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The Research and Application of DNA Computing by Self-assembly

Author: SongBoSheng
Tutor: YinZhiXiang
School: Anhui University of Technology
Course: Applied Mathematics
Keywords: DNA computing satisfiability problem matrix addition Tile self-assembly
CLC: O242.1
Type: Master's thesis
Year: 2011
Downloads: 41
Quote: 0
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Abstract


In recent years, great concerns have been raised by inventions in the fields of quantum computer, bio-computer and DNA computing. Among them, bio-computing, because of its large scale parallel computation and potential storage capacity of huge data, has been one of the important methods which are used to develop the non-traditional and high-performance computing. Thus it has attracted the attention of the scientific community. DNA computing is a fresh way of calculation, which simulates biologic molecular structure and use molecular biologic technology to compute. It also initiates such a precedent, which is based on biochemical reactions as computing tools. DNA computing is a new method which is used to solve calculation problems that are hard to solve, especially its great potential in solving difficult problems of NP.DNA molecular self-assembly is one of the important research branches in the field of DNA computing. It is such a procedure that under the action of a certain temperature, concentration, ph value and specific enzymatic, some DNA molecules with input information, according to Watson-Crick complementary matching principle, self-assembly generate new DNA molecular with output information. Self-assembled DNA computing model is combined with DNA computing, Tiling theory and DNA nanotechnology, thus become one of the most concerned model. In this context, the innovation points are as follows:Firstly, DNA Tile self-assembly calculation model is applied to solve NP-totally problem. In order to discuss a 3-satisfiability problem containing only 3 variables, it is divided into "not" operation subsystem and "or" operation subsystem. At the same time, calculation example of "not" operation and "or" operation of DNA Tile self-assembly are given respectively. Through the combination of these two operations, according to computation rules of the DNA Tile self-assembly, it can automatically judge whether it meets the paradigm for any given group of solution. Because DNA computing is equipped with highly parallelism, so for satisfiability problem all solutions can simultaneously be judged.Secondly, in the practical computing science, for a satisfiability problem, each clause and the number of variables of its paradigm often are random. Therefore, in the ideological basis, make a list for all variables in this paradigm, then add each clause with variables which it does not originally contain,and make it become k-satisfiability problem that contains n variables. For the added variables, which are marked specially, they have no influence on the true value of the paradigm in the process of operation.Thirdly, discuss the applications of DNA Tile self-assembly calculation model to solve matrix addition. For a matrix addition, it is mainly the continuation of the addition operation of two numbers. At the very beginning, illustrate the process of the addition operation of two numbers by taking advantage of an example, and then undertake the addition operation with all the numbers of a matrix as the initial line, all the numbers of another matrix as the initial column.In the last section of this context, DNA molecular self-assembly is used to solve satisfiability problems. Its principle is mainly in the bases of complementary matching principle. Through the formation and launching of hairpin structure in corresponding DNA chains, use gel electrophoresis operation to separate different lengths of DNA chain, and obtain the solution of the problem in the end.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation > Mathematical modeling
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