If I understand your question, it is how much higher must be the Ki of substance 2 than the Ki of substance 1 for substance 2 to be considered to have lower affinity?

The mathematical answer is that it is a question of statistical significance. After measuring both Kis at least 3 times each in order to estimate the experimental variation, you can determine to the desired degree of statistical significance (P-value, usually 0.05) whether the two values are different from each other using a t-test.

Another way to pose the question is, how big a difference in Ki is of interest to the project? From experience, I would say that about a 5-fold decrease in Ki is enough to generate interest.

You gave a wide range of baseline values in the question. The only thing I want to bring up with respect to that is that binding assays and enzyme activity assays have lower limits to the potencies they can measure, which is one-half the active site concentration. For example, if you have 10 nM receptor in a competitive binding assay, the lowest possible IC50 for an inhibitor is 5 nM. You could have very potent inhibitors with large differences between their Kis, but they could all have the same IC50 of 5 nM because of this limitation.

With weak inhibitors, you may run into the limit of solubility of the compound when you are looking at inhibitors with IC50s above about 10 µM. At high inhibitor concentrations, there is also an increased likelihood of non-specific inhibition and detection artifacts giving misleading results.

If I understand your question, it is how much higher must be the Ki of substance 2 than the Ki of substance 1 for substance 2 to be considered to have lower affinity?

The mathematical answer is that it is a question of statistical significance. After measuring both Kis at least 3 times each in order to estimate the experimental variation, you can determine to the desired degree of statistical significance (P-value, usually 0.05) whether the two values are different from each other using a t-test.

Another way to pose the question is, how big a difference in Ki is of interest to the project? From experience, I would say that about a 5-fold decrease in Ki is enough to generate interest.

You gave a wide range of baseline values in the question. The only thing I want to bring up with respect to that is that binding assays and enzyme activity assays have lower limits to the potencies they can measure, which is one-half the active site concentration. For example, if you have 10 nM receptor in a competitive binding assay, the lowest possible IC50 for an inhibitor is 5 nM. You could have very potent inhibitors with large differences between their Kis, but they could all have the same IC50 of 5 nM because of this limitation.

With weak inhibitors, you may run into the limit of solubility of the compound when you are looking at inhibitors with IC50s above about 10 µM. At high inhibitor concentrations, there is also an increased likelihood of non-specific inhibition and detection artifacts giving misleading results.

So-called tight binding is a relative concept. If Kd is much larger than the concentration of the protein in the binding assay, it is a weak binding. When the Kd approach, equals or even less than the protein concentration, it becomes tight binding. This is because free ligand concentration can no longer be treated as the total ligand concentration for tight binding in calculation:

for binding reaction: P+L=PL,

Kd=([P]-[LP])([L]-[LP])/[PL]

Therefore:

Kd=1uM, [P]=10nM, weak binding

Kd=1uM, [P]=1uM, tight binding

Kd=10nM, [P]=0.1nM, weak binding

Kd=10nM, [P]=10nM, tight binding

Cydi from EZBiolab

Very good points Adam! The problem is that I want to process automatically multiple assays from CHEMBL and hence I don't know the protein concentration or the experimental error. However, for the former, wouldn't be possible to estimate it roughly from the range of binding affinities in the assay? Also wouldn't be possible from the range of values to set a threshold binding affinity value to determine if a molecule is a binder or not? Below are 2 real examples from aspartice protease BACE:

assay CHEMBL946838 (IC50s in uM): 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.012, 0.014, 0.026, 0.065, 0.07, 0.089, 0.12, 0.13, 0.187, 0.191, 0.33, 0.44, 0.61, 0.63, 0.77, 1.35, 2.0

assay CHEMBL944848 (IC50s in uM): 0.5, 0.6, 0.6, 0.6, 0.6, 0.7, 0.7, 0.8, 0.9, 0.9, 1.0, 1.1, 1.2, 1.2, 1.3, 1.3, 1.3, 1.3, 1.3, 1.4, 1.4, 1.4, 1.5, 1.6, 1.6, 1.7, 1.8, 1.8, 1.9, 2.0, 2.0, 2.8, 3.0, 3.5, 3.7, 4.6

I would claim that the protein concentration is lower in assay CHEMBL946838. The same claim could be made for the threshold binding affinity value (lower in CHEMBL946838) to separate binders from non-binders. In general, would you claim than any compound that has binding affinity n-times higher (e.g. x1000) than the minimum binding affinity in the same assay, is a non-binder?

Can you be sure that all the IC50s reported for each assay were measured at the same protein concentration? Can you be sure that the other conditions were also the same? Is there a way in CHEMBL to obtain the protocol that was used in the assay, which would hopefully give the protein concentration and other conditions? I see that CHEMBL provides literature references for specific assays, but I'm not clear on whether all the data listed come from that specific paper.

You can't conclude that the protein concentration was lower in the first assay. It could be that the substrate concentration with which the inhibitor had to compete was much higher in the second assay. The two assays may be entirely different in many respects, and therefore the IC50s are not comparable. Moreover, the compounds being tested may be different.

Adam, when you do systematic analysis of thousands of records, you have to make several assumptions. Here the assumptions are that all the measurements of each assay were done in the same conditions (protein concentration, buffers, etc.). The only way to find this out is to read the cited publication, but in my case, this is out of option. I have to devise an automated way to create training sets of as high fidelity as possible, in order to train machine learning models.

So going back to the threshold value that separates binders from non-binders, would you agree with 1000 x min(IC50) or would you choose another value? Of course, this value will assay-specific, not a global threshold value. Or would you also set a "twilight zone", e.g. 900 x min(IC50) - 1100 x min(IC50), where one cannot be sure of the molecule binds specifically or not?

The choice of threshold is arbitrary. I can't think of any meaningful way to set it. You could consider adding another piece of information that is often considered, ligand efficiency, which normalizes inhibitory potency for molecule size (number of heavy atoms).

Is this information (number of heavy atoms) really useful in practice? If I normalize by number of heavy atoms then shouldn't I do the same to the binding affinities in my primary question? In that case, the 5-fold decrease in Ki that you mention in your answer would not apply anymore.

Yes, binding affinities can also be normalized by heavy (i.e. non-hydrogen) atom count (N). Ligand efficiency (LE) = ΔG of binding/N and

ΔG = -RTlnKi. Since IC50 is usually directly proportional to Ki in a given assay for a set of inhibitors with the same mode of inhibition, IC50 is sometimes substituted for Ki.

LE is on a different scale than Ki, so the somewhat arbitrary 5-fold difference that applies to Ki or IC50 is not relevant. One way to use LE is in conjunction with Ki or IC50. If Ki or IC50 decreases but LE also decreases, it is not a good situation. It is usually possible to increase inhibitor potency by adding lipophilicity, but doing so is a trap, because it leads to compounds with poor solubility.

Coming back to this question, but for % inhibition or % enzyme activity data. What would be a good rule to claim that one compound is stronger binder that another compound? In the case of Ki, a 5-fold difference prooved in practice to be a good rule. Hope to get some interesting answers like last time.

The same rule-of-thumb applies for inhibitors of ligand bindind as for inhibitors of enzyme activity. Care should be taken to make sure you are comparing inhibitors with the same mode of inhibition, however.

You mean at least 5-fold increase in % inhibition? This is a real case:

molname assayID

chembl3970075 CHEMBL3874242 7.7 % Inhibition

chembl3931481 CHEMBL3874242 33.2 % Inhibition

chembl3966260 CHEMBL3874242 52.4 % Inhibition

chembl3922571 CHEMBL3874242 53.8 % Inhibition

chembl3958985 CHEMBL3874242 74.8 % Inhibition

chembl3910684 CHEMBL3874242 92.1 % Inhibition

chembl3929614 CHEMBL3874242 92.4 % Inhibition

chembl467399 CHEMBL3874242 96.1 % Inhibition

chembl3922135 CHEMBL3874242 96.4 % Inhibition

chembl3940517 CHEMBL3874242 97.0 % Inhibition

chembl3901656 CHEMBL3874242 103.7 % Inhibition

chembl3891745 CHEMBL3874242 105.1 % Inhibition

chembl200102 CHEMBL3874242 106.2 % Inhibition

chembl109480 CHEMBL3874242 107.0 % Inhibition

107.0/33.2 = 3.22, so according to you, compound chembl109480 is not significantly stronger inhibitor than chembl3931481? Wouldn't the difference (instead of the ratio) be more suitable is such cases (e.g. the difference between the % inhibition between two compounds must be at least 20% in order to claim that one compound is stronger inhibitor than the other)?

Sorry to cause confusion. I was talking about IC50 or Ki, not % inhibition. % inhibition is useful when screening many compounds to identify positives, but when measuring potencies of inhibitors you should use IC50s or Kis.

I am not interested in the absolute value of the potency but in the ranking. I want to sort the molecules based on the % inhibition. Obviously, when their inhibitions are 52.4 % and 53.8 % (as in the example above) you cannot be sure that compound chembl3922571 is more potent than CHEMBL3874242. According to your experience, what would be a reasonable difference in % inhibition to claim that molecule1 is more potent that molecule2? I am not an experimentalist, that's why I am asking here.