**Ligation reaction:**

**For sticky ends:**

x ul DNA insert

y ul DNA vector

2 ul 10x T4 Ligase Buffer (make sure it is well dissolved)

z ul H2O to 20 ul total

1 ul T4 DNA Ligase (400U/ul) very temperature sensitive (keep cold at

all times)

10 minutes at RT (20-25C), then put on ice for transformation

**Desired Insert to Vector MOLAR ratio is 3:1**

y ul of vector = (t * SizeVec/SizeIns) / (3 + SizeVec/SizeIns)) / [vector]

z ul of water = 20 – x – y

_{Vec}= size of the vector in bp, Size

_{Ins}= size of the insert in bp, [insert] is the concentration of the insert in ng/ul, and [vector] is the concentration of the vector in ng/ul.

**If volume of insert + vector > 17 ul then set t less than 100ng**

**(example t = 20 ng)**

[python filename=”ligation2.py”]

in ng, and then use the known concentration of X/ul and Y/ul to

calculate volumes x and y.

**Desired Insert to Vector MOLAR ratio is 3:1**

Want to use 20-200ng total DNA in rxn, aim for 100ng first if possible

v = ng of vector (mass)

i +v = t , where t=100 ng, t is total mass (

**equation 1**)

**equation 2**

^{9}ng/1g

v = moles vector * MWvector (g/mol) * 10

^{9}ng/1g

MW is proportional to size

_{Ins}= size of insert in bp

_{Vec}= size of vector in bp

_{Vec}/Size

_{Ins}) = 3

**(equation 2)**

**i = 3* v (Size**_{Ins}/Size_{Vec}) ** (equation 3)**

_{Ins}/Size

_{Vec})

**(equation 3)**

**(equation 2)**

_{Vec}/Size

_{Ins}) = 3 (equation 2a)

solving for i.

_{Vec}/Size

_{Ins}= 3 (t-i)

i * Size

_{Vec}/Size

_{Ins}= 3t – 3i

i * Size

_{Vec}/Size

_{Ins}+ 3i = 3t

i * (Size

_{Vec}/Size

_{Ins}+3) = 3t

**i = 3t/ (Size**(

_{Vec}/Size_{Ins}+3)**equation 4)**

**i = 300/ (Size**

_{Vec}/Size_{Ins}**+3)**(

**equation 4a)**

**v= (t * Size**_{Vec}/Size_{Ins}) / (3 + Size_{Vec}/Size_{Ins}) (**equation 5)**

_{Vec}/Size

_{Ins}) / (3 + Size

_{Vec}/Size

_{Ins})

**v= 100 * Size**_{Vec}/Size_{Ins}) / (3 + Size_{Vec}/Size_{Ins}) (**equation 5a)**

_{Vec}/Size

_{Ins}) / (3 + Size

_{Vec}/Size

_{Ins})

#### Practical equations:

**x ul of insert = (300/ (Size**_{Vec}/Size_{Ins} +3)) / insert [concentration]**(equation 6)**

_{Vec}/Size

_{Ins}+3)) / insert [concentration]

**x ul of insert = (3t/ (Size**_{Vec}/Size_{Ins} +3)) / insert [concentration] **(equation 6a, general version, where t = total DNA)**

_{Vec}/Size

_{Ins}+3)) / insert [concentration]

**y ul of vector = (****100 * Size**_{Vec}/Size_{Ins}) / (3 + Size_{Vec}/Size_{Ins})) /vector** [concentration] ****(equation 7) **

**y ul of vector = (**

_{Vec}/Size

_{Ins}) / (3 + Size

_{Vec}/Size

_{Ins})) /vector

**[concentration]**

**y ul of vector = (t**** * Size**_{Vec}/Size_{Ins}) / (3 + Size_{Vec}/Size_{Ins})) /vector** [concentration] ****(equation 7a, general version, where t = total DNA) **

**y ul of vector = (t**

_{Vec}/Size

_{Ins}) / (3 + Size

_{Vec}/Size

_{Ins})) /vector

**[concentration]**

**z ul of water = 20 – x – y ****(equation 8) **

**If volume of insert + vector > 17 ul then set t less than 100ng in**

**equations 3, 4 and 5**

**(example t = 20 ng)**