Percent inhibition / activation — theory
Many enzyme assays test how a treatment (an inhibitor, activator, mutation, salt, pH shift, etc.)
changes the observed reaction rate. If \(v_0\) is the control rate (no treatment) and \(v_i\) is
the treated rate, we quantify the change as a percent difference relative to the control.
The key idea: compare rates through the ratio \(v_i/v_0\). A ratio below 1 means inhibition; above 1 means activation.
1) Definitions
The commonly used definitions are:
\[
\%\,\text{inhibition}=100\left(1-\frac{v_i}{v_0}\right)
\]
\[
\%\,\text{activation}=100\left(\frac{v_i}{v_0}-1\right)
\]
These two formulas are negatives of each other:
\[
\%\,\text{activation} = -\,\%\,\text{inhibition}
\]
That is why an “auto” reporting mode can label results based on whether \(v_i \le v_0\) or \(v_i > v_0\).
2) Interpreting the ratio \(v_i/v_0\)
The ratio determines both direction and magnitude:
Notice that percent inhibition is defined to be positive when the treated rate is lower than the control.
Percent activation is defined to be positive when the treated rate is higher than the control.
3) Why replicates matter (recommended mode)
Rates typically vary from run to run due to pipetting error, instrument noise, temperature drift,
or biological variability. With replicate measurements, we summarize each condition with a mean and a standard deviation:
\[
\bar v = \frac{1}{n}\sum_{k=1}^{n} v_k
\]
\[
s = \sqrt{\frac{\sum_{k=1}^{n}(v_k-\bar v)^2}{n-1}}
\]
The calculator then computes percent inhibition/activation using the means:
\[
\%\,\text{inhibition}=100\left(1-\frac{\bar v_i}{\bar v_0}\right),\qquad
\%\,\text{activation}=100\left(\frac{\bar v_i}{\bar v_0}-1\right)
\]
Interpretation tip: the SD does not directly enter the percent formula, but it tells you how stable your assay is.
Large SDs can make a small “percent change” unconvincing.
4) Dose series: inhibition vs concentration
In a dose series, you measure a rate at multiple inhibitor (or activator) concentrations, then compute the percent change
relative to a baseline control rate \(v_0\). If the dataset includes a “no compound” row (dose \(=0\)),
that row is often used as the baseline.
For each dose point:
\[
\%\,\text{inhibition at dose } D = 100\left(1-\frac{v(D)}{v_0}\right)
\]
Plotting “% inhibition vs dose” is useful even before fitting an IC50 model:
you can visually inspect monotonicity, saturation, and the dose range where effects appear.
A horizontal 50% line is a handy reference because it shows where an IC50 would lie if you later fit a curve.
This calculator shows that line even without a full IC50 fit.
5) Validity checks and common pitfalls
-
\(v_0\) must be > 0 because it appears in the denominator. If your “control rate” is near zero,
percent change becomes unstable and not meaningful.
-
Rates should be positive for these formulas. Negative rates can happen after blank subtraction or drift correction
(especially in absorbance assays). In that case, fix the baseline/data processing first.
-
Units cancel in the ratio \(v_i/v_0\), so any consistent rate unit is acceptable.
However, do not mix different units across conditions.
-
Large variability (large SD) can hide or exaggerate apparent percent effects. Use replicates and report mean ± SD.
6) Reporting: inhibition vs activation
Many lab reports choose a single convention:
- Inhibitor experiments often report % inhibition, where positive values indicate decreased activity.
- Activator experiments often report % activation, where positive values indicate increased activity.
This is why the calculator can “auto-label” the result based on whether \(v_i \le v_0\) or \(v_i > v_0\),
or show both if you want a symmetric view.
