# Problem on Probabilty of a restriction enzyme cutting a random DNA sequence

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I think its a silly question to ask here. When I came to this site all I could see were the questions which asked detailed explanation behind a phenomenon and reasoning was there at first place. I am bringing quite math here!!!

First, I am a beginner.

Second, I would like to mention some problems…

1. Genomic DNA is digested with AIU I, a resrtiction enzyme which is a four base pair cutter. What is the frequency with which it will cut a DNA assuming a random distribution of bases in genome?

2. Eco RI and Rsa I restriction endonucleases require 6 bp and 4 bp sequences respectively for cleavage. In a 10 kb DNA fragment how many probable cleavage sites are present for these enzymes?

These questions were solved by my teacher using some probability results or rules. I would like to mention it here… [you know already… !!! ;-)]

(1/4)^n *10,000 or simply (1/4)^n. By putting n = number of base pair cut by enzyme.

I get the frequency with which enzyme will cut a DNA assuming a random distribution of bases in genome by using (1/4)^n and I get probable cleavage sites are present for Eco RI and Rsa I in 10 kb DNA fragment.

But why do I do that? I mean why that formula? How to understand how it was derived? Can you explain me that?

Please suggest some good books containing concepts and numerical problems like these so that I can work on it… [Please let me know your source]. Thank you.

EcoRI recognizes, binds to, and cleaves the hexamer 5'-GAATTC-3'. In a completely randomized DNA sequence, with 25 % A's, 25 % C's, 25 % G's, and 25 % T's we would expect to randomly discover the sequence GAATTC, once every 4,096 base pairs, on average. The actual distribution of EcoRI fragments (a fragment where each end contains a cleaved EcoRI site) in our random genome will vary and yield a normal distribution, or curve, with some fragments longer and some shorter. The mean value should be 4,096.

The expectation of 1 site per 4,096 bp is indeed (1/4)^6.

1/4 = 25 %

6 = the number of contiguous base pairs in the recognition site.

In a model like this it is important to keep in mind that the probability of one base occurring in the sequence is completely independent of the sequences before that base, and the sequences after that base. In other words, for each and every position the probability of getting a base that will contribute to an EcoRI site is 25 %, or 1 out of 4 = 1/4.

75% of the time, the next base will not contribute to an EcoRI site (and a quarter of the time it will).

Let's start with your 10 kb fragment, and go through from one end to the other, and mark every time a 'G' occurs. Theoretically those could all be the beginning of EcoRI sites, right? There will be approximately 2500 such 'G's. Now to match our pattern, we need an 'A' in the second position, so let's mark all those sites that contain the dinucleotide 'GA', there will be about 2500 x 0.25 = 625 of them. The next match we need is position 3, another 'A', so in a similar fashion, let's go through the positions of all those GA dinucleotides, and just mark the ones that have an 'A' at the next position. So that will be about 625 x 0.25, or approximately 156 'GAA's distrubuted randomly along the 10 kb fragment.

If we continue, essentially filtering out more and more of those 'G' sites in our initial list then we will find, on average, that there are

39 sites with GAAT

10 sites with GAATT

2 sites with GAATTC

If you don't believe me just pick a sequence and try it yourself.

10,000/4,096 ~ 2.5

## Question: 1.What Is The Probability That Any Base In A Sequence Is An Cytosine, C? __________________ How Many Times Do You Expect To Find Adenine In The Human Genome? ___________________ 2. What Is The Probability Of Finding A Particular Two-base Sequence? ____________________ How Many Times Do You Expect To Find That Sequence In The Human Genome? ______________ .

4. How many times would you expect to find a specific 20 base pair sequence in the human genome?

5.Write out a complete equation to calculate the predicted occurrence of a sequence of n length within a DNA fragment of X length.

6.Using mathematical evidence, explain why CRISPR-Cas9 gene-cutting technology, which uses a target sequence of 20 base pairs, is more specific than classic restriction enzymes.

7.Write three different ideas you have about why CRISPR-Cas9 technology could be more useful for gene therapy and/or research than other gene-cutting tools.

8. In actuality, the DNA sequence of the human genome is NOT random. Some sequences, including some very large sequences, are repeated many times throughout the human genome. Write two ideas you have for how this fact complicates the use of CRISPR gene-editing technology in humans.

## Stanley N. Cohen: Transforming Molecular Biology

“Grow faster, you little bugs,” Stanley Cohen recalls begging his bacteria, in jest, because he was so eager to see the results of his experiments. It was a heady time in early 1973, as scientists shuttled DNA back and forth between Cohen’s laboratory at Stanford School of Medicine and Herbert Boyer’s group at the University of California, San Francisco.

Cohen in the lab
[Courtesy of Jose Mercado, Stanford News Service]

Cohen, who trained as a physician, started his research with an interest in infections. The discovery of penicillin in 1928, and other antibiotics subsequently, seemed to herald the end of infectious diseases. “That turned out not to be the case,” says Cohen. “The reason is that bacteria developed resistance to the antibiotics.” Furthermore, bacteria could swap that resistance amongst themselves, sometimes sharing resistance to multiple drugs at the same time.

This resistance was carried on something scientists called the ‘R-factor’, a piece of DNA bacteria could transfer between themselves. Bacteria have one large chromosome, containing most of their genes. But they can also store genes on smaller, circular pieces of DNA called plasmids. R-factors rode on these plasmids. Only a handful of labs were working on plasmids at the time, and in 1968, Cohen set out to understand how R-factor resistance genes were arranged, controlled, and acquired.

First, researchers in his lab tried to move the R-factor plasmids around themselves. Cohen and technician Christine Miller started by purifying the R-factor plasmids. Then, research technician Annie Chang and Leslie Hsu, a medical student working in the lab, succeeded in putting the purified plasmids into new bacteria in 1971.

Cohen with research associate Annie Chang
[Courtesy of Chuck Painter, Stanford News Service]

Chang and Cohen also figured out how to chop up the plasmids, hoping to separate the genes therein, but the process was random and haphazard. Sometimes the fragments would stick back together into a new circular plasmid, but the researchers could not consistently replicate their results. It was like stirring a big pot of broken spaghetti, hoping some strands would stick together in desired combinations. They needed a method to control the subtraction and addition of genes in plasmids.

A cartoon depicts the famous Honolulu deli meeting. Stanley Falkow (thinking ”D”), Herbert Boyer (“N”), Stanley Cohen (“A”), with Charles Brinton (lower left) and Ginger Brinton (bottom)

Boyer was working on restriction enzymes, protein-based machines that cleave DNA at specific sequences. For example, the enzyme EcoRI cuts only the sequence GAATTC. Those cuts create ‘sticky ends’, so scientists can then glue two EcoRI-cut sequences together in new combinations. Boyer’s group had identified the enzyme in 1968 after isolating it from E. coli cultured from a patient with a drug-resistant urinary tract infection. In Honolulu, Boyer and Cohen plotted their experiments on a napkin.

Back in California, Cohen’s group purified the plasmids from E. coli. Then Chang, who lived in San Francisco, delivered them to Boyer’s lab, where researchers cut the plasmids with restriction enzymes and then glued the pieces together in a different arrangement. They sent the DNA back to Stanford with Chang, where Cohen’s group inserted it into bacteria. Then the scientists isolated the plasmids from those bacteria and sent them back to Boyer for analysis.

Boyer recalled the moment he saw the evidence of rearranged plasmids in a 2009 interview with PLoS Genetics:

“It actually brought tears to my eyes…I knew we’d be able to isolate any piece of DNA that was cut with EcoRI, regardless of where it came from.”

But could they transfer DNA from a different organism into the plasmids carried by E. coli? Many scientists doubted it, assuming that the DNA would be incompatible.

Cutting Cohen’s plasmid, pSC101, with the restriction enzyme EcoRI leaves ”sticky ends.” Other pieces of DNA, cut with the same enzyme, can fit into the sticky ends to create a new plasmid, pSC105.

Nonetheless, Cohen and Chang managed to insert a piece of DNA from the plasmid of another bacterium, Staphylococcus aureus, into E. coli via a plasmid. Then they rejoined forces with Boyer, and in 1973 the collaborators took a piece of DNA from the African clawed frog, a common lab animal, and put that into E. coli with a plasmid too. This linking of disparate DNA sequences would quickly come to be called ‘recombinant DNA technology.’

The Rise of Recombinant DNA Technology

These studies showed that scientists could use plasmids and restriction enzymes to ‘clone’ DNA sequences from any creature. They could make large amounts of the plasmid for further study. Other scientists were excited and requested that Cohen send them his plasmid for their own experiments.

But researchers were worried, too. This new approach also meant that scientists could conceivably create potentially hazardous ‘Frankenorganisms’ expressing unnatural and potentially hazardous genes. What if they transferred antibiotic resistance into bacteria that didn’t already have it, creating new superbugs? Or what if they put cancer-causing viral genes into bacteria and created novel cancer agents?

A committee that included Cohen and Boyer, as well as Paul Berg, evaluated the possible dangers of mixed-DNA organisms. In a 1974 article, the group proposed that scientists should not insert antibiotic resistance genes into species of bacteria that weren’t already known to harbor such resistance, nor should they transfer animal viral genes into plasmids. The National Institutes of Health also issued guidelines, requiring that the riskiest experiments be conducted in airlock-secured facilities, the same kind used to study the Ebola virus and other very-high-risk pathogens.

In a 1977 article in the journal Science, Cohen argued that the risks of genetic engineering were mostly speculative, whereas the benefits were much more likely.

“It really was an experience in trying to educate the political community scientifically,” he recalls. “I did spend a lot of time working with congressmen and senators and their staffs.”

Scientists followed the guidelines, and with time it became clear that Cohen was right about the positive potential of DNA recombination.

Electron micrograph of plasmid DNA

In 1976, Boyer made an initial investment of \$500 to co-found Genentech, a pharmaceutical company in Oceanside, California. Genentech scientists copied the human insulin gene into a plasmid and put that into bacteria. The bacteria then used that gene to pump out insulin for people with diabetes. Next, Genentech made human growth hormone, which is used to treat short stature and other related conditions in the same way.

The recombinant DNA revolution had begun. Today, hundreds of biotechnology companies use recombinant DNA technology to make medications for conditions ranging from cancer to hemophilia. In the lab, restriction enzymes and plasmids have become standard tools, enabling scientists to study genes in detail. Scientists transfer new genes into crop plants to make foods more appealing or nutritious. The list goes on.

“You couldn’t do any of the things that people are doing now if you didn’t have the cloning technology and the plasmids,” says Miller, who was a research associate in Cohen’s lab until her retirement in 2011.

Meanwhile, Cohen is still working on the problem of antibiotic resistance, studying how bacteria adapt to stressful conditions. He’s also investigating how repetitive DNA sequences contribute to diseases such as Huntington’s disease and muscular dystrophy.

“He’s just motivated to learn things, to find things out,” says Miller. “He’s still working as hard as ever.”

## Problem on Probabilty of a restriction enzyme cutting a random DNA sequence - Biology

1) Bacterial plasmids range in size from 1,000 to 200,000 bp, and are used extensively for cloning purposes. The plasmid drawn below has cutting sites for the following restriction enzymes: EcoR1, Sal1, and BamH1. The distance in base pairs (bp) between cutting sites is listed between the sites. Answer the following questions based on your knowledge of biology and the diagrams labeled (a) through (e).

a) Which of the gel electrophoresis results would you expect after cutting the cloning plasmid with the restriction enzyme EcoR1? Why?

Introducing restriction enzymes EcoR1 to the proposed plasmids would result in separations at each restriction site. This would separate the plasmid into 3 different parts. The lengths of these fragments would be 500bp, 800bp, and 1000bp. Lines at around 500, 900, and 1000bp will be shown in a gel electrophoresis block next to the known DNA marker strand. The only gel block selection that has exactly 3 separate lines on it that correspond with the lengths predicted is block B.

b) Which of the gel electrophoresis results pictured above would you expect after cutting the cloning plasmid with the restriction enzyme Sal1? Why?

Using the same procedure as above but now with the restriction enzyme Sal1, two fragments of length 800bp and 1600bp are created. The gel block that displays this relationship in comparison to the known DNA marker is block C. It has exactly 2 lines and the first line seems to be, on the block, slightly greater than the 500bp mark while the second line is a bit less than the 2000bp mark. This fits with the calculated fragment lengths.

c) Which of the gel electrophoresis results pictured above would you expect after cutting the cloning plasmid with all three restriction enzymes-EcoR1, Sal1, and Bam1-all at the same time? Why?

If I was to “cut” the plasmid using restriction enzymes EcoR1, Sal1, and Bam1, I would create six fragments. There would be two of length 300bp, two of length 500bp, one of length 200bp, and one of length 600bp. The gel block that has four different lines in the test lane that most closely correspond in base pair length at the given lengths with the DNA marker is block D. The only other block with four lines is block E which has its longest fragment at 10,000bp, more than four times longer than the plasmid itself.

2) A linear piece of DNA is cleaved with the individual restriction enzymes HindIII and SmaI and then with a combination of the two enzymes. The fragments obtained are:

HindIII and SmaI 2.5 kb, 3.0 kb, 2.0 kb

b) The mixture of fragments produced by the combined enzymes is cleaved with the enzyme EcoRI, resulting in the loss of the 3-kb stained band (on an electrophoresis gel) and the appearance of a 1.5-kb stained band. Mark the EcoRI site cleavage site on the restriction map.

3) *NEW VERSION* Explain Sopie's hair.

3) Duchenne muscular dystrophy is an X-linked recessive disease. Victims of the disease become progressively weaker, starting early in life.

a) What is the probability that a woman whose brother has the disease will have an affected child?

I am going to assume that the mother does not have the disease. There exists another variable which is whether or not her parents were also affected. If a woman’s brother has the disease then the woman's mother must be at least a carrier if not have it herself. Therefore there actually lie two different situations within the question. If the woman’s mother has the disease then the woman is certainly a carrier and the probability of having an affected child would be 1/4. If the woman’s mother was just a carrier but did not express the disease then the woman has a ½ chance of being a carrier (because 1 in 2 female offspring are probable carriers) and a ¼ chance of her child being affected, making the total probability of the event 1/8.

4) The accompanying pedigree concerns a certain rare disease that is incapacitating but not fatal.

## The restriction mapping problem revisited

In computational molecular biology, the aim of restriction mapping is to locate the restriction sites of a given enzyme on a DNA molecule. Double digest and partial digest are two well-studied techniques for restriction mapping. While double digest is NP-complete, there is no known polynomial-time algorithm for partial digest. Another disadvantage of the above techniques is that there can be multiple solutions for reconstruction.

In this paper, we study a simple technique called labeled partial digest for restriction mapping. We give a fast polynomial time ( O(n 2 log n) worst-case) algorithm for finding all the n sites of a DNA molecule using this technique. An important advantage of the algorithm is the unique reconstruction of the DNA molecule from the digest. The technique is also robust in handling errors in fragment lengths which arises in the laboratory. We give a robust O(n 4 ) worst-case algorithm that can provably tolerate an absolute error of O( Δ n ) (where Δ is the minimum inter-site distance), while giving a unique reconstruction. We test our theoretical results by simulating the performance of the algorithm on a real DNA molecule.

Motivated by the similarity to the labeled partial digest problem, we address a related problem of interest—the de novo peptide sequencing problem (ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000, pp. 389–398), which arises in the reconstruction of the peptide sequence of a protein molecule. We give a simple and efficient algorithm for the problem without using dynamic programming. The algorithm runs in time O(k log k) , where k is the number of ions and is an improvement over the algorithm in Chen et al.

In the end, we all want to do the best science we can, on the budget we have.

(A) Figure 3 of Lowry et al. (2016) and (B) an extension of that figure by McKinney et al. (2017). Edited to add:Each panel plots the proportion of a simulated genome “covered” by a given number of randomly distributed RAD loci, given different average linkage distances. Different line styles indicate different sizes of simulated genomes.

Of course, it is unrealistic to expect that the 30 species in this table broadly represent all species and all populations of interest for scientific study, and Lowry et al. (2016) fail to point out that six of the species in their Table 1 (20%) have LD estimates either equal or much greater than 100 Kb, three of which even had LD estimates of 1 Mb or greater …

Using code from the Supporting Information of Lowry et al., McKinney et al. extend a key figure from the Breaking RAD paper to show that, if linkage really does extend farther than Lowry et al. assume, a typical RADseq protocol can account for 100% of multi-gigabase genomes. I’d characterize the thrust of their argument as, why assume the worst? And, when candidates from a RADseq-based genome scan show evidence of functional roles or a history of selection based on independent data, I’d say they’ve got a point. Even if RADseq can’t find every part of the genome driving adaptation, finding some parts is a good start, and can be a major breakthrough. Still, if we want to understand how adaptation works in general, we ultimately want to build up a comprehensive picture of even individual cases.
Are the alternatives any better?
The second response paper is by several of the original RADseq authors, let by Julian Catchen, and they argue that even if RADseq has its limitations, the alternatives are not necessarily better. Lowry et al. suggest, rather than the random genome reduction of RADseq, taking a targeted approach to reduce sequencing costs — either using RNAseq to sequence only expressed genes, or exome capture to sequence protein-coding genes identified from RNAseq or from the annotation of a reference genome. The logic here is that, if you can’t afford to sequence the whole genome, you might as well know what you’re missing. (In this case, targeting protein-coding regions with the understanding that non-coding regions, including potentially important regulatory elements, will be missed.) It’s also possible to estimate population allele frequencies with whole-genome coverage using pooled sequencing, in which individual genomic samples are mixed in equal proportions to produce a “pool” that is then sequenced — as long as enough samples are pooled and the pooling process is precise, this can give good estimates of allele frequencies with a lot less sequencing than would be needed to sequence every sample individually.
Catchen et al. argue that the limitations of RNAseq, exome capture, and pooled sequencing put them out of reach in many cases where RADseq can still work. RNA sequencing is potentially biased by variable gene expression, while exome capture and pooled sequencing are more reliant on a good reference genome, or at least a transcriptome, as a starting point for capture array design or to align pooled sequences for genotyping. They also point out that it’s perfectly possible to assess the extent of linkage using RADseq data — so RADseq users can evaluate the suitability of their data before running a genome scan. This isn’t possible with pooled sequencing, because the protocol elides individual genotypes.
It takes a village (of genomic resources)
In their response to these responses, Lowry et al. emphasize that their argument is not against RADseq as a method, but against its use without proper understanding of the biology and genome structure of the species to be studied. While it is clear that many individual studies using RADseq take this precaution, others have not. They recommend that molecular ecology studies of previously un-sequenced species — based on RADseq or otherwise — start by building the infrastructure of an annotated reference genome or a linkage map, or both that study designs be informed by model-based power analysis and that candidate loci found in genome-scan analyses be validated by data beyond population genomics. As they conclude

We did not and do not advocate for any ascertainment method across all scenarios, only that investigators responsibly assess different ascertainment designs including RADseq, whole-genome pooled sequencing, RNA-seq, and sequence capture in the context of a study question, genome size, and expected patterns of LD. We do advocate for careful consideration of experimental designs and acknowledgement of errors when they occur.

## User input to check a DNA sequence for restriction sites with BioPython

I wish to write a script that accepts a user inputted restriction enzyme name (therefore a string) and parses a given DNA sequence (also a string) for instances of the restriction enzyme sequence. The input would access the library of restriction enzymes contained in the Bio.Restriction module. A very simple example:

The problem, of course, is that the variable enzyme is a string object, not the RestrictionType object required to access the class.

I tried using the importlib package. The enzymes appear to be classes instead of modules, however, so importlib can't help.

I'm also fairly new to Python, so I didn't get too much from reading the Restriction source files.

There are obvious limitations to being forced to access restriction enzyme in the command line. One solution to this problem is to have two python scripts where one prompts the user for the enzyme and then subsequently replaces code and imports output from another script. Another solution is to simply create a dictionary of all possible restriction enzymes and their sites. Both of these solutions are hideous. The ideal solution for me would be to convert the user inputted string into the proper RestrictionType object which could then be used to access the sites. Thanks for reading, and I would appreciate any help with this problem.

## Using PaqCI&trade for Golden Gate Assembly - What Makes it a Special Addition to the NEB Assembly Portfolio?

Before we get into the specifics about PaqCI, let&rsquos delve into a bit of enzyme background to set the stage: Golden Gate Assembly is directly dependent on Type IIS restriction enzymes that have asymmetric DNA recognition sites and cleave outside of their recognition, or binding, sequences. We currently offer 50 Type IIS restriction enzymes, of which a subset have the necessary favorable characteristics for Golden Gate Assembly. Enzymes such as BsaI-HF®v2, BsmBI-v2, and BbsI-HF® have been our Golden Gate workhorses as they have historically been featured in published assembly protocols in the scientific literature, plus we have extensive experience using them here at NEB. During this time, and with input from our customers, we recognized how useful it would be to the research community to offer an enzyme with a 7-base recognition site for assembly, but one done the &ldquoNEB Way&rdquo &ndash with fully optimized protocols and enzyme recommendations, for assemblies ranging from simple to complex, and at a reasonable price.

And that is where the PaqCI Golden Gate story begins, as we set down the path of finding a Type IIS enzyme with a highly desirable 7-base recognition site (see Figure 1), whose sites are less likely to be present in DNA sequences being assembled, yet is capable of the full range of assembly complexity that scientists require for their experiments. Through a collaboration between laboratories in our Research, Applications Development, and Production Departments, PaqCI was identified and cloned, and its expression was optimized. We also optimized a DNA activator for the enzyme, and developed protocols for single inserts, and simple-to-complex assemblies. All this &ndash from discovery, to optimization, to being available for sale &ndash despite the challenges we have all been facing conducting our science during a pandemic!

Figure 1: Type IIS enzymes recognize asymmetric DNA sequences and cleave outside of their recognition sequence

### What is domestication? And why is PaqCI important when considering domestication?

Domestication refers to converting any DNA fragment that will be part of an assembly into &ldquoGolden Gate-ready&rdquo form - flanking the DNA at both ends with the Type IIS restriction sites that will direct the assembly and removing any internal sites for that enzyme that might be present in the DNA and are not tolerated well in GGA. For PaqCI it&rsquos all about the 7- base recognition site statistically any 7-base sequence will appear in any given DNA sequence less often than the 6-base sequence of the more commonly used Type IIS restriction enzymes. The Achilles&rsquo Heel of Golden Gate Assembly has always been that internal sites significantly decrease assembly efficiency, as they would allow the finished construct to be susceptible to digestion by the restriction enzyme present in the assembly reaction at best, and could lead to incorrect and unwanted assemblies at worst.

This is less an issue when using Golden Gate for single insert cloning because the overall efficiency for single inserts is SO high you would get your desired construct even if many of your successfully cloned inserts became linearized and did not transform well simply by screening a few colonies from your transformation plate, you would find cloned single inserts. But typically, researchers are using Golden Gate for multiple inserts. And the more inserts you have&mdashthe greater the assembly complexity&mdashthe more you need maximal efficiencies. So, having an internal site for your chosen restriction enzyme is a big problem for Golden Gate Assembly.

There are proven methodologies for eliminating internal sites while domesticating DNA sequences. We have a video (below) that shows the options for domestication: (1) site-directed mutagenesis to eliminate an internal site in advance of the assembly reaction, or (2) designing an assembly junction point right at the internal restriction site with a base change to eliminate the site upon assembly.

This video explains Domestication, or the removal of Type IIS cut sites naturally occurring in vector or insert sequences, as it relates to Golden Gate Assembly.

But all this sequence manipulation to deal with internal sites takes thought and time. Hence the attractiveness of a 7-base recognition site enzyme, which significantly decreases the probability of internal sites. And that is where PaqCI comes into the picture &ndash a 7-base recognition restriction enzyme that has been optimized for Golden Gate assembly, and is supplied at a concentration that enables use for complex assemblies up to 20+ fragments. We&rsquore very excited about this!

### The mechanism of multi-site enzymes and why they benefit from the addition of an activator

Some enzymes have more intricate ways of interacting with their recognition sites in DNA than others. Most homodimeric enzymes, like the standard Type IIP restriction enzymes EcoRI and HindIII, have two identical subunits that bind cooperatively at the symmetric site with each subunit cutting one strand to result in a double-stranded cut. In contrast, multi-site enzymes like PaqCI have a more complex structure and mechanism. It is presumed that PaqCI utilizes multiple subunits to interact with two recognition sites in order to cleave a single target site. To make sure that PaqCI cuts all the sites during Golden Gate assembly, we supply an inert short oligonucleotide activator containing an extra PaqCI binding site, which functions in trans as an activator for PaqCI cleavage (see Figure 2).

Figure 2: Presumed mechanism for how the PaqCI activator assures complete cutting via trans binding if needed

One would think that for Golden Gate, where by definition, every insert and every destination plasmid has its assembly active DNA fragment flanked by two sites, there would be no need for any added sites. But Golden Gate is a very dynamic process, with cutting and ligation taking place in the assembly reaction, and situations can arise where PaqCI binds and cuts sites on different DNA molecules, which means on each of those DNA molecules there would be another site remaining to be cut. So having an optimized number of extra sites available in the form of the PaqCI activator ensures that complete cutting in your assembly reaction occurs. It should be noted that the activator does not get cut or interact in any way with the assembly &ndash it only provides a second binding site that can activate cutting. Different levels of complexity call for different levels of PaqCI and T4 DNA Ligase in addition we have carefully optimized how much PaqCI and its activator are needed for different assembly complexities.

Now, it gets interesting when we think about what exactly constitutes the right amount activator. The cutting of DNA in a typical DNA restriction digest, where cut DNA remains cut, is different from what happens in Golden Gate assembly reactions, where sometimes cut sites are nonproductively reannealed and ligated, so that any one DNA cut site can require being cut more than once throughout the assembly reaction. This is why the optimal amount of the activator can be different from what is recommended for a standard restriction digest with PaqCI, where using 1 µl of the enzyme (10 U) requires 1 µl of the activator (20 pmoles). Because of the dynamic nature of GGA, these regenerated sites translate to less supplementary sites in the form of the activator being needed.

From over a thousand test assembly reactions, we can recommend just the right amount of PaqCI, activator, and T4 DNA Ligase for everything from simple single insert cloning to a complex 24-fragment assembly (see Table 1).

1. Based on 5 fragment assembly test system
2. Based on 24 fragment assembly test system
3. The activator solution is in a Mg-free buffer for best long-term storage. For short-term working stocks, if desired, dilute an appropriate amount in 1X T4 DNA ligase buffer to achieve more easily pipettable volumes (e.g., a four-fold dilution = 5 µM, 5 pmoles/µl activator.)

Table 1: Recommendations for PaqCI Golden Gate Assembly

As assembly reactions increase in complexity, more units of enzyme are required for maximal performance our range is from 5 to 20 U of PaqCI paired with 200-800 U of T4 DNA Ligase. We also have recommendations for how much of our activator to add to each assembly reaction, within a range of 5-10 pmoles. We provide a 20 µM stock of the activator with each PaqCI enzyme, more than enough for all your assembly needs.

One note about the buffer requirements: CutSmart buffer is the best buffer to use for setting up a simple DNA digest with PaqCI, but for Golden Gate Assembly, there are better efficiencies achieved maximizing the PaqCI and T4 DNA ligase enzyme activities using T4 DNA Ligase Reaction Buffer.

### New England Biolabs Golden Gate Assembly tools are here to help

Webtools make our scientific lives simpler by facilitating workflows, and our Golden Gate Assembly tool keeps to that tradition.

After designating the DNA fragments you would like to use for any given assembly, the tool can design optimal unique four base overhangs between the inserts that have been independently verified through T4 DNA Ligase fidelity studies to work at high fidelity. It will also automatically check your inserts for the presence of any internal sites that might affect the choice of Type IIS restriction enzyme to direct an assembly, or alert the user to remove such internal sites via domestication. The program will also automatically generate a set of primers for your inserts to add the flanking bases and recognition sites required either for amplicon generation of inserts to be directly used or for pre-cloning purposes. Finally, a report can be generated describing your full assembly with a color-coded graphical read out, your final assembly sequence, and descriptions of each junction between inserts.

In addition, there are also useful programs available under the &ldquoUtility&rdquo tab within the tool. Those programs can take an uploaded sequence and make suggestions for different desired insert or module design and can also provide you with vetted lists of what overhangs have been found to support high efficiencies and fidelities during Golden Gate Assembly. Together the Golden Gate Assembly tool makes assembly design easy, even for the first time user!

Check out our video outlining the Golden Gate Assembly workflow, our usage guidelines for GGA using PaqCI, or our protocol for GGA using PaqCI and T4 DNA Ligase.

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## Problem

Say that you place a number of bets on your favorite sports teams. If their chances of winning are 0.3, 0.8, and 0.6, then you should expect on average to win 0.3 + 0.8 + 0.6 = 1.7 of your bets (of course, you can never win exactly 1.7!)

More generally, if we have a collection of events \$A_1, A_2, ldots, A_n\$ , then the expected number of events occurring is \$mathrm(A_1) + mathrm(A_2) + cdots + mathrm(A_n)\$ (consult the note following the problem for a precise explanation of this fact). In this problem, we extend the idea of finding an expected number of events to finding the expected number of times that a given string occurs as a substring of a random string.

Given: A positive integer \$n\$ ( \$n leq 1,000,000\$ ), a DNA string \$s\$ of even length at most 10, and an array \$A\$ of length at most 20, containing numbers between 0 and 1.

Return: An array \$B\$ having the same length as \$A\$ in which \$B[i]\$ represents the expected number of times that \$s\$ will appear as a substring of a random DNA string \$t\$ of length \$n\$ , where \$t\$ is formed with GC-content \$A[i]\$ (see “Introduction to Random Strings”).

## VI. Conclusion

DNA-based circuit design is continually evolving as DNA paradigms can be developed to represent their digital counterparts. Current efforts of our research team are dedicated to the utilization of these developments in the design of security applications. This presentation demonstrates how a microfluidic device can act as a random number generator, a fundamental element in security circuitry. Oligonucleotide synthesis is used to randomly generate a nucleotide sequence, plasmid vectors enable temporary storage of the sequence, and chromatogram analysis enables the translation from a sequence to its digitally equivalent random number. Long term storage is achieved through spotted microarray fabrication, which enables each sequence's expression levels to be permanently stored.