# Re: [AMBER-Developers] Origin of dihedral term

Date: Tue, 20 Oct 2015 10:51:48 -0400

Hi All

Two quick things, more to come.

1. Indeed, it was Dave Cerutti that presented the dihedral fitting.
Chad, Dave and I discussed this quite a bit.
2. We did publish a paper with Chad on this, please see
doi:10.1021/ci500112w

I will expand a bit later on on my own thoughts on this discussion, but
let me state clearly that it is PURELY semantic. Of course, using either
functional form gives the exact same answer.

On 10/20/15 10:26 AM, Ross Walker wrote:
>> Hi Carlos,
> What do you fit to then? The forces? Or the second derivatives?
>
> The issue is that when you expand out the 1+cos(n.theta - phi) terms you get
>
> ndih n[1] n[1]
> sum ( sum Vn + sum Vn.cos(n.theta - phi) )
> i=1 j=1 j=1
>
> The issue here is that if your fitting algorithm varies Vn in order to fit the energy to a QM reference - even if you have an offset so you are are only fitting relative energies - so your mean energy of all your MM terms (essentially the offset from the QM energies) also changes.
>
> I think Jason is right that one should also fit the n=0 term but I 'think', need to look more closely, that this still has the same problem. For now I am just discarding the 1+ term and fitting just to Vn.cos(n.theta - phi) under the premise that this fitted against relative energy differences yields Vn terms that one can just use in the standard force field equation given that the 1+ falls out in the derivative.
>
> I am interested to hear what others do though.
>
> All the best
> Ross
>
>> On Oct 20, 2015, at 03:18, Carlos Simmerling <carlos.simmerling.gmail.com> wrote:
>>
>> For the protein force fields we don't fit the absolute energies, so the
>> offset doesn't matter.
>> Carlos
>> On Oct 19, 2015 7:30 PM, "Jason Swails" <jason.swails.gmail.com> wrote:
>>
>>> On Mon, Oct 19, 2015 at 6:25 PM, Ross Walker <rosscwalker.gmail.com>
>>> wrote:
>>>
>>>> Hi All,
>>>>
>>>> I am wondering if anyone knows the origin or why the dihedral term we use
>>>> in the AMBER force field has the 1+ term in it.
>>>>
>>>> I.e. we have:
>>>>
>>>> ndih n[i]
>>>> sum sum( 1/2 x Vn(1+cos(n.theta - phi)) )
>>>> i=1 j=1
>>>>
>>>> Specifically we have the 1+cos term in there which is I guess to make the
>>>> cos term oscillate between 0 and 2 rather than -1 and +1 and then we have
>>>> the 1/2 in front of the Vn to get rid of the 2 making it between 0 and
>>> Vn.
>>>> However, as far as I can tell this is purely cosmetic. Is that correct?
>>>>
>>> ​I always thought of it more as making it *look* a little more like the
>>> other bonded terms (which are harmonic, and have the 1/2 term in front of
>>> the force constant, and as a result have a minimum energy at 0). But
>>> obviously the 1+ has no effect on forces, and the 1/2 can be pulled into
>>> the Vn term (which, in Amber, it already is).
>>>
>>> As in I could ditch the 1/2, and ditch the 1+ and just have
>>>> V[i,j].cos(n.theta-phi). The question is if that is true why don't we do
>>>> this - does anyone know?
>>>>
>>> ​At this stage, it would be historical.​
>>>
>>>
>>> The issue arrises not in MD but when we try and refit the torsion terms. If
>>>> we try to fit energies against quantum energies we always have an offset
>>> in
>>>> the mean due to the origins not matching - that doesn't matter since it
>>>> would be constant during an MD run. However, if we are fitting Vn terms
>>> the
>>>> 1+cos term here causes our mean to drift as we adjust Vn. This is a pain
>>> in
>>>> the butt when it comes to getting a good fit. Thus I propose to just fit:
>>>> Vn.cos(n.theta-phi) which, I believe would give perfectly transferable
>>>> parameters to the 1+cos equation.
>>>>
>>> ​Lachele actually addressed this precise problem in her presentation at the
>>> Amber developer's meeting last year. The solution is simple: fit the
>>> zero-periodicity term. That *gives* you an arbitrary constant to improve
>>> your fit -- it doesn't contribute to an overfitting problem and solves the
>>> issue you're describing. Then you're free to simply throw that term away
>>> when making the frcmod file since it has no effect on forces. It seems to
>>> me you are rediscovering her problems :). I'm sure she'd be happy to share
>>> her slides if she can find them and you wanted them. </throwing Lachele
>>> under the bus>
>>>
>>> Am I missing anything here? - Is there any reason why we couldn't go the
>>>> whole step and just ditch the 1/2 and 1+ terms from the entire force
>>> field?
>>>> - Seems to me all that would happen is for a given set of parameters (say
>>>> FF14SB) we just shift the energy origin but everything else would still
>>>> work.
>>>>
>>> ​A couple things. If you do a QM scan, you're certainly not going to get
>>> an energy of zero at the midpoint -- the zero point energy will be
>>> arbitrary. The easiest thing to do with your QM scan is simply scale the
>>> whole potential by the minimum energy value, which will give you the same
>>> minimum as the 1+cos() series at 0 (maybe that's why it's done?).
>>>
>>> Y
>>> ​ou can fit however you'd like, but changing how Amber computes this
>>> internally would break from how every other package calculates proper
>>> torsions. It would make cross-program conversion validation much harder
>>> than it currently is. This is a big deal IMO.
>>>
>>> All the best,
>>> Jason
>>>
>>> --
>>> Jason M. Swails
>>> BioMaPS,
>>> Rutgers University
>>> Postdoctoral Researcher
>>> _______________________________________________
>>> AMBER-Developers mailing list
>>> AMBER-Developers.ambermd.org
>>> http://lists.ambermd.org/mailman/listinfo/amber-developers
>>>
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