DOI 10.1007/s00500-006-0137-8 O R I G I NA L PA P E R
Primer design for multiplex PCR using a genetic algorithm
Li-Cheng Wu · Jorng-Tzong Horng ·Hsi-Yuan Huang · Feng-Mao Lin · Hsien-Da Huang · Meng-Feng Tsai
Published online: 24 October 2006 © Springer-Verlag 2006
Abstract Multiplex Polymerase chain reaction (PCR) is the term used when more than one pair of primers is used in a polymerase chain reaction. The goal of multi-plex PCR is to amplify several segments of target DNA simultaneously and thereby to conserve template DNA, save time, and minimize expense. The success of the experiment is dependent on primer design. However, this can be a dreary task as there are many constrains such as melting temperatures, primer length, GC con-tent and complementarity that need to be optimized to obtain a good PCR product. In our investigations, we found few primer design tools for multiplex PCR and there was no suitable tool for our partners who want to use a multiplex PCR genotypic assay. The tool draws on a genetic algorithm where stochastic approaches based on the concept of biological evolution, biological genet-ics and genetic operations on chromosomes are used to find an optimal solution for multiplex PCR. The pre-sented experimental results indicate that the proposed algorithm is able to find a set of primer pairs that not only obey the design properties but also work in the same tube.
L.-C. Wu· J.-T. Horng (
B
)Institute of System Biology and Bioinformatics, National Central University, 320 Taoyuan, Taiwan e-mail: [email protected]
J.-T. Horng· F.-M. Lin · M.-F. Tsai
Department of Computer Science and Information Engineering, National Central University, 320 Taoyuan, Taiwan
H.-Y. Huang· H.-D. Huang
Department of Biological Science and Technology,
Institute of Bioinformatics, National Chiao Tung University, 300 HsinChu, Taiwan
1 Introduction
Polymerase chain reaction (PCR) is a very powerful technique in molecular biology and is widely used today for an increasing number of applications such as in clin-ical diagnostics, in identification of individuals, in vitro DNA amplification and so on (Griffin and Griffin 1994). It was discovered in 1983 by Kary Mullis who was work-ing at that time for the Cetus Corporation. The first pub-lication of the procedure appeared in 1985 and Mullis was awarded the Nobel Prize for Chemistry in 1993.
A PCR experiment is a method for the fast and mass amplification of a specific DNA sequence. It is an itera-tive process, consisting of three steps: denaturation of the double-stranded DNA by heat, annealing of the oligonucleotide primers to the single-stranded target sequences, and extension of the annealing primers by a thermostable DNA polymerase. These three steps are repeated between 24 and 45 times usually in order to complete the DNA amplifying process and this is able then to generate enough sequences to allow subsequence experimental protocols. The PCR proce-dure is shown in Fig. 1. In addition, in reverse transcription-PCR (RT-PCR) (Burke 1996), it is used to quantify mRNA levels from much smaller samples. The process is roughly same as the PCR experiment. The additional first step in RT-PCR is the production of a sin-gle-strand complementary DNA (cDNA) of the RNA through the action of the retroviral enzyme, reverse transcriptase (Sambrook and Russell 2001).
Multiplex PCR is the term used when more than one pair of primers are included in a polymerase chain reac-tion. Many research and diagnostic assays involve the analysis of multiple loci. Rather than perform singleplex PCR amplification reactions for each locus, it is often
Fig. 1 The PCR procedure
desirable to amplify all sequences of interest simulta-neously in a “multiple” reaction (Innis et al. 1999). Mul-tiplex PCR thus conserves template DNA, save time, and minimize expense. Reducing the number of tubes to which aliquots of DNA need to be added also minimizes the possibility of contamination and sample mix-up dur-ing reaction setup.
The success of the above-mentioned methods is dependent on primer design. Developing a better tool for this has become an active research issue. Therefore, various kinds of approaches and tools for the design of primers have been proposed in the last few decades. The ideal length of the primers is expected to be in a range from 18 to 30 bases. The percentage of GC con-tent ought to be between 40 and 60% to obtain specific binding, yet also allow efficient melting during the PCR. In addition, the base distribution of the primers should be random, with polypurine and poly pyrimidine tracts being avoided (Griffin and Griffin 1994). The primers must avoid forming any self-complementary and com-plementary sequences. The specificity of PCR depends strongly on the melting temperature (Tm) of the prim-ers. Generally speaking, good results are obtained when the difference in Tm within one primer pair does not exceed 5◦C. PCR products that are between 100 and 2,000 base pairs long are desired. Although the above
mentioned tools have satisfied various parameters, most of them do not relate to multiplex PCR (Sambrook and Russell 2001).
Multiplex PCR primer design is a great challenge. Multiple primer annealing events need to occur under the same annealing conditions without interfering with one another. In order to analyze the PCR products by electrophoresis, the products should have different lengths. In practice, it is preferable that the difference in the lengths of the PCR products is more than 50 bp. In addition, the constraints of PCR have to be satisfied.
Traditionally, the researcher finds a primer that satis-fies the primer design constraints using manual primer design. However, it may take a lot of time to find a good primer and this will lead to lower accuracy and unreli-able results through human error. Since experiments are expensive, and a minor mistake may cause the experi-ment to fail, the manual primer design method is con-sidered to be potentially a poor approach.
To save time, and minimize problems, the use of computer programs to optimize the design, selection, and placement of oligonucleotide primers is supported (Sambrook and Russell 2001). Many different primer design programs have been developed. According to our surveys, there are approximately 70 programs available for primer design. Some of them are used on the internet, and some of them are simple stand-alone programs. In addition, some are free, while others require payment. “Primer3” (Rozen and Skaletsky 2000) picks primers from a DNA sequence, and it can avoid choosing prim-ers in transposable elements and can pick an oligonu-cleotide as a probe or primers. The “Amplicon” (Jarman 2004) is a program for designing PCR primers on aligned groups of DNA sequences. The most important applica-tion for Amplicon is the design of ‘group specific’ PCR primer sets that amplify a DNA region from a given tax-onomic group, but do not amplify orthologous regions from other taxonomic groups. The “CODEHOP” (Rose et al. 1998) was developed for PCR amplification of dis-tantly related gene sequences. An interactive program has been written to design CODEHOP PCR primers from conserved blocks of amino acids within multiply aligned protein sequences. “ExPrimer” (Sandhu and Acharya 2005) is a web-based computer program to design primers mainly from a specified exon–exon junc-tion (E-E-jn) of a gene of interest. The tool suggests the optimum primer-pair(s) of which the right (reverse) primer represents a particular E-E-jn of the mRNA. “Expeditor” (Hu et al. 2005), that can be used to com-bine known gene structure information from human and coding sequence information from farm animal species for a streamlined primer design in target farm animal species. Although these existing tools can find feasible
solutions for many problems in PCR, they do not sat-isfy some of the constraints, for example, specificity or multiplex PCR.
Compared with primer design for singleplex PCR, multiplex PCR primer design is difficult. In our surveys, we only found approximately six programs for multi-plex PCR primer design. Most of them require payment. “MultiPLX”1groups PCR primers groups according to their compatibility. The program calculates the opti-mal combinations of primer pairs for PCR primer mul-tiplexing. Primer compatibility is tested against each other as well as against each other’s products. Addi-tionally, the Genome Test is performed with all possible PCR primer pairs in each multiplex group. This avoids the appearance of unwanted PCR products from mul-tiplexed groups. “Primer Primer 5”2 is able to design primer pairs for PCR and multiplex experiments. It inte-grates multiple-sequence alignment with primer design to facilitate the design of primers for amplification. A proprietary algorithm is used to calculate a minority consensus that uses degenerate bases to represent all possible bases in a particular sequence position. Based upon this consensus, primers are designed in highly conserved regions of the sequences. “Fast PCR”3 has specific, ready-to-use templates for many PCR and sequencing applications: standard and long PCR, inverse PCR, degenerate PCR directly on amino acid sequence and multiplex PCR. The program is convenient when searching homology in a personal database by local alignment and other bioinformatics tools are included.
In general, the above programs are not free, nor do they consider all of the necessary constraints. If a primer is able to anneal in several locations of a DNA template, specificity is violated. In addition, some software pack-ages state that they can design primers for multiplex PCR, but they do not. “Primer Primer 5” is a conspicu-ous example. It does assist the user in selecting multiple or nested primers from a pool by ensuring that they are free of cross dimers, but multiplex PCR primer design is not supported. The main motivation for this study was the need by a group at the Taipei Veterans General Hos-pital, Taiwan, to carry out multiplex PCR as part of their tuberculosis research. The group was examining isoni-azid resistance in Mycobacterium tuberculosis by sin-gle nucleotide polymorphism analysis of various genes. They wanted to use a multiplex PCR genotypic assay to increase the efficiency of their experiments. Therefore,
1 MultiPLX http://www.asperbio.com.
2 Primer Primer 5 http://www.premierbiosoft.com/primerdesign/
index.html.
3 Fast PCR http://www.biocenter.helsinki.fi/bi/bare-1/html/
oligos.htm.
a new tool for multiplex PCR primer design needed to be developed.
The aim was to develop a primer design tool for mul-tiplex PCR. The user can input the multiple regions or the multiple loci of interest. The tool will return the opti-mal and specific groups of primers quickly according to user’s requirements such as primer length, GC content, and so on. It will reduce the time and error in developing the assay. Finally, the tool is also designed with a friendly interface that will allow easy use by scientists.
In this paper, we use the genetic algorithm (GA) to design primers for multiplex PCR. Genetic algorithms were formally introduced in the United States in the 1970s by John Holland at University of Michigan. He described the “genetic algorithm”, as a control struc-ture with representations and operations that can be managed in order to evolve bit strings that were adapted to the problem to be solved. Genetic algorithms tend to converge on solutions that are globally optimal or nearly so (Davis 1987).
2 System and Methods 2.1 Unique region searching
The proposed tool contains three parts, which are shown in Fig.2. They are “unique regions searching”, “multi-plex PCR primer design” and “result verification”. First, we find unique regions in the target sequence. In addi-tion, these regions need to also satisfy some parameters of primer design such as the length of primers at 18–30 nucleotides and GC content between 40 and 60%. We select candidate primers from these regions.
The length of the amplified fragment needs to be between 100 and 2,000 nucleotides and the melting tem-perature tolerance should be about 5◦. If the primer pairs satisfy these limitations, the pairs are legal prim-ers. In multiplex PCR primer design, we determine the legality of primer pair repetitively. In order to reduce execution time, we record the legality between candi-date primer and candicandi-date primer in advance.
Excessive regions of complementarity between primers should be avoided as they allow the forma-tion of primer-dimers, where the primers bind to one another instead of the template (Schoske et al. 2003). Therefore, we calculate the number of matching nucle-otides between primers. The matching nuclenucle-otides are one of the calculated fitness components in multiplex PCR primer design. Table1shows a set of primer pair interactions with the highest degree of cross reactivity.
Fig. 2 System flowchart
Table 1 Cross-checking Sequence Information Potential Interaction A1 vs. A2
Matches = 12 Alignment score = 5
*Alignment score which is defined as the number of complementary base pairs minus the number of mismatched base pairs between two primers
2.2 Multiplex PCR primer design using a genetic algorithm
In this section, we describe the main components used in our genetic algorithm, namely, crossover, mutation, and fitness.
2.3 Chromosome
Each chromosome is one of the solutions of the multi-plex PCR primer design. It was defined as serial integers and the number of integers is three times the number of target regions. Every three contiguous integers, includ-ing the number of the forward primer, the number of the reverse primer and experimental tube number, are presented to amplify one target region. For example, five target regions cost 15 integers in chromosome. Definition 2.3.1 (Chromosome) A chromosome is com-posed of target regions T1, T2,. . . , Tn, denoted as T1#T2# · · · #Tn, can be represented by
T1#T2#· · · #Tn
= (G1, Pf1, Pr1)(G2, Pf2, Pr2) · · · (Gn, Pfn, Prn)
where
• n is the number of target region; • Tiis the ith target region of genome;
• the symbol # is represented for concatenation; • Gi is the tube of multiplex PCR for the ith target
region;
• Pfiis the number of forward primer for the ith target
region;
• Priis the number of reverse primer for the ith target
region; 1 i n
Figure3shows that there are five target regions we want to amplify. Among the chromosome, the 21st primer and the 54th primer can amplify the 1st tar-get region and the 4th primer and the 23rd primer can amplify the 4th target region. These primers both act in the 3rd tube.
2.3.1 GA process flow
The system processing flow is depicted in Algorithm 1. The symbol |P| represents the size of the population. The concept of the system process flow is based on the architecture of a simple genetic algorithm (Goldberg 1989). In each chromosome, the length of amplified frag-ment should be between 100 and 2,000 bases and the difference in melting temperature between each primer
Algorithm 1 The Flow of Our Approach
Generate the initial population P
Let Pm be the probability of mutation; Pe be the probability of crossover; while not satisfy the termination condition do
for i 1 to |P| do
Select two chromosomes X and Y from population by the Roulette Wheel method Let X’ X and Y’ Y
Mutation( X’ ) Mutation( Y’ ) Crossover( X’ , Y’ )
Add X’ and Y’ into mating pool
end for
Select the best top |P| chromosomes to replace the original population
end while
should not exceed 5◦ for any target regions. In addi-tion, the primer pairs in same tube should have a similar melting temperature.
Elitism is used. This means, that at least one of the best solutions in each generation is preserved without change to a new population. Therefore, the best solution can survive to the succeeding generation. The crossover and mutation operators are repeatedly applied until the termination conditions are satisfied. The following are termination conditions:
• The number of generations exceeds the maximum number of generations permitted.
• The best fitness does not improve over a given num-ber of generations. The default is 500 generations.
2.3.2 Fitness
To evaluate their fitness, the chromosome must be applied to a sum-of-pairs function (Setubal and Mei-danis 1997). The sum-of-pairs function is defined as the sum of the scores of all primer pairs in same tube. If the difference of length of amplified fragment is less 50 bases and the number of complementary sequences is not zero, then the fitness receives a lower score. The fit-ness values of chromosomes are recomputed after the mutation and crossover process.
2.3.3 Crossover operator
The purpose of crossover is to exchange information from the chromosomes to produce offspring, which it is hoped will possess an advantage over the parental gen-eration. However, the offspring also can inherit a dis-advantage from the parental generation. The crossover does not promise to produce good offspring. Then, based on the principle of survival-of-the-fittest, the worse off-spring are eliminated by competition.
In the crossover process, two parent chromosomes, denoted as X and Y, are selected by Roulette Wheel Selection and are used to produce two daughter chro-mosomes, denoted as X and Y. The common cutting point is randomly selected in parent chromosomes. It will cut every chromosome into two parts, called the longer part and the shorter part. We reserve the longer part and exchange the shorter part. The identifier of tube must be reassigned. The assignment order is the same Tm of the group, no member of group, and new group
in turn. Algorithm 2 describes, in detail, the crossover operator 1.
An example of crossover is shown in Fig.4. Two par-ent chromosomes X and Y are used to produce two daughter chromosomes X and Y. When the cutting point is selected, we exchange the shorter part and reas-sign the group. In the chromosome Y, the melting tem-perature of the 12th primer and the 2th primer is 66◦C.
Algorithm 2 Crossover(chromosome X , chromosome Y)
Randomly select a cutting point L, L % 3 0, 1 L 3n
if L n L then
Exchange the rear-end part of two chromosomes and Reassign groups.
In reassigning process, we select the group which has the same Tm with the
primer pair first. If the group can’t be found, the empty groups will be considered. We can select one from them. When the above-mentioned methods can’t work, we will assign a new group until the maximum number of group is reached.
else if L 3n L then
Exchange the front-end part of two chromosomes and Reassign groups. The reassigning process is same with the above-mentioned process.
end if ≥
Fig. 4 Crossover operator example
According to the assignment order, we finally assign a new group to it.
2.3.4 Mutation operator
Evolution can’t produce novel individuals by crossover and reproduction alone because the offspring only mix the properties of parents. Evolution under these cir-cumstances only moves ahead slowly and is limited to a small group of individuals. In nature, organisms use mutation to create new variants. Therefore, we made use of a mutation operator to increase the diversity of population and this allows evolution to act fully through diversification.
There are two kinds of mutation operators in our approach. In the mutation process, each selected chro-mosome is mutated by randomly using one of the fol-lowing mutation operators.
The mutation operator 1 chooses one of integers to change. After mutating, we test if the Tmof
correspond-ing target region is the same as the original. If the muta-tion point is the group, we use another group to replace it. First, we find the candidate groups, the Tm of which
is the same as the group that we want to change. We randomly choose one of candidate groups to replace the mutation group. This action doesn’t change the Tm of
target region. It is aimed to let the primer pair change their reaction environment. If the mutation point is the primer, we randomly choose another primer that must obey the constraints of primer design. Algorithm 3 describes the detail of mutation operator 1.
An example is given in Fig.5. Figure5a shows muta-tion operator 1 where it chooses a group to change. After deciding the mutation point, we identify the other
Fig. 5 Mutation operator example
groups whose Tmis 60◦C as the candidate groups. Then,
we randomly select one group from them to replace the original group. Unfortunately there are no candidate groups, so we assign a new group or mutate another loca-tion. In the same way, mutation operator 1 can choose a primer to change as depicted in Fig.5b.
Mutation operator 2 whose detail is depicted in Algo-rithm 4 replaces group and primer at the same time. We choose one target region to rearrange the group and primer pairs. This action must obey the constraints of primer design.
2.3.5 Result verification
Finally, we check the solutions again to optimize the number of primer pairs in same tube and to avoid non-specific PCR amplicons.
Algorithm 3 Mutation operator 1(chromosome X)
Randomly select a mutation point L, 0 L 3n
If L % 3 0 then
Find groups whose Tm is the same with the group we want to change Randomly select one to alter the origin
else
Randomly choose the other primer which must obey the constraints of primer design to alter the origin
Algorithm 4 Mutation operator 2(chromosome X)
Randomly select a mutation point L L 3n, L % 3 0 Randomly select a group G
According to the Tm of the group G, find the primer pair Pr and Pf for target region TL Replace the G, Pr, and Pf to L, L 1, and L 2 respectively
Table 2 The result of case study I
Target Region Forward primer Reverse primer Product size
Start Len Tm GC Start Len Tm GC
Group 0→ Tm: 86 katG (110) 2155779∼2155782 2154867 25 86 59 2156566 25 90 55 1672 kasA (77) 2518341∼2518344 2517673 25 88 57 2519532 25 86 59 1831 kasA (413) 2519349∼2519352 2519283 25 90 50 2519532 25 86 59 219 Group 1→ Tm: 62 inhA (194) 1674779∼1674782 1674046 25 64 52 1675177 25 62 40 1110 katG (463) 2154720∼2154723 2154062 25 64 60 2155953 25 62 55 1871 katG (90) 2155839∼2155842 2155454 25 66 57 2155953 25 62 55 478 ahpC (176) 2726341∼2726344 2725564 25 62 55 2726502 25 62 55 918 Group 2→ Tm: 80 ndh (110) 2102710∼2102713 2101383 25 82 51 2102976 25 80 48 1566 ahpC (174) 2726716∼2726719 2725630 25 82 57 2727461 25 80 60 1805 Group 3→ Tm: 76 kasA (312) 2519046∼2519049 2517688 25 76 58 2519273 25 80 60 1561 ahpC (61) 2726371∼2726374 2726304 25 76 58 2727303 25 76 58 975 ahpC (51) 2726476∼2726479 2726304 25 76 58 2727461 25 80 60 1133 Group 4→ Tm: 86 katG (434) 2154807∼2154810 2154691 25 88 51 2154867 25 86 59 147 kasA (269) 2518917∼2518920 2517673 25 88 57 2519532 25 86 59 1831 Group 5→ Tm: 64 inhA (21) 1674260∼1674263 1674046 25 64 52 1675157 25 64 60 1090 katG (397) 2154918∼2154921 2154062 25 64 60 2156068 25 68 54 1986 katG (315) 2155164∼2155167 2154062 25 64 60 2155454 25 66 57 1372 katG (91) 2155836∼2155839 2155454 25 66 57 2157329 25 64 52 1854 Group 6→ Tm: 78 katG (529) 2154522∼2154525 2154302 25 82 57 2154727 25 78 56 399 kasA (66) 2518308∼2518311 2517678 25 78 56 2519273 25 80 60 1570 Group 7→ Tm: 70 ndh (268) 2102236∼2102239 2101770 25 70 52 2102708 25 70 59 915 katG (438) 2154795∼2154798 2154224 25 70 59 2155514 25 70 59 1268 katG (336) 2155101∼2155104 2153914 25 74 60 2155514 25 70 59 1577 katG (138) 2155695∼2155698 2155514 25 70 59 2157283 25 72 56 1747 3 Results
The tool runs on a PC with an AMD K7-1200 Mhz CPU, 750 MB RAM and an OS consisting of a Linux 9.0 plat-form. It is written by C++.
3.1 Case study I
Isoniazid (INH) is a central component of drug regimens used worldwide to treat tuberculosis. Previous studies show that a variety of single nucleotide polymorphisms in multiple genes are found exclusively in INH-resis-tant clinical isolates. These genes are either involved
in mycolic acid biosynthesis or are overexpressed as a response to the buildup or cellular toxicity of INH (Ramaswamy et al. 2003). Up to the present, 24 poly-morphisms have been published. These target regions and the Mycobacterium tuberculosis genome are the inputs for this case study. The default parameters are used. Table2shows the detailed results for this case. In the target region column, we display the start and end locations of every target region. The detail primer infor-mation includes start location, length, melting tempera-ture, GC content and the length of amplified fragment for any primer pair. These are shown in the second and third column. The constraints for singleplex PCR and
Table 3 The result of case study II
Target Region Forward primer Reverse primer Product size
Start Len Tm GC Start Len Tm GC
Group 0→ Tm: 72 ybbH 191182∼192033 191032 25 74 48 192279 25 72 44 1222 ybdE 219594∼220019 218454 25 72 44 220067 25 74 48 1588 mdr 332260∼333540 331789 25 72 44 333796 25 76 52 1982 Group 1→ Tm:76 gcaD 56350∼57720 55905 25 78 56 57928 25 76 52 1998 rpmC 139922∼140122 138521 25 76 52 140483 25 76 52 1937 Group2→ Tm: 74 ksgA 50638∼51516 50092 25 74 48 51979 25 76 52 1862 yazB 87398∼87607 86124 25 74 48 87862 25 76 52 1713 adaB 204337∼204876 204227 25 74 48 205572 25 76 52 1320 Group 3→ Tm:72 holB 40663∼41652 39923 25 72 44 41838 25 76 52 1890 gltX 111044∼112495 110748 25 74 48 112512 25 72 44 1739 Group 4→ Tm: 72 ybxB 121065∼121670 120125 25 74 48 121888 25 72 44 1738 ycbD 268838∼270304 268474 25 76 52 270466 25 72 44 1967 Group 5→ Tm: 74 phoD 283555∼285225 283286 25 76 52 285243 25 74 48 1932 yceA 309554∼310396 308841 25 78 56 310623 25 74 48 1757 Group 6→ Tm: 78 dnaX 26812∼28503 26659 25 78 56 28636 25 78 56 1952 rpsI 154299∼154691 153407 25 78 56 154895 25 78 56 1463 Group 7→ Tm: 70 mpr 245179∼246120 244896 25 74 48 246483 25 70 40 1562 ycbA 265537∼266700 265448 25 74 48 266905 25 70 40 1432
multiplex PCR are satisfied. For example, the differ-ence in product size between each target is at least 50 bases in same tube. We also observe other phenomena. Some primers can be shared and some primer pairs can amplify regions that include many targets. These are due to the short distance between some target regions.
3.2 Case study II
We select Bacillus subtilis genome as our material and choose 30 genes as target regions. The designated primer length was 25 nucleotides. The result also satisfies the constraints of singleplex PCR and multiplex PCR as shown in Table3. In this experiment, we find that there are no legal primer pairs close to certain the target regions, thus no primers for these genes are generated. Our approach filters this in advance.
4 Discussion and Conclusion
We present a novel tool to design primers for multiplex PCR. It can design primers for target regions and group the primer pairs to achieve the purpose of multiplex PCR primer design. We were able to find unique regions
in the target sequence and select candidate primers from these. We use this method to avoid primers annealing in several locations. Most programs don’t pay attention to the area of specificity.
Our tool uses “unique regions searching” to find can-didate primers. This action ensures uniqueness of the primers. Primers will not anneal in several locations of a template. However, there is a defect in this method. If there is no unique region close to the target regions, we will fail to find primer pairs for these regions. We need new approaches to solve this problem. Addition-ally, we need to consider further constraints, such as the fact that the base at the 3end of each primer should be G or C. Such changes, we believe, will increase the accu-racy of any experiments carried out after primer design for multiplex PCR using the program outlined here.
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