NMRlipids III: Quantitative measure for the force field quality needed

Progress in the NMRlipids III project about lipid-cholesterol interactions has been slow because the focus has been recently in improving ion binding to PC lipid bilayers and charged membranes.

After revisiting the manuscript with a serious intention to finalize the project, I think that we need to define a quantitative measure for the force field quality to simplify the discussion. For example, Berger model gives the best agreement with form factor data with high cholesterol content, but too large order parameters. On the other hand, Slipids give better order parameters with and without cholesterol but the form factor with high cholesterol concentrations is less good, and so on. This kind of discussion could be significantly simplified with a quantitative quality measure for the force field quality.

The quality measure could be also used to rank the force field quality in the databank collected from the contributions to the NMRlipids project and in further automatic force field development. The simplest measure to start with could, for example, sum up the deviation from the experimental order parameters for different segments and the deviation from experimental form factor using equation (3) from the SIMtoEXP publication. Similar measure has been recently introduced for proteins in solution.

Any kind of ideas and contributions about measuring the force field quality are welcomed.

NMRlipids IV: Challenges in evaluating counterion binding affinity to PS bilayers

Counterion binding to POPS lipid bilayers is signifincantly different between simulation models, as seen from density profiles along membrane normal in figure 1.

Figure 1:    Counterion densities of POPS lipid bilayer along the membrane normal from simulations with different force fields.

In the NMRlipids IV manuscript, we are trying to figure out which one these is the most realistic. In the NMRlipids II project we evaluated the sodium binding affinity to PC lipid bilayers using the changes of headgroup order parameters and electrometer concept. Similar experimental data is available for POPC:POPS (5:1) mixtures as a function of KCl, NaCl and LiCl concentration. This data is compared with different simulations in figure 2.

Figure 2:     Changes of the PC (left) and PS (right) headgroup order parameters as a function of added NaCl, KCl and LiCl from POPC:POPS (5:1) mixture at 298 K (except Berger simulations are (4:1) mixture at 310 K).

Rough conclusions could be that the binding of sodium and potassium is overestimated in Berger and CHARMM36 models, while Lipid17 performs better. Changes in MacRog model with potassium are somewhat overestimated but not systematically. However, these results are more difficult to interpret than the corresponding figure for PC lipids in the NMRlipids II, because zero point of the x-axis (added salt concentration) is not free of ions in this case. The systems always contain counterions when PS lipids are present and the binding affinity of these counterions differ between simulation models. Therefore, the changes of order parameters in figure 2 cannot be plotted against completely ion free state and the interpretation is more complicated.

The changes of PC headgroup order parameters with increasing amount of PS lipids give additional information about counterion binding affinity. According to the electrometer concept, the headgroup order parameters increase with increasing amount of negatively charged PS lipids, as seen in experiments and MacRog simulations with potassium in figure 3.

Figure 3:  Changes of PC (left panel) and PS (right panel) headgroup order parameters from POPC:POPS mixtures with increasing amount of POPS.

However, POPC headgroup order parameters are unaffected by POPS in CHARMM36 simulations with potassium and sodium counterions, and decrease in Berger simulations with sodium. This can be explained by overestimated counter ion binding in these simulations, which cancel the negative charge by the PS headgroups.

In conclusion, the results would suggest that sodium clearly overbinds in Berger simulations, both sodium and potassium slightly overbind in CHARMM36 simulations and most realisistic binding to PS containing bilayers is observed in MacRog simulations with potassium. The case of Lipid17 is little bit unclear because the relatively strong counterion binding in Figure 1 is not seen in Figure 2. The Lipid17 results are yet missing from Figure 3 because we do not have pure POPC simulation with Lipid14 at 298 K.

ToDo: My current suggestion is to do following. We conclude from this data that the MacRog simulations with potassium probably represent the most realistic counterion binding affinity to PS containing bilayers and compare its density profile to the results from other simulations in Figure 1. To finalize this part we still need the following data:

1. Pure POPS MacRog simulation with potassium counterions at 298 K
2. Pure POPC Lipid14 simulation at 298 K
3. Ion density profiles from Lipid17 POPC:POPS (5:1) simulations with different ion concentrations for figure: https://github.com/NMRLipids/NMRlipidsIVotherHGs/blob/master/Figs/CIdensPSOCmixt-eps-converted-to.pdf (we already have the data in Zenodo in Amber format but we need to calculate the density profiles.)

Maybe we should also move current figures 7 and 8 to the supplementary information.

Fortunately, the calcium binding results seems to be more clear because changes in both simulations and experiments are larger.