**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

For ligations containing blunt ends, this is modfied to 2 hours at RT (see NEB catalog).

For ligations with low amounts of material, this is modified to 14-16 C o/n.

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

decide on total DNA, t in ng (100 ng is desirable)

x ul of insert = (3t/ (SizeVec/SizeIns +3)) / [insert]

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

z ul of water = 20 – x – y

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

z ul of water = 20 – x – y

where t = total DNA mass (ng) of insert + vector, Size

_{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)**

If there is no insert, then just use 10-100 ng of the vector as x in the reaction.

A more formal description of how to ligate DNA in the context of cloning is here.

[python filename=”ligation2.py”]

More information

Use these equations

For a 20 ul reaction:

z=20- x -y -2 -1 = 17 -x- y

z=20-x-y

To calculate volumes x, y, and z, we need to find the mass of X and Y

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

calculate volumes x and y.

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

i= ng of insert (mass)

v = ng of vector (mass)

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

v = ng of vector (mass)

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

**equation 1**)(example, t can be substituted with 20-200 ng as needed)

i + v = 100

(moles insert)/(moles vector) =3 (3:1 ratio) (ratio, can be changed, for example use 5:1 for blunt-end cloning)

**equation 2**i = moles insert * MWinsert (g/mol) * 10

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

^{9}ng/1gv = moles vector * MWvector (g/mol) * 10

^{9}ng/1g(i /MW(insert)/(v/MW(vector)) = 3

MW is proportional to size

MW is proportional to size

(i / v) * ((size of vector in bp)/(size of insert in bp)) = 3

Size

_{Ins}= size of insert in bpSize

_{Vec}= size of vector in bpi/v * (Size

_{Vec}/Size_{Ins}) = 3**(equation 2)**solve for I (insert)

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

_{Ins}/Size

_{Vec})

**(equation 3)**

so for example if the vector is 3000 bp and the insert is 1000 bp , then the vector is 3 times bigger than the insert. Using 100 ng of insert, requires 100 ng of vector to achieve a 3 fold molar excess.

v = t – i

i/v * (SizeVec/SizeIns) = 3

**(equation 2)**(i/(t-i)) * (Size

solving for i.

_{Vec}/Size_{Ins}) = 3 (equation 2a)solving for i.

i * Size

i * Size

i * Size

i * (Size

_{Vec}/Size_{Ins}= 3 (t-i)i * Size

_{Vec}/Size_{Ins}= 3t – 3ii * Size

_{Vec}/Size_{Ins}+ 3i = 3ti * (Size

_{Vec}/Size_{Ins}+3) = 3t**i = 3t/ (Size**(_{Vec}/Size_{Ins}+3)**equation 4)**for t=100 ng:

**i = 300/ (Size**

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

**equation 4a)**

The corresponding equation is:

use I = T- V to get

**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})

i /(concentration of insert) = x ul of insert

#### 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)**