Hi guys, i have a doubt regarding a calculation example proposed by illumina in its protocol "16S Metagenomic Sequencing Library Preparation" link here: https://support.illumina.com/documents/documentation/chemistry_documentation/16s/16s-metagenomic-library-prep-guide-15044223-b.pdf
On page 16 there is the formula for the Nanomolar concentration (nanomoles/liter in theory but non specified) and an example with 15 nanogr/microlt and 500 average library size. When i try to redo this calculation i obtain 45 (like illumina) but in nanomoles/microliter and not in nanomoles/liter.
My calculation steps are: 1) (15 nanogr/microlt / ( 660 gr/mole 500)) 10^6 (the initial formula) 2) (15 nanogr/microlt / 330.000 gr/mole) 10^6 3) 15 nanogr/microlt / (0.33 gr/mole) 4) 15 nanogr/microlt (1/0.33) mole/gr 5) 15 10^(-9) (1/0.33) mole/microlt 6) 15 (1/0.33) nanomole/microlt 7) 45 nanomole/microlt 8) 45 10^6 nanomole/liter, and not 45 nM as Illumina.
Can someone help me to understand my mistake? Thanks a lot
Maybe easier if you consider the x10^6 represents the ng/uL to ng/L conversion.
So, you really start with
Density: 15,000,000 ng per liter = 0.015 g / L
Molar mass: 330,000 g / mole
(0.015 g / 1 L) * (1 mole / 330,000 g)
(0.015 mole / 330,000 L)
(4.5x10^-8 mole / 1 L)
(45x10^-9 mole / 1 L)
(45 nmole / 1 L)
45 nM
Sorry but 15 nanogr/microlt 10^6 is either 0.015 g/microlt or 15.000 gr/L or 15 10^12 nanogr/L right? It's not a conversion if we multiply a fraction by an "external" number, we can pass from 15 nanogr/microlt to 0.015 g/L internally without the need of 10^6 in the formula. Or am i missing something?
Thank you for the answer!
Sure thing. The formula itself is confusing since it's not apparent the goal.
One point you might be missing is that the formula is a shortcut for manual conversion. So you plug in all values as is with no need for conversion. So X ng/uL is actually (X ng/uL) as a single variable, not a variable with units.
So the x10^6 is the correction factor to account for inputting variables with mismatched units.
May also help to consider the real formula for converting from mass/volume to molarity(moles/volume) using molar mass (mass/moles):
(mass/volume) x (moles/mass) = (moles/volume) = M
So doing manually you will need to convert mass and volume units to make them equivalent.
In summary:
filling in the variables, units mismatch, equation not balanced.
(ng/uL) x (moles/g) != (nmole/L)
expand unit prefix
(10^-9 g / 10^-6 L) x (moles/g) != (10-9 mole / L)
simplify
(10^-3 g / L) x (moles / g) != (10^-9 mole / L)
(10^-3 moles / L) != (10^-9 mole / L)
(mmoles / L) != (nmole/L)
convert mmole to nmole
(mmole / L) x (10^e6 nmole / mmole) = (nmole/L)
So you can see the x10^6 constant comes from simplifying/shortcutting the conversion steps. Another way to think about it is to simplify all the constants you would multiply by to converts units (e.g. (1g/10^9 ng) x (10^6 uL / 1L) x (10^9 nmole / mole) => cancel units from actual equation = x10^6
Edit: corrected some math.
Ok, i need to reason on that, thank you for your help!!
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