I know that the Stoke's relationship gives the relationship I am looking for but that requires me to know the viscosity of the molecule in the solvent right? I don't know that. It is a large protein molecule. Can I make an estimate for its viscosity value?
In principle, the diffusion coefficient depends on the geometry of the object, and on the viscosity of the solvent. It does nor depend directly on the mass (except if you find a relation between mass and geometry). For large protein molecules you could do a coarse graining and represent the protein as several spheres linked, forming a chain. From that, you could estimate some kind of diffusion coefficient. The problem that I see is that a large protein molecule is usually bending in many ways, and the geometry is not always the same. From the non-experimental point of view, the simplest possibility that I can imagine (not so simple as you can see) is to simulate the protein and obtain, if it were exist, some sort of "averaged diffusion coefficient". Even doing that, it is very probable that you would need more quantities than a single diffusion coefficient to describe the thermal interaction of the protein. So I think that there is not a simple way to estimate the diffusion coefficient of a large protein molecule.
You need the viscosity of the medium/continuous phase at zero shear - not the viscosity of the protein. From a knowledge of the molecular mass and an assumed shape you can calculate a particle size. In the Stokes-Einstein equation, viscosity appears (as you know) but in dilute solution the actual viscosity of the continuous phase can be used as your input. This should give you the ball-park for the number you require. For a solvent molecule you could use the kinetic theory of gases for an estimate.
Ahh thank you so much! I was under the impression that in the equation it is the viscosity of the protein itself that is required rather than that of the medium. I will use the medium (in my case it is water so I should have readily available values) viscosity to get an estimate. Thank you once again!
Regards,
Appy
So I tried doing the calculation but it gives me a really strange number. Here are the parameters I used:
Equation: Diffusion Coefficient = (kT/3*mu)*(rho/6*pi^2*M)^1/3
(source: http://www.math.utah.edu/~keener/classes/math5120/homework/homework1.pdf)
Values Used:
k = 1.38x10^-23 m^2.kg.s^-2.K^-1
T = 298 K
rho = 1300 kg/m^3 (typical value for large molecular weight proteins)
viscosity of water = 0.001 N.s/m^2
Molecular Weight = 64,500 g (hemoglobin)
Using these values in the above eqn I get a DC of 8.7x10^-15 cm^2/s for hemoglobin whereas its actual DC has been calculated previously to be ~7.0x10^-7 cm^2/s. Is there something I am doing wrong?
Thanks,
Appy
First, check that your units are correct. You have meters mixed with cm....
I may find time to look at the equations from a different perspective, but can't promise.
Hi Dr. Rawle,
I can confirm my units are correct. I just reported that final answer in cm^2/s so as to compare with the published values in the literature. Thank you once again for looking into this.
Regards,
Apratim
Not sure how you're evaluating your calculation - perhaps some numerator and denominator issues? This is what I have:
- D = kT/6 π μ rh (Stokes-Einstein)
- For a molecular mass 64.5 kDa for a globular protein we expect a particle radius around 3.5 nm . Using 273K and SI units:
- Thus, D = 1.38E-23*273/[6π*10E-6*(3.5E-9)]
- This makes D ~ 5.7E-8 m2/s
And here's something else on diffusion:
August 13th, 2015 The importance of the measurement of diffusion in 2-phase systems
https://www.brainshark.com/malvern/vu?pi=65736585&b=1&tx=120486&c1=22
Thank you Dr. Rawle! I was making some mistakes with converting from the molecular weight to the effective size.
Regards,
Appy
Alan F Rawle in your calculation of D the viscosity of water you report in SI units should be on the order of E-4 not E-6 correct? The viscosity of water at 25C is 1 centipoise which is 10E-4 kg/m*s.
Thank you both for this discussion.
Nicholas Moringo
1 cP = 0.001 kg/m*s
I have 10E-6 above which is 1E-5
1 Pa s = 1 kg/(m s) = 1 (N s)/m2 = 10 P = 1000 cP
Yes, I've probably screwed up my units. After all this time I can't relate my thought process. Thanks for spotting!
Alan F Rawle yes I agree for unit conversions you have shown above. To correct the calculation you should use 10E-4 kg/m*s for the viscosity of water not 10E-6=10E-5.
A literature value (attached) for hemoglobin diffusion in solution is 3.4× 10−8 cm^2/sec and you are reporting something 4 orders of magnitude faster. It is just a units issue.
Thank you again for your input it helped guide this calculation for my current work.
Article The Diffusion Coefficient of Human Hemoglobin at High Concentrations
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