DNA based in silicon (Inchrosil)

From Watson-Crick discovered DNA structure; there are lot researches in several fields of science about this topic, in special biology. Computer science is not an exception, Professor Adleman with his research and experimentation about new computation with DNA, opened new research way with organic DNA strands (which is called DNA Computing). In this article, we would like to give another point view, with artificial materials, by this reason, the document relates to an electronic system for emulating the DNA strand of a chromosome, which is characterised in that it includes means for the binary coding of the four types of nucleotides (A, G, C, T) that form the strands, such that the nucleotides that form complementary links are assigned complementary codes. Furthermore, with one minimal electronic module to emulate pair of nucleotides, it is possible to create complex electronic structures to solve NP and NP-Complete problems in polynomial times.

In 1953, Watson and Crick described structure of DNA (Watson & Crick, 1953), this fact is a revolution in the science, and consequently, several science areas use DNA structure for their studies. In special, Computer Science and Mathematics have used this simple structure of DNA to create a complex paradigms or methodologies to calculate unsolvable problem (Hamiltonian path problem, SAT, etc.). The new branch of science is called DNA Computing, which is a form of computing, using DNA strands and biochemistry methods. DNA computing is inside of Natural Computing (G.Rozenberg, T.Back, & J.Kok, 2012), is a fast developing interdisciplinary area. Big hit in this area is in 1994, when Professor Adleman at University of Southern of California demonstrated using organic DNA can solve seven-point Hamiltonian problem (Adleman, 1994) in polynomial time.

The Adleman experiments demonstrated to have more advantages of actual machines, based in Von Neumann architecture (Von Neumann, 1945) and Harvard Architecture (Furber, 1989). Consequently of initial Adleman experiment, several searchers have developed machines, using Turing machine models (Turing, 1936) or similar machines with same power, but using DNA (Boneh, Dunworth, Lipton, & Sgall, 1996), (Kari, Gloor, & Yu, 2000).

In 1997, Mitsunori Ogihara and Animesh Ray described an implementation about Boolean Circuits using organic DNA (Ogihara & Ray, 1999). Later in 2002 at Israel, Professor Ehud Shapiro Yaakov Benenson, Binyamin Gil, Uri Ben-Dor, and Rivka Adar had constructed a DNA device coupled with an input and output module, which would theoretically be capable of diagnosing cancerous activity within a cell, and releasing an anti-cancer drug upon diagnosis. (Benenson, Gil, Ben-Dor, Adar, & Shapiro, 2004).

In general, DNA computing is similar to parallel computing, because it’s possible to solve any logical-mathematical problem in linear time. This is because, DNA structure consists in two chains of nucleotides (main and its complementary), and in nature both chain are linked in its nucleotides by hydrogen links. Sometimes by artificial or natural way, one DNA chain is not linked with complementary (In future, this chain could be called incomplete chain), first action of this incomplete chain is to look for its complementary chain, because its natural state of DNA strand. If in specific moment, there are lot incomplete chains, first action of theses chains is assembling with their complementary at the same time, due massive parallelism inherent in DNA reactions, by this reason, if one mathematical problem is codified with incomplete chains (inputs, variables and equations), when all these chains are introduced in same place react creating a full strand, which is final result of mathematical problem. Consequently, complex problems as NP and NP-complete could be solved in linear times, using this procedure.

Note, all methodologies are based in organic DNA and chemical procedures, thus high knowledge in mathematics. Main idea of DNA Computing to be strong alternative of silicon computing (traditional computers), but DNA computing has several walls to cross, material used dies over time, because it’s organic and perishable and it doesn’t work at industrial environments, by this reason, it is very difficult to move outside of laboratories. Almost, there are several organic devices, which are working as a silicon computer, but only in scientific environments.

This article describes an electronic system emulate DNA structure without chemical reactions, using artificial components as silicon, creating with it an inorganic DNA with electronic circuits, by this reason, the electronic system is called InChroSil (Inorganic CHROmosome based in SILicon). On the other hand, the system can be reused lot times, because it is composed by electronic circuits, there are not ethical or moral implications with cloning DNA (note, some countries are prohibited to manipulate human DNA). Also, this computation is not a pure DNA Computing; it is a mixture between both worlds (silicon and DNA), by this reason, it takes the best parts of one and another.

Nucleotide code and DNA strand structure.

To understand the electronic system, it is necessary to make a genetic introduction of chromosomes, which are formed by DNA, RNA and proteins. In turn, DNA is composed of two longitudinal fibres joined by centromere. These fibres are called chromatids and represent two identical chains of the duplicated DNA.

Therefore, DNA is composed of chains (set of nucleotides), which are differentiated in four types which are listed below:

• Adenine is represented by the letter A.
• Guanine is represented by the letter G.
• Cytosine is represented by the letter C.
• Thymine is represented by the letter T.

Consequently, DNA is composed of two linked chains and each chain contains innumerable nucleotides. There are no complementary nucleotides on the same chain, i.e. they can join without any restriction. However, on linking the two chains, there are restrictions of complementarity, so that an Adenine (A) of a single chain can only join with Thymines (T) of the complementary chain, in the same way as Guanines (G) can only link with Cytosines (C). All above descriptions in this section are obvious and incomplete for any Biotechnical, geneticist or similar technical professional, but it’s necessary for other readers to take a general idea. 

On the other hand, emulating to nature, the electronic system is characterised in that it comprises means of binary encoding of the four different types of nucleotides which compose the strands, so that the nucleotides which form complementary linkages are assigned complementary codes by the inversion of one of them.

Binary encoding consists in two bits corresponding to each nucleotide acquire the decimal quantities of 0 of 3 so that it permits forming a plurality of numerical presentations determined by the position of the two bits and by the value each position receives. This encoding permits that any encoding system which has correspondence with the decimal or binary can be encoded with the numeration and encoding system of this electronic system. Next list shows codification for each nucleotide:

• Adenine (A) is assigned the value of “00” or in decimal 0.
• Guanine (G) is assigned the value of “01” or in decimal 1.
• Cytosine (C) is assigned the value of “10” or in decimal 2.
•  Thymine (T) is assigned the value of “11” or in decimal 3.

Next figure shows a circuit represents pair of nucleotides (one nucleotide and its complementary):

Inchrosil Unit

Electronic schema of Figure consists mainly in four bi-states and logical gates. Note one bi-stable can be used to store state information, by this reason, each bi-stable store one bit of nucleotide codified. Also, the two bi-stables connect with SEL₀ signal represent one nucleotide and the two bi-stables connect with SEL₁ signal represents codification of both nucleotides, so this codification permits to obtain different structures of both nucleotides, next list shows all possible combinations:

1. Both nucleotides are active (state normal in nature).
2. Top nucleotide is missing, hole in top of DNA strand.
3. Bottom nucleotide (complementary) is missing, hole in bottom of DNA strand.
4. Both are missing, not genetic information in place, break point of DNA strand.

All combinations are necessary to do holes in DNA strands, this skill very important to do DNA computing, because one mathematical-logical problem could be represented by incomplete chain or chain with holes.

Furthermore, the system cans read/write one specific nucleotide or both, depending of R/W signal and Chip/Select signal. Also, Figure 1 is a conceptual model, by this reason; it could be developed in several technologies as CMOS, quantum or future technologies.

So the above electronic system is the unit to represent two nucleotides of DNA strand (one nucleotide and its complementary). Connecting these units in serial, it is possible to obtain full DNA strands, because there are not restrictions to join between nucleotides in same level, by this reason, the length of DNA strand depends only of number of units connected, creating with this way, a three-dimensional DNA database with different access it (by columns, rows and one simple nucleotide).

References

• Adleman, L. M. (1994). Molecular computation of solutions to combinatorial problems. Science , 1021–1024.
• Benenson, Y., Gil, B., Ben-Dor, U., Adar, R., & Shapiro, E. (2004). An autonomous molecular computer for logical control of gene expression. Nature , 423-429.
• Boneh, D., Dunworth, C., Lipton, R. J., & Sgall, J. I. (1996). On the computational power of DNA. Discrete Applied Mathematics , 79–94.
• F, G., M, F., & C, B. (1996). Making DNA add. Science , 220–223.
• Furber, S. B. (1989). VLSI Risc Architecture and Organization. CRC Press.
• G.Rozenberg, T.Back, & J.Kok. (2012). Handbook of Natural Computing. Springer.
• Kari, L., Gloor, G., & Yu, S. (2000). Using DNA to solve the Bounded Post Correspondence Problem. Theoretical Computer Science , 192–203.
• Knuth, D. (1962). Positional Number Systems. In The Art of Computer Programming (pp. 194–213). Addison–Wesley.
• Ogihara, M., & Ray, A. (1999). Simulating Boolean circuits on a DNA computer. Algorithmica , 239–250.
• Turing, A. (1936). On Computable Numbers, with an Application to the Entscheidungsproblem., (pp. 230–65).
• Von Neumann, J. (1945). First Draft of a Report on the EDVAC.
• Watson, J., & Crick, F. (1953). Molecular structure of nucleic acids; a structure for deoxyribose nucleic acid. Nature , 737–738.
• Wu, G., & Seeman, N. C. (2006). Multiplying with DNA. Natural Computing , 427–441.