Re: questions regarding ABF sampling in a DMPC bilayer

Date: Wed Jan 18 2012 - 12:27:31 CST

Hello all,

I have a somehow related question with the last topic here. We are trying to do some PMF calculation of the binding (really detachment) of a protein-DNA complex with umbrella sampling. As a collective variable we are using the minimal distance between the groups as implemented in this paper: J Am Chem Soc. 2009 131(29):9864-5. The forces are applied thorugh the tcl forces module. The sampling problem is not so bad when the two groups are very close, but it gets really nasty when they are far apart and both molecules are somehow "free" to diffuse. The thing is that this portion of the PMF is needed to compare against experimental dG values. Do you think that accelerated MD will be a good way to help this issue? In principle, it is possible to unbias the aMD simulation and also the umbrella potential, but i am not sure wether they will work well together.




----Mensaje original---- De: Fecha: 18-ene-2012 15:00 Para: "Ajasja Ljubeti?"<> CC: "namd-l"<> Asunto: Re: namd-l: questions regarding ABF sampling in a DMPC bilayer Dear Ajasja,

Good questions! I hope other users find them interesting.

On 18 January 2012 15:12, Ajasja Ljubeti? <> wrote:
Dear all,

For the past half-year I had a lot of fun building a GPU cluster and running some ABF MD simulations in a DMPC bilayer. The system simulated is a spin-labelled peptide composed of alanine either in water or in a DMPC membrane (Fig1). The colvars (theta and phi) are the polar angles from the C-beta to the center of mass of the ring of the spin label. (Fig1).

And in that time I have gathered quite a few ABF related questions:

Why is the diffusion along the colvars so much slower in a DMPC bilayer than in water? For example compare the colvar trajectories of Fig2 (water) and Fig3 (DMPC). If the PMF along the colvars is approx flat, should it still matter that one system is in DMPC and another in water? So, is the slower diffusion an intrinsic property of the system or am I perhaps not setting some ABF parameters correctly?

This is correct, the slow diffusion is an intrinsic property of the lipid environment, and ABF does not change that. If you model the unbiased process as 2D diffusion on an effective potential (i.e. the PMF), then ABF will (in time) erase the barriers, but not change the intrinsic diffusion properties. For that reason, if your problem is slow diffusion on a flat energy landscape, then ABF will do absolutely nothing. Remember that the spirit of ABF is to remain close to equilibrium. Forces that increase diffusion speed would be acting against friction, they would be dispersive, non-equilibrium forces.

Why are there spikes in the forces applied by ABF in DMPC? If one plots the applied forces in water and DMPC the patterns seems quite different. Larger forces are probably required to move lipid tails so perhaps this is normal. Fig3 (fa_theta and fa_phi)

Indeed this is due to slow relaxation of the lipid tails. ABF forces have to push lipids that are in the way. Incidentally these force spikes are non-equilibrium, so this is when the objective mentioned above is (locally) defeated. Once the lipid tail has moved out of the way, there is no barrier anymore, and the forces registered by ABF have to be averaged out - that's part of the deal, usually it happens fast enough to be tractable. So this is purely a timescale problem, not one of underlying PMF.

Why are there such small energy differences in PMF between water an DMPC? (Fig4). If the diffusion along the colvars is slower and more energy is needed to move lipids out of the way, then this should be seen in the PMF as higher energy barriers, right?

No, see above. To be more precise, things that appear as slow diffusion (i.e. friction) in the reaction coordinates are actually fluctuations in other degrees of freedom that couple to the RCs. Barriers in those directions, if they are too high, will kill diffusion in the RCs.

But i'm seeing differences of only 2 kt, which does not seem that much. I thought this might be due to the fact that I'm running the simulations above the DMPC transition temperature. So I tried to lower the temperature (perhaps a bit too much), but at the lower temperature ABF fails to sample the phase-space very well (Fig5).

Well... see above. Each of your questions is the answer to the one before! Once the "fast" degrees of freedom become slow, there is no separation of timescales and all the coordinates might as well mix. Each time ABF comes back to a point in (theta, phi) that has been visited before, it sees a different landscape, because the other coordinates don't have time to average out. So ABF just fails.

How are gradients merged using InputPrefix? From some quick plots (Fig6) the algorithm seems to adjust the offset (how?) and make the gradient continuous. Overlapping regions are probably averaged over and the counts of the overlap summed.

The center of each bin is mapped onto the new grid, and all data from that bin is added to the new bin. If several bins map into a larger one, the data is combined (with proper statistical weights). The gradients should be continuous given sufficient sampling; I really don't know what's happening in the plot on the left, but it looks wrong. Are you sure the color scale is the same everywhere?

Is it possible to use Accelerated MD with ABF (and get correct results)? This is more of a brainstorming question. Using aMD I could "soften up" the lipid tails, but this seems very similar to increasing the temperature, which means I would not know at what temperature and what phase (liquid ordered, liquid disordered) the lipids are. If indeed this is even technically possible.

If by "correct results" you mean the same results you would get from longer standard MD, the answer is: not without some coding. ABF relies on a canonical average to get the free energy gradient. If you do non-Boltzmann sampling, you need to modify ABF to reweight that average on-the-fly. It could be fun to try, but it might not be worth your time.



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