activities in our body are being nucleobases considering epigenetic layer data. In other words, by adding methylated cytosine and adenine as the 5 th and 6 th bases, the DNA sequence is composed of 6 bases. In the hidden virtual layer, the new DNA sequence scheme is operated by the senary numeral system rather than the quaternary system. In the transcription process for protein synthesis, 216 types of RNA triple codons are presented rather than 64 types in conventional biology.
Thus far, it is understood that if the nucleobase sequences of the genetic layer are the same, the results of protein synthesis are the same.
However, if the data of the epigenetic layer are different, the results must be different. The role of epigenetic data has not yet been identified in the process of protein synthesis. It is postulated that epigenetic data may be used for the regulation of gene expression and for the sustainable cellular blockchain ecosystem with cryptocurrency.
Cryptographic private and public key pair provides the cell with a complete authentication process over blockchain network. Additionally, the cellular secure hash algorithm is defined for the process of taking the input nucleobase sequence of any length and turning it into a cryptographic nucleobase sequence output of the fixed 18-digit length.
For the consensus algorithm, it is postulated that stochastic interactions among the cells create the random game of competition and that the selfish nature of the cell which is its sustainable influence on the population, provides the motivation to participate in the game more.
The winning reward is suggested to be a degree of epigenetic plasticity such as the amount of DNMT in cellular cryptocurrency.
This study helps to understand the principle of gene expression in cell populations. The conclusion has not been verified by biological experiments, but it will be clearly confirmed mathematically. It is sure that the biological hidden algorithm inside the DNA sequence will be revealed from the binary bit-logic with physical on and off states which is mathematically proven. The results will contribute to epigenetics, including future disease treatment and medicine development.