Serial dilutions

Take a spoonful of Cheerios and add it to a spoonful of milk, stir it up well, take a spoonful of this new mix and add it to a spoonful of fresh milk, stir that up & add a spoonful of it to another spoonful of new milk and… You’ve got yourself a SERIAL cereal DILUTION! Which I have to admit would have been a lot more fun than the actual serial dilutions I spent part of my morning doing…
blog form: bit.ly/serialdi...
note: text old, video new
We’ve looked at a lot of “glamour” experiments - and that’s the type of stuff you see in the news too - how CRISPR gene editing is being used to treat patients with sickle cell disease, how scientists are determining the atomic structures of key biological molecules, etc. What you don’t usually hear about is all the hard, less-glamorous, work that goes into those discoveries. A lot of day-to-day lab life isn’t “glamorous” in any sense of the word, but it’s still important - and doesn’t have to be boring. And, sometimes if you make seemingly boring tasks more fun you can come to appreciate them more, understand them at the molecular level, and even perform them better. One such task is the serial dilution.
In a serial dilution you perform a series of stepwise dilutions where you’re diluting by the same factor each time (e.g. 1:2 in this cheerio-y example), so the concentration (relative amount of the thing to the non-thing) decreases “exponentially.” We can put some terminology on it and say that each mix has a Dilution-Factor-times less than the one before it. So in this case, our Dilution Factor (DF) is 2, each new Cheerio mix has 1/2 as many Cheerios per spoonful than the one before it.
If instead of mixing 1 spoonful to 1 spoonful each time we’d mixed 1 spoonful to 9 spoonfuls of milk (a 1:10 dilution) our Cheerios would dilute out a lot faster. We’d have a Dilution Factor of 10, so each new spoonful would have 10-times-less Cheerios than the one before.
Serial dilutions are kinda like pyramid schemes with the opposite effect - if you start out with a certain amount of money it gets distributed to more and more people - but you can’t give out more money than you started with so people end up with less and less money.
When we have something changing by a constant multiplier (like 1/2 or 1/10) we call it geometric, or exponential, growth/decay. And it gives us shortcuts to work with as we’ll see…
So, how do serial dilutions work & why do we use them? You keep diluting the same thing over and over but in a constant-stepwise fashion, stepwise being key & they’re useful for lots of things - like helping with accuracy & creating “standard curves” which are a series of things of known concentration that allow you to compare yours to. More on these why’s after we discuss the how
But let’s get back to the how for now, skipping the part where you milk the cow - say you want to do 1:2 dilutions of Cheerios, we’ll call them H for shortness, since C will mean something else (concentration) later and I don’t want anyone to get confused.
So take the starting solution, which is all H. And you mix it with an equal amount of milk. e.g. if you took 1 spoonful of H + 1 spoonful of milk you’d get 2 spoonfuls of of a 50% H solution
Then you take that 1st dilution and do the same thing with it - but now since you’re starting with a 50% solution, when you have it, you get a 25% solution. And if you do the same thing with the 25% solution, you’ll get a 25/2= 12.5% solution, and you can keep doing this, each time getting a solution half as dilute as the one before.
100% → 50% → 25% → 12.5% → 6.25%
So in the span of 5 samples you can cover a spread from 100% to 6.25%
If that’s not big enough for you, you can keep on diluting (e.g 6.25% → 3.125%…) But you’ll still only be decreasing by 1/2 each time. If you want to “move faster” you can choose a higher dilution factor.
Dilution factor (DF) refers to the amount by which you’re diluting by each step. So in this example, the dilution factor was 2/1 = 2. What if instead of 2 you chose a dilution factor of 10? Now over the span of 5 samples you go from 100% → 10% → 1% → 0.1% → 0.01%
So, for example, if you started with 100 spoonfuls of Cheerios (H), the 5th tube would have 1 spoonful-worth of Cheerios and 99 spoonfuls-worth of milk. But you didn’t get there by mixing 1 spoonful of Cheerios with 99 spoonfuls of milk - you got there stepwise.
solution 1) 100 H
solution 2) 10 H + 90 milk
solution 3) 10(10 H + 90 milk) + 90 milk
solution 4) 10(10(10 H + 90 milk) + 90 milk)
solution 5) 10(10(10(10 H + 90 milk) + 90 milk)) + 90 milk
finished in comments

[@thebumblingbiochemist]

If you were to take samples of equal volumes (like equal spoonfuls), each sample will have 1/10 of the molecules of the diluted thing as the one before it → so if solution 1 has 100 Cheerios, solution 2 has 10, 3 has 1, 4 has 0.1? I guess you can cut a Cheerio, but how do you have 0.1 molecules? Well, we’re usually dealing with waayyy more than 0.1 molecules because our “solution 1” usually has way more than 100 molecules per “spoonful”
In fact, molecules are so tiny and abundant that we often speak of their concentrations in “moles,” where a mole (mol) is 6.02x10²³ (Avogadro’s number) of something (anything - like how a dozen can be used for donuts or bagels). Molarity (M) is a unit of concentration corresponding to 1 mol per liter (L). So if our solution of Cheerios is 1M that would mean that 1L of it has 6.02x10²³ Cheerios in it and 100mL has 6.02x10²² Cheerios, so solution 4 will still have plenty! bit.ly/dimensionalanalysising
Even when we speak in terms of millimolar (mM), you have 1/1000 of a mol/L, micromolar (μM) you still have 1/1000,000, and nanomolar (nM) still has 1/1000,000,000 mol/L which is 6.02x10¹³ Cheerios per L which is still a lot! (definitely more than physically possible but that’s never stopped the bumbling biochemist!)
Say you want to know the Cheerios concentration without having to count them out which would be even more tedious than serial dilutions! Thankfully there’s an easier way because serial dilutions follow the same dilution “rule” as “normal” dilutions → C₁V₁ = C₂V₂
What this says is - the initial concentration times the initial volume equals the final concentration times the final volume. I actually learned this as M₁V₁ = M₂V₂, where M stand for molarity, so that’s how I usually think of it, but the concentration doesn’t have to be in terms of molarity - it can be any concentration unit (even Cheerios per spoonful), as long as the units are the same on both sides of the equation. In past posts I’ve used M₁V₁ = M₂V₂ more, but I’m going to use C₁V₁ = C₂V₂ here to avoid any confusion. Going back to our serious cereal counting conundrum…
With a serial dilution, C₁V₁ still equals C₂V₂ but for each dilution your C₁ is the C₂ from the previous dilution. Instead of having to calculate out the C₂ stepwise, you can take advantage of the “geometric progression” of the dilution series → each time you dilute, C₂ gets divided by the dilution factor (DF), which is the same as multiplying by (1/DF) (e.g. in our initial cereal example, where our DF is 2, we multiply C by 1/2 each time). So, starting with some initial stock (C₁)
∙ C₁
∙ C₁*(1/DF)
∙ (C₁*(1/DF))*(1/DF)
∙ ((C₁*(1/DF))*(1/DF))*(1/DF)
∙ (((C*(1/DF))*(1/DF))*(1/DF))*(1/DF)
That’s supposed to be helpful?! Bear with me - that’s all just multiplication, so we can order/group it however we want, so we can rearrange things a bit and get…
∙ C₁
∙ C₁((1/DF))
∙ (C₁)((1/DF)*(1/DF))
∙ (C₁)((1/DF)*(1/DF)*(1/DF))
∙ (C₁)((1/DF)*(1/DF)*(1/DF)*(1/DF))
A little better, but here’s where it really clicks - Exponent form
∙ C₁
∙ C₁((1/DF))
∙ (C₁)((1/DF)²)
∙ (C₁)((1/DF)³)
∙ (C₁)((1/DF)⁴)
Now we don’t even have to worry about calculating any of the concentrations of the previous dilutions in order to find the concentration of a later one. We just need to know the starting concentration, the dilution factor, and the number or dilutions
Say you want to graph the average # of Cheerios per spoonful of each of the mixtures. If you were to try to graph that on a “normal”, linear scale (where the tick marks are evenly spaced by addition (e.g. 1, 2, 3, 4, 5,….) you’d have a bunch of dots squished together near the origin (0,0) and then that 100% way out on the right. If you want to get the values in a better-seeable form, you can instead plot it on a logarithmic scale. Logarithmic scales use tick marks that are spaced apart based on exponents that you’re raising something to. So if you have a DF of 2 you’d use a log2 scale to get a line. If you had aa DF of 10 you’d use log10. more on exponents & logs: bit.ly/logarithmsandexponents
Normally, instead of diluting Cheerios, I’m diluting things like RNA or protein and instead of spoonfulling them I pipet them. Today I was doing serial dilutions of RNA for slot blot assays, which are a way to test protein-RNA binding. bit.ly/bindingaffinity
I did a serial dilution of a dye to show you, but most of the serial dilutions I do for my stuff involve diluting things that are “invisible” to us, so it’s important to have a good system in place to make sure you don’t lose track of where you are in your dilution!
Depending on the volumes you want it’s helpful to do them in strip tubes (like PCR strip tubes) or deep well blocks, etc. - something where the liquid-holders are connected so you don’t mix them up & you don’t have to worry about numbering tons of tubes, etc. I recently found these awesome “cluster tubes” which are kinda like giant PCR strip tubes - they’re strips of 8 tubes that fit in a deep well block frame and are great for doing larger-volume dilutions without wasting a whole block. For today’s experiments I was doing 2-and-a-half blocks worth of cluster tube strips.
I can start by
1. make the highest concentration at the concentration you want to start at then pipet the diluent (buffer (pH-stabilized salt water) in this case) into all the tubes except the first one which I save for the starting, highest concentration one that doesn’t need to get diluted. Then stick the starting one into the first tube and the 2nd tube.
or
2. make a 2X initial concentration and then add that to diluent in the first well. so, in that case, you would add the same amount of diluent to all of the wells and then you add your sample to the first well and use that as your initial dilution. But, since you’re then diluting it, you need it to be 2X the desired starting concentration before you add it. For example, if you want to have 100uL of each concentration want to start at 400nM, either start by pipetting 100uL of 400nM sample into empty first well, or start by pipetting 100uL of 800nM sample into 100uL of buffer.
Usually what I do is I transfer then pipet up-down-up-down-up-down… (usually I do 5 times) ending on “up” then transfer to the next tube for the down
When you’re making dilutions, you have to remember that you’re taking out part of your “V₂” each time - so if you do 10uL + 10uL = 20uL and then take 10uL of that for the next one you only have 10uL of that one left - not 20. So if you need 20, you should be doing 20 + 20 (actually if you need 20 you should be doing 25+25 or something because it’s always good to have a little extra to account for evaporation, tube/pipet sticking-to-ness, etc.) more practical tips: bit.ly/bblabtips
And speaking of that stickiness, another reason to do serial dilutions is that they aid with accuracy. We don’t want one of those Cheerios boxes that’s “BONUS - 10% more FREE!”
As I talked about in a previous post, each instrument & measurement tool you use has a bit of error (e.g. if you pipet out 1mL it could *really* be 1.01mL or 0.99mL instead of 1.00mL). And the smaller the thing you’re measuring the bigger relative error a “small” error can make. (think of a drop in a pool vs a drop on a ladybug). bit.ly/accuracyprecisionerror
And if you’re pipetting a concentrated solution, 1 drop packs a lot of punch. So that little drop of liquid stuck to the outside of the pipette holds a lot of molecules that you aren’t accounting for. So it’s better to be pipetting larger volumes of more dilute things.
But sometimes you need to make a really dilute solution. Say you want to make a million-fold dilution of something (e.g. you have something that’s 1M and you want to get it to 1uM). Even if you pipetted just 1uL, you’d have to dilute that in a whole L of water to get 1uM. Instead of doing it that way you can do it stepwise.
Another time serial dilutions are great is for making “Standard curves.” These are where you take solutions of known concentration and you make a plot of them and then you compare a sample of unknown concentration to the plot of known concentrations to see where it falls along the line. Like, if it’s easier to measure Cheerio taste than count individual Cheerios in a spoonful, you could make a standard curve of the taste-ness of known Cheerio concentrations. Then you could taste a spoonful of unknown concentration and see where it falls in the curve to figure out the concentration without having to count Cheerios. more on these here: blog: bit.ly/standardcurves ; TH-cam: th-cam.com/video/9ZAWm5xm6gc/w-d-xo.html
 
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