A microfluidic systems-based DNA algorithm for solving special 0–1 integer programming problem
Introduction
Though the speed of computing becomes faster and the capacity of memory becomes more immense, many complex problems (e.g. difficult NP-complete problems, prediction of protein structure and function, and so on) cannot be solved by electronic computer. Many novel methods for computational purpose have been developed in order to settle these kinds of problems efficiently. For example, inspired by nature, the idea of computing with DNA has been proposed.
Using DNA molecules for computing is based on its high density of information storage and the amount used for parallel computation. An interesting property of DNA is that particular bases are jointed together to form pairs: A with T and C with G. This process, known as hybridization or annealing, causes self-assembly of DNA fragments. It occurs when two DNA strands are composed of matching (complementary) nucleotide sequences. Due to interactions among favored intermolecular, particular molecules can recognize each other. As a result, a kind of key-lock decoding of information is possible. The other important feature of self-assembling is that particular molecules may be considered as processing units to perform computing.
The idea of computing with DNA had not been realized until 1994 [1], when Adleman published an original work for making a general-purpose computer with DNA molecules. Since then, many achievements have been published on DNA computing. Lipton [2] proposed a method to solve the Boolean satisfiability problem (SAT) by using DNA experiments. Ouyang et al. [3] solved the maximal clique problem by means of molecular biological techniques and building a pool of DNA molecules corresponding to the total ensemble of six-vertex cliques. Liu et al. [4] designed a DNA computation system where a set of DNA molecules encoding all candidate solutions to the computational problem of interest was synthesized and attached to the surface. And, Wu [5] analyzed and improved their surface-based method. All of these efforts made use of molecular biology and demonstrated the feasibility of carrying out computation at molecular level.
Microfluidic systems provide the basis for new types of rapid chemical and biological analyses. There is much previous work on DNA computing using microfluidic systems. Ledesma et al. [6] proposed a linear time DNA algorithm for the Hamiltonian path problem on a microfluidic system which was suited for parallel implementation. Gehani and Reif [7] studied theoretical lower bounds on the quantities of DNA strands and the time needed to solve a problem in a microflow biomolecular computation model, and proposed methods to efficiently route strands between chambers. McCaskill [8] took a brute-force approach to encode each possible subgraph in a DNA strand. The algorithm used the so-called selection transfer modules (STM) to retain all possible cliques of the graph. Then it determined the maximum clique by a sorting procedure. Chiu et al. [9] proposed a novel approach where subgraphs and edges of the graph were codified with wells and reservoirs, respectively. These wells and reservoirs were connected by channels and contained fluorescent beads. The readout was a measure of the fluorescence intensities associated with each subgraph. Livstone and Landweber [10] proposed an application of microreactors to implement Boolean functions AND and OR.
In this paper, we propose a microfluidic systems-based DNA algorithm for solving the 0–1 integer-programming problem. In our method, all possible values of each variable are encoded with DNA strands with different lengths. CE is used to transfer and separate DNA strands, and the solutions are distinguished by analyzing the fluorescence imaging obtained by LIF. Under the control of CE workstation, DNA strands with different lengths are separated and transferred according to an advanced program. Unlike other existing DNA computing algorithm [11], there is no need to construct probes and the number of chamber and channel on chip is linearly increased with the complexity of the problem.
The rest of this paper is organized as follows. Section 2 introduces the 0–1 integer-programming problem and the DNA solution. Section 3 describes the microfluidic systems. Section 4 describes in detail the microfluidic systems-based DNA algorithm. An example of the DNA algorithm based on microfluidic systems for solving 0–1 integer programming problem is given out in Section 5. Section 6 gives the conclusions.
Section snippets
0–1 Integer programming problem
Linear programming is an important problem of operational research. It is widely applied in production schedule, materials requirements planning, network analysis and so on. An integer-programming problem is one of linear programmings. Generally speaking, there are two kinds of integer programming problems. If all variables are required to be integers, the problem is called a pure integer-programming problem. If some variables are restricted to be integers and some are not, then the problem is
The microfluidic systems
Microfluidic systems, also known as lab-on-a-chip or miniaturized total analysis systems, were developed by Manz et al. [16] in the early 1990s. These systems incorporate many of the necessary components, such as sensors, on to a small chip [17]. They are becoming increasingly popular for DNA analysis [18], [19], clinical diagnostics [20], [21], and detection or manipulation of bio-molecules [22], [23].
The use of microfluidic systems have a number of significant advantages. (1) Because the
The microfluidic systems-based DNA algorithm
Here, we consider the following special 0–1 integer-programming problem:where aij is 0 or 1, xi is 0 or 1 and bi is non-negative integer (i = 1, 2, … , m; j = 1, 2, … , n).
An example of 0–1 integer programming problem
In this section, we discuss in detail this model with a simple 0–1 integer-programming problem as below:
Based on the method mentioned above, the microchip for this example is designed in Fig. 7.
In this example, the oligonucleotide encodings for variables x1, x2, x3, x4 are listed in Fig. 8. All these DNA fragments have sticky ends. The number in the box in Fig. 8 represents arbitrary base pairs. The differences between these
Conclusion
Advantages of performing analytical and diagnostic tasks in microfluidic-based systems include small sample volume requirements, rapid transport times, and the promise of compact, portable instrumentation.
In this paper, we propose a DNA computing model based on microfluidic systems to solve an instance of 0–1 integer programming problem. In our model, the chip CE is used to transfer and separate DNA strands. To test constraint terms and get the final optimal solution, the only biology operation
Acknowledgements
This work was supported in part by the National Nature Science Foundation of China (Nos. 60474037 and 60004006), Program for New Century Excellent Talents in University (NCET-04-415), and Specialized Research Fund for the Doctoral Program of Higher Education from Educational Committee of China (No. 20030255009).
References (26)
Molecular computation of solutions to combinatorial problems
Science
(1994)DNA solution of hard computational problem
Science
(1995)- et al.
DNA solution of the maximal clique problem
Science
(1997) - et al.
DNA computing on surfaces
Nature
(2000) An improved surface based method for DNA computation
Bio-Systems
(2001)- et al.
A DNA algorithm for the Hamiltonian path problem using microfluidic systems
Lecture Notes in Computer Science
(2004) - et al.
Microflow bio-molecular computation
Biosystems
(1999) Optically programming DNA computing in microflow reactors
Biosystems
(2001)- et al.
Using three-dimensional microfluidic networks for solving computationally hard problems
Proceedings of National Academy of Sciences USA
(2001) - et al.
Mathematical considerations in the design of microreactor-based DNA computers
Lecture Notes in Computer Science
(2004)
The general form of 0–1 programming problem based on DNA computing
BioSystems
Combinatorial Optimization: Algorithms and Complexity
Cited by (11)
Investigating simultaneous effects of temperature, surface heterogeneity and geometry on fluid mixing in electroosmotic flow considering temperature dependent properties by Nernst–Planck Poisson method
2023, Communications in Nonlinear Science and Numerical SimulationNature-inspired intelligence: A review of selected methods and applications
2009, International Journal on Artificial Intelligence ToolsAn improved cuckoo search algorithm for integer programming problems
2018, International Journal of Computing Science and MathematicsInteger programming problem based on plasmid DNA computing model
2017, Chinese Journal of ElectronicsRotate-vector method for integer programming
2012, Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Systems Engineering and ElectronicsUsing 10-23 DNAzyme to solve simple 0-1 programming problem
2012, Proceedings of 2012 IEEE International Conference on Information Science and Technology, ICIST 2012