[gmx-users] HB lifetime
David van der Spoel
spoel at xray.bmc.uu.se
Thu Oct 2 17:20:03 CEST 2008
Christopher Daub wrote:
> Hi Omer,
>
> We are aware of your work with Dr. Agmon, and I believe Dr. Luzar has
> spoken with him about it. I don't understand it enough to say much, but
> I don't think we have substantive disagreements with it. Of course, the
> questioner was asking about the implementation of the Luzar model in
> Gromacs, so I tried to explain some of the background of her ideas.
> Perhaps they'll implement your HB model in Gromacs 5...
I would encourage anyone to contribute implementation of this algorithm
to the current g_hbond code. Please get in touch with me off-list if
you are interested.
>
> Cheers,
> Chris.
>
> On Oct 2, 2008, at 4:45 AM, Omer Markovitch wrote:
>
>> Please see my comments below.
>>
>>>
>> Hi,
>>
>> The HB definitions and associated lifetimes are a bit arbitrary,
>> so there' s always going to be some ambiguity here. That being
>> said, the reason the integral of the HB correlation function C(t)
>> isn't an ideal definition is that C(t) is only roughly
>> exponential. Same argument goes for getting the lifetime from a
>> fit to C(t), or looking for the time where C(t)=1/e, or similar
>> simple approximations.
>>
>>
>> I disagree. HB lifetime is only slightly dependent on the exact values
>> of the geometric parameters, around the usual values of R(O...O)= 3.5
>> Angstrom & angle(O...O-H)= 30 degrees, please see JCP 129, 84505 (a
>> link to the abstract is given below).
>> C(t) of a HB obeys the analytical solution of the reversible geminate
>> recombination (see a short review in JCP 129), and so its tail follows
>> a power law: C(t) ~ Keq*(D*t)^-3/2, which is indicative of a 3
>> dimensions diffusion.
>>
>>
>> What Luzar recommends is to think about an equilibrium between
>> bound and unbound molecules, so that they interact with a forward
>> and a backward rate constant k and k'. k gives the forward rate,
>> ie. the HB breaking rate, and k' gives the HB reformation rate...
>> they are not equal due to the diffusion of unbound molecules away
>> from the solvation shell. There are a few advantages of going
>> this route, not the least of which is that you tend to get similar
>> lifetimes regardless of small changes in the HB definition, and
>> whether you use geometric or energetic criteria, etc.
>>
>>
>> The reversible geminate recombination deals with the A+B <---> C, here
>> A=B=H2O & C=(H2O)2, the bound water dimer.
>> From a single fit to C(t) one receives the bimolecular forward &
>> backward rate constants, which are well defined.
>> k' you suggest is an apparent unimolecular rate constant, which
>> appears to be more suited for short times.
>>
>>
>>
>> Extracting these rate constants is a bit tricky (I usually do it
>> by hand), but I guess gromacs has a scheme to do it... I haven't
>> actually looked at it (though I really should!). I'd recommend
>> some caution though, a scheme that works well for HB's between
>> water molecules in bulk may need to be adjusted to properly model
>> HB's between water and polar atoms.
>>
>>
>> I have to disagree again. The A+B=C problem has an analytical
>> solution. Technically, ones only need to know how to calculate an
>> error-function and to solve a cubic equation, please see eq. 9, 10 at
>> JCP 129.
>> The geminate problem is robust in the sense that it describes C(t) of
>> ANY 2 particles, as long as their behavior is controlled by diffusion,
>> it describes the water pair, but should describe also, for example,
>> liquid argon. For the second case, ofcourse, different rate constants
>> are expected.
>>
>> One should NOT see JCP 129 as a "proof" that previous works were
>> absolutly wrong !
>> Instead, it shows that the postulate by Luzar & Chandler, that C(t) of
>> water is controlled by diffusion, is right, and that with the
>> analytical solution of the geminate problem one can understand some
>> aspects of the water dimer. For example - what causes the activation
>> energies of the forward & backward rate constants to be about similar
>> rather then being different by the strength of 1 HB?
>>
>> Hope I was clear.
>> Omer Markovitch.
>>
>> ** a link to JCP 129, 84505 (2008) http://dx.doi.org/10.1063/1.2968608
>> ** supporting information includes a short trajectory movie
>
>
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--
David.
________________________________________________________________________
David van der Spoel, PhD, Professor of Biology
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596, 75124 Uppsala, Sweden
phone: 46 18 471 4205 fax: 46 18 511 755
spoel at xray.bmc.uu.se spoel at gromacs.org http://folding.bmc.uu.se
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