Interplay of relaxation and kinetics

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Posts: 49
Joined: Tue Jul 13, 2021 8:33 am

Interplay of relaxation and kinetics

Post by faq_user »

I came over the activation barrier and downloaded your program, and installed the latest version of matlab, and started reading the documentation and running the example scripts. It is indeed well documented. I would like to simulate a rather complex problem. I believe, Spinach is capable of performing these tasks, I just have to figure out which modules should I combine. In the documentation you wrote that the users should not change the kernel functions. Therefore, I was wondering, whether my problem could be solved by just writing new "experiments" and functions, or something more dramatic is required. So, here is my problem:

I would like to simulate 1H rotating frame relaxation (on-resonance, simple spin-lock, no special shape pulse yet), under MAS at high spinning speed. I'm interested in the conditions, when the effective rf field strength matches the half-rotary and rotrary-resonance conditions and the timescale of motion is in the microsecond regime.

I derived analytica relaxation rate equations for these scenarios by solving the master equation. (A simple example was also shown on my poster.) These equations predict that if the correlation time of the motion sensed by a proton is on the timescale of 1-100 us, then the 1H R1rho profile (recorded as a function of the irradiaiton frequency) will show two bumps at the resonance conditions (there might be three bumps when off-resonance spin-lock is applied). Resonance condition is when the effective rf field (or the half of it) equals the spinning speed (or the half of it).

This analytical solution has three major problems, firstly, it neglects that at the resonance conditions the dipolar and CSA interactions are recoupled, which would raise the observed relaxation rate; secondly, it assumes that we are still within the Redfield-limit, which is certainly not true; thirdly, it assumes an effective apparent 1H-1H distance (aka 1H density), but I'm not sure how good this approximation is.

I would like to disentangle the above problems and devide the observed relaxation contributions into coherent (recoupling) and incoherent (dynamics) part, so that I could at least estimate the relative ratios, and also to get a picture what does it mean if a certain proton displays significant bumps in the relaxation rate profiles, is it indeed an indicaiton of microsecond timescale motion, or it is rather a sign, that certain residues are more prone to recouling.

What I see in Spinach, that it handels the relaxation (R) and the exchange kinetics (K) separatly. I think, the solution of my second concern lies somewhere in between R and K, when the exchange process is so fast that it is rather a stochastic motion and not a simple exchange.

I have plently experimentally recorded 1H relaxation profiles with which I could compare the results of the simulations. The experiments were done for a perdeuterated and partially (30%) backprotonated sample (this partial backprotonation also makes some headache, but that is not so important for the current simulations), at 27777 and 55555 Hz spinning speed (i.e. fast enough spinning and little enough protons to avoid coherent contributions).

What do you think? Is the problem complex enough that I ask for your help? Would you be interested in solving this? If not, or you don't have time for this, then could you please provide me with some suggestions where to start, which moduls and functions to use, what to modify.
I would really appreciate your help (e.g. co-authorship). I can also provide you with more data, or for example with the full form of the analytical equations
Posts: 72
Joined: Mon Mar 29, 2021 4:26 pm

Re: Interplay of relaxation and kinetics

Post by kuprov »

The first question of course is which relaxation model you are going to use and how. Indeed Spinach can handle any combination of relaxation and kinetics, and they would interfere correctly, including with magic angle spinning. I would suggest the following:

1. Look through the description of the relaxation theory options in the documentation ( ... parameters) and see if there’s already something that would be satisfactory. If not, add your own option to relaxation.m function.

2. Look through the kinetics module options and see if your kinetics is there, it likely is – Spinach supports arbitrary kinetics with linear ODEs.

3. The magic angle spinning module (singlerot.m) would do the following:

(a) Replicate your relaxation and kinetics superoperators at each rotor orientation.
(b) Set your dipolar and CSA tensors appropriately for each rotor orientation.
(c) Cycle through rotor orientations.
(d) Provide all necessary infrastructure to the pulse sequence function – see the description of singerot.m context in the documentation.

Off-resonance irradiation is performed by shaped_pulse_af function. A good starting point would be the standard pulse-acquire pulse sequence, just add a call to that function. So, numerically, of course this is possible and Spinach would have no problem replicating your experiment.
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