One-phase association fit / rate constant value comparison

Question

Currently, I am writing my thesis (in molecular biology - not mathematics), and I am puzzled over the results.

I measured an increase in a signal and did a one-phase association fit in GraphPad. Now, I have four curves, and they look as we would expect.

The bit that puzzles me is: why does the rate constant K not correlate to the steepness of the curves? I would have expected the rate constant to increase in the order 1, 2, 3, 4 because they do have an increasing steepness. Am I getting the meaning of K wrong?

Thanks for your help

Edit: Thank you for your answer. Here are the equations: $$Y=Y0 + (Plateau-Y0)*(1-exp(-K*x))$$

One-phase association information from GraphPad Prism:

X: Time

Y: Y starts at Y0, then goes up to Plateau with one phase

Y0 and Plateau: Same units as Y

K: Rate constant in units that are the reciprocal of the X axis units.

1. $Y=0 + (20.11-0)*(1-exp(-0.006995*x))$
2. $Y=0 + (43.89-0)*(1-exp(-0.005735*x))$
3. $Y=0 + (58.24-0)*(1-exp(-0.009574*x))$
4. $Y=0 + (98.02-0)*(1-exp(-0.009438*x))$

Answer 1

The rate constant determines the speed with which the value of $Y$ approaches the plateau. In your data that seems not to correlate with the value of the plateau - the plateau can be larger without being attained faster. If that contradicts something you think should be true you may need to examine the data collection or the model. Some but not all the datapoints have error bars.

The half-time column is the time it takes to get halfway to the plateau. That's inversely proportional to the rate constant; the constant of proportionality is $\ln(2) \approx 0.7$.