[gmx-users] HB lifetime

[David van der Spoel]

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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