Re: questions regarding ABF sampling in a DMPC bilayer

From: Jérôme Hénin (jhenin_at_ifr88.cnrs-mrs.fr)
Date: Wed Jan 18 2012 - 12:00:28 CST

Dear Ajasja,

Good questions! I hope other users find them interesting.

On 18 January 2012 15:12, Ajasja Ljubetič <ajasja.ljubetic_at_gmail.com> 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<http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig1.GIF>
> ). 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<http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig1.GIF>
> ).
>
> 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 <http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig2.GIF> (water)
> and Fig3<http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig3.GIF>(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<http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig3.GIF> (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<http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig4.GIF>).
> 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<http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig5.GIF>
> ).
>
> 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 <http://lbf.ijs.si/ajasja/mails/ABF/enhancing-abf-DMPC/Fig6.GIF>)
> 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.

Best,
Jerome

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