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normal Diffusion Coefficients and Effective Time

  • ram74656
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8 years 4 months ago #5316 by ram74656
Diffusion Coefficients and Effective Time was created by ram74656
I'm currently doing a simulation of coarse-grained peptides in nonpolarizable water at 298 K/1 atm, and repeated measurements of the diffusion coefficients get me a diffusion coefficient of ~5X bigger for the atomistic than the coarse-grained system for a system that is mostly water (a single peptide in a box). I'm using gromacs g_msd to extract the mean-square-displacements and then inspecting the results by hand, so I believe I'm approximately in the linear regime. Does anyone have any idea why this might be happening? I can't find much in the literature on actual data of calculations of effective time, and I'm getting pretty confused.

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8 years 4 months ago #5318 by jbarnoud
Replied by jbarnoud on topic Diffusion Coefficients and Effective Time
It is expected to have diffusion coefficient 2 to 10 times larger with CG simulations than atomistic ones. This is due to the smoother energy landscape and the lack of friction in CG simulations. See Marrink et al. (2007) for more details.

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8 years 4 months ago #5319 by ram74656
Replied by ram74656 on topic Diffusion Coefficients and Effective Time
I understand that; however, my atomistic diffusion coefficient is about five times larger than my coarse-grained one. Surely it ought to be the other way around?

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8 years 4 months ago #5320 by jbarnoud
Replied by jbarnoud on topic Diffusion Coefficients and Effective Time
I am sorry, I misread your message. What diffusion coefficient are you calculating? Water in water or peptide in water? Anyway, what diffusion coefficient do you get in the atomistic case for the water? It should be around 2 to 3e10-19 m2s-1. Finally, did you try to be more stringent in what you consider the linear regime of the MSD?

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8 years 4 months ago #5321 by ram74656
Replied by ram74656 on topic Diffusion Coefficients and Effective Time
Okay, just to check, I ran a 100 ps simulation of a 7x7x7 nm water box in atomistic and in coarse-grained. Running g_msd from Gromacs on the whole system and looking at the msd.xvg output to make sure I'm fitting to the linear region, I get a diffusion coefficient of 5.8648 * 10^-5 cm^2/s for atomistic, versus a diffusion coefficient of 1.9116 * 10^-5 cm^2/s for Martini non-polar water, which seems pretty much exactly backward to me.

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8 years 4 months ago #5322 by mnmelo
Replied by mnmelo on topic Diffusion Coefficients and Effective Time
Hi,

The comparison of Martini vs atomistic diffusions takes into account that each Martini bead corresponds to 4 waters. The comparison then dictates that CG diffusion be multiplied by 4, as that'll be the relation between the individual diffusion rate of each of four water molecules and their center-of-mass (see J. Phys. Chem. B 2004, 108, 750-760 ).

Whether this scaling is the most realistic way to compare diffusions is probably subjective, but the reported CG speedup is relative to that. In your case you'll be comparing 5.9*10^-5 cm^2/s (AA) to 7.6*10^-5 cm^2/s (CG). There's your CG speedup. Also note that the experimental value for water self-diffusion is 2.13*10^-5 cm^2/s, and the CG speedup is greater (almost 4x) compared to that.

As you can also tell, the choice of AA water model (and probably electrostatic treatment) will likely play a role. Your water self-diffusion is probably a bit too high (I get 3.9*10^-5 cm^2/s at 300K with SPC, at a constant volume corresponding to the average density).

Manel

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8 years 4 months ago #5323 by ram74656
Replied by ram74656 on topic Diffusion Coefficients and Effective Time
That makes MUCH more sense! Thank you for the clarification.

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7 years 8 months ago #5768 by nilusha
Replied by nilusha on topic Diffusion Coefficients and Effective Time
Hello,

I also have calculated the self diffusion constant of CG water in polypeptide system and got 8 x 10-5 cm2/s after multiplying by four. According to the 'J. Phys. Chem. B 2004, 108, 750-760' paper self diffusion of CG water is
2 x 10-5 cm2/s after multiplying by four. So do you think it is okay to have four times fast self diffusion constant for water in a polypeptide system?

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7 years 8 months ago #5779 by Pim
Replied by Pim on topic Diffusion Coefficients and Effective Time
In short: yes. Just to avoid confusion though: this means that your water is diffusing at roughly the same speed in the peptide system as in pure water. Your results are in line with what is discussed above. Both polarisable and normal coarse grain water give you a diffusion constant of roughly 2 x 10-5 cm2/s from g_msd, which would fit nicely to the experimental data. However, if you take into account that the CG dynamics are inherently faster, you multiply this value by four and you could argue you make the agreement worse and the model is not 100% fantastic. This is life. The way it's written in the paper is confusing (see post by mnmelo).

FYI: I recently performed simulations of sticky polypeptides at concentrations up to ~30 weight% in water, and I find that the diffusion of water drops to about 0.8 x 10-5 cm2/s (not multiplied by anything). This is the range you could expect at high peptide concentration.

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7 years 8 months ago - 7 years 7 months ago #5781 by ploetz
Replied by ploetz on topic Diffusion Coefficients and Effective Time
Hi,
Sorry, but I am confused by this thread! Can you help me understand how both ram74656/nilusha and the published literature are both right?
Thanks,
Elizabeth

ram74656 & nilusha:
  • ~2x10-5cm2/s (from g_msd) x 4 = ~8x10-5cm2/s
  • Conclusion: CG water has almost 4x faster diffusion than experimental water.

    • JPCB 2004, 108, 750-760 & PLoS Computational Biology 2010, 6, e1000810:
  • 0.5x10-5cm2/s x 4 = 2x10-5cm2/s
  • Conclusion: CG water agrees with experimental water diffusion.

    • JPCB 2004, 108, 750-760 excerpt (Regular Martini Water):

    The self-diffusion constant of the CG water sites at 300 K is DCG = 5×10-6cm2s-1. The CG water sites, however, represent the center-of-mass of four real water molecules. The average mean squared displacement of the center-of-mass of four molecules is 4 times less than the average mean squared displacement of four independently diffusing molecules.15 The effective diffusion constant of individual water molecules as represented by the CG particles is therefore 4 times larger. The self-diffusion rate of water as modeled by the CG particles is therefore 2×10-5cm2s-1. For pure water the experimental diffusion constant Dexp = 2.3×10-5cm2s-1 (at 300 K).


    PLoS Computational Biology 2010, 6, e1000810 excerpt (Polarizable Martini Water, but comments on Regular Martini Water):

    Diffusion constant. The self-diffusion coefficient of a polarizable water bead is DCG = 6.25x10-6 cm2 s-1 at 300 K, as calculated from the mean-square-displacement (msd) over effective time. As one CG bead represents four real water molecules, and the average msd of the center of mass of four molecules is four times smaller than the average of the individual msd’s of these molecules, the effective diffusion coefficient of individual water molecules represented by a CG water bead is 4 x DCG = 2.5x10-5cm2s-1. This value is slightly higher than the self-diffusion coefficient of the original MARTINI water model of 2 x 10-5 cm2 s-1 and compares well to the experimental diffusion coefficient of 2.3x10-5cm2s-1 at 300 K [30].

    Last edit: 7 years 7 months ago by ploetz. Reason: mistake in exponent

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    7 years 8 months ago #5808 by Pim
    Replied by Pim on topic Diffusion Coefficients and Effective Time
    The way I understood it, is in the quote "as calculated from the mean-square-displacement (msd) over effective time" That implies that g_msd gave 2.5e-5 over Martini time, that value was divided by 4 to calculated the MSD over effective time, and then multiplied by 4 to compare again to experiments. That's why I called it confusing :D.

    But... Manel may have additional insight?

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    7 years 7 months ago #5816 by mnmelo
    Replied by mnmelo on topic Diffusion Coefficients and Effective Time
    Additional insight on the historic use of the 4x multiplier:
    The trend up until recently was to incorporate the time multiplication factor in all reported times, yielding 4x slower rates. It's indeed confusing, as Pim pointed out, but I can see the appeal of saying you got to 4x longer timescales.

    The more recent approach is to mention the time compression in a qualitatively way, acknowledging the fact that there is no easy answer to 'How much faster does Martini go?'. Reasons for this change are:
    • Not all systems/solvents display such a 4x speedup. Some might have no speedup at all;
    • For some atomistic forcefields/solvent combinations diffusions can depart just as much from the experimental values;
    • The comparison of the center-of-mass diffusion vs. 4 free particles is not necessarily the best one to judge these rates. An alternative (of equally subjective quality) is to compare to bundled SPC systems. Fuhrmans et al. found a bundle diffusion around 1.25e-5, vs. 1.92e-5 of (unscaled time) Martini.

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    7 years 7 months ago #5818 by ploetz
    Replied by ploetz on topic Diffusion Coefficients and Effective Time
    Okay, thanks Pim and Manel. I get it now: The values from g_msd were both multiplied and divided by 4 in the references for regular and polarizable water, but that may not always be the case. Thanks again.

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    7 years 7 months ago #5855 by nilusha
    Replied by nilusha on topic Diffusion Coefficients and Effective Time
    I got it now.Thank you Pim, Manel and Ploetz.

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