A microfluidic systems-based DNA algorithm for solving special 0–1 integer programming problem

Abstract

In this paper, based on microfluidic systems, we propose a DNA algorithm for solving the special 0–1 integer programming problem, which has n variables and m constraint terms. In our method, capillary electrophoresis (CE) is used to transfer and separate DNA strands, and the solutions are distinguished by analyzing the fluorescence imaging obtained by laser-induced fluorescence (LIF). Under the control of CE workstation, DNA strands with different lengths are separated and transferred according to an advanced program. This method has advantages such as low cost, low error, short operation time, and simple experimental steps. Moreover, there is no need to reconstruct probes and the size of biochip is linearly increased with the complexity of the 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.