# Primer Dimer / Hairpin Algorithms

What are the algorithms / methods in use for the calculation of primer dimers and hairpins?

As an example, IDT's OligoAnalyzer tool will generate these analysis given particular sequences.

The homo-dimer analysis seems to me to just be a sliding scan of two sequences across each other. I assume this doesn't take into account possible hairpin issues? or are such structures less likely compared to the myriad of other more common problems. In addition, how are the ΔG values calculated given a particular dimerization pattern?

It is important visualize more faces to design primer or oligo and PCR experiments:

- calculate thermodynamic parameters of DNA Hybridization (Oligo/Template)

• compute hairpin-loop, dimer, bases penality and melting temperature about primer or pair primer

• calculate statistics about melting temperature with the change in composition and mix PCR concentration

with google you could find more tools but you must choose a tool of a sequencing team. almost all tools use mfold algorithm, it's simple and effective:

M. Zuker, D. H. Mathews & D. H. Turner. Algorithms and Thermodynamics for RNA Secondary Structure Prediction: A Practical Guide In A Biochemistry and Biotechnology, 11-43, J. Barciszewski and B. F. C. Clark, eds. , NATO ASI Series, Kluwer Academic Publishers, Dordrecht, NL, 1999.

I worked in a sequencing team and there was a programmer. he developed a fantastic tools. he is a little english, but he could support you: http://promix.cribi.unipd.it/cgi-bin/promix/melting/melting_main.exe

## Biology:Primer dimer

A primer dimer (PD) is a potential by-product in the polymerase chain reaction (PCR), a common biotechnological method. As its name implies, a PD consists of two primer molecules that have attached (hybridized) to each other because of strings of complementary bases in the primers. As a result, the DNA polymerase amplifies the PD, leading to competition for PCR reagents, thus potentially inhibiting amplification of the DNA sequence targeted for PCR amplification. In quantitative PCR, PDs may interfere with accurate quantification.

## Running AutoDimer

1. Prepare an input file containing at least two sequences following the input file format.

Note: You must use an input file. Sequences cannot be entered manually in the blue text box.

2. Open file from “File” menu.

3. Confirm that the proper number of sequences have been read in by reviewing the “# of Sequences box”.

4. If desired, vary the parameters for Score, [Na+] or total DNA strand concentration (CT).

5.Click either “Primer Dimer Checker” or “Hairpin Checker” the meter will indicate progress.

6. Potential structures are displayed in the text box in the lower portion of the program screen.

7. If you wish to save the screening results go to “File” and “SaveAs”. The information can be opened later in Word, Excel, Notebook etc.

8. The results can also be printed directly from the AutoDimer program.

As the algorithm runs, AutoDimer saves temp files to your “C” (C:) drive. It erases these files when you exit the program. However, if you load the program onto a D, E (non C) drive or if your “C” drive is full then you will have problems running the program.

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## Materials and methods

### Assumption

To create training data on RNN, the entire PCR reaction was schematically planned. (Fig.  1 ). Primer binding to the template is not limited to its full length and is assumed that only a part of 3′ may bind (Fig.  1 B). Hairpin structure of the primer and its dimer are assumed to be formed before binding the primer to the template (Fig.  1 B). Thus, it is assumed that DNA synthesis occurs from some hairpin structures and dimers 21 , 22 . As DNA synthesis from partially bound primers proceeds, PCR products that are completely complementary to the primers began to be synthesized (Fig.  1 C). Eventually, most PCR products become completely complementary to the primers (Fig.  1 D).

PCR process diagram of primers with incomplete homology with the template. Schematic diagram of the reaction assumed by PCR from partially matched primers. DNA elongation may start from primers on which partially 3′-end matches (B). On the end of second cycle, the 3′-end of the elongated DNA completely match with a primer (C). On the end of third cycle, synthesized DNA are completely matched on both ends of synthesized DNA (D).

To express the relationships of these schemas as words, we decided to express the hairpin, primer dimer, primer-template bond, and primer-PCR product bond as words. The strength of the primer-template bond on the forward and reverse flanks greatly influences the establishment of the PCR reaction. For combinations that are not of the original primer-template, the binding position needs to be determined by PCR from the possible binding of multiple primer-templates. With this, we constructed the words for the learning RNN.

### Templates for PCR

A part of the 16S rRNA nucleotide sequence (v6-v8) (Supplement 1 Table 1 ) was synthesized by OE-PCR (Supplement 1 Table 2 ) for 30 phyla as templates for PCR model experiments. Of the 30 phyla, 16S rRNA sequences in Firmicutes were synthesized into two genera, the Bacillus and the Calditerricola. These sequences were significantly different in v6-v8. Thirty-one double-stranded DNAs with 435 to 481 bases were prepared as a template for PCR model experimentation utilized the standard thermodynamic index.

### PCR experiment as basic data for primer design using RNN

#### Design of primer sets for preliminary learning of RNN

We designed 72 sets of PCR primers capable of amplifying 31 DNA templates, according to the specifics of the primer sequence to the specific template and the amplification size of about 100� (Table ​ (Table1). 1 ). In a preliminary trial when primers were designed using Primer3 primer-design software, all primers amplified all 31 templates (data not shown). From its result, we designed 72 sets of PCR primers at this stage ignoring some of the conventionally known annealing temperatures and some indicators such as avoiding single base repetition. The size of the primers was set to 19� bases. The most important index is high homology to the target template and low homology to others.

### Table 1

Primer sets for the main experiment.

Primer no.Primer nameSequence
1aim_1fGTCCAGGGCTTCACACATGCTA
aim_22rTGTTACCAACTTTCATGACGTG
2aim_71fAGCGCAACCCTCACCTTATGTT
aim_94rGGGACCGGATTTTTGAGATTAG
3aim_122fTTCAGTTGGGCACTCGTAAGGA
aim_94rGGGACCGGATTTTTGAGATTAG
4aim_94fCTAATCTCAAAAATCCGGTCCC
aim_143rCCTTCACGAGTTTCACCTTAGT
5aim_94fCTAATCTCAAAAATCCGGTCCC
aim_147rCTTCACCCCCTTCACGAGTTTC
6aim_161fGAGGTGGAGCGAATCCCAGAAA
aim_194rCTTACCAAGCATACCTTAGGCA
7aim_263fCAAATCCCAGAAAGCCGCTCTC
aim_250rACCAGCCCTGCCGTCGGCGCCT
8aim_348fGTGTTGCCTAGCAATAGGATCT
aim_282rTGCTGCCCTCTGTCTATGCCAT
9aim_386fGCTGAGGACTCTAATTGAACTG
aim_394rAGACAGCTTTTAAGGGATTTCC
10aim_386fGCTGAGGACTCTAATTGAACTG
aim_461rCCGATCCGGACTGAGACAGCTT
11aim_394fGGAAATCCCTTAAAAGCTGTCT
aim_436rCGAGCGTCTTTGGGTACTCCTG
12aim_468fGGCGGAGGAAATCCTAAAAACT
aim_515rCTTCAGATACTTCGGGTGCGAC
13aim_555fACGGGACTGCCCGCGAAAGCGG
aim_562rGGGCCCACCTTTTTGCGATTAG
14aim_599fGTGCTACAACGGGTAGCGAAAC
aim_652rCCGCCGAGGCGGAGTTGGGTCA
15aim_764fCTTATCCTTTGTTGCCAGCGGT
aim_744rCGACATACTTTATGAGGTCCGC
16aim_812fCTGCCAGTGATAAACTGGAGGA
aim_744rCGACATACTTTATGAGGTCCGC
17aim_842fTCTCATAAAACCGTTCTCAGTT
aim_848rTGTTACAAACTCTCGTGGTGTG
18aim_1016fCTAATCGGAAAAAGCCGGCCTC
aim_1036rATGAATTACACCTTGGGCGGCT
19aim_1209fGTGTCGGTAGTTACAGGTGTCT
aim_1159rATTGTCGTGGCCATTGTAGCGT
20aim_1248fCGCCGTGACCGGCGGAGGAAGG
aim_1193rCCGCGCCATGGCTGATACGCGG
21aim_1175fTCGCCTAAACGTGGTCTCAGTG
aim_1264rTCCCAGTCGCGGCCCCTGCCCT
22aim_1177fGCCTAAACGTGGTCTCAGTGCA
aim_1264rTCCCAGTCGCGGCCCCTGCCCT
23aim_1316fCTAGTGGGACAGCCGGAGTAAT
aim_1285rTGCAATCCGAACTAAGACAAGG
24aim_1332fCCGGAGTAATCCGGAGGAAGGT
aim_1276rAGGTTTTTGAGGTTGGCTCACT
25aim_1285fCCTTGTCTTAGTTCGGATTGCA
aim_1293rGCTTCTGGCAAAACCGACTTTC
26aim_1401fTGAGGTGTCGGCTTAAGTGCCA
aim_1368rGCTAGCTGCCTTCTGTACCCCC
27aim_1401fTGAGGTGTCGGCTTAAGTGCCA
aim_1383rTTTGGGATTAGCATACGGTCAC
28aim_1415fGAGGTGTCGGCTTAAGTGCCAT
aim_1368rGCTAGCTGCCTTCTGTACCCCC
29aim_1447fAGGTCATGCTGAGGACTCTGGA
aim_1368rGCTAGCTGCCTTCTGTACCCCC
30aim_1447fAGGTCATGCTGAGGACTCTGGA
aim_1391rTTCGATCCGAACTGAGAGAGGA
31aim_1391fTCCTCTCTCAGTTCGGATCGAA
aim_1465rCCCTAGGACGATCCTTGCGGTT
32aim_1549fGGGTAATGCCGGGTACTCACAG
aim_1504rCATTGTCCCTGCCACTGTAGCG
33aim_1504fCGCTACAGTGGCAGGGACAATG
aim_1550rTAGCTCGGGGACTTCCGATGAA
34aim_1758fGCCAATACAAACAGTTGCAAAT
aim_1775rTACCAGCTCTCATAGTTTGACG
35aim_1770fCTGTAAAGTTGGTCTCAGTTCG
aim_1775rTACCAGCTCTCATAGTTTGACG
36aim_1770fCTGTAAAGTTGGTCTCAGTTCG
aim_1811rCTACCCTAGACATGCGCTTCCT
37aim_1948fCAAAGGGCAGCGACATAGTGAT
aim_1984rATGAGCCGTAGCTGATGCCCAT
38aim_2085fAGTACAGAAGGTAGCAAGATCG
aim_2138rAACGTATTCACGGCGTTATGGC
39aim_2109fGATGGAGCAAATCCTTAAAGCT
aim_2164rTCAACGACTTAAGGTAAAACCA
40aim_2292fGGTTAAGTCCCCTAACGAGCGA
aim_2247rATGACTTTGCAGCCTAGCAACG
41aim_2547fTCGAGTACATGAAGTTGGAATC
aim_2581rTACGGTTAGGCCTGCTACTTCA
42ai2_1242_fTACTTTGTCTAACGAGACTGCC
ai2_1242_rCGAACTGAGACCAACTTTACAG
43ai2_100_fACGAGCCGGAGGAAGGAGG
ai2_100_rACCCCGGGAACGTATTCACC
44ai2_1213_fCCTAAACCCTGTCGTGGTGCAG
ai2_1213_rTAGCTCGGGGACTTCCGATGAA
45ai2_1325_fTAAGGGGACTGCCCCGGATAAC
ai2_1325_rGCGCTTTCTGAGATTCGCTCAG
46ai2_6_fCAAGTCGAGCGGAGAAGATTT
ai2_6_rGGTATTACCCATCCTTTCGGAT
47ai2_1194_fGCGGGTGACCGTATGCTAATCC
ai2_1194_rCTTGCGGTTACGTACTTCAGGT
48ai2_1315_fCGTTGCTAGGCTGCAAAGTCAT
ai2_1315_rGCGGCTCCGGCGACTTCGGATG
49ai2_1147_fCGCCGTGACCGGCGGAGGAAGG
ai2_1147_rCACTGAGACCACGTTTAGGCGA
50ai2_23_fGAGACTGCCGGTGACAAACC
ai2_23_rAGTTGCAGACTCCAATCCGGA
51ai2_1244_fGCCAATACAAACAGTTGCAAAT
ai2_1244_rTACCAGCTCTCATAGTTTGACG
52ai2_1125_fACCGCTGCAACCCCGCGAGGGT
ai2_1125_rTGGGCGGCTGCTCCCTTGCGGT
53ai2_1238_fGGCACAGGTGGTGCACGGCCGT
ai2_1238_rGGCATAAGGGGCACGAGTACCT
54ai2_1166_fCCGGAGTAATCCGGAGGAAGGT
ai2_1166_rTGCAATCCGAACTAAGACAAGG
55ai2_1143_fTGCCGCCGTGACCGGCGGAGGA
ai2_1143_rCACTGAGACCACGTTTAGGCGA
56ai2_1124_fACCGCTGCAACCCCGCGAGGGT
ai2_1124_rAGCGCACCGACTTCTAGTGCAA
57ai2_1284_fACGAGACTGCCTGGGTTAACCA
ai2_1284_rAGCTTTAAGGATTTGCTCCATC
58ai2_1288_fCTGCCTGGGTTAACCAGGAGGA
ai2_1288_rGAACTGGGGCCAGCTTTAAGGA
59ai2_1090_fAAAGGAGACTGCCAGTGATAAA
ai2_1090_rTCCAATCCGGACTACGACATAC
60ai2_1142_fGTGTCGGTAGTTACAGGTGTCT
ai2_1142_rCAACTCCGCCTTCACGGGGGCG
61ai2_1195_fGCGGGTGACCGTATGCTAATCC
ai2_1195_rCCCTAGGACGATCCTTGCGGTT
62ai2_101_fGTCGTCGTCAGCTCGTGCC
ai2_101_rCTCCTTCCTCCGCCTCGTC
63ai2_1189_fCGTCGTAAGATGTGAGGAAGGT
ai2_1189_rTTCGATCCGAACTGAGAGAGGA
64ai2_1088_fCTTATCCTTTGTTGCCAGCGGT
ai2_1088_rTCCAATCCGGACTACGACATAC
65ai2_1192_fGGGGGTACAGAAGGCAGCTAGC
ai2_1192_rCTTGCGGTTACGTACTTCAGGT
66ai2_1303_fGCCATAACGCCGTGAATACGTT
ai2_1303_rCTTCATCCTAGTCATCAGCCTC
67ai2_1102_fAAGTTGGGCAGTCTAAGGTGAC
ai2_1102_rTCTTGCAGCTCTTTGTACCGTC
68ai2_54_fCGGGTGAGTAACACGTATCTAA
ai2_54_rTCTCAGTTCGGCTACGTATCAT
69ai2_1275_fTGATATGGAGCGAATCCCCAAA
ai2_1275_rGTCTGCCTCCTGCAAGCAGGTT
70ai2_1327_fCTGAGCGAATCTCAGAAAGCGC
ai2_1327_rTTGCCTGGGTTGGGCCACCGGC
71ai2_10_fCTGGCGGCGTGGATAAGACA
ai2_10_rATGGGCTATTCCCCACTTCAG
72ai2_1071_fAGCGATGCCACCCGGCAACGGG
ai2_1071_rCCTGCCCGTAGGCTCCCGGCGA

Primer pair number, primer name and base sequence (5′ →𠂓′) used in the experiments for RNN-training are shown. Primers with the same primer pair number are used as a set of primers.

We also designed 54 sets of phylum-specific primers, which were designed based on analysis with preliminary test primers (Table ​ (Table2). 2 ). As a design method, a plurality of primer candidates was firstly extracted from the template sequence, and a combination of the extracted primer candidates was used as a primer pair candidate. A primer pair for which PCR is expected to occur only in a specific bacterial phylum by RNN was determined as a primer set for a test experiment.

### Table 2

Primer set no.Primer namePrimer sequence
11_f_180AACGCGCTGCGAGCCTGTGA
1_r_369CCCACAAGGGTTAGGCCACT
21_f_180AACGCGCTGCGAGCCTGTGA
1_r_397ATCGCCGATCCCACCTTCGA
31_f_180AACGCGCTGCGAGCCTGTGA
1_r_400CCAATCGCCGATCCCACCTT
41_f_180AACGCGCTGCGAGCCTGTGA
1_r_408ACTTCGTCCCAATCGCCGAT
51_f_186CTGCGAGCCTGTGAGGGTGA
1_r_369CCCACAAGGGTTAGGCCACT
61_f_186CTGCGAGCCTGTGAGGGTGA
1_r_397ATCGCCGATCCCACCTTCGA
71_f_186CTGCGAGCCTGTGAGGGTGA
1_r_400CCAATCGCCGATCCCACCTT
81_f_186CTGCGAGCCTGTGAGGGTGA
1_r_408ACTTCGTCCCAATCGCCGAT
92_f_50TCAGTTGGGCACTCGTAAGG
2_r_342TGGCAAAGACCACTTCGGGT
104_f_251CTAAAGCCACCCCCAGTTCA
4_r_395CTCTTCGCCTGACTTCGGGT
114_f_251CTAAAGCCACCCCCAGTTCA
4_r_403TCGGCAGGCTCTTCGCCTGA
125_f_0TGCCTGGGAGCCCTAGCACA
5_r_228CCCCTTACGGGTTCGCTTCC
135_f_223CAGAGGGAAGCGAACCCGTA
5_r_410TCCGGGGGTTGGGATAGCGA
146_f_66GCCTAGCAATAGGATCTCTC
6_r_211GGGCATAGTTTAGGGATTGG
156_f_211CCAATCCCTAAACTATGCCC
6_r_363AGACGACCTGAGCACTTCTG
166_f_211CCAATCCCTAAACTATGCCC
6_r_385TACTAATCACAACTTAGGGC
177_f_205AATCCCTTAAAAGCTGTCTC
7_r_347AGCGTCTTTGGGTACTCCTG
188_f_78ACTGCCCAGATCAACTGGGA
8_r_349TGGCTTCAGATACTTCGGGT
198_f_78ACTGCCCAGATCAACTGGGA
8_r_359TCCTTGCGGTTGGCTTCAGA
209_f_87GACTGCCCGCGAAAGCGGGA
9_r_181GTTGCCGGGTGGCATCGCTT
2110_f_226TCCCTAAAAAGCATCCTCAG
10_r_381AGGCGGAGTTGGGTCACTGA
2212_f_190GGCATATACAAAGAGAAGCG
12_r_395TAAGCGCCCTCCCGAAGGTT
2312_f_216CGAGAGCAAGCGGACCTCAT
12_r_395TAAGCGCCCTCCCGAAGGTT
2412_f_236AAAGTATGTCGTAGTCCGGA
12_r_395TAAGCGCCCTCCCGAAGGTT
2513_f_203GGTACAAAGAGCTGCAAGAC
13_r_397CTCCAAAAAGGTTACCCCAC
2614_f_64GCAAGGGGGCCCTCTGGAGA
14_r_341TAGAGCACTCCCTTCTCCCA
2715_f_60TGGCGAAACCGCCTCGGATA
15_r_349CTCCCTTGCGGTTAGCGCAC
2818_f_17TGTCGGTAGTTACAGGTGTC
18_r_177GATCTGCACTGAGACCACGT
2918_f_173CTAAACGTGGTCTCAGTGCA
18_r_330TCCCCGACTGGGGTTAGCAC
3019_f_83TAGTGGGACAGCCGGAGTAA
19_r_177AGGTCGCATCCCGTTGTCCT
3119_f_90ACAGCCGGAGTAATCCGGAG
19_r_371CTATCCGAAGATTCGGTCAC
3219_f_196TCGCGAGAGTGAGCCAACCT
19_r_346TCTGGCAAAACCGACTTTCG
3319_f_196TCGCGAGAGTGAGCCAACCT
19_r_371CTATCCGAAGATTCGGTCAC
3420_f_225ATCCCAAAATCCTCTCTCAG
20_r_382GACGATCCTTGCGGTTACGT
3521_f_61GGGTAATGCCGGGTACTCAC
21_r_211ACCACGACAGGGTTTAGGGG
3621_f_61GGGTAATGCCGGGTACTCAC
21_r_217ATCTGCACCACGACAGGGTT
3721_f_61GGGTAATGCCGGGTACTCAC
21_r_227GCAACCCTCAATCTGCACCA
3821_f_179AATGGGCTGCAACGCCGTAA
21_r_359GTTAGCTCGGGGACTTCCGA
3921_f_216AAACCCTGTCGTGGTGCAGA
21_r_348GACTTCCGATGAACCCGACT
4023_f_151ATGACGTCAGGTACTCGTGC
23_r_437CCCCCCTCACCAGGTTCTCC
4124_f_84CTGCCAACGTAAGTTGGAGG
24_r_360CTTGCGGTTAGCAACACGGT
4226_f_74AGACTGCCCGTGTTAAGCGG
26_r_169TCACTATGTCGCTGCCCTTT
4326_f_74AGACTGCCCGTGTTAAGCGG
26_r_358CTGCAAGCAGGTTGGCGCAA
4428_f_165AATGGGGCGGACAGAGCGTT
28_r_333CCCCCGCTTTGGTGGCTTGA
4528_f_165AATGGGGCGGACAGAGCGTT
28_r_397ACTTAGTCCCCATCACGGGT
4628_f_170GGCGGACAGAGCGTTGCTAG
28_r_339GGATGCCCCCCGCTTTGGTG
4728_f_173GGACAGAGCGTTGCTAGGCT
28_r_333CCCCCGCTTTGGTGGCTTGA
4828_f_192TGCAAAGTCATGCTAATCGC
28_r_333CCCCCGCTTTGGTGGCTTGA
4928_f_192TGCAAAGTCATGCTAATCGC
28_r_397ACTTAGTCCCCATCACGGGT
5028_f_204CTAATCGCAAAAACCGTTCC
28_r_397ACTTAGTCCCCATCACGGGT
5129_f_237GCGAATCTCAGAAAGCGCTC
29_r_437CCCAGTCGCCAGCCATACCA
5230_f_128CAATGCTACGGACAAAGGGC
30_r_306TTCGGGCGTGGCCAACTTCC
5330_f_128CAATGCTACGGACAAAGGGC
30_r_328CCACAAGGGTTGGAGTAACG
5430_f_128CAATGCTACGGACAAAGGGC
30_r_342TTCGGCGTCCTCCTCCACAA

Primer pair number, primer name and base sequence (5′- >𠂓′) used in the experiments for RNN-test are shown. Primers with the same primer pair number are used as a set of primers.

#### PCR amplification experiments

Using the 72-primer sets for learning and validation of RNN and 54-primer sets for testing RNN, we tried to amplify all 31 templates. PCR was carried out using 2× GoTaq Green Hot Master Mix (Promega) for a total of 3,906 PCRs with 31 templates and 126 (72 plus 54) sets of primers. The PCR solution contained 0.5 µM primer, 100,000 copies of the template, and was adjusted to 1× GoTaq Green Hot Master Mix by adding water and 2× GoTaq Green Hot Master Mix. After adjustment, the PCR solution was subjected to denaturation at 95 ଌ for 2 min and followed by 33 cycles at 95 ଌ for 30 s, 56 ଌ for 30 s, 72 ଌ for 30 s, and followed by incubation at 72 ଌ for 2 min. After cooling to 8 ଌ, it was stored at 4 ଌ until processed in agarose gel electrophoresis. The PCR products were electrophoresed using 1.5% agarose in 1× TBE buffer at 100 V for 40 min. The agarose gel was stained in 1 µg/ml Ethidium Bromide solution and photographed under UV.

### Symbols for RNN learning

The data for RNN learning consisted from a symbol (Table ​ (Table3) 3 ) generated from the hairpin structure of the primer, the primer dimer, and the homology between the primer and the template, and multiple 5-character codes (pentacode) generated from the symbol (Fig.  2 ). The correct answer data for RNN was the PCR result for each primer set and template. Since the RNN is optimized for learning natural language sentences, which were composed of words, the generated pentacode is called a pseudo-word, and the pentacode listed according to the nucleotide sequence of the template is called a pseudo-sentence. Specific design methods are described in the creating pseudo-words and pseudo-sentences section.

### Table 3

Base pair characters for sense or antisense direction.

Base pair (primer base–template base)Primer-templatePrimer hairpin or dimer
Initial stageMiddle stage
ForwardReverseForwardReverse
A-T, T-Aafpuk
C-G, G-Cbgqvl
A-A, A-G, G-A, G-G, C-Cchrwm
T-T, T-C, C-Tdisxn
C-A, A-C, G-T, T-Gejtyo

A symbol for generating pseudo-words for RNN learning. The codes are set in the nucleotide duplex on each base pair at the complementary position. Mismatched base pairs such as A-A, T-T and C-A may appear within the partially complementary region. Base-pairs are grouped based on influence for stability of partially complementary strands.

The process of generating pseudo-words and pseudo-sentences is shown. Pseudowords are generated in relation to a particular primer pair and template. First, prepare the primer pair and template data in a format that can be read by the analysis program (A). Then, the base sequence alternatives which synthesized on the primer hairpin (B) and dimer (C) are added to the original primer sequences. The plausible double-strand formation which is expected between the primer sets and template is assumed and expressed as letters (DE). First, a part of the complementary primer including a part of the primer and the template and the position of the template are listed (D), and their interaction is expressed by a letter for each base-pair (E). The one-character code used to express the interaction used at that time is shown in E. In order to do machine learning with RNN, it is necessary to predict the primer-binding position on the template, which is the source of the PCR product production. On the prediction other primer-binding positions are classified to unrelated binding positions the PCR product production. In this study, the free energy of each plausible primer binding position on the template was calculated for all possible primer binding positions. Referring to the free energy of binding positions, two primer binding positions, which have minimum free energy, were identified as the PCR-amplifiable primer binding positions. For these determinations, the free energy was calculated on nested dimers and sum free energies on the primer-template binding positions (F). The free energies are calculated from Enthalpy, Entry, and absolute temperature of the nested dimers. According to the free energies on the primer-template binding positions, we determined two primer-template binding sites, from which PCR is most likely to proceed, and capitalize nucleotide-interaction-letters (G). Similar to primer-template interactions, the program searches hairpin or dimer formation in a primer and primers. One-letter codes are generated for each base pair in these hairpin and dimer (H). Strings of interactions between primers or between primers and templates were broken down into 5 letters (five-character codes) as words and duplicated to reflect their importance depending on their length and position from the 3'end (I). Similarly, the interaction is predicted for the PCR product and primers shown in Fig. ​ Fig.1D, 1 D, and characters different from the interaction assumed in the middle of the process are assigned (J). A pseudo-sentence is generated by arranging all the five-character codes assigned in this way at positions based on the array of templates (K).

### Creation of pseudo-words and pseudo-sentences from the relationship between primers and templates

For hairpins and dimers, DNA synthesis from the complementary region was predicted and the synthesized primers were added to the primer set. For the complementary region between the hairpin, dimer, primer-template, and primer-PCR product, characters corresponding to the complementary base pair were set for the entire complementary region, and a pseudo-code sequence was generated. The corresponding character string was divided into 5 bases in order from the 3′ end, and 5 bases were repeatedly generated according to the length of the complementary region between the primer-template and the primer-PCR product (pseudo-word). The final pseudo-words were generated in the order of hairpin, dimer, and template forward strand positions.

Hairpin was searched on each primer. Dimers were searched also on possible combinations of primers included in the primer set. The hydrogen bond between primer and template was sought for by any combination of primer-template, primer-primer and 5′-end and 3′-end of a primer.

In probing assumed primer set, the search was performed for both the primer set, and the double-stranded template (Fig.  2 A). A complementary region with 5 or more bases was assumed to form a hairpin or dimer, and the relevant region is searched. If present, a 3′-end terminal of the partial duplex was searched. Assuming that complementary strands were synthesized from the partial duplex. When the synthesis of DNA from the partial duplex primers, the additional primers were sequentially incorporated into the primer set (Fig.  2 B,C).

As a general rule, the homology between the primer sequence divided into 5 to 22 bases and the template sequence was confirmed, and when the number of bases in Supplement 2 Table 1 was the same (about 80%), a pseudo-code was generated (Fig.  2 D). Regarding the homology, area to be generated as a pseudo-code, the pseudo-code was determined by referring to Table ​ Table3 3 for the entire homology, and all lower-case pseudo-codes were generated (Fig.  2 E).

Many primer set-template combinations have multiple complementary regions that require priming positions to be determined. Since the complementary region for which such a priming position needs to be determined is short enough, the most stable combination of complementary regions is expected to be the priming position. To determine the most stable complementary region, the combination of complementary regions with the minimum Gibbs energy was set as the priming position (Fig.  2 F). The Gibbs energy was calculated according to the formula of DG =𠂝H-TDS by sequentially calculating the entropy and enthalpy of the two bases of the primer and the two bases of the template at the complementary position, assuming an annealing temperature of 56 ଌ. Therefore, after calculating for all combinations of two complementary bases, the total value was minimized, and the complementary positions of forward and reverse, which are separated by 100 bases or more, were set as the priming positions. Using reference numerical values 23 , complementary dimer set calculations for entropy and enthalpy were done where their original and our extrapolated values were used (Supplement 2 Table 4 ). The pseudo-code for the complementary position, which was predicted to be the priming position, was converted to uppercase (Fig.  2 G). Homologous positions of 6 bases or more were searched for hairpins and dimers, and pseudocodes were generated for the corresponding homologous regions (Fig.  2 H). For the pseudo-code sequence generated between the primer and the template, 5 characters were sequentially extracted from the 3𠌮nd of the primer to obtain a pentacode. The pseudo-code was generated by repeating a part of the pentacode according to the length of the homologous region to express the strength of the binding between the primer and the template (Fig.  2 I).

As for the PCR product, the complementary region of the primer is also completely complementary to the primer because the synthesis proceeds using the primer as a template in the extension reaction (Fig.  1 D). For the pseudo-code in this region, a pseudo-code different from the relationship between the template and the primer was set, and a pseudo-code was generated in the same manner as in the complementary region of the primer-template (Fig.  2 J). The pentacodes generated from hairpins, dimers were placed first, followed by the primer-templates, and the pentacodes generated from the primer-PCR products in the order of the forward strands of the template. The pentacode was generated and placed from a set of primers and a template was used as pseudo-sentences of the primer set-template (Fig.  2 K). Pseudo-sentences were generated for all primer and template combinations and used as learning data during machine learning.

### Scripts for pseudo-sentence generator

A Ruby and Python scripts were used to generate pseudo-sentences in the order shown in Fig.  2 (Supplement 3 , List 1𠄹). The Ruby script read the structure of the template base sequence, primer base sequence, and primer set, and generated pseudo-sentences according to the order shown in Fig.  2 . SeqKit (https://bioinf.shenwei.me/seqkit/, v0.14.0) was used to search for homology between the primer and the template. The pseudo-sentences generated for each template-primer set were first categorized by PCR results, and each was categorized into 5 groups. One of the five groups was not used for learning as a group to verify RNN learning but was used to predict the prediction accuracy for each epoch.

We noted that a particular primer set produced many positive PCR results and organized the group to disperse its effects. Five groups were randomly constructed for each PCR positive and negative results after collecting the results for each template. To divide the overall result into 5 groups, the primer-pair template data, which is the unit of data, was combined so that the total number was even for each group. When we equalize the ratio of PCR positives and negatives, the acquired data is adjusted so that the numbers are even at the stage of collecting the results for each template (undersampling).

Axlsx (https://github.com/randym/axlsx, v3.0.0) was used for colorizing spread sheets (Tables ​ (Tables4, 4 , ​ ,7). 7 ). MatPlotLib (https://matplotlib.org/, v3.3.3) was used for creating line-graphs on epochs-accuracy (Fig.  4 ). GnuPlot (http://www.gnuplot.info/, v5.4) was used to create the scatter plot for Gibbs energies (Fig.  5 ).

### Table 4

PCR results with a combination of 72 primer sets and 31 templates.

PCR results are expressed by the following numerical values based on observation on agarose gels. Number 0: No PCR product, 1: PCR product can be confirmed. Results on the primer pairs which have positive results on more than 20 templates are shown with pink background. Similarly, primer pairs which have results with single or no positive on 31 templates are shown with lime or blue background, respectively.

Average prediction accuracy on validation groups in cross-validation. Average of prediction accuracy was calculated on 5 validation groups in cross-validation. (A) Whole sets in 72-primer-31template sets were used for learning or validation. (B) The number of primer pair-template sets in 72-primer-31template was controlled to 1:1 by undersampling. Groups are Orange: PCR positive primer pair-template sets, Green: PCR negative primer pair-template sets, and Blue: all primer pair-template sets. Standard deviation within validation groups was shown as error bars.

### Table 7

Color summarization of PCR results and predictions, (A) predictions from whole-data, (B) predictions from undersampling data.

Color presentations for PCR-result and RNN-prediction. Colors show the following results and predictions red: PCR-positive-prediction-positive, pink: PCR-positive-prediction-negative, blue: PCR-negative-prediction-negative, light blue: PCR-negative-prediction-positive, white: primer pair-template sets excluded from predictions during undersampling.

Scatter plot of PCR-results and predictions. Plot the PCR results and RNN-predictions against the Gibbs energy at the hydrogen bond at the forward (horizontal axis) and reverse (vertical axis) priming positions determined at the time of pseudo-sentence determination (Fig.  2 ). Colors and shape show the following results and predictions red triangle: PCR-positive-prediction-positive, pink triangle: PCR-positive-prediction-negative, blue circle: PCR-negative-prediction-negative, light blue circle: PCR-negative-prediction-positive. Primer pair-template sets excluded from predictions during undersampling were not plotted.

### Learning results

The PCR results performed with the annealing temperatures set at 56 ଌ were set as pseudo-texts generated from each primer-template set and were trained by RNN. For its learning, the pseudo-sentence created for the combination of primer and template was used as input data, and the PCR results were arranged as a teacher. For the RNN, an RNN-Long short-term memory (LSTM) module of PyTorch (https://pytorch.org/, v1.7.1) was used. Python scripts for learning pseudo-sentences and extracting prediction results were written based on the scripts published in a book (Shinqiao Du, "Can be used in the field! Introduction to PyTorch development Creation of deep learning model and implementation in application", Shosuisha 2018/9/18 in Japanese). After reading the pseudo-sentences and PCR results of each primer-pair template, RNN generated a decision algorithm that matched the output results for all input pseudo-sentences (learned algorithm) (Fig.  3 ). As the negative control of sentences, randomly selected nucleotide pentamers were aligned as nonsense pseudo-sentences.

Learning and prediction by RNN. Schematic diagram of how to learn pseudo-sentences by RNN. The upper row shows the processing during learning, and the lower row shows the processing during testing. The learning results are saved in the file specified by PyTorch, read during the test, and used for prediction step.

The prediction accuracy of the generated trained algorithm was confirmed by split verification (cross validation). The primer pair-template sets were divided into five groups, and the RNN was learned using four groups among them and the learning. The remaining one group was not used as learning data but was utilized as verification data. Verification was made during the learning steps.

When evaluating the prediction by RNN, whether the expected PCR band was found on agarose-gel electrophoresis was treated as the true conditions, and the prediction by RNN was treated as the predictive conditions. A true positive, false negative, false positive, true negative, sensitivity, specificity, and accuracy were calculated accordingly. Significant differences in sensitivity, specificity, and accuracy between conditions were made based on Student's and Welch’s t-test 24 .

## Primer Dimer / Hairpin Algorithms - Biology

DNA oligonucleotides are essential components of a high number of technologies in molecular biology. The key event of each oligonucleotide-based assay is the specific binding between oligonucleotides and their target DNA. However, single-stranded DNA molecules also tend to bind to unintended targets or themselves. The probability of such unspecific binding increases with the complexity of an assay. Therefore, accurate data management and design workflows are necessary to optimize the in-silico design of primers and probes. Important considerations concerning computational infrastructure and run time need to be made for both data management and the design process. Data retrieval, data updates, storage, filtering and analysis are the main parts of a sequence data management system. Each part needs to be well-implemented as the resulting sequences form the basis for the oligonucleotide design. Important key features, such as the oligonucleotide length, melting temperature, secondary structures and primer dimer formation, as well as the specificity, should be considered for the in-silico selection of oligonucleotides. The development of an efficient oligonucleotide design workflow demands the right balance between the precision of the applied computer models, the general expenditure of time, and computational workload.

This paper gives an overview of important parameters during the design process, starting from the data retrieval, up to the design parameters for optimized oligonucleotide design.

## How do you detect primer dimer?

Watch out a lot more about it. Besides, what causes primer dimer?

Causes of PCR/Primer Dimers in Sequencing Reactions Contamination of the template, primer stock or other sequencing reagents with primer dimers. Too low an annealing temperature during the PCR. Two primer binding sites present in the template. Direct sequencing of PCR products where there is more than one band.

1. Avoid complementary clamps on the 3' end of your primers, e.g. GC or GCGC, etc.
2. Measure and adjust your primer and template concentrations to recommended values.
3. Use touchdown PCR (temperature gradient) to take guesswork out of annealing temperatures.
4. Use high-fidelity DNA polymerases, e.g. Pfu.

Thereof, how do I get rid of primer dimer?

1. increase the annealing temperature.
2. increase time temperature of template denaturation.
3. decrease primers concentration(10 pmol will be OK)
4. use a PCR enhancer such as DMSO.
5. Check out your template. (
6. use high quality Tag.

Mark K Chee. Martin Methodist College. Hi Deepthi, Hairpins form when your primer is able to form a number of base pairs between two separate regions along its length after it folds back on itself.

## An Alternative Mechanism for Primer Dimer Artifacts

There are some additional observations that provide clues for an alternative mechanism for primer dimerization.

1. Generally, homodimers (i.e., dimers involving the same strand) are rarely observed.
2. Primer dimer artifacts typically occur at a large threshold cycle number (usually > 35 cycles), which is higher than the threshold cycle number for the desired amplicon.
3. Primer dimers increase markedly when heterologous genomic DNA is added.
4. Primer dimers are most often observed when one or both of the primers bind inefficiently to the target DNA (e.g., due to secondary structure of the target or weak thermodynamics).
5. When the primer dimers are sequenced, there are often a few extra nucleotides of mysterious origin in the center of the dimer amplicon.

Observations 1 and 2 suggest that DNA polymerase does not efficiently bind to or extend primer duplexes with complementary 3′-ends. Observation 2 could also be interpreted as meaning that the concentration of the primer duplex is quite low compared with the normal primer-target duplex. In the early stages of PCR, however, observations 3 and 5 suggest that background genomic DNA may play a role in the mechanism of primer dimer formation. Observation 4 suggests that primer dimerization needs to occur in the early rounds of PCR to prevent the desired amplicon from taking over the reactions in the test tube. Figure 9 illustrates a mechanism that involves the genomic DNA in the early cycles of PCR and that provides an explanation for all five observations.

The mechanism presented in Fig. 9 can also be checked for by computer, but searching for such a site in a large genome can be quite computationally demanding. The ThermoBLAST algorithm developed by DNA Software, Inc. can meet this challenge (see myth 5).

## Primer Design Using Software

A number of primer design tools are available that can assist in PCR primer design for new and experienced users alike. These tools may reduce the cost and time involved in experimentation by lowering the chances of failed experimentation.

Primer Premier follows all the guidelines specified for PCR primer design. Primer Premier can be used to design primers for single templates, alignments, degenerate primer design, restriction enzyme analysis. contig analysis and design of sequencing primers.

The guidelines for qPCR primer design vary slightly. Software such as AlleleID and Beacon Designer can design primers and oligonucleotide probes for complex detection assays such as multiplex assays, cross species primer design, species specific primer design and primer design to reduce the cost of experimentation.

PrimerPlex is a software that can design ASPE (Allele specific Primer Extension) primers and capture probes for multiplex SNP genotyping using suspension array systems such as Luminex xMAP® and BioRad Bioplex.

## How to get rid of PCR primer dimer - (Mar/17/2003 )

For a Mg2+ titration, what concentrations are best to pick? I mean, exactly what values should I be trying?

Mg2+ at a final concentration of 1.5, 2.0, 2.5 and 3.0 mM should be tried.

I'm trying to make more efficient an RT-PCR because, albeit i have my desired PCR product, i wish to get a better reaction. I think the problem is that the primers are getting in dimers. I've heard about the use of detergents or DMSO in the reaction mix but i'm not sure about this. Does anyone knows a way to do it without change the Tm?

Dimers tend to form when the template concentration is low. If you can, try titrating in more of the template.

Adding yeast tRNA carrier can reduce the amount of template that sticks to the tube walls, making more of it available for amplification.

When designing your primers, check them for homo-dimer and hetero-dimer formation with the Oligo Analyzer program at the IDT website www.idtdna.com.

dmso can be used between 2-10%, but the higher you go the less active the polymerase becomes so you may no get the same amount of cylces. u can try at 2 and 5% to be safe.

100bp sounds too big for primer dimer - your oligos would need to be >50 bases each to get that - looks like a proper pcr product. MgCl2 titration might help, as well as trying different Tms.

1) Try the DMSO up to 5%. Some polymerases are ok with DMSO and others aren't. You never know until you try.

2) Try a two step PCR. There is a paper in Biotechniques about a two step PCR reaction but I don't have the reference with me since I'm at home and it's in lab. Its worth looking up. Basically you've got template plus forward primer in one tube and template plus reverse primer in another tube and then do between 1-15 rounds of PCR. Then combine the contents of the two tubes and do your normal 25 rounds of PCR. Sometimes this allows the primer to bind to the template effectively and allow you to get some initial transcripts which will then bind to each other when you combine the contents of the two tubes.

3) If you're not using a polymerase for high GC content, then get one. It will save you a lot of hassle. It won't solve your problem but it will help you narrow down things when troubleshooting. KOD XL polymerase (novagen) isn't sensitive to DMSO up to 5% and it helped me get all of my mutants but not without a lot of tries just because the GC content of primer and template were over 60%. Some people like the quik change kit by stratagene but I never got it to work, which is really expensive when its 軸 a kit for 30 rxn or something like that. To each his own.

4) I wouldn't go below 55 deg for an annealing temp. 50 might be fine but below that you're pushing your luck with trying to have a high enough temp to resolve any hairpin structures which are common in high GC rich primers not to mention possibly decreasing the specificity of matching primer and template.

good luck! it takes a lot of troubleshooting and its hard to get consistent results.

It might be as simple as using a Hot-Start polymerase. I think that Vent is for higher fidelity, whereas hot-starts help to remove any impurities or non-specific bindings, dimers, etc. We had dimers in our gels, and switched to a hot-start called RepliTaq Thermal and it did the trick.

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