選取一組適當的引子在多重聚合酶反應的技術當中扮演相當重要的角色，我們稱之為引子選取的問題。而引子選取問題的目的就是以最少個數的引子去複製一組DNA序列，若我們能使用較少個數的引子來複製DNA序列，則實驗所花費的時間和金錢都能夠降低。
在本論文當中，我們發展出一種有效率的啟發式演算法來幫助使用者挑選適合的引子，而這些引子可以用來複製一條以上的DNA 序列，故所需要的引子數量就可以降低。
我們以weight參數來加入原來Gibbs samplers的計分方式，而這個觀念使得Gibbs samplers能夠由觀察整體的概念慢慢收斂到只觀察部分的概念，藉此去發現DNA序列當中部分共同區域，這裡所提到的部分共同區域即為上述所提到的引子。我們也將我們的方法放在人造的DNA序列和真實的gene family當中作測試，也都顯示了不錯的結果。
我們的方法是用在偵測gene family的特性而不是單純的去對某段基因做引子設計的工作。

Multiple polymerase chain reaction (multiple PCR) is one of the most important
techniques in molecular biology. The selection of a suitable set of primers is very important
for multiple PCR experiments. The primer selection problem is to minimize the
number of primers required to amplify a set of DNA sequences. If the minimum set can
be used to amplify the entire target DNA sequences, the experimental costs and time will
be reduced. But the primer selection problem was proved to be an NP-complete problem.
In this thesis, we develop an efficient heuristic algorithm for selecting a set of
primer candidates, each may be able to amplify more than one target sequence. Those
primers are called universal primers. The universal primer finding can be viewed as the
local motif finding in our method.
We modify the score function of the original Gibbs sampler method to find local
motifs. The new score function is added a new parameter, weight parameter. The weight
parameter can guide the Gibbs sampler method to find local motifs with the local view.
Then, the complementary sequences of those local motifs are input into the binary integer
programming. Thus we can reduce the size of the solution space. We also test our method
on some artificial domains and two gene families. All the results show that we get some
improvements on the problem.

TABLE OF CONTENTS

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Significance of Primers and Ploymerase Chain Reaction (PCR) . . . . . . 3
2.2 The Features of Primer Selection in PCR . . . . . . . . . . . . . . . . . . 5
2.2.1 GC-Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Mismatches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.4 Complementary Sequences . . . . . . . . . . . . . . . . . . . . . 6
2.2.5 Universal Primers . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Some Methods for Primer Selection . . . . . . . . . . . . . . . . . . . . 7
Chapter 3. Related Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1 The Motif Finding Problem . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 The Gibbs Sampler Method . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 The Ant Colony Optimization Algorithm . . . . . . . . . . . . . . . . . . 12
3.4 An Algorithm for Sequence Motif Finding . . . . . . . . . . . . . . . . . 14
Chapter 4. Our Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1 Local Motifs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 A Local Motif Finding Algorithm . . . . . . . . . . . . . . . . . . . . . 19
4.3 Binary Integer Programming . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 5. Experimental Results and Accuracy Analysis . . . . . . . . . . . . 28
5.1 Experiments on Artificial Domains . . . . . . . . . . . . . . . . . . . . . 28
5.2 Experiments on Real Domains . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

BIBLIOGRAPHY

[1] http://www.informatics.jax.org/mgihome/nomen/genefamilies/trim.shtml.
[2] http://www.gene.ucl.ac.uk/nomenclature/genefamily/TBX.shtml.
[3] T. Bailey and C. Elkan, “Unsupervised learning of multiple motif in biopolymers
using expectation maximization,” Machine Learning, Vol. 21, pp. 51–80, 1995.
[4] K. Doi and H. Imai, “Greedy algorithm for finding a small set of primers satisfying
cover length resolution condition in PCR experiments,” Proc. of the 8th Workshop
on Genome Informatics, Tokyo, Japan, pp. 43–52, 1997.
[5] M. Dorigo and L. M. Gambardella, “Ant colony system: A cooperative learning
approach to the traveling salesman problem,” IEEE Transactions on Evolutionary
Computation, Vol. 1, No. 1, pp. 53–66, 1997.
[6] F. Hillier and G. Lieberman, Introduction to Operations Research. McGraw-Hill,
Seven ed., 2001.
[7] L. Hillier and P. Green, “Osp: a computer program for predictions of DNA duplex
stability,” PCR-methods and Applications, Vol. 1, pp. 124–128, 1991.
[8] M. H. Hsieh, W. C. Hsu, S. K. Chiu, and C. M. Tzeng, “An efficient algorithm for
minimal primer set selection,” Bioinformatics, Vol. 19, No. 2, pp. 285–286, 2003.
[9] Y. J. Hu, S. B. Sandmeyer, and D. F. Kibler, “Detecting motifs from sequences,”
In Proceedings of the 16th International Conference on Machine Learning (ICML),
Bled, Slovenia, pp. 181–190, 1999.
[10] T. kampke, M. Kieninger, and M. Mecklenburg, “Efficient primer design algorithms,”
Bioinformatics, Vol. 17, No. 3, pp. 214–225, 2001.
[11] C. E. Lawrence, S. F. Altschul, M. S. Boguski, J. S. Liu, A. F. Neuwald, and J. C.
Wootton, “Detecting subtle sequence signals: A Gibbs sampling strategy for multiple
alignment,” Science, Vol. 262, pp. 208–214, Oct. 1993.
[12] Y. J. Liao, C. B. Yang, and S. H. Shiau, “Motif finding in biological sequences,” in
Proc. of 2003 Symposium on Digital Life and Internet Technologies, Tainan, Taiwan,
pp. 18–27, Sep. 2003.
[13] C. Linhart and R. Shamir, “The degenerate primer design problem,” Bioinformatics,
Vol. 18, pp. s172–s180, 2002.
[14] P. Nicodeme and J. Steyaert, “Selection optimal oligonucleotide primers for multiplex
PCR,” Proc. Fifth International Conference on Intelligent Systems for Molecular
Biology, Halkidiki, Greece, pp. 210–213, 1997.
[15] W. pearson, G. Robins, D. Wredgs, and T. Zhang, “A new approach to primer selection
in polymerase chain reaction experiments,” Proc. International Conference on
Intelligent Systems for Molecular Biology, Cambridge, England, pp. 285–291, 1995.
[16] W. pearson, G. Robins, D. Wredgs, and T. Zhang, “On the primer selection problem
in polymerase chain reaction experiments,” Discrete Applied Mathematics, Vol. 71,
pp. 231–246, 1996.
[17] E. Rocke and M. Tompa, “An algorithm for finding novel gapped motifs in DNA
sequences,” Proc. of the Second Annual International Conference on Computational
Molecular Biology, New York, USA, pp. 228–233, Mar. 1998.
[18] G. Stormo and G. Hartzell, “Identifying protein-bindign sites from unaligned DNA
fragments,” National Academy of Sciences, Vol. 86, pp. 1183–1187, 1989.
[19] A. Talaat, P. Hunter, and S. Johnston, “Genome-directed primers for selective labeling
of bacterial transcripts for DNA microarray analysis,” Nature Biotech, Vol. 18,
pp. 679–682, 2000.
[20] A. Tobin and J. Dusheck, Asking about Life. Harcourt College Publishers, Second
ed., 2001.