[gmx-developers] Re:Re:Re: Energy Minimization

Mark Abraham Mark.Abraham at anu.edu.au
Fri Jun 12 06:22:12 CEST 2009

Leontyev Igor wrote:
>> Igor Leontyev wrote:
>>> There is no rigorous prove in the manual section 3.10 that the finer
>>> energy minimization is not essential for MD of complex biological 
>>> system.
>> Tsjerk Wassenaar wrote:
>> There doesn't need to be. The point of doing MD is to see a system cross
>> energy barriers (or, rarely, to see that it doesn't). Thus it is
>> expected to move from the starting position, and at a certain point of
>> EM, the structure is good enough, i.e. close to one in the ensemble of
>> interest so that equilibration happens reasonably quickly and without
>> failures of the integrator.
> The goal of doing any simulation is modeling actuality. In real proteins a
> rate of crossing some potential barriers can be in a scale of microseconds
> or even larger, which is not feasible for MD. Therefore, we should start
> simulation from the configuration which is close to "the ensemble of
> interest" to explore an essential part of the phase space. However, it's
> even not always known what part of the phase space is essential. Therefore,
> we may just want to find the lowest energy local minimum. A finer EM
> algorithm suppose to results to lower energy. If it's not the case we 
> always
> can use optimized structure from the previous gruff minimization step. But
> if the finer EM algorithm would bring our system to another (lower energy)
> local minimum separated from the first one by a high barrier (>>kT) then we
> will observe in MD a different dynamics (explore a part of the phase space
> different from the one corresponding to the gruffly minimized
> configuration). Or, is there any indication that the finer EM algorithm can
> not bring us to other local minimum?

EM algorithms are unlikely to cross any energy barriers. They all work 
by looking at the value of the function and/or (approximations to) 
various derivatives, deducing a likely direction to move, following a 
heuristic to guess how far to move, and then trying again. In the limit 
of a continuous target function (true for MM), accurate energies and 
forces (true for MM), accurate second derivatives (often true for MM, 
but perhaps not for some EM algorithms), and a sufficiently conservative 
heuristic for choosing step sizes, then an EM algorithm cannot leave the 
local minimum. Thus there can exist a point when the system is in the 
region of a suitable minimum, and further EM won't affect the quality of 
the starting structure for MD on an MM force field. However if the 
assumptions don't hold, as they might for systems with frozen atoms, 
constraints, or an EM algorithm that starts with an approximation to the 
Hessian (matrix of second derivatives), or an EM stepsize that is too 
large, then EM might cross barriers.

>> Tsjerk Wassenaar wrote:
>> There doesn't need to be. That section describes the methods. By the
>> way, I haven't seen rigorous prove against the existence of
>> leprechauns or the monster of Loch Ness yet.
> Sure. Thus, the section 3.10 can not be used as an argument or theorem to
> prove something.

Sure - I introduced it as supporting evidence for my assertion that 
there exists a point when preparing for MD, beyond which further EM is a 
waste of time.

>> Tsjerk Wassenaar wrote:
>> Sorry, I'm not sure what the "second example" or "simple option" to
>> which you refer are.
> "Second example" is an optimization of hydrogen positions with frozen heavy
> atoms which typically is employed for continuum electrostatic pKa
> calculations. The "Simple option" is a capability to carry out the "cg"
> minimization with constraints.

I've forgotten the original context for this. The "second example" was 
outside the original context of the discussion, which I understood to be 
EM preparing for MD. The "simple option" is something the developers did 
not envisage being needed, for the reasons they describe in 3.10.2. If 
enough people want it, it might get added. The joy of free software is 
that if you want it, you can write it too!

>> Tsjerk Wassenaar wrote:
>> You did steepest-descent EM on a system with lots of frozen atoms, if I
>> understand correctly. You then switched to L-BFGS with frozen atoms,
>> which starts with an estimated Hessian. The Hessian updates then are
>> based on calculated forces whose components are unbalanced because of
>> the constraints. Such a procedure could well be numerically unstable.
>> You may be proving that. Try a second L-BFGS from your first L-BFGS
>> endpoint and see where it goes. If it's some different place, then you
>> may be demonstrating that this minimizer can't deal with the
>> (artificial) problem you have constructed.
> Similar problem has been observed for polarizable benzene molecule without
> constraints. After finer optimization of a single benzene molecule, 2 shell
> particles were relocated from the position of their heavy atoms (ground
> state) to position of neighboring heavy atoms (very high energy local
> minimum due to a large bond stretching energy penalty). The artifact I have
> reported earlier in the thread "Polarizable simulations in Gromacs"
>> "Frozen" might have meant with respect to the initial configuration, or
>> as someone pointed out, that the atomic positions were merely never
>> updated. So (for example) if the initial frame was translated for some
>> reason, it could still be translated in the output. This could produce a
>> deceptive frameshift. You can test for this by doing what I said -
>> centering the input and output structures on the same frozen atom
>> post-mdrun.
> Anyhow, the terminology does not affect the problem: the
> optimization of water-hydrogens with frozen positions of water-oxygens
> results to the structure with shifted water-oxygens.

The terminology does affect the problem if your description of the 
existence of a problem is confounded by a frameshift artifact.


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