Brownian motion isn’t about Brownie Scouts going around trying to sell Girl Scout cookies, but just like the Brownies might leave a meeting where there’s a bunch of them & end up spread out evenly over town even if they don’t have an explicit strategy starting out (they’re young -and I was a Brownie back in the day – so no judgment here!) – molecules move about randomly through “Brownian motion” with the end result that you get a net flow of molecules from areas of high concentration to areas of low concentration until all the areas have equal amounts. At this point, the molecules still move around, but there’s no net movement because for every molecule going left one’s going right. We call this process DIFFUSION and it need not cause confusion! (But waiting for it to de-dye your gel may cause boredom….)
For those unfamiliar with the Girl Scouting system, Brownies are one of the younger age groups of Girl Scouts and they, like all the age groups, sell cookies to raise money to do cool fun and educational activities. Imagine you had a big conference of Brownie scouts, so you have a ton of Brownies in a small space (a high Brownie concentration). And then the conference ends, doors open, & the Brownies spill out to go try to sell cookies. They don’t have any strategy (and for the sake of the analogy pretend that they’re not even trying to sell cookies), they just go one way until they bump into something (or someone) and get deflected to go another way.
If they go to a crowded place, they’ll get bounced away but if they go to a less crowded place, they can travel further without bouncing. As a result, the Brownies get evenly spread out. Once an even spread is reached, the Brownies still move around (they’re still high-energy kids!) but they’re just as likely to run into another Brownie no matter where they go so all their random motions cancel each other out and you get no net movement.
If there’s a bigger area to spread out into, it will take them longer, because it’s hard to get to the boondocks, especially when you keep getting “bumped off course” on the way but if they have more energy (maybe they’re nibbling their ware along the way…), the spreading out will happen more quickly.
This might seem like a really bizarre analogy, but it came to me as I was thinking about Brownian motion while impatiently relying on diffusion to de-stain my SDS-PAGE gel (more on this later), which relies on this Brownie-like stuff happening on a much much smaller scale – molecules moving instead of Girl Scouts.
Molecules constantly move around randomly, but they can’t move through other molecules (that’d be like walking through really tiny walls). So they start going one way, and move that way until they collide w/another molecule which deflects them so they change course (like in ping pong or pinball). This eventually leads to molecules spreading out evenly.
This phenomenon whereby molecules move around randomly and get bumped around by each other wasn’t named after the Girl Scouts (shocker, right?!). Instead, “Brownian motion” gets its name from a botanist, Robert Brown who, in 1827, looked at pollen “swimming” under a microscope because they were getting moved around by water molecules banging into it.
Why move in the first place? Molecules like to move about randomly, so if they *can* they will – this which is where we get that whole 2nd law of thermodynamics from (nature tends towards increasing entropy). “Entropy” refers to “randomness” or “disorder” – I like to think of it as freedom – if molecules have more freedom to act independently and move at will, they will, and the end result of this molecular anarchy that occurs when you let them be might look random or disorderly.
But random movements at the individual molecule level can lead to “non-random” large-scale effects. Like when you stick a drop of food coloring on one spot on a glass of water and the coloring travels all the way down to the bottom.
So we often talk about diffusion as molecules moving from ⬆️ to ⬇️ concentration to “even things out” BUT, although this even-ing *is* the end result we see, the molecules aren’t really “trying” to do this just like prehistoric fish weren’t “trying” to grow legs. It’s just that randomness can provide variety needed to find optimalness. And for molecules, optimal ness often means high entropy (freedom to move freely without distraction)
In DIFFUSION, molecules move about randomly but keep running into other molecules, causing them to change course (like pong) 🏓. The more other molecules around (more crowded the solution) the more it will get deflected 🏓🏓 BUT if there are fewer molecules, it can travel further interruption-free. So when molecules happen to be traveling in a less-crowded direction they can go further in that direction & if they try to travel into a crowded area they get bounced back to a less crowded area. So you end up w/a NET MOVEMENT towards less crowded place.
But then those get crowded too, so there’s less difference. The molecules get bumped around the same amount anywhere so they get evenly spread out. They reach a DYNAMIC EQUILIBRIUM where molecules are still moving but there’s no NET movement
If you have a lot of other molecules you can bump into, you’ll get deflected more, so the bigger the difference in concentrations between the high and low concentration areas, the “steeper the concentration gradient.” You can think of this gradient like a see-saw ramp with ⬆️ concentration area at the top & low concentration area at the bottom. The steeper the ramp (bigger the conc difference), the faster molecules will move ⬇️ it.
You can think of piles of molecules “propping up” the ends of the ramp – more molecules means higher ramp. But as molecules move to the other side the piles get smaller, so the ramp gets less steep, and eventually you reach a point at which conc are = on both sides – the ramp is level – this is called EQUILIBRIUM and I spent a lot of today fighting it…
And although I’m gonna talk about manipulating diffusion for geeky things like getting dye into and out of my gel, diffusion isn’t just some obscure labby thing – it happens all around us all the time – from food coloring or flavor drops spreading out in your water to pollution from factory smokestacks spreading through the air.
I spent a lot of time this morning at the gel rocker, staining and de-staining an SDS-PAGE gel. SDS-PAGE is a method we use to separate proteins by size by unfolding them, coating them with a negatively-charged detergent (SDS) & using a + charge to motivate them to travel through a gel mesh made of PolyAcrylamide that slows them down along the way (with bigger proteins getting slowed more)
The proteins are invisible to us, but we can use various staining methods to visualize them. But for the stains to work they have to get to the proteins trapped in your gel. So you put the gel in a little “bath” (liquid in a gel staining box) and then let diffusion step in to get the dye to sites of protein in our gel and then let diffusion get the unbound dye out. So 1 end of the see-saw is in the pores of the gel & the other end is in the surrounding bath.
When I pour on the dye, the concentration of it is really high outside the gel and 0 inside, so the dye molecules (thanks to random motion) will have a a NET movement from areas of ⬆️ concentration (stain) to areas of ⬇️ concentration (gel’s pores). This journey “down the concentration gradient” will continue until there are = amounts of dye inside & outside gel. Once this EQUILIBRIUM is reached, molecules will continue moving about randomly so some will go into gel ⤵️ & some will go out ⤴️ BUT there won’t be any NET movement (FLUX)
To make the dye move out we need ⬇️ concentrations outside gel 👉 simply swap out stain solution for water ⏩ dye moves out of gel until a new equilibrium is reached (@ ⬇️ concentrations) ⏩ repeat 🔂 until there’s practically no dye in the gel
We *could* just pour on stain, let it sit, & it’d eventually reach equilibrium BUT could take a long time (and if you really wanted to, you could use Fick’s laws to calculate how long…
FLUX, more specifically, FLUX DENSITY (sometimes called J) is the net movement of molecules over a specific area over a specific time
We can describe J numerically using something called FICK’s 1st LAW: J = -D(Δc/Δdx)
🔹 ΔC/Δdx (if you want to get calculus-y, dC/dx) is how “steep” concentration (C) gradient is. Δ is pronounced “delta” and it means change in. So this ratio looks at the change in concentration over a change in distance (x) (how steep is our see-saw?)
🔹🔹 the ➖ in the equation is there because the movement’s opposite gradient direction
🔸D is DIFFUSION COEFFICIENT (DIFFUSIVITY). It takes into account how big the molecules are, how viscous (syrupy) the fluid they’re moving through is & TEMPERATURE
You can ⬆️ flux by ⬆️ steepness (using higher concentration of stain) &/OR heating it (which is one reason why you might see a microwave in a biochemistry lab). Heating gives molecules more energy, so can “shake off” interactions w/other molecules that are holding them back, & molecules all move faster so they can “get out of the way.” So you’ll get to equilibrium faster, ⚠️ make sure stain (& box) are “microwave-safe” & won’t let off toxic fumes or melt ☠️
If you’re wondering about Fick’s 2nd law, it tells you how fast concentration’s changing @ any point & time, so you can calculate how long it’ll take for molecules to diffuse a distance. The time needed to diffuse increases w/square of distance, so it takes 100X as long to travel 10X as far. (Remember that this see-saw we’re imagining is in 3D so it gets “taller” in all directions)
Thankfully DIFFUSION is just 1 contributor to MASS TRANSPORT ( movement of “stuff” from 1 place to another). DIFFUSION occurs on the small scale & is due to RANDOM motion of INDIVIDUAL molecules. But we can help dye out by manually adding another type of mass transport, CONVECTION. Convection is bulk fluid motion – it involves movement of ALL molecules such as you get by mixing, shaking, etc.
Think about putting a drop of food coloring in water – it’ll eventually spread out evenly thru diffusion, but you can speed it up by stirring (add CONVECTION). For some things, we use magnetic stir bars to help us out on with convection. We drop one of these little magnets into our beaker and, stick it on a magnetic stir plate. The stir plate makes the magnet spin, which leads to convection. We can’t really use a stir bar with our gel (talk about ripping danger!). Instead of stirring We use a rocking platform to keep gel agitating while we stain it. Because we’re controlling the movement with the platform, it has non-random direction. We help direct dye into gel -> get it close to the protein & then diffusion takes it the last stretch, letting it move in all directions so it reaches everywhere protein could be hiding.
We put our platform through a LOT of wear & tear – it had to get some “WD-40-ing” from equipment services a while back because it started making super loud screeches. Shaker’s fixed now, but our hot dog roller died 🙁 so we’ve been making do with an orbital shaker platform and this end-over-end rotator (the marshmallow roaster one) until the new “hot dog one” comes in. RIP roller. You were always so good to me.
I’m currently rotating a tube with a protein I’m purifying with another protein that’s cutting off the affinity tag/fusion protein combo (Strep-Sumo) that I used for the first purification step. In this case all the molecules are free to move anywhere – but this isn’t always the case. Like in my gel – the proteins can’t move because I’ve “fixed” the gel by getting the proteins to aggregate (clump up) inside the gel mesh so they can’t wriggle free – but the little things, like the water and salts and dye molecules can get through. The gel is “permeable” to the dye but not to our clumped protein.
This is similar to the situation we have in dialysis – but in that case we let the proteins keep swimming, but in a membrane pouch that acts kinda like a shark cage that only small things can get through (penetrate) – a semipermeable membrane. The BASIC CONCEPT 👉 put protein in membrane pouch ⏩ put pouch in big bath that doesn’t have that thing we’re trying to get rid of (we call this bath liquid the DIALYSATE) ⏩ If membrane’s permeable to that thing it’ll leave pouch & enter bath 🛁 but our protein can’t get through the membrane, so will stay put
When it’s WATER diffusing, NOT what’s dissolved in it (solutes), we call it OSMOSIS 👉 diffusion of water thru a semipermeable barrier (only some things can get through (penetrate)) to balance out overall concentrations of “stuff” (solutes) on either side ⚖️
and speaking of moving all over the place sorry today’s post is kinda all over the place!