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Dimerization of the receptor-ligand complex with negligible dissociation of L from the RL dimer.
U_R2L2 model

In this model the receptor binds ligand and forms a dimerization-competent complex. By definition, the ligand cannot dissociate from the complex in a dimer, only when dimer dissociates.

 

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Concentration dependence of RL<=>R2L2 equilibrium

Here I will have make saturated complex and change concentrations to see redistribution of the species. LRratio will have tiny increment to separate points on L/R axis.

Slow dissociation

Fast dissociation

Simulate setup_conc_dep U_R2L2_As_Bs_conc_dep

NOTE: All graphs scale L/R from 0 so I have to resave FIG and PNG files to have L/R=[3.000 - 3.006].

Simulate setup_conc_dep U_R2L2_As_Bf_conc_dep

 

Conclusion:
The model adequately predicts distribution of species and their line shapes upon successive dilutions.

 

 

 

 

U_R2L2 example 1: Slow dimerization, slow binding

Simulate setup U_R2L2_As_Bs

Report: summary_report

Slow exchange, three peaks  with new peaks growing non-proportionally to each other.

 

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U_R2L2 example 2: Slow dimerization, fast binding

Simulate setup U_R2L2_Af_Bs

Report: summary_report

This spectral appearance is very similar to U_RL in the similar exchange regime and to U_R2 with fast dissociation and slow binding

If the fast-exchange peak is taken to fit 2-site exchange it would NOT fit for the reason of non-linearity of the chemical shift change and that the maximum broadening is achieved at 0.6 rather than 0.4 for 2-site line shapes.

Let's try:

(truncate the spectral width in a new simulation to only leave the fast-exchange peak)

Simulate setup_truncated_range1 U_R2L2_Af_Bs

Fit is EXTREMELY POOR, indicative one has to look for a more complex model.

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U_R2L2 example 3: Fast dimerization, fast binding

Simulate setup U_R2L2_Af_Bf

Report: summary_report

We may predict that fitting will fail with 2-site model unable to reproduce line width pattern:

Optimum norm: 2.17e-01
[1] Kd: 1.09457e-06 +/- 1.8e-07
[2] Koff: 1.17928e+02 +/- 5.5e+00
[3] Scale Factor: 2.17523e+00 +/- 2.8e-02

Fit is poor, indicative that the model is more complex than U.

 

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U_R2L2 Example 5: Fast dimerization, intermediate binding

Here we place R2L2 chemical shift in between R an RL so the fast exchange peak crosses its position. When dissociation is in fast-intermedate exchange the peculiar 'transient narrowing' of the averaged peak at L/R=0.9 is observed.

Simulate setup U_R2L2_Af_Bi

Report: summary_report

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U_R2L2 example 4: Fast dimerization, slow binding

Simulate setup U_R2L2_As_Bf

Report: summary_report

This spectrum is similar to U_R and U_R2 in slow isomerization/dissociation and fast binding.

 

 

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Conclusions

Looking at the different cases we may notice that we have a limited pattern of spectral appearances that can be accounted for by different models. In another chapter I will investigate how to tell apart the models doing additional data analysis.

 

 

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