04 / 06 · Decreasing 4PL
Teaching example. Synthetic data.
At what concentration is the response halfway between the plateaus?
The response decreases as concentration rises. Find the concentration at the midpoint between the model’s upper and lower plateaux.
Theory: Dose-response curves: the four-parameter logistic model →
10 concentrations · 4 parameters
- Half-response concentration: IC50, µM
- 2.491
- 95% confidence interval
- 2.422 … 2.561
Inspect the original observations
| Concentration, µM | Response |
|---|---|
| 0.01 | 98.0729 |
| 0.03 | 97.2267 |
| 0.1 | 96.4243 |
| 0.3 | 90.8103 |
| 1 | 74.3169 |
| 3 | 44.37 |
| 10 | 17.4914 |
| 30 | 6.5321 |
| 60 | 4.2227 |
| 100 | 2.9341 |
Calculated by the Linza engine from this example’s data. Opening it in the editor runs a fresh calculation.
Why this method
A decreasing four-parameter logistic model describes two plateaus and the transition between them. A straight line cannot represent that shape. Reliable IC50 estimation depends on doses covering both plateaus and the transition; an attractive curve is insufficient.
Explore the theory: Dose-response curves: the four-parameter logistic model →Work through it in Linza
Open the chart with its logarithmic X axis. Locate both plateaus, then the halfway response and its corresponding concentration. In Analyses, check the interval and fit warnings. Do not transfer the IC50 to other conditions without validation.
Open a copy and recalculateTry changing one condition
Add 10 to every response Y. Should this shift alone change IC50?
Show the explanation
In the ideal model, both plateaus move up by 10 while the midpoint concentration stays the same. IC50 is defined relative to the plateaus. Sparse data and unstable fitting can affect numerical estimates, so inspect the warnings.
Data and reproducibility
Teaching studies with synthetic data. The scenarios reflect practical questions, but do not report real experimental findings.