Diffusion = sedimentation at 1g?

[twall11347243]

At Earth's 1g, is the rate of diffusion equal to the rate of sedimentation for cellular molecules (or proteins)? The diffusion rate is higher, correct?

Thanks.

 

[Omega0]

I would love to answer this question more quailified but from my gutt feeling: If you drop fluid on a ground it will sink into the ground by gravitation first, depending on what the ground is made of. It definitely depends from the ground. If you have glas it might take forever for diffusion. If you have a sandy beach it takes not much time if you shed liquid there but this again depends from the ground. It additionnaly depends on chemical reactions...

Could you reformulate your question more presicely?

 

[twall11347243]

I'm wondering if you look inside the cell at any given molecule (say an enzyme that's in the cytosol of the cell) - is the diffusion rate for that molecule higher than its sedimentation rate? Are molecules in our cells sedimenting at the same rate as they diffuse around?

If they do... that's called sedimentation equilibrium (or isothermal settling). This is what happens in the atmosphere and is why more molecules are closer towards the ground even though they're not sedimenting all they way (due to the balance in diffusion) - however this creates what's called a 'barometric distribution' where the density in molecules decreases exponentially as you get higher and higher into the atmosphere.

Ultimately, I'm wondering if this distribution happen inside our cells? Are there more molecules located towards the 'bottom' of our cells? This doesn't make any sense to me but I think this is true (see attached screen shots). I thought solutions (such as the cytosol in the cell with its proteins, DNA, etc) were homogenous? Having less molecules at the top of cell is not a homogenous solution, is it? And wouldn't this affect cellular processes in a bad way?

 

[mfb]

What is the density of the particles discussed there? Organic molecules have a density that is not so completely different from water. It is certainly possible to find their typical scale height.

 

[twall11347243]

They don't say the densities. I'm trying to figure out is what they're trying to tell me is that everything (all atoms, molecules) in the air or water or cytosol of the cell undergoing this 'isothermal settling' or sedimentation equilibrium... where it creates this barometric distribution of more at bottom than top?

Doesn't that directly contradict the definition of a solution? A true solution is homogenous throughout. I mean, if more dissolved solute particles are concentrated progressively towards the bottom of a solvent... how is that homogenous? And I want to know if this happens in our cells with various organic molecules like enzymes and RNA and ribosomes (small solutes that shouldn't be affected by gravity whatsoever, regardless of their density due to their small size and being soluble). I mean, are their literally more transcription factors concentrated towards the 'bottom' of the nucleus than the top? Surely I'm missing something here, because that seems like it would cause problems.

The definition of this isothermal settling/sedimentation equilibrium is that the sedimentation rate is in equilibrium with the diffusion rate... (not sure if this means they are the same value) hence my original question.

 

[mfb]

They don't say the densities. I'm trying to figure out is what they're trying to tell me is that everything (all atoms, molecules) in the air or water or cytosol of the cell undergoing this 'isothermal settling' or sedimentation equilibrium... where it creates this barometric distribution of more at bottom than top?

If there is nothing else influencing the position (and usually there is), and if the object is denser than water, sure.

A true solution is homogenous throughout.

Why should it?

I would expect the effect to be tiny even for large molecules, and negligible compared to other processes in a cell (e.g. places where the molecules are produced and destroyed, active transport mechanisms and soon).

 

[twall11347243]

So let's say that in a 100 um cell (diameter of your typical muscle cell) there is a gradient where there is 10% less enzymes at the 'top' of this cell compared to the bottom.. due to this isothermal settling. You don' think this would affect cellular processes?

What about intercellular transport between the synapse? Is the influence of gravity strong enough to 'pull' molecules down slightly as they diffuse across to the degree that it negatively affects cellular communication?

Thank you for the advice too.

 

[mfb]

I don't expect a 10% concentration difference, and I don't see calculations that would suggest this.

 

[twall11347243]

Okay, I'm sorry. I just did a calculation now, (see my file #1) So according to the formula

Lg is the length by which the density decreases by 37%. And let's use a massive particle (say 1,000 kDa).

Lg = KbT/mg

(1.38 x 10^-23) x (310 Kelvin for body temperature) / (1.66 x 10^-21) x (9.8) = 0.262970 meters ... or 262,970 um. (over this length the density would decrease by 37%).

It's an exponential curve but at this length I think I could treat this as pretty much linear for the first part of the curve - in order to figure out what % it decreases at say 100um.

262,970 um / 37% = 7107um (this would be the length for 1% density decrease)

7101um / 100 = 71um (length for 0.01% density decrease or 1/10,000) ... so for a 71um cell there is 0.01% less at the top then there is at the bottom. And this shouldn't be enough to affect anything in a deleterious way. Would you agree with this?

So basically, the strength of Earth's gravity on intracellular position or scale height is negligible.. would you agree with that? So all in all I need to quit worrying about the 'influence' of Earth's gravitational strength on cellular processes. These kinds of questions are the crap that's been bothering me.

 

[twall11347243]

But when Perrin did these calculations... he was dealing with colloids (grains) that are insoluble in water. But I'm talking about molecules that are dissolved in the cytosol forming a solution. This should create even more homogeneity (as far as density distribution at the top vs. bottom) because they are dissolved and can interact with the water molecules to diffuse around even more vigorously, in contrast to what that formula accounts for. Basically, I don't think that formula is accounting for small molecules that are dissolved in a liquid (I think it has to do with gas particles in the atmosphere or insoluble colloidal particles), correct?

So, the density change would actually be even less than what I calculated... it's virtually 100% top versus bottom?

Thanks.

 

[mfb]

Lg = KbT/mg

I think that assumes the surrounding medium is a gas and doesn't take up volume. The actual effect should be even smaller.

 

[twall11347243]

I attached a few pics. Can someone tell me, if this 'isothermal settling' happens even for very small molecules (say proteins inside the cell) at normal gravity?

Something that small's thermal energy (KT) would be >>> much greater than it's gravitational potential energy (mgh) so it should never reach sedimentation equilibrium.

Or, since technically our cells are isothermal (our cells do maintain a constant temperature) does this mean that for even the smallest molecules, they will be subject to 'isothermal settling' and thus display a concentration distribution?

 

[mfb]

Something that small's thermal energy (KT) would be >>> much greater than it's gravitational potential energy (mgh) so it should never reach sedimentation equilibrium.

It does (in the absence of active transport, production or destruction mechanisms), but the equilibrium is a nearly homogeneous distribution.
1MDa * 10 µm * g = 1µeV, and 1GDa * 10µm * g = 1 meV, still significantly below the thermal energy - and that does not even take buoyancy into account.

 

[twall11347243]

It should not. In your example, for the 10MDa it's thermal energy is significantly greater than its gravitational PE. Thus, rate of diffusion >>> rate of sedimentation.
The definition of sedimentation equilibrium is that thermal energy = gravitational PE (and diffusion rate = sedimentation rate).

How can at one point in time a molecule's TE >>> GPE and then later TE=GPE. You don't just lose thermal energy and diffusion over time.

However, I am confused, because there are experiments where sedimentation can happen once GPE gets within 200-fold of TE. I don't understand even if it's close it's still should sediment to the point of achieving equilibrium. Diffusion should still be dominate enough to oppose and be greater.

 

[mfb]

The definition of sedimentation equilibrium is that thermal energy = gravitational PE (and diffusion rate = sedimentation rate).

That is an odd definition if potential energy is limited.

 

[twall11347243]

See attached.

 

[twall11347243]

I'm really not sure about TE = GPE... there's other factors like a 'Peclet number'... it's all really confusing.

I am sure that diffusion = sedimentation at equilibrium, and that at equilibrium all the particles have the same kinetic energy and are in arrested state, not moving. But if diffusion is proportional to KT and sedimentation is proportional to GPE then KT=PE when diffusion = sedimentation, right?

 

[twall11347243]

The peclet number is a ratio: gravitational potential energy/thermal energy
Isothermal settling is done in situations where the peclet number is small (less than 0.1) (see attached) - which means that KT > mgh ... so how can you get isothermal settling (aka sedimentation equilibrium) if KT > mgh ... because at equilibrium diffusion = sedimentation (but yet KT is greater?)

 

[mfb]

That is getting a matter of definitions, and I think those discussions are pointless.
"A is called QKAH" - "no, we should call it GJEJW!".

 

[twall11347243]

I appreciate your help. Thank you, Could you take a shot at interpreting this for me? See attached.

I think it's saying that for a 1MDa protein who falls so slowly that you would never see the gradient in a realistic amount of time. But then that's why they started using shorter columns such as 1mm - to reduce the time needed to see the gradient. It mentions:

"However the gradients thus obtained, can only be detected if the dispersed particles are large (> 1um), due to 'analytical limitations'."

It implies that for the 1MDa reducing the column size down to 1mm WOULD EVENTUALLY get you a gradient, it would just still take a long time to see it, due to 'analytical limitatations'? But as we've said, the PE for that is so small compared to the thermal energy it shouldn't EVER settle enough to give the gradient of barometric/isothermal distribution. IDK, how do you interpret that

 

[mfb]

Larger particles are heavier and lead to larger gradients, maybe that's the analytical limitation. Also, 1µm particles scatter light nicely, which helps measuring their concentration.

Ultracentrifuges easily reach accelerations of 10^5 g over a range of centimeters, where many molecules will get a notable concentration gradient.

 

[twall11347243]

So the 1MDa will give a gradient eventually even at 1g? It's just so small we can't detect it? Or is it saying that because it under 1um it settles so slowly we can't detect the gradient because there is no gradient. The context of this excerpt is talking about 1g. It's not talking about in an ultracentrifuge.

 

[twall11347243]

I am confused on how this whole 'isothermal settling' process is even possible in the cell. I attached a screeshot, of a published work saying that isothermal settling is possible effect within the cell. It's condition is that the temperature T does not change over the height of a group of particles, such that the average KT is then the same for all particles at all heights. UHhh what about exothermic, endothermic reactions... that releases heat and absorbs heat - the cell overall may not change in overall temperature, but within at the molecular scale, heat is being released/absorbed all the time and thus local temperture fluctuations happen everywhere.

 

[twall11347243]

Plus the defintion is that once at equilibrium, there is no net mass transfer, no net transfer of chemical potential energy... we wouldn't be able to sustain life under these conditions. But, I'm confused because then why is the paper EVEN TALKING ABOUT THIS in the mammalian cell?

The link (google preview) https://books.google.com/books?id=YbSw-MdA4WYC&printsec=frontcover#v=onepage&q=isothermal&f=false

 

[mfb]

So the 1MDa will give a gradient eventually even at 1g? It's just so small we can't detect it? Or is it saying that because it under 1um it settles so slowly we can't detect the gradient because there is no gradient. The context of this excerpt is talking about 1g. It's not talking about in an ultracentrifuge.

Everything will give a non-zero gradient if you wait long enough. Even oxygen and nitrogen in the atmosphere would have a tiny gradient if we would switch off wind completely.
That does not mean it is relevant. The gravitational force of Pluto on us is non-zero as well, but completely irrelevant, for example.

Living cells are never in equilibrium (that is one of the key points of life), which makes this hypothetical situation even more pointless.

 

[twall11347243]

Everything will give a non-zero gradient if you wait long enough. Even oxygen and nitrogen in the atmosphere would have a tiny gradient if we would switch off wind completely.
That does not mean it is relevant. The gravitational force of Pluto on us is non-zero as well, but completely irrelevant, for example.

Living cells are never in equilibrium (that is one of the key points of life), which makes this hypothetical situation even more pointless.

Right, we are not isothermal at the molecular scale hence endothermic and exothermic reactions, and there are other processes to prevent the equilibrium for ever happening but then why does the paper say it can affect cells? I don't understand why it's evening mentioning it- it makes me think that we are in isothermal equilibrium.