[gmx-users] how to calculate kinetic constant?

Christopher Neale chris.neale at mail.utoronto.ca
Sat Oct 5 23:03:57 CEST 2013

Dear Rajat:

I just checked the first two papers that you mentioned and they both get kinetics from standard equilibrium simulations. As for the Arrhenius law, with k, A, and the energy of activation (Ea) all unknown for each T, how do you obtain a unique solution for k given T ? Even if you assume that Ea is some function of the maximum of your PMF (which is not always true), I presume that you can only then get the relationship between k and A, not the absolute value of k, even with information from many temperatures. However, I've never worked on this directly. Can you provide a reference so that I can take a look?

Thank you,

-- original message --

Hi Chris,
I have never done this and I may be missing something. But here is what I
I have seen a few papers use the Arrhenius law, k=A*exp
(-deltaG/kB*T)...-deltaG/kB*T can be obtained from the PMF...Now, if you do
this for different temperatures, you can back out the activation energy and
hence the rate constant.
I would love to learn more about this. Any inputs will be welcome.


On Sat, Oct 5, 2013 at 11:44 PM, Christopher Neale <
chris.neale at mail.utoronto.ca> wrote:

> If you want K_on and K_off, then I think you need to look at long-time
> equilibrium simulations or massively repeated simulations connected with a
> MSM. Beyond that, I believe that you will need to understand all of the
> important free energy barriers in all degrees of freedom (hard, to say the
> least).
> Rajat: how are you going to compute kinetics from a PMF? Barriers in
> orthogonal degrees of freedom don't show up on your PMF but can greatly
> affect the kinetics. Even relatively minor roughness of the
> multidimensional free energy surface and off-pathway kinetic traps are
> going to affect the kinetics but not the PMF. Some people have tried to
> circumvent this limitation by using the PMF in addition to computing the
> local diffusion at each small section of the order parameter (e.g.,
> http://www.nature.com/nnano/journal/v3/n6/full/nnano.2008.130.html ) but
> unless there is excellent sampling overlap and lots of transitions between
> all relevant states, I see this as a way to calculate an upper bound of
> rates that I think could easily be much slower. See, for example,
> http://pubs.acs.org/doi/abs/10.1021/jp045544s . Finally, I am not sure
> how rates can be usefully extracted from a non-equilibrium method like REMD.
> Unless I missed it, the paper that David cites:
> http://pubs.acs.org/doi/abs/10.1021/ct400404q doesn't compute kinetics.
> Perhaps the OP can provide more information on what they are trying to
> obtain, exactly.
> Chris.
> -- original message --
> If you are looking at binding/unbinding as a function of temperature
> (hopefully with REMD), you can use g_kinetics. If you are looking at
> unbinding/binding events in a single simulation with temperature, etc
> constant (no annealing), you will need to calculate binding probabilities,
> from which you can back out a rate constant. A simple google search gave me
> these papers (http://www.pnas.org/content/90/20/9547.full.pdf,
> http://pubs.acs.org/doi/abs/10.1021/jp037422q)
> Of course, the best approach is to calculate the PMF and back out the rate
> constant from the free energy. Hope that helps.

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