# Error rate in Taq pol. 1:270?

Tom Chappell t.chappell at ucl.ac.uk
Wed Feb 12 08:24:57 EST 1997

```>Dr. Duncan Clark (duncan at genesys.demon.co.uk) wrote:
>
>> Anyone have a formula for actually calculating the real no. of errors
>> one would see after so many cycles for a fixed target size. I use a
>> published one for determining fidelity (similar to Wayne's) on a lacI
>> assay but my algebra is not good enough to know how to reverse the
>> formala and for a given error rate get an actual. no. of errors for so
>> many cycles for a fixed target size. It would be nice to have a table in
>> the FAQ showing no. of errors to be expected after say 10, 15, 20, 25
>> and 30 cycles for targets of 100, 500, 1000, 2500bp etc. Any offers?
>
By straight probability:

Assuming Taq makes an error at 1 in 10,000 (0.0001), the probability of it
NOT making an error is 0.9999

on a target of X bp, the probability of it not making an error is
(0.9999)^X, the probability of it making 1 or more errors is 1-(0.9999)^X

100 bp : 99% / 1%
500 bp : 95% / 5%
1000 bp : 91% / 9%
2500 bp : 78% / 22%

This is for 1 cycle. You can generate a probability distribution for Y
cycles by using the formula:

Probability of n errors =  (Y!/((Y-n)!*n!))*(0.9999^X)^(Y-n)*(1-(0.9999)^X)^n

This formula is somewhat of a simplification, in that I've assumed the Taq
makes either 0 or 1 errors each cycle. This is a faulty assumption once
you get above about a kb.  You could generate the proper formula, but the
factorials at the beginning would start to choke Excel (although
Mathmatica should handle it fine...)

For 25 cycles, the probability of making zero errors are:

100 bp : 78%
500 bp : 29%
1000 bp : 8%
2500 bp : 0.2%

This is just the mathematics. I would assume that the error rate of Taq
actually increases during a PCR reaction as you differentially use up and
heat destroy the nucleotides. In addition, I would also assume that very
few of the products at the end of the PCR reaction have actually been
amplified at EACH cycle (a nanogram of target would end up as 32+ mgs of
product after 25 cycles).

If the error rate is 1 in 3,333 (from Kunkel's numbers of 300 opal
reversions / million) the above numbers are:

100 bp : 47%
500 bp : 2%
1000 bp : 0.06%
2500 bp : really, really small

```