DNA fragmentation and directed evolution experiments using nucleotide exchange and shearing techniques
DNA fragmentation and directed evolution experiments using nucleotide exchange and shearing techniques
The use of DNA mashups to mimic natural evolutionary processes is a common approach to optimize DNA and protein properties. Here we present a new development in such methods, namely the use of standard polymerase chain reaction (PCR) to amplify gene libraries by mixing dUTP with four other standard dNTPs as an exchange nucleotide for the determination of DNA fragmentation sites. The source of this experiment is the "Laboratory Guide to Modern Protein Engineering" [Germany] K.M. Arndt, K.M. Miller, eds.
Operation method
DNA fragmentation and directed evolution using nucleotide exchange and shearing techniques
Materials and Instruments
T4 DNA Ligase Receptor Cells Move 3.1 Cloning For more product details, please visit Aladdin Scientific website
Taq polymerase PCR buffer Ethidium bromide (EB) solution Ammonium persulfate (APS) aqueous solution
Agarose gel
During the NExT hybridization process, the pairing sites of the hybrid primers containing restriction sites should be set on both sides of the target gene, and the ideal annealing temperature is about 60°C. The annealing temperature is estimated by the 4 plus 2 rule: 4°C for each G and C base and 2°C for each A and T base. Annealing temperatures for primers are estimated by the 4 plus 2 rule: 4°C for each G and C base, and 2°C for A and T bases.
我们在 NEXT 混编过程中使用的基因包括：含 657 个碱基的野生型 CAT 基因 ( CATwt；SwissProt 编号： P00 483；蛋白质数据库（PDB) 编号：1NOC：B)，编码 N 端 10 个残基截短的突变体，C 端 9 个碱基截短和 N 端、C 端双截短 CAT 突变体 ( CAT_ Nd10, CAT_Cd9 and CAT_ Nd10_Cd9) and a C-terminal 26-base truncation mutant (CAT_Cd26). These genes and all of the mashup genes were cloned into the plasmid vector PLiSC-SAFH1 [7], and partial fragments of the original plasmid were replaced using Xba l and Hind III double-enzymatic cleavage sites. Diversity was generated by error-prone PCR and uridylic acid exchange PCR ( see section 10.3.2). Amplification of wild-type and N-terminal truncated genes was performed using a mix of Pr-Nshuffle ( 5'- ATTTCTAGATAACGAGGGCAA-3' ) and Pr-C-shuffle ( 5'- ACTTCA CAGGTCAAGCTTTC-3' ) primers; while for amplification of C-terminal truncated and double truncated mutant genes, Pr- N-shuffle was used. genes, Pr- N-shuffle and Pr-Cdx-shuffle (5'-CTTCACAGGTCAAGCTTATCA-3') primers were used. These plasmids were transformed into E. coli receptor cells by conventional methods [8].
3.2 Uridine exchange PCR
Uridine was chosen as the exchange nucleotide because many types of DNA polymerases can introduce dUTP into the gene sequence [9]. Uridine exchange PCR introduces the exchange nucleotide, uridylic acid, while amplifying the target gene library. The desired DNA breakage can be achieved by varying the dUTP: dTTP ratio. This step can be achieved either by analyzing experiments with different U:T ratios, as described in Section 10.3.4, or by using our program developed for this purpose (see Section 10.3.9). The use of dUTP at ratios up to 50% does not affect the yield of PCR products. It is only when dUTP is used exclusively that the yield of PCR products is approximately 1/4 that of other reactions (Figure 10.1A).
(1) For accurate spiking, the 100 mmol/L nucleotide reservoir was diluted with water to a final concentration of 10 mmol/L for dATP, dGTP, and dCTP, and 1 mmol/L for dUTP and dTTP.
( 2 ) The ureide exchange PCR mix consisted of 50 ng of template (0.017 pmol for plasmid containing 4340 bases), 25 pmol of each primer, 0.4 mmol/L each of dATP, dGTP, and dCTP, 0.4 mmol/L dUTP: dTTP mixture with different ratios, 5 U of Tag DNA polymerase, 5 μl of 10 X PCR buffer, and 1 μl of dUTP and dTTP. PCR buffer. Add to a final volume of 50 μl with water (see Note 1 and Note 2).
( 3 ) The temperature cycling program was 1 min pre-denaturation at 94°C, denaturation at 92°C for 30 s, annealing at 62°C for 20 s, extension at 72°C for 2 min for a total of 25 cycles, and a final extension at 72°C for 4 min, where the extension time was extended to 2 min because it was tested to significantly increase the yield (data omitted). Depending on the yield of the PCR, four or more 50 μl reactions should be done simultaneously to obtain sufficient product (preferably about 7 μg of DNA after gel recovery; see Note 3 ).
( 4 ) The resulting PCR products are combined and purified by 1% agarose gel electrophoresis (see Note 4). If the amount is large enough, a light red band can be seen on the gel in daylight. The bands are cut off and added to the centrifuge column of one or two gel recovery kits and eluted with 50 μl of elution buffer.
( 5 ) Determine the concentration of the PCR recovery product by detecting the baseline calibration absorbance value at 260 nm using a spectrophotometer with a wavelength range of 220~350 nm. We usually measure the concentration in a 140 μl cuvette at a dilution of 1 : 30. The optimal yield of the NExTDNA hybrid product is 7 μg of DNA. lower yields may be possible, but a sufficient amount of DNA is required to ensure that the next step in the recombination process goes smoothly (see 10.3.7 ). All of the desired DNA is used in the next step.
In this study, we have used uridylic acid as the exchange nucleotide, but this technique is equally applicable to the introduction of other analogues. For example, 8- oxoguanine can be removed by the 8-oxoguanine DNA glycosylase FPG (foramidopyrimidine-DNA glycosylate) [10]. This minus group can be used in AT-rich regions, where UDG enzymes frequently cleave DNA, and in GC-rich regions lacking thymine. Thus, the use of multiple exchange nucleotides in combination can produce fragments of the desired size for the next step of reassembly. In addition, the introduction of exchange nucleotides into PCR primers should ensure that these regions of the gene pool are similarly muxed. 
3.3 Enzymatic reactions and chemical cleavage
Uridine exchange PCR purified products are subjected to UDG enzymatic digestion to cleave DNA at the exchange nucleotide site. the enzyme is effective on both double- and single-stranded DNA and initiates hydrolysis by nucleophilic attack on the C1' site of the dideoxyuridine, removing the uracil moiety with a high degree of specificity [12] . Piperidines are used to remove the backbone after uracil cleavage by UDG enzyme [13]. The results of the above cleavage reaction were analyzed by high-resolution urea denaturing polyacrylamide gel electrophoresis, where the ratio of dUTP ranged from 100% to 0% (Fig. 10.1B ), which in turn was quantified by image analysis software (Fig. 10.1C). For very small fragments, better visualization can be achieved by introducing radiolabeling (see Note 2 ).
( 1 ) The UDG enzymatic reaction system consists of 45 μl of PCR purification product (containing approximately 7 μg of DNA, see step 4 in section 10.3.2), 6 μl of 10 X UDG reaction buffer, and 2 U E. coli UDG enzyme. Add water to 60 μl and digest at 37°C for 1 h (see Note 6).
( 2 ) The reaction system for DNA cleavage with piperidine consists of piperidine at a final concentration of 10% (m/V) (6.7 μl of piperidine reservoir in 60 μl of system), and the reaction is carried out in a thermal cycler with a heated lid for 30 min at 90°C (see Note 7).
As an attempt to adopt relatively mild reaction conditions, some other endonucleases were used instead of piperidine to cleave the backbone DNA [11], such as endonuclease IV [14], nucleic acid exonuclease III [15], or T4-endonuclease V [16]. We tested the last one but rejected its use; T4-endonuclease V cleavage of UDG-activated DNA results in incomplete breaks, as shown by the size distribution of the products (Fig. 10.2A ). More problematically, this reaction is bound to give rise to a high error rate. The CAT wild-type gene was cut by UDG and T4 endonuclease V, recovered from the gel, reassembled, and six of the clones, totaling 3930 bp, were sent for sequencing, resulting in a mutation rate of 1.75%. We gave two reasons for this result. First, T4 endonuclease V cleaves the DNA backbone by its cleavage enzyme activity, which catalyzes a β-elimination reaction, leaving an unsaturated aldehyde group (4-hydroxy-2-pentanal) at the 3' end attached to the phosphate group [ 11, 17]. Further chemical reactions to generate the free phosphate group were not completed, and the resulting fragment was not favorable for polymerase initiation. Second, a comparison of the fragments revealed that not all backbones introduced into the uridylic acid site completed cleavage. However, the uracil at these sites was cut, and such base-deficient templates can result in the introduction of erroneous nucleotides.Miyazaki [18] suggested the use of E. coli endonuclease V, but as seen from the data provided, the cutting was even less efficient, and even with an extended cutting time (12 h) and an increased rate of dUTP (75% ) short fragments could not be obtained. Although further experiments could have been designed to address these issues, there was no need to try again as the piperidine cuts were i.e. good and cost-effective.
As a chemical alternative to piperidine, we tested the effect of sodium hydroxide. The piperidine reservoir was replaced with a 0.5 mol/L sodium hydroxide solution spiked to 10% by volume (V/V) of the DNA and reacted at 90°C for 30 min. The same uridylic acid-exchange PCR products were cleaved using piperidine and sodium hydroxide, and the results were compared between the two products by denaturing polyacrylamide gel electrophoresis followed by EB staining. The intensity distributions of the fractured fragments obtained by image analysis software were essentially identical. Similar results were obtained for recombinant loading reactions performed in parallel. These demonstrate that the main reaction initiated by piperidine is the base-catalyzed β-elimination reaction, which removes the two remaining phosphate groups from the sugar base of DNA. Therefore, sodium hydroxide could be used in place of piperidine if safety considerations are important. However, we did not sequentially analyze whether the product of sodium hydroxide cutting the fragment after reassembly produced mutations. In principle, piperidine is more suitable for triggering nucleophilic attack on the sugar moiety and the cleavage is more complete. 
3.4 Urea denaturing polyacrylamide gel electrophoresis
Use urea denaturing polyacrylamide gel electrophoresis to analyze the size distribution of the broken fragments and to purify fragments in specific size ranges (see 10.3.5). This step is optional and recommended only for fracture reactions requiring tight control.
( 1 ) The gel contains 6.7 mol/L urea, 11% to 12% polyacrylamide, and 1 X TBE buffer [8]. The size of the analytical gel is 10 cm X 8 cm X 1 mm and the size of the preparative gel is 10 cm X 8 cm X 2 mm (see 10.3.5.2 ). Since urea degradation can affect electrophoresis, all gels are required to be freshly prepared. We typically use 31.5 g of urea, 29.2 ml of gel reservoir containing 30% polyacrylamide, 0.8% methacrylamide (37.5 : 1 ), 17.1 ml of water, 7.5 ml of 10 X TBE buffer, 500 μl of 10% APS in water, and 50 μl of TEMED; this is enough to prepare 9 analytical gels in a single maker simultaneously (see Note 8 ).
( 2 ) Electrophoresis was performed at 56°C. We use a Hoefer Mighty small basic electrophoresis tank (Amersham) with a temperature-controlled water bath.
( 3 ) The gels were pre-electrophoresed for 10 min in 1 X TBE buffer at 100 V. The gels were pre-electrophoresed for 10 min in 1 X TBE buffer.
( 4 ) Concentrate the fractured DNA to 7 μl, add to the speed-vac vacuum centrifugation volatilizer, add 25 μl of deionized formamide, and heat at 80°C for 3 min in the PCR instrument (see Note 9). Add 3 μl of 60% sucrose solution and 7 μl of water to aid in sampling (see Note 10). The final sample volume is 15-20 μl (about 3 μg of DNA).
( 5 ) The Oligonucleotide Mix and 100 bp DNA Scale can be used as molecular mass standards (see Note 11). For at least one scale, use a sample buffer with dye.
( 6 ) Electrophoresis is performed at 170 V after sampling and ends when the bromophenol blue in the scale is 0.5 cm from the edge (see Note 12).
( 7 ) Stain in 30 ml of 1 μg/ml EB solution (1 : 5000 dilution) for 5 min and observe under UV light (see Note 13).
Analytical gel electrophoresis showed that the size distribution of fragments produced by breakage had a fixed peak, determined by the ratio of dUTP. As shown in Fig. 10.1B, multiple length-distribution bands are readily available, including very small and large fragments for short genes and long gene clusters of mixes, respectively. Such a test is only used to initially determine the appropriate dUTP ratio to obtain the target fragment size distribution. The optimal ratio for dUTP use in the test library was finally determined to be 33.3% and the results were reproducible. Therefore, this step of analyzing electrophoresis can be omitted in the following directed evolution experiments.
3.5 Fragment purification
Gene fragments obtained by enzymatic and chemical cleavage (see 10.3.3 ) can be purified either directly from the cutting reaction solution by silica gel resin (see 10.3. 5.1) or by preparative urea denaturing polyacrylamide gel electrophoresis (see 10.3.5.2).
Initially, it was thought that purification by gel electrophoresis was necessary to obtain fragments of a specific size to ensure that no longer fragments, or even full-length fragments, were present in the reassembly reaction, so as not to affect the probability of collision. In practice, it is not possible to amplify full-length products directly from purified fragments without multiple rounds of recombinant loading, which suggests that the cutting reaction was performed thoroughly (see 10.3.7). Therefore, purification by gel electrophoresis is only necessary if there are very stringent requirements for the size range of the fragments.
3.5.1 Purification directly after piperidine excision
( 1 ) The easiest way to purify the fragments is to use the Qiaex II kit (Qiagen) for direct purification from the piperidine excision reaction solution (see 10.3.3). Follow the kit instructions (see Note 14) and neutralize with binding buffer (approx. 20 μl of 3 mol/L acetate buffer).
( 2 ) After two washes, elute in two steps by adding 25 μl of Elution Buffer. Mix the two eluents.
( 3 ) Centrifuge twice, each time in a clean centrifuge tube (see Note 15).
3.5.2 Purification by urea denaturing polyacrylamide coagulation electrophoresis
Note that this step is optional. Two methods were tried to recover the fragments from the gel. One was the classic water extraction followed by acetic acid/magnesium ion precipitation, and the other was using Qiagen's Qiaex II kit. However, both were found to suffer from incomplete extraction by staining the gel after gene extraction.
( 1 ) After electrophoresis on a preparative urea denaturing polyacrylamide gel (see 10.3.4, step 1), the target-sized bands were cut off under low-intensity UV light (Fig. 10.2B). After thorough mashing in a centrifuge tube and addition of extraction buffer (QiaexII Extraction, step 2 ) or 1 ml of water (Water Extraction, step 3 ), the sample was incubated in a hot mixer (Eppendorf ) at 37°C, 1000 r/min overnight.
( 2 ) If extracting with QiaexII extraction buffer, see section 10.3.5.1.
( 3 ) If water extraction is used, precipitate DNA with 1/10 by volume of acetate buffer, 1/100 by volume of MgCl2, and 1 volume of isopropanol; react at -20°C for 1 h; centrifuge at 4°C for 15 min at 20,000 g; resuspend precipitate in 50 μl of 90% ethanol in a thermal mixer at 37°C for 1 h at 1,000 r/min; let stand at -20°C for 1 h; centrifuge at 4°C for 15 min at 20,000 g; and incubate overnight at 37°C for 1,000 r/min in a thermal mixer. After drying the precipitate in air, add 30 μl of elution buffer and incubate for 1 h at 37°C, 1000 r/min.
In order to obtain the crossover rate of the gel extraction step, we designed a mix-and-match assay of three maternal clones (CAT_Nd10 mutant). Two of the clones contained 1 specific mutation within 100 bp and the other contained 2 specific mutations within 100 bp. Eight clones were selected for sequencing after mixing and amplification by Tagase, and the results showed that six of the clones had a crossover in the 100 bp range. This is comparable to the crossover rate obtained by direct rapid purification (see 10.3.5.1 and 10.3.8). A total of 3851 bases were sequenced and 12 errors were found, giving a mutation rate of 0.31%. Such an error rate is much higher than that of the rapid purification and could be due to UV irradiation (even with a weak 366 nm light source) or chemical modifications in the gel. We therefore removed the gel purification step from our final NExT DNA hybridization method because the extra work did not provide benefit, but rather a loss of yield and an increased error rate.
3.6 Quantification of purified fragments
In order to analyze and compare the yields of purified DNA, we first used SYBR Greenn reagent for quantification. Because of the high reproducibility of the NExT DNA mixing method, it is sufficient to quantify only once (see Note 16). Usually, we can obtain DNA fragments with a concentration of 40-60 ng/μl.
( 1 ) Take 2 μl of purified DNA fragments (see 10.3.4) and add 50 μl of 1 : 5000 diluted SYBR GreenII solution, which is very sensitive to single-stranded DNA (see Note 17).
( 2 ) Detect the fluorescence signal after 5 min of reaction in a dark box (we use a 96-well Perkin Elmer LS 50B phosphor photometer; see Note 18). The excitation wavelength of the dye is 480 nm, and emission values can be detected at 515 nm.
( 3 ) Calibrate the concentration of DNA contained in the fragments by plotting a concentration standard curve using standard oligonucleotides in the fragment size range, diluted at different multiplicities.
3.7 Recombinant assembly and amplification
Full-length genes are recombined from purified gene fragments by internal primer extension reactions (see 10.3.5), with increasing annealing temperatures and preferably using a DNA polymerase with a calibrating function, such as Vent (Fig. 10.3). During internal primer extension PCR, fragments can be used as primers for each other, and are therefore lengthened after each cycle of the reaction until the full-length gene is finally obtained. Finally, the product of the assembly reaction is amplified by a conventional PCR reaction with the addition of two terminal primers, and clones are constructed and sent for sequencing. The results of the recombinant loading reaction were continuously detected by agarose gel electrophoresis during the method building process (Fig. 10.3 ). The recombinant loading reaction is stopped after a number of rounds, and the resulting product is amplified by PCR on this basis. The basic principle of the last step of the reaction is the same as the rest of the gene assembly process, but with very important changes. The assembly reaction using high-fidelity DNA polymerase is efficient despite the drastic chemical cleavage conditions experienced.
( 1 ) Remove about 2 μg of purified DNA fragments (see 10.3.5) for reassembly. In fact, less than 1 μg of DNA fragments is sufficient if Vent polymerase is used. Usually we use 20-25 μl of fragment solution without checking the concentration.
( 2 ) Add 4 μl (see Note 19) of a 10 mmol/L mixture of dATP, dTTP, d CTP, and dGTP (final concentration 800 μmol/L) to the DNA fragments, as well as 4 U of Vent DNA Polymerase (NEB), 1 to 4 μl of 25 mmol/L magnesium sulfate, 5 μl of 10X Reaction Buffer, and dissolve to 50 μl with water.
( 3 ) Cycling reaction was 94°C for 3 min; denaturation at 92°C for 30 s, annealing at 30°C for 60 s, increasing 1°C (cooling rate 1°C/s) in each round, extension at 72°C for 1 min, adding 4 s more in each round, totaling 36 cycles; and finally extension at 72°C for another 3 min. 
( 4 ) Take 10 μl of the recombinant loading product ( see Note 20 ) and use the appropriate primer for the gene (25 pmol primer, 0.2 mmo/L dNTP, 25 cycles, 40s extension time) to perform the conventional PCR reaction.
( 5 ) Clone the amplified gene into the vector using appropriate restriction sites.
To the best of our knowledge, most of the published fragment reassembly procedures use Taq enzyme.The 3'→5' proofreading nuclease activity of Vent DNA polymerase is based on its ability to remove mismatched nucleotides on the synthesized strand at the 3' end only until the polymerization reaction can be initiated from the annealed end. This means that point mutations on the nucleotide chain, even immediately adjacent to the 3' end, are not a problem [19] . To compare the action of the two polymerases, two sets of recombinant loading experiments were performed in parallel using Tag and Vent enzymes, respectively, both using the same library of fragments as a starting point. An appropriate amount of the reassembled product was used as a template for PCR amplification, and when Taq enzyme was used, the product was subjected to agarose gel electrophoresis with only one band, which was then quantified by image analysis. As a result, the DNA yield obtained with Vent enzyme was 35 times that of Taq enzyme. Interestingly, sequencing of the 6988 bases obtained with Tag enzyme revealed only 5 additional mutations (0.075%). Thus, within the statistical errors of the available sequences, NExT DNA mixing with Tag and Vent enzymes produces essentially the same error rate (see 10.3.8 ). The significant difference in yield can be explained by the nature of the calibrated enzymes. Vent enzyme, for example, has strand displacement activity [ 20 ], which may aid in many hybridization reactions, and Vent enzyme has a half-life of about 8 h at 95°C, which is better suited for prolonged reassembly reactions than Tag enzyme, which has a half-life of 1.6 h [ 20 ]. In addition, Taq enzyme has the habit of adding extra dATP at the 3' end [21], which is also a possible reason for hindering the reassembly reaction. In addition to the above factors, it was found that although Tag enzyme is suitable for fragment reassembly, its reassembled product serves as a template for the next amplification reaction, and it is difficult to be amplified by DNA polymerase with a correction function.
3.8 Analysis of crossover rate, average length of fragments and mutation rate
The NExT DNA hybridization technique described above was applied to the study of directed evolution of the 600 bp long CAT gene, in which the N-terminal and C-terminal were truncated by 10 and 9 amino acid residues, respectively (CAT_Nd10_Cd 9 ). In the experiment, five clones with different mutation patterns between 12 and 383 bases were selected and mixed with a truncated wild-type clone for backcrossing as a stationary library, and mixed by 33.3% uridylic acid exchange PCR. The fragments are purified directly from solution (see 10. 3.5.1 ) and then subjected to a recombinant loading reaction by Vent polymerase (see Section 10.3.7). Eight hybrid clones were selected for sequencing in control plates without resistance selection pressure (Fig. 10.4A ). The unique mutation patterns of these clones showed that all clones tested evolved from 2 ( e.g., clone 1 ) ~4 (e.g., clone 4 ) parent clones. Of the 372 bp fragments involved, there was a crossover every 93 to 186 bp, with an average fragment length of 114 bp.
The mutation rate was calculated from the sequencing results. Of the 4425 bases sequenced, four mutations (an A to G, a T to C, a 1 bp insertion and a 1 bp deletion) were found, and the mutation rate was calculated to be 0.09%. This is much lower than the 0.7% error rate previously reported for DNAzyme mix-ups. As discussed in Section 10.3.7, Vent polymerase is not the only enzyme that can achieve such a low mutation rate. Since we obtained fragment size distributions and crossover rates comparable to those obtained in the DNA enzyme mixing experiments, we analyzed the possibility that the high error rate reported earlier was caused by UV damage during DNA digestion and gel observation, rather than fragment size and polymerase type. The low mutation rate is particularly important for the mixing of long fragments of DNA, because we want to avoid as much as possible the introduction of dysfunctional or unwanted molecules into the gene pool.
In further experiments, four truncated CAT gene (CAT_ Cd26 ) parents were selected for the same mixing experiments described above, all of which contained a single mutation distributed from 9 to 575 bases, and five clones were finally selected for sequencing (Fig. 10. 4B). The average length of detectable fragments was 86 bp, including many short fragments. In the "Control 5" clone, mutants were separated by only 6 bases (positions 324 and 330), 12 bases (positions 364 and 376) and 11 bases (positions 404 and 415), respectively. The average length of fragments obtained in this experiment was smaller than in the previous experiments because more mutations facilitated the detection of fragment length. There are two possible reasons for the large number of fragments obtained: the QiaexII kit used allows for efficient recovery of short fragments of DNA, or crossover during gene amplification is a complex process that involves strand swapping as in the case of the PCR base.
3.9 NEXT Fragment Breakage-Prediction Procedure
Since the incorporation of dUTP and the resulting fragment breaks are based on deducible principles, we have developed a computational program called NExTProg. This program predicts the NExT breakage pattern of double-stranded DNA, allowing researchers to design appropriate dUTP: dTTP ratios without the need for experimentation. By reading in a DNA sequence file and the dUTP: dTTP ratio, the program calculates all possible fragments, their probability of occurrence, and their relative distribution. The complementary strand of a given DNA is automatically generated by the program and added to the calculation. The results of the calculations are displayed in the form of a bar chart, and all data can be output in tabular form for use (Fig. 10.5A). When it is necessary to set upper and lower limits for fragment size (e.g., for gel purification), the program calculates the probability of material loss and adjusts the relative distribution of each fragment. 
3.9.1 Mathematical Principles
( 1 ) Set the probability that a thymine is replaced by a uracil in a given DNA sequence to p. The probability of a thymine being replaced by a uracil in a given DNA sequence is set at p.
( 2 ) When both thymine are replaced by uracil, a fragment between the two is created with probability p X p.
( 3 ) The fragment can exist only if none of the n thymine between the two thymine mentioned above is substituted, obtained with probability p X p X ( 1-p) n.
( 4 ) For fragments containing 1 or 2 DNA ends, 1 or 2 p in the p X p probability is set to 1 ( see Note 21 ).
( 5 ) For the purpose of comparing breakage results, we define the fragment probability as the sum of all the values divided.
Our calculations differ from all previous calculations [23] in that we take into account that both ends of the fragment need to be produced, but do not consider issues such as sequence bias and uncertain enzymatic conditions, which can severely hamper calculations for DNAzyme digestion.
For a gene containing x uridylic acids, the maximum number of possible fragments can be produced [ which, according to Gauss's theorem, is equal to (x + 1 ) X (x + 2 ) / 2 when x is odd; see Note 22]. Thus, for a typical gene 1000 bp long containing 250 thymine and 240 adenine (also counted as thymine in the complementary strand), the program soon calculates to produce 31626 + 29161 = 60787 fragments, including their probabilities and sequences.
Because most users are likely to be interested in the generalization of the results, the program pools all fragments with the same size, sums their probabilities, and gives the distribution of the percentage of the sum of all probabilities against the length, which is denoted in the program as "%mol". To visualize the electrophoretic bands, a "mass" distribution is calculated by multiplying the probability of a segment by its length. These values are homogenized to represent base ratios, defined as "mass", and are displayed in the program as "%mass" if the length is fixed in the base pair. The output file of fragment sequences lists all fragments in descending order of probability of occurrence. The same sequences are listed only once, and the probability is their sum.
3.9.2 Calibration of the program and comparison with experimental results
Before comparing the results of measurements and calculations, there is one very important value to consider: it is the ratio of uridylic acid to thymidylate doped by the polymerase during exchange PCR. This value may depend not only on the dUTP : dTTP value, but also on the type of polymerase used, the absolute concentration of nucleotides and the buffer used. It is therefore necessary to set this value when using the program. Uridine incorporation can be measured either directly by calculating the radioactivity of the PCR product from radiolabeled dUTP or indirectly by quantitatively analyzing the fracture profile. We chose the latter method because it also provides basic principles similar to those of our software. However, it is important to note that this dual utilization of information is only valid if the fracture is complete.
To quantitatively analyze the cleavage experiments, we used commonly used conditions (standard Tag polymerase [ 24 ], 200 μmol/L dNTPs).
( 1 ) In the uridylic acid exchange PCR reaction (see 10.3.2, see Note 2), 32P-dCTP-labeled DNA was used.
( 2 ) Perform denaturing polyacrylamide gel electrophoresis (see 10.3.4 ).
( 3 ) Radiographic energy imaging of the gel is performed by an imager (see Note 23). This avoids signal distortion caused by inefficient staining of small fragments.
( 4 ) Each band is passed through image analysis software such as QuantityOne ( BioRad ) or NIH Image/Scion Image/imagej ) to generate a line density profile.
( 5 ) The relative migration values of the fragments and radiolabeled molecular quality standards were calculated from the line density curves.
( 6 ) Substitute the variable parameters a and b, representing the relative distance and length of the marker, into the equation: relative distance = a X In (base pair length) + b .
( 7 ) Convert the relative distance values of the fragments to nucleotide lengths using the above equation.
( 8 ) Convert the intensity signal/continuous length distribution to intensity signal/integer by combining th