SpinDynamics.org User Support Forum

Dear Spinach community,

I have a molecule undergoing exchange in which I wonder if the effects of scalar relaxation of the first kind are visible in 2D NOESY. There is definitely exchange, and I see a strong cross peak with same sign as the diagonal between two spins which are coupled (meta protons on an aromatic ring), whilst normal NOE cross peaks are opposite sign to the diagonal as expected for small molecules. However, I'm having difficulty making a sensible simulation of the spectrum.
From the NOESY and from 1D spectra the rate constant for the exchange should be around 2Hz; certainly not much faster as exchanging carbon signals 10Hz apart are not noticeably broadened.
I've constructed a simulation setup with just the two relevant proton spins in each exchanging form, starting from the aziridine example, with suitable coordinates, and the experimental shifts and approximate couplings (attached). If the rate constant is set to 2 and modulation depth is set small, the simulation works and I see the exchange cross peaks as well as antiphase artefacts between the coupled spins. This is the same as if SRFK is turned off. However, if I try to increase the modulation depth to the point where I see a strong SRFK signal, I get an error:

Error using relaxation
T1,2>>srfk_tau_c validity condition violation in Redfield theory

For example at rate constant of 2 I am limited to modulation depth of about 0.6, and at this point the SRFK cross peaks are insignificant.

Where does this limitation come from? Is it occurring because my spin system only contains the two spins for each conformer? Is there something trivially wrong with my setup (quite likely!)?
It's of course possible that SRFK as I'm attempting to simulate, is not in fact the cause of the cross peaks I see, and maybe the fact that I can't reach conditions that reproduce the spectrum, is really telling me that, but I don't have a good idea about other mechanisms. I'm relatively confident about the exchange rate given the various data I have, but not at all about the relaxation theory.

Thanks for any assistance/ suggestions anyone can provide
Pete

Long story; see Section 6.3.2 here:

https://link.springer.com/chapter/10.10 ... -05607-9_6

Redfield type relaxation theories (of which the SRFK model is an instance) have validity conditions. One of them is that the stochastic noise that causes relaxation must have a short memory time - much shorter than the characteristic response time of the physical system. In practice this means that Redfield theory is dangerously close to a breakdown when T1 or T2 is similar to tau_c. This is the condition that Spinach checks; it throws an error if it detects a violation. This is what you see.

The good news is that I don't think you actually need to manually turn on SRFK in that system: because you are treating chemical exchange explicitly, its secondary relaxation effects will be accounted for automatically, similarly to how it happens in Stochastic Liouville Equation treatments where explicit treatment of rotational diffusion already covers Redfield theory.

Thus, delete the SRFK option and simply make sure that the two instances of your spin system on the two sides of the reaction arrow have different spin interactions. The kinetics superoperator in Spinach will make sure that the relaxation effects proceeding from this difference are accounted for in the dynamics.

Dear Ilya,

Thanks for the clarification, I see your point about timescales. I guess (although I am as you can see not super clear on the theory) that the breakdown of the theory doesn't mean that the effect is not there; rather that we can't quantify or predict it.

I tried the calculations with the SRFK turned off, and I don't see the same effect, even with the coupling constants in the two forms set to be substantially different. With srfk turned on I see an effect even for a modulation depth of about 1Hz, but with the same exchange rate I see no effect with srfk turned off even if the difference in coupling constant is a few Hz. So not sure what to conclude from that.

I also don't have any clear basis for expecting a modulation of the coupling; I'm not even sure what exchange process is going on here so it could quite well be there is some other source of the experimental result.

This is really an incredibly powerful tool, thanks to you and your fellow developers for all your effort and support!

Yes, essentially you are at the safety margins of SRFK as a physical model. One way to proceed there is to observe that SRFK type processes only create one type of cross-relaxation Lz <-> Sz process, same as Overhauser effect. This means that the experimental data may be fitted with respect to the elements <Lz|R|Sz> and <Sz|R|Lz> of the relaxation superoperator. Find that element and alter it manually until you have a good match. Then the argument is "Redfield is not a good model for this process anymore, but we can of course just vary the rate of the process without an ab initio model".