Buffer you start judging me, I’m not hoarding all these bottles and cylinders, instead I’m making pH-stabilizing salt waters (aka buffers!)  for a protein purification. You know how you’re most likely to run into people you know in “common areas?” Well, our glassware cabinets are in a common hallway and it seems like most of the times I run across prominent scientists (frequently including members of my thesis committee) is when I’m balancing like 5 graduated cylinders and as many bottles as I can squeeze in. Carrying a lot of bottles and cylinders and beakers and flasks is like the biochemist’s version of a waiter being able to hold a bunch of plates. We get good at it because we have to do it a lot…

A lot of the buffers I make are made to serve as nice soothing baths for the proteins I’m working with – and just like you wouldn’t want to take a bath in lye (super basic (high pH)) or vinegar (super acidic (low pH)), you shouldn’t ask the proteins and other molecules you’re working with to do so! And you certainly shouldn’t expect them to act the same in those different conditions. Instead, you usually make up baths for them that resemble their native homes (like the inside of cells) but with minimum molecular “clutter.” While it’s easy to focus on the protein we put in the buffer and forget everything else, the buffer itself matters too! A lot! And it’s precisely because of its buffer-ness that we’re able to “ignore it.” 

Since I do a lot of protein purifications, I need to make a lot of buffers – and it’s not just for protein purifying that buffer-making is required. Basically (no pun intended (this time) – honestly!) every time you want to see how molecules act and interact, you have to make sure that they’re in an okay environment, and you want to make sure that environment stays consistent – especially if you’re trying to compare things. 

Just like (unless you’re looking for effects of temperature) you wouldn’t want to compare a reaction performed in a cold room to one performed at “room temp,” you don’t want to compare reaction performed at different pHs (unless that’s the only variable you’ve changed because you’re looking for effects of pH). Bottom line – don’t change anything you aren’t interested in – this is what we refer to as “controlling variables.” A variable we commonly control is pH, and we keep it in a narrow range using chemicals called “buffering agents.”

By acting as both an acid (proton-giver) and a base (proton-taker), buffering agents like Tris, sodium phosphate, HEPES, CHAPS, & MOPS, are able to maintain a steady pH so that we keep our molecules happy and don’t have to worry about fluctuations in how many “free” protons (H⁺) are floating around. That’s what pH is a measure of, acidity, which refers to how many free protons (H⁺) are hanging out in a solution. I say “free” but in reality most protons in a water-based (aqueous) solution quickly latch onto a water molecule to become a hydronium ion (H₃O⁺). An acid (in one definition) is something that donates proton(s) and a base (in one definition) is something that accepts protons. So the pH is a combination of the effects of all the acids &  bases present in a solution.

pH is an inverse log of the proton concentration: pH = log10(1/[H⁺]). Dividing by something bigger gives you something smaller, and all the log part does is make the numbers smaller and easier to deal with, so the more protons there are (the more acidic the solution) the lower the pH.  We call pH 7 “neutral” – above it (fewer protons) & we call a solution BASIC or ALKALINE – lower than 7 (so more protons) and we call it ACIDIC 

I like to think of a sort of “proton cookie jar” where the jar fullness corresponds to pH (fuller jar -> lower pH -> more acidic) & how full the jar is at any time depends on how many proton-givers (acids) & proton-takers (bases) there are. But that’s not all – it also depends on how “stingy” they are – how willing are to give or take? 

An acid is a molecule that *can* donate a proton (H⁺), but that doesn’t mean it always wants to…Instead of thinking in terms of acids *wanting* to get rid of H⁺, it sometimes helps to think of how reluctant they are to give them up. An acid’s willingness to give up H⁺ depends on its surrounding environment – how much “free” H⁺ is already out there. If there are plenty of H⁺ around, the acid’s desire to donate is low. BUT if there aren’t many H⁺ around, the acid “feels guilty” & donates 1 to help out. pKa is a measure of “how extreme” (i.e. basic/alkaline) conditions must be in order for an acid to give up its H⁺

Before we get into it, a quick note on notation. An acid can be anything that can donate a proton, so we often use “HA” as a generic shorthand for an acid and A⁻ as a generic shorthand for its deprotonated form. So HA -> H⁺ + A⁻. But this is reversible. A⁻ can now snatch up a proton to become HA again, H⁺ + A⁻ -> HA, and since proton-snatchers are called bases, we can call A⁻ the “conjugate base” of HA.

This HA/A⁻ notation is typically used for what are referred to as “weak acid/bases.” Theoretically, any acid/base reaction can go both ways, but some acid/bases are sooooo much happier in one form (i.e. a strong acid is way happier deprotonated and a strong base is way happier protonated) that protonation/deprotonation is virtually “irreversible.” Examples of such strong acids are: HCl (hydrochloric acid), HNO3 (nitric acid), and H2SO4 (sulfuric acid) and a couple strong bases are: NaOH (sodium hydroxide) and KOH (potassium hydroxide).

You might come across these in the lab in biochemistry, but when it comes to our bodies, we’re usually dealing with weak acids & bases, which can be in either their conjugate acid or conjugate base forms. And figuring out how much of which form is present means dealing with their pKa. 

⚠️ Don’t confuse pKa w/pH. pH is a measure of the *total* concentration of protons ([H⁺]) from *any* source. This includes:

  •  water itself: H₂O ⇌ H⁺ + OH⁻ check out this post for more on such “auto-ionization of water:” http://bit.ly/phacidbase
  • AND/OR acid(s)(HA) dissolved in it: HA ⇌ H⁺ + A⁻

⚠️ pKa & pH are different: pKa is a (constant) property of a *molecule* while pH is a (changeable) property of a *solution*

pH & pKa are different BUT directly related through the Henderson-Hasselbalch equation: pH = pKa + log[A⁻]/[HA]

pKa is the pH @ which 1/2 of the acid molecules have given up a H⁺

  • @ any pH higher than an acid’s pKa, a molecule of that acid is more likely to be deprotonated than protonated 
    •  the chances increase the further above pKa you are. For example, 1% deprotonated @ 2pH units below pKa & 99% deprotonated @ 2pH units above pKa.

Different acids have different “willingness thresholds”

  • STRONGER acids are more generous & have LOWER pKas –  even a slight deficit of H⁺ in surroundings & they’ll give 1 up
  • WEAKER acids are “greedier” – they have HIGHER pKas meaning they won’t give up H⁺ until there’s a big deficit

For example, say you have 3 acids: X w/pKa of 3, Y (pKa of 7), & Z (pKa of 9)

  •  at neutral pH (7), most of X will be deprotonated, 1/2 of Y, BUT almost none of Z
  •  But if we raise pH (so there’s fewer free H⁺ available) even stingy Z will give up its H⁺ 

If you want to know what proportion of an acid will be deprotonated ([A⁻]/[HA]) you can calculate that using a rearrangement of the Henderson-Hasselbalch equation (if you know the pH and the pKa)

pH = pKa + log[A⁻]/[HA]

[A⁻]/[HA] = antilog(pH-pKa)

when pH = pKa, you get a ratio of 1 (equal amounts of protonated form (conjugate acid) & deprotonated form (conjugate base)

when pH > pKa, [A⁻] > [HA]

when pH < pKa, [A⁻] < [HA]

You can plug in numbers to get values.

Some acids can give up  more than 1 H⁺. We call such acids “polyprotic.” So you have more than one pKa (1 per donatable H⁺). Usually they give up 1st much easier, so the “pKa1” will be much lower than “pKa2”

BUFFERS are weak acids that you use near their pKa, where you have almost even numbers of the acid & base forms at the point where they’re “on the fence” about giving or taking protons so they’re easy to “convince” with small changes in proton concentration.

You can adjust the pH the buffer keeps things at by adjusting how many protons are in the “proton jar” when you start the experiment – for sodium chloride (NaCl)(table salt)-containing buffers, you can lower pH by adding HCl or raise the pH by adding sodium hydroxide (NaOH)

But you can’t get too far from the buffer’s pKa and still get stabilization. That’d be like asking the cookie monster to give up a cookie when it doesn’t have any (too far above the pKa) or asking it to take one when it’s stuffed (too far below the pKa) – going back to Henderson-Hasselbalch, we can see that at 1 pH unit above pKa, we’re already at a 10-fold excess of base and when we’re 2 pH above pKa, that shoots up to 100-fold. 

Different buffering molecules have different buffering ranges. So your choice of buffering molecules depends in large part based on what pH you’re aiming for. You want to use a buffering molecule that has a pKa about where you want the pH to be because this means that about 1/2 the molecules will be available to give & half to take, so you have plenty of both.

For example, Tris has a pKa of 8.06 at 25C. So it’s good for things around there. This is the high end of physiological pH range (~6-8) ~7.4 is typically considered “standard” biological pH – this is below the pKa of Tris, Tris is slightly outside of its comfort range. But it’s cheap, easy to use, & often does the trick.

But buffering capacity alone isn’t the only thing to consider when selecting – the proton give/take-ing part is just a part of the molecule – you still have the whole rest of the molecule that proton is or isn’t attached to. And that “rest of the molecule” can do things too – some of which you might not want… So let’s look a little at a couple commonly-used buffers and their pro/con lists

When biochemists debate PBS & TBS, they’re probably not arguing about the TV channels – they’re talking about two common liquids we use for steadily mimicking biological conditions when we want to study things that come from cells while they’re outside of cells.

PBS stands for Phosphate-Buffered Saline & TBS stands for Tris-Buffered Saline. Saline’s just salt water and, as we now know (possibly in more detail than you’d wished to know) a buffer is something that keeps pH constant. So both PBS & TBS are pH-stabilized salt waters, they just use different stabilizers – phosphate in the case of PBS & Tris (Tris (Tris(hydroxymethyl)aminomethane)) in the case of TBS.

The “Tris” is for 3 as in 3 hydroxymethyl groups (hydroxy is -OH and methyl’s CH₃ – when you combine them you get CH2OH since C can only bind 4 things happily and one’s already taken by the carbon acting as the central “hub”

I said carbon can hold 4 things happily – the 4th in this case is an amine group (NH₂). In this form it can act as a base -> accept a proton to become NH₃⁺. Now this conjugate acid version is able to serve as an acid if the need arises (the proton jar runs low), returning it to its base form. And then, if more H’s become available (pH drops), the NH₂’s can act as bases to take protons “back” to raise the pH again

When preparing Tris buffers you want to make sure you read the label – are you using Tris base or Tris HCl (aka Trizma)? Tris HCl already has hydrochloride added to neutralize it. The difference biochemically is that, without adjustment, the pH of Tris-HCl will be lower. So if you want a lower pH, you won’t have to add as much HCl because they’ve already done that! Another practical difference is that they’ll have different formula weights so you need to take this into account when calculating how much to add to get different concentrations

In the Tris base form, Tris has a formula weight of 121.14 g/mol & a 50mM solution of it (unadjusted) has a pH of ~10.4. Tris-HCl has a formula weight of 157.6 g/mol & a 50mM solution of it (unadjusted) has a pH of ~4.7. So if you calculate based on the wrong one you’ll end up adding too much or too little.

These forms are basically at the extremes – so they won’t be useful as buffers as is – so you blend them (there are mixing tables to help) or adjust with HCl and/or NaOH. Problem with starting with the HCl form and “going up” is that you’re also adding sodium, so you’re adding more salt, increasing ionic strength and changing the salt concentration not just the pH, so it’s better to “go down”

Typically, what I’ll do when preparing Tris buffer is weigh out the amount of Tris base I need to get the desired molarity, and then I stick that in a beaker with a magnetic stir bar and fill it ~80% of the way full (e.g. if I’m making 1L I put it in a 1L beaker but only fill it to the 800mL line) with water. This gives me room to add HCl to adjust the pH until I get to the desired value without having to worry about “going over.” I add HCl drop-wise while stirring it with the stir bar and monitoring the pH with a pH meter. Once it settles on the right value, I pour the solution into a graduated cylinder (I hold a big stir bar on the bottom outside the beaker to keep the stir bar from falling in (learned the hard way). And then I adjust to the desired volume and filter it using a bottle-top vacuum filter. 

It’s convenient to make high concentration stock solutions (like 1M Tris at pH “X”) that you can then add to other solutions get to whatever final concentrations of it you want without having to weigh it out & adjust it over and over each time.

I love the podcast Science Friday, and they do this “Good Thing/Bad Thing” segment. A bad thing” about Tris is that the pH it maintains changes slightly with temperature. And this temperature dependence is a bigger problem for Tris than other buffers because Tris deprotonation has a high enthalpy – it requires more energy to overcome the attraction between the proton and the nitrogen its attached to. At lower temperatures, there’s less energy available, so molecules are less willing to give up their protons at lower temperatures and, as a result, the pH will increase at a lower temperature. So you want to adjust the pH to the value you want at the temperature you plan to use it at.

Another potential problem with Tris is that, because it has a primary amine, it can form Schiff bases with aldehydes & ketones – those sort of interactions are the basis of fixation/cross-linking reactions that use glutaraldehyde or formaldehyde to do things like attach things to lysine residues on proteins. So if you use Tris you’re kinda introducing “false targets”

Speaking of “false targets” – that other commonly-used buffer I mentioned, PBS has as its conjugate acid/base pair H₂PO₄ (dihydrogen phosphate & HPO₄³⁻ (monohydrogen phosphate). And that phosphate can trick things that are affected by phosphate. One place this can come into play is with Western blotting – where you look for specific proteins by probing a membrane with little proteins called antibodies that recognize specific parts of things you’re looking for.  Before we talked about cross-reaction from the antibodies you add (e.g. an antibody meant to recognize protein X also sticking to protein Y), but you can also get interference from the liquid you add them in.

You don’t want to use PBS if you’re going to use alkaline phosphatase detection – or anything that’s sensitive to phosphates (don’t want that P raising false alarms!). On the other hand, you don’t want to use TBS for anything that’s sensitive to amines because Tris is one!

Another con of PBS is that can also form complexes with metal ions, with a couple consequences – 1) it gives up protons to do this, making the solution more acidic & 2) the complexes can be insoluble and can hide them from enzymes that need them. For example, PBS can cause calcium to precipitate.

But don’t worry – if neither of these two will do, there are lots of buffering agent options – other common ones include HEPES, CHAPS, & MOPS. 

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉 http://bit.ly/2OllAB0

2 Thoughts on “pH buffers & the Henderson-Hasselbalch equation”

  • Loved the article! It made so much more sense than a lot of the other sources out there. I have a question regarding the use of the Henderson-Hasselbach equation: I noticed that you prefer to titrate Tris instead of using the amount calculated from the HH equation. Is there a reason for that? Can simply using the amount of acid calculated from the HH equation give a decent approximation of the desired pH?

    • Thanks! You can use HH to get a starting point if you want to go the mixing route. That can be good to get close – but then you’re going to have to adjust it anyways. It depends on the pH you want so if you’re close enough to one of the 2 forms’ pH it can be easier to start from just one.

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