Ligand binding in Spinach

[faq_user]

A friend of mine is doing competitive protein binding experiments and I am sure there is a way to define it in the spinach but can't see how. I'd like to give him simulated spectra from which he can do whatever analysis he is planning to do with experimental spectra. And since it is simulated spectra we can check if he gets the correct binding constant out of it.

Your asymmetric exchange example looks quite close to me to describe a single ligand saying spin -1 is the free and spin-2 is the bound state. But I don't understand the rate and concentration definitions. To calculate equilibrium spectra for a given binding constant example, how should I set concentrations and rates?

Can I define the rates and take their ratio to be my binding constant, and use the equilibrate function with initial conc. of 1 for free and 0 for bound state, and let it work out the equilibrium concentrations?

And how can I add the protein in the system? And multiple ligands but keep bound with the same protein. I was planning to define a short T2 for the bound state and look how that effects the resulting linewidth of the free ligand which is the only observed signal because it is fast exchange and ligand is in large excess.

Chemically what we have is:

ligand(free) + protein(free) <--> ligand(bound)-protein

As an input, I'd like to use a fixed value for total concentration for ligand and protein, and define the Kd binding constant which would be the ratio of on/off rates.

[kuprov]

Spinach supports both equilibrium and non-equilibrium kinetics. If you begin with arbitrary concentrations, that does of course mean that a mostly unidirectional chemical reaction will be going on during the pulse sequence and distortions will occur. For specifically equilibrium kinetics, there are two alternatives:

1. Solve your reaction kinetics equations for equilibrium concentrations manually (set time derivatives to zero and solve for concentrations), and specify those in Spinach.

2. Start with any concentrations and use equilibrate.m function to shake them down into an equilibrium, and then use the equilibrium values in Spinach.

The reaction looks fine. You will need to specify two spin systems back to back in Spinach input: [protein + ligand, unbound] and [protein + ligand, bound], and tell spinach which spins in the input correspond to which system.

[fidgetspinner]

Hey!

Continuing on the same topic, how would one deal with the concentrations using this approach when there is an excess of the ligand? Taking the reaction:

Protein(free) + Ligand(free) <--> Protein-Ligand (bound)

Let's say that in chemical equilibrium the concentrations are:

Protein(free): 1 mM
Ligand(free): 100 mM
Protein-Ligand (bound): 10 mM

Now, if I specify the two spin systems back to back, I can only set the concentrations of those two systems, corresponding to [Protein(free) + Ligand(free)] OR [Protein-Ligand (bound)]. However, that would assume that the proton/ligand ratio is equal, right? How could one overcome this kind of problem?

[kuprov]

This is an instance of non-linear kinetics where the process is not chemical exchange. The developer version of Spinach can handle such cases (we implemented that feature a few months ago). Get the developer version and look at the Diels-Alder cycloaddition example in the kinetics example set. That reaction is mathematically identical to your case; use that script as a starting point.