MBAR prediction accuracy for LJSF-C12

[mostafa-razavi]

I ran the following direct simulations and I used the first as a reference simulation to predict the Z and U^res using MBAR (N=500) at the parameter set of the second and compare to the second direct simulation results. Both direct simulations are run for 2 million steps and averages and uncertainties are obtained using 5 blocks of the last 1 M steps.

Reference: C12_s3.760e120.0_s4.00e60.0 Prediction: C12_s3.780e120.0_s4.00e60.0

Only sigma_CH_3 was changed and sigma CH_2 was not changed. Note that only 2 sites out of the total 12 sites in C12 are CH_3, so one would expect a reasonable agreement between direct simulation and MBAR prediction.

Also, the sigma_CH3 difference between the reference and the prediction is 0.02 A which is less than the recommended value of 0.025 A.

!#The Z and U^res of C12_s3.760e120.0_s4.00e60.0 (ref.sim.)

Conclusions:

1) The MBAR predicts U^res better than Z. This was also mentioned in Messerly2018.

2) Even though the value of N_eff is way larger (~400) than the minimum recommended value of 50, the predicted Z values at some ITIC points disagree with direct simulation results.

3) The intra method (as opposed to single molecule) gives reasonable U^res values when MBAR is used.

4) Uncertainty of direct simulation Z is largest for the meta-stable point, and the MBAR prediction is the best for this point.

[mostafa-razavi]

Hypothesis and Questions:

1) What will happens if the study is repeated at two different sets of parameters that avoid the meta-stable points.

2) What if the sigma of CH_2 is changed, but the sigma of CH_3 is constant. The disagreement must be even larger.

3) Check if the direct simulations are properly equilibrated. Maybe run longer simulations (e.g. 5 M steps) and see if the MBAR prediction of Z is any better. Done!

4) Repeat the plot using N=1000 instead of 500 and see if the MBAR prediction is improved. Done!

[mostafa-razavi]

Equilibraion Plot for C12

3. Check if the direct simulations are properly equilibrated. Maybe run longer simulations (e.g. 5 M steps) and see if the MBAR prediction of Z is any better.

Here is the equilibration plot of the meta-stable point. 2 M steps seems to be enough for

C12_s3.760e120.0_s4.00e60.0

C12_s3.780e120.0_s4.00e60.0

[mostafa-razavi]

N=1000 results

4) Repeat the plot using N=1000 instead of 500 and see if the MBAR prediction is imoroved.

The N=1000 results shows that using higher number of snapshots does not change the agreement between MBAR and direct sim. for IT points. However, there a significant and rather random difference between N=1000 and N=500 for near saturation temperature points on IC's. One of them get better and the other gets worse. These points have large uncertainties, so the big difference is justifiable.

[mostafa-razavi]

sigma CH_3 vs. sigma CH_2

What if the sigma of CH_2 is changed, but the sigma of CH_3 is constant. The disagreement must be even larger.

It turns out that the N_eff heavily depends on the number of sites of the sigma that has changed. When sigma_CH_3 and sigma_CH_2 are changed 0.02 A, N_eff in MBAR is 373-717 and 710-927. However, the MBAR performance seems to be similar.

Predicted at s3.760e120.0_s4.02e60.0:

Predicted at s3.760e120.0_s4.02e60.0

[mostafa-razavi]

LJSF-C12: Ref: s3.850e127-s4.000e60

s3.850e127-s3.92-4.08e60

s3.850e127-s4.00e56-64

Conclusions: 1) U^res is much more predictable using MBAR than Z even for large eps variations of C12 CH_2 site 2) Z is hard to predict when sigma varies a lot, but when epsilon varies up to 4 K Z is still predictable

[mostafa-razavi]

I used the following Mie simulations as references:

sig_CH3	eps_CH3	sig_CH2	eps_CH3
3.74	118	4.03	62
3.763	120.25	3.97	59.5
3.783	121.25	3.99	61
3.803	122.25	4.01	61.5
3.84	120	3.96	59

to predict the MiPPE Z and U^res, i.e. 3.783 | 121.25 | 3.99 | 61 and here is the result:

C2: All points are perfect

C4: high rho low T point is a little off

C12: high rho low T point is way off. Low rho point is a little off

Conclusions: 1) In all cases, U^res is perfect. 2) For small simple molecules such as C2, Z is more predictable using MBAR. For larger molecules, MBAR is not very accurate.

Todo: 1) Figure out a way to to systematically show the inaccuracies of MBAR for large molecules 2) Maybe incorporate higher temperatures at high densities to avoid meta-sable region?