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Weak, fast-off binding , intermediate isomerization

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General comparison of models

Here we will compare outcomes of the four alternative models for conditions when binding is weak and the off-rate is fast. The isomerization is chosen to be slow here. I choose binding affinity of 106 M-1 and the off-rate constant of 500 s-1. R and RL are separated by 100 s-1 and R* or R*L - by 100 s-1 from corresponding species. Isomerization equilibrium is shifted 5:1 toward *-forms. The reverse isomerization rate is 17 s-1 to make kex =100 s-1 .

Location:Af_Bi/

Simulate setup U_Af

Simulate setup U_R_Af_Bi

Simulate setup U_L_Af_Bi

Simulate setup U_RL_Af_Bi

  Note remarkable narrowing of the peak in the very beginning of titration! Similar to U model Notice remarkable narrowing of the peak near the end of titration!

 

NOTE: The transient narrowing of the line shapes in U_R and U_RL models is only happening if *-isomer chemical shift is in between the R and RL chemical shifts as can be seen below:

Simulate setup U_R_Af_Bi_reverse_chem_shifts

Simulate setup U_RL_Af_Bi_reverse_chemical_shifts

Shifting of the final peak is a remarkable feature. Shifting of the initial peak is small inversely proportional to the R*/R. Shifting of the initial peak is a remarkable feature. Shifting of the final peak is small inversely proportional to the RL*/RL. The FWHH of the final peak sharply decreases at the end.

 

The models produce very feature-rich lineshapes. Forward and reverse titrations will enable sensitive distinction between the models.


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Evolution of complex line shapes in U_R system

k2(B), s-1

k2(B)= 0.1 s-1

 

k2(B)= 1 s-1

 

k2(B)= 10 s-1

 

k2(B)= 30 s-1

 

k2(B)= 60 s-1

 

k2(B)= 120 s-1

 

k2(B)= 240 s-1 k2(B)= 500 s-1 k2(B)= 1000 s-1
 

Setup setup_U_R_fancy_lineshapes

U_R_Af_Bi_fancy_lineshapes1

Setup setup_U_R_fancy_lineshapes

U_R_Af_Bi_fancy_lineshapes2

Setup setup_U_R_fancy_lineshapes

U_R_Af_Bi_fancy_lineshapes3

Setup setup_U_R_fancy_lineshapes

U_R_Af_Bi_fancy_lineshapes4

Setup setup_U_R_fancy_lineshapes

U_R_Af_Bi_fancy_lineshapes5

Setup setup_U_R_fancy_lineshapes

U_R_Af_Bi_fancy_lineshapes6

Setup setup_U_R_fancy_lineshapes U_R_Af_Bi_fancy_lineshapes7

Setup setup_U_R_fancy_lineshapes U_R_Af_Bi_fancy_lineshapes8

Setup setup_U_R_fancy_lineshapes U_R_Af_Bi_fancy_lineshapes9

  slow exchange conditions help us see the average resonance of R and RL moving through the R* resonance   Exchange between R and R* is in intermediate regime (kex=60) and significant narrowing of the overlapped line is seen at L/R=0.1, 0.2   Exchange between R and R* is faster so the peak at L/R=0 becomes narrower while the overlapped resonance at 0.1 and 0.2 stays same narrow (visual narrowing effect disappears). The R-R* exchange is fast now, now visual narrowing is seen but the line widths are significantly different from what U-model would produce      
 
 
 

Display line width evolution

comparisons/

plotdatasets 'U_R_fancy_lineshapes6' 'L/R' 'FWHH,/s'

Reason to the significant narrowing of the peak in the initial steps after ligand addition is that the fast-exchange resonance between R and RL shifts and overlaps with the position of R*. When k2 accelerates so the exchange between R and R* becomes intermediate and the significant narrowing of the average peak between all three states is observed. As k2 further accelerates the initial broadening of R-R* peak reduces so there is no visual narrowing any more.

Another large effect is that the maximum of broadening is at L/R=0.5 when exchange in R-R* is intermediate and shifts even further away to 0.6 when exchange becomes fast so no initial narrowing is seen any more. Only when exchange rate exceeds 3000/s  the maximum of broadening returns to the 0.4 observed in the 2-state model.

These are very significant effects indicative of the U_R model.

 


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Evolution of complex line shapes in U_RL system

k2(B), s-1

k2(B)= 0.1 s-1

 

k2(B)= 1 s-1

 

k2(B)= 10 s-1

 

k2(B)= 30 s-1

 

k2(B)= 60 s-1

 

k2(B)= 120 s-1

 

k2(B)= 240 s-1 k2(B)= 500 s-1 k2(B)= 1000 s-1
 

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes1

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes2

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes3

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes4

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes5

 

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes6

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes7

 

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes8

 

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes9

 
 
 
                   

Plot line width evolution

comparisons/

plotdatasets 'U_RL_fancy_lineshapes6' 'L/R' 'FWHH,/s'

U_RL system gives rise to much more significant line broadening than U system. Visually, when k2(B) brings B-transition into intermediate regime we see narrowing of the average peak at the end of titration (L/R=0.9) followed by a new broadening process. As k2(B) accelerates the effect is reduced and the maximum of broadening in the titration series shifts from L/R 0.4-0.5 to 0.4 (relatively minor shift) and the end-point broadening is reduced as well.

 


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Difference between U_R and U_RL in the fast exchange

If isomerization is fast then we only see a shifting peak. However, these two cases as still markedly distinct

Simulate setup U_Af

k2(B)= 240 s-1

Setup setup_U_R_fancy_lineshapes U_R_Af_Bi_fancy_lineshapes7

k2(B)= 240 s-1

Simulate setup_U_RL_fancy_lineshapes U_RL_Af_Bi_fancy_lineshapes7

Plot line width evolution

comparisons/

plotdatasets 'LW_lineshapes7' 'L/R' 'FWHH,/s'

 

Kd=1e-6

Koff=500

[1] Kd: 1.58777e-06 +/- 1.4e-07 
[2] Koff: 3.94176e+02 +/- 1.9e+01

[1] Kd: 1.30095e-07 +/- 1.4e-08
[2] Koff: 7.68534e+01 +/- 5.2e-01
  Kd and Koff are roughly in the range but pattern of discrepancy between U and U_R is remarkable due to significant differences in line broadening distribution across L/R range Discrepancy between U and U_RL is smaller because line broadening effect is distributed similarly along L/R but much larger line width dictate significantly smaller Koff. Pattern of mismatch between the line shape is less remarkable and very different from what U_R shows.

 


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Conclusions

  1. Weak binding with intermediate isomerizaition is a regime with the very rich information content. Narrowing of fast-exchange averaged peaks is a remarkable feature of U_R in the beginning of L/R range and for U_RL in the end.
  2. U_R and U_RL mechanisms produce remarkably different line shapes and forward and reverse titrations undoubtedly capable of setting U_R/U_L system aside.
  3. U_RL system is very distinguishable in slow and intermediate exchange. In fast exchange it is closer to U but still has signature deviation of line widths at the end of titration, which may be enhanced by choice of L/R points at the end.

 


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