If the concentration is too low, the initial contact between and insert fragment and a vector fragment will be a rare event, resulting in very few intact plasmids.
If the concentration is too high, fragments will collide more frequently, resulting in long molecules composed of many fragments.
If you want a high insert:vector ratio, you may need to use less vector DNA. If ligation proceeds more quickly at room temperature, why would I take the time to do it at a lower temperature? Thus, a lower temperature is the optimum environment for sticky ends to anneal.
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Agarose gels 1. Band intensities were quantified with Kodak molecular imaging software v4. For each image, the relative intensities of each band were obtained by averaging quantification at three different aperture and exposure settings. Circular ligation was carried out by ligating this vector to digested off7 insert prepared as described above at specific molar ratios and concentrations. Transformations were performed using XL1-Blue cells as described above and the resulting colonies were counted manually.
The detailed thermodynamic model of linear ligation is provided in the Supplementary methods. The values of K 1 and K 2 were used in all subsequent simulations. Four thermodynamic equilibrium equations S1—S4 and three mass balance equations S5—S7 were solved in Matlab for molar concentrations of each species based on input DNA concentrations.
Experimental determination of these quantities is described in the Supplementary methods. As in the linear model described above, a thermodynamic model of circular ligation was characterized by K 1 and K 2 , but also included the Jacobson—Stockmayer factor j to capture the probability of circularization Jacobson and Stockmayer, The detailed mathematical model is provided in the Supplementary methods section.
The ribosome display vector pRDV was chosen as the vector template, and off7, a gene evolved from ribosome display to bind maltose-binding protein, was chosen to be the model insert Binz et al. In a directed evolution experiment, these two sites would be used for assembling the initial library into pRDV, reattaching the T7 promoter and tolA regions to the library insert between selection rounds, as well as analyzing selection results by transformation and subsequent sequencing of individual clones Zahnd et al.
Each of the above steps requires high ligation efficiency and fidelity to preserve the diversity of the library as the success of any selections depends heavily on the quality of the construction, propagation and analysis of the library. We thus picked a directed evolution application as the motivation of our study, although our results are generally applicable in any context where ligation efficiency is important.
Identical palindromic ends in different DNA molecules, usually caused by digestion with the same restriction enzyme, can anneal by forming complementary base pairs. However, a molecule can also anneal to another copy of itself in reverse orientation as palindromic ends are self-complementary. This leads to the loss of molecules and unwanted homodimer byproducts which is an inherent limitation of any Type IIP restriction enzyme. Since the Type IIS restriction enzyme BbsI cuts at sites 2 and 6 bp away from the recognition sequence, it allows us to custom design the sequence of each cutting site.
First, they are non-palindromic and eliminate homodimer formation. Second, they cannot recombine with each other within mismatch tolerance of T4 DNA ligase. In contrast, the use of sub-optimal cutting sequences ACTA and GCTT, which have two out of four correctly positioned complementary bases between sense and anti-sense overhangs, gave a very high misannealing of the two sites results not shown.
The selection of CGAA and GCTT overhangs provides a simple solution to the above two problems, as the two sites are identical in overall base composition thus providing similar annealing temperatures but have opposite sequence orientations thus minimizing spurious annealing.
Third, the first BbsI site was inserted between the T7 promoter and RBS so as not to perturb transcription and translation, while the second site was inserted at the beginning of tolA preserving in-frame glycines and serines to maintain the flexibility of the spacer Fig. Single-clone ribosome display was carried out using pRDV2-Off7 to demonstrate that insertion of the BbsI sites had no adverse effect on selection see Supplementary methods and Fig. Lastly, the BbsI sites were positioned next to the original NcoI and HindIII sites to generate similar fragment sizes, which facilitated direct comparison of the methods.
A constant amount of vector with different molar ratios of insert : vector were ligated and the products were resolved and visualized with agarose gel electrophoresis. Even without insert, many high molecular weight products were formed through vector—vector annealing events. As the amount of insert increased, high molecular weight products remained and additional lower molecular weight bands were visible.
The presence of circular species and the exponential combination of linear and circular products make determination of the identity of these bands extremely difficult the sizes of products containing up to four ligated molecules are provided in Table I. In contrast, ligation of off7 and pRDV2 cut by BbsI shows a faint product band at the same distance as the nicked pRDV2-Off7, and this band is strongest for a 1 : 1 insert : vector ratio Fig. In the BbsI ligation, excess insert at 0.
The sizes of the product bands are provided in Table I. V represents Nb. Products at bp full-length product are shown. D Vector 8 or 3 nM ligated with the corresponding amount of insert was transformed into XL1-Blue cells. Shown here is the number of colonies relative to the number obtained for 1 : 1 BbsI ligation of the same vector concentration.
A one-tailed t -test was used to examine statistical significance. For comparison of the relative amount of correctly ligated product, each ligation mixture was subjected to 10 cycles of PCR amplification with outer primers that anneal to insert-flanking regions of pRDV2 Fig.
This procedure should selectively amplify circular vector—insert products and not linear vector—insert products or other undesired products vector—vector, insert—insert, etc. In addition, the ligation mixture was transformed and the number of bacterial colonies were counted Fig.
To minimize any variability in transformation efficiencies across experiments, colony numbers were normalized to the result for the 1 : 1 insert : vector ligation reaction at the same vector concentration.
All these results suggest that it is preferable to use Type IIS restriction enzymes in generating fragments for ligation to yield more full-length product. In order to gain more understanding of the ligation reaction, a minimal system consisting of the linear ligation of three DNA fragments was developed. This scheme is also particularly useful for applications in which transformation is not needed and linear ligation products can be directly used e.
A constant amount of digested off7 was ligated to digested T7 and tolA at the specified molar ratios, and the products were resolved and visualized on an agarose gel Fig. Quantification of the gel confirmed this observation, indicating a 1. It should be noted that the smallest increase 1. With excess T7 and tolA 10 : 1 : 10 and 2 : 1 : 2 , T7—T7 and tolA—tolA homodimers are the major products, but the desired product is also maximized since off7 is less likely to homodimerize when T7 and tolA are in such abundance.
In contrast, with excess off7 1 : 2 : 1 and 1 : 10 : 1 , many high molecular weight products could be seen, likely due to the undesired formation of off7 multimers, which can further circularize or anneal to T7 or tolA fragments to generate further species diversity.
A closer look at ligation following BbsI digestion Fig. More full-length products were observed with higher molar excesses of T7 and tolA, as there was no risk of byproduct formation. Representative 1. The arrow shows full-length ABC product at bp. Arrows in B indicate positions of selected species; locations of higher order species can be found in Table I. Arrows in C indicate positions of all of the species. No lig. Viewing ligation as a two-step process, a thermodynamic model was developed for both the minimal three-piece ligation and the more complicated vector—insert ligation for fragments generated by Type IIS restriction enzymes Fig.
We modeled each ligation reaction as a reversible equilibrium process with the free energy defined by the identity of the sticky ends involved in that particular reaction. This thermodynamic model was used to estimate output from input when ligation had proceeded for a sufficiently long time to reach equilibrium.
Assuming that both sealing events after an annealing event occur in rapid succession and that only ligated products, but not annealed and nicked products, are stable enough to proceed to the next ligation reaction, a system of thermodynamic equations was written. Schematic of the thermodynamic model proposed in this study. Refer to Supplementary data Table S2 for nomenclature used. All possible species are shown in the diagram. A: T7, B: off7, C: tolA. Only products containing up to four reactant molecules were included in the model.
Cir: circular product. Although free energies of annealing for specific sequences could, in principle, be determined using available calculators, there remains some uncertainty in the accuracy of these predicted values under different experimental conditions e. Additionally, the free energy of sealing would still be required. These two values were used for all subsequent simulations. Figure 4 A shows the three-piece linear ligation model for non-palindromic sticky ends.
All possible species were considered. We assumed no homodimer formation, no cross-reactivity between sites 1 and 2, and no blunt-end ligation. Figure 4 B shows the vector—insert ligation model for non-palindromic sticky ends. Species containing up to four fragments were explicitly included and any higher order molecules were assumed to be insignificant. This assumption is valid in the range of concentrations and molar ratios that were most commonly used, and accounting for higher-order species would have a minimal effect on the optimizations that were examined in this work.
The probability of circularization is reflected by the Jacobson—Stockmayer factor j which represents the effective concentration of one end of a linear molecule with respect to the other, which is dependent on length of the linear molecule but independent of DNA concentration Jacobson and Stockmayer, If the competing DNA concentration is above j , linear multimers will be favored; conversely, circularization will be favored if the DNA concentration is below j Dugaiczyk et al.
To test the validity of the model, we compared its predictions to experimental results. First, three-piece linear ligations with five different molar ratios were simulated by solving the system of equations to obtain equilibrium molar concentrations for the reactants, intermediates and products in each ligation Fig.
For each reactant molar ratio, product molar concentrations were converted into product molar ratios by normalizing to full-length product and further converted to mass ratio based on the number of base pairs.
This was done to facilitate direct comparison with experiments in which mass ratios were determined by quantifying product bands in agarose gels. Across all reactant molar ratios, the model predictions were in good agreement with the experimental results. The only major difference between predictions and experiments was for 1 : 10 : 1, where predictions generated mass ratios much higher than those obtained by experiments Fig.
This was likely due to inaccuracy from saturating gel signals and further error amplification from the small amount of full-length product compared with intermediates and reactants. Validation of thermodynamic model with experimental results.
For more information on cloning, consult the Subloning chapter of the Protocols and Applications Guide. Sara is a native Wisconsinite who grew up on a fifth-generation dairy farm and decided she wanted to be a scientist at age She was educated at the University of Wisconsin—Parkside, where she earned a B.
She has worked for Promega Corporation for more than 15 years, first as a Technical Services Scientist, currently as a Technical Writer. Sara enjoys talking about her flock of entertaining chickens and tries not to be too ambitious when planning her spring garden. This site uses Akismet to reduce spam. Learn how your comment data is processed. Skip to content. About the author Related posts. Sara Klink. September 28, Like this: Like Loading One thoughtful comment nice piece!
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