First you can just use the DLS to measure exactly what is the diameter of your globular particle, its a very easy measurement and takes a few minutes to do. Secondly, there are equations to do the conversion but you have to remember it depends on many parameters such as the type of particle (polymers, proteins etc.), shape (most important, since you wrote globular than its easier since most equations are for spherical), solvent interaction and temperature and viscosity. I would say that the best fit for skin studies which involves usually proteins this would be the best correlation for you (spherical proteins):

Rmin=0.066M^(1/3)

M in Dalton; Rmin in nm

I also attached an article you might find useful (contains the above formula too).

Hope this helps.

Roni

Dear Roni,

I used to read that article, and I found it to be very useful in my area of research (nanoparticle for protein-based drug delivery). And instead of using the formula I used the table (table I) to get the rough estimate regarding my protein's size compared to the nanoparticle size. And after you mentioned the formula, I give it a shot, and I found it to be incorrect (or perhaps I calculate it in the wrong way).

For example, for Bovine Serum Albumin, which is around 60s kDa, and I know that the size is around 7nm x 5 nm x 5 nm, and it is somewhat go together with the table (Rmin slightly larger than 2.4 nm), but when I try and calculate with the formula in the article:

Rmin = (60,000 * 0.066)^1/3

Rmin = 15.82 nm

I've got a completely different result than the one in the table, but there's something more interesting. I tried to cube root it again and the result is pretty much correct:

15.82^1/3 = 2.51

Am I doing it wrong Roni?

Radif

Update (5 hours later):

My apology, I'm doing it wrong, M supposed to be cube rooted before multiplying it by 0.066, not multiplying M by 0.066 then cube root it.

Thank you, the calculations are giving 9.2 nm for 12 KDa MWCO dialysis membrane. My particles are around 300 nm. So what size DM (Dialysis membrane) should I use for these size particles?

Hi Shreya, as stated above, I believe that the formula is incorrect. And now I am more convinced since your result is obviously incorrect too (because I remember that IgG with molecular weight 150 kDa has the length of 10 nm, means the mean radius should be around 4-5). Check Table I from the article shared by Roni.

Actually the MWCO choice for dialysis membrane is depends on what you're trying to separate, if it is just to purify the nanoparticle from small molecule (salt, buffer, etc) then I think it is fine to use the dialysis membrane with 12 kDa MWCO. I used to be using 3.5 kDa MWCO to separate the acetic buffer from nanoparticle (my nanoparticle size distribution was between 180-260 nm).

Thank you Radifar. I was planning to use the dialysis membrane as a model for skin diffusion experiment of my 300 nm drug loaded particles and I have 12 KDa membrane only with me. I guess it'll be too small and should use bigger MWCO DM or actual skin for the experiment. 

I remember my friend was doing transdermal transport study, and he is using vertical diffusion cell with rat skin. But I'm wondering if it will suit your need, since I've never seen it being used for studying the transport of nanoparticle. Maybe you need some more literature study regarding the transdermal transport of nanoparticle.

I'm using DM for purifying quantum dots. I used DM with MWCO at 8-10 KDa, which is 1-2 nm based on a correlation attached below between Dalton to diameter(I suppose).

Empirically,it is probably right but I still need to further prove it. 

http://www-user.uni-bremen.de/koelling/dalton.html

Muhammad the formula is correct. The way you are using it is wrong.

1 Kilo=6.0221366568E+23 kilodalton (kDa)=1.0E+12 nanogram

Dear shreya

nm is for length and Dalton is for WT

so the formula ,  i think can work as estimation in exact fixed density .

"For example, the aquaporin 3 channel has a pore width of 8-10 Ångströms and allows the passage of hydrophilic molecules ranging between 150-200 Da"

(From-- https://en.wikipedia.org/wiki/Aquaporin)

This statement doesn't fit into Rmin=0.066M^(1/3) as well. 

This equation probably only applies to protein. 

I am working on nanocarrier and is wondering what equation can be used to relate MW to the size? Anyone has any idea?

Dear all,

The formula I have mentioned before regards a globular protein if it is in a different shape (sometimes due to different pH) then the formula won't work. This formula won't work (in my opinion and based on other projects I tried using this formula) for polymers. Polymers shape varies by the nature of the solvent (whether it is a "good/bad" solvent or teta solvent). For polymers try this paper (attached) for size estimation Mark Hawkonian or Flory-Fox. The article attached found specific correlation for different polymers, for example for PS the correlation is:

Rg(nm)=0.0138(M)^0.59

and for PS4M the power is 0.58 and the coefficient is 0.0118. In general the prediction I believe with power of 0.6. The solvent affects this correlation too, this is for TCB or teta solvent I believe. Hope this help.

Roni

How will I manipulate the equation when I have to measure silica nanoparticles of size 20 nm diameter?

hi

i wanna to know is it useful for niosome or not?

Refat, I'm sorry but silica has the same Mw so I fail to understand why do you need this equation. Sahar, same for you, this equation is to switch from Mw to size. since you already know your size just use any filter with that cut-off. Usually the suppliers will provide you with data about the size and Mw correlation they have.

Though they are different I would still use the same equation as for proteins.

Ranthi, what is the purpose of your question? the equations are merely estimations under specific conditions. If you are trying to figure out which MWCO you need in order to do that then translate the MWCO to size, usually they are meant for purifying proteins.

Well sizes you already have....did you make NPs of the polysacharides or are you purifying these sacharides?

Dear Magela,

The Mw is in Da not kDa as you you used it. it needs to be (500,000)^(1/3). Hope this helps.

I recommend Aharon's answer

Best Regards

Aharon already gave a nice answer, I am adding the following as an additional support:

1. density = mass*volume (Equation 1)

2. oftentimes, protein density is ~1.35 g/cm^3 (assumption 1)

3. since we assumed the protein to be globular, volume = 4/3*pi*r^3 (assumption 2)

4. substitute the assumptions into eqn 1 and rearrange, we have:

r = (0.066)*(mass)^(1/3) (Equation 2)

where r is the radius of the protein in nanometer, and the input (mass) is in the unit of dalton (g/mol).

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To see how well Equation 2 work, let’s look at the following proteins:

Example 1

IgG: 150 kDa in molecular weight, shape like a “Y, with the each Fab (the upper arm) portion 8.9 nm in length and the Fc (the stem at the bottom) portion 7.7 nm in length. The “thickness of the “Y” is ~ 4 nm [Ref 1].

r = (0.066)*(150,000)^(1/3)

r = 3.51 nm. Base on Equation 2, IgG is roughly a sphere with a diameter of 7.02 nm, which is actually pretty close to its real physical size).

Example 2

BSA: 66 kDa in molecular weight, with a Stokes radius of ~ 3.57 nm according to [Ref 2].

r = (0.066)*(150,000)^(1/3)

r = 2.69 nm, which is kind of close to the Stokes radius (note: Stokes radius is not the close to but not necessarily equal to the physical size of the radius).

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Ref 1: Pease III, L. F., Elliott, J. T., Tsai, D. H., Zachariah, M. R., & Tarlov, M. J. (2008). Determination of protein aggregation with differential mobility analysis: application to IgG antibody. Biotechnology and bioengineering, 101(6), 1214-1222.

Ref 2: Axelsson, I. (1978). Characterization of proteins and other macromolecules by agarose gel chromatography. Journal of Chromatography A, 152(1), 21-32.

You can check both of these links in which show the approximate conversion between MWCOs and Dialysis Tubes Pore size:

https://www.sedgeochem.uni-bremen.de/dalton.html

and for the following link, go to the page P.7/17 for conversion Dalton to Microns:

http://www.interchim.fr/ft/D/Dialya.pdf

Following

kDa is an unit of molecular size, while, Microns is an unit of distance or in other words molecular diameter. Simply, a solution containing 2 or 100 molecules or two elements A ,B with MW 2 KDA,100 KDA, respectively can have the same size in microns but MW may vary though. One cannot arrive at a direct relationship between kDa and Microns. Always get your membranes from manufacturers who are willing to divulge pore size in microns instead of just kDa