The biphasic equation is a double-sigmoid curve fit commonly employed to model processes that exhibit two distinct phases. These processes may include dose response studies for PROTACs that do not follow a normal distribution, dose-response curves where a drug may have two different mechanisms of action, or a kinetic scenario where a ligand may have an initial binding phase and then a secondary action.
To implement the accumulation and exponential decay curve fit, users can follow these steps:
- Creating readouts for input data such as concentration and % response (with or without normalization)
- Creating a plot type readout to generate the curve fit
- Data calculations for different intercepts (optional)
- Editing and saving the curve
Lets work through an example where we will implement this curve fit within our “Dual Mechanism Agonists” protocol.
Create a numerical readout for the X-axis values:
Create a numerical readout for the Y-axis values:
Create a readout to plot the curve and calculate any optional intercept values:
Our protocol now captures our input data and automatically generates a biphasic curve fit for each entity per run of the protocol. As shown below, be sure to customize your report to include relevant calculated parameters such as log center 1 and 2, IC50, or slope.
The Biphasic equation curve fit is performed using the following equation where the x-axis must be in log scale:
plateau1 + (plateau2 - plateau1)*frac/(1+10**((center1-x)*slope1)) + (plateau2 – plateau1)*(1-frac)/(1+10**((center2-x)*slope2))
Where
Plateau 1= plateau at the left end of the curve in units of Y
Plateau 2= plateau at the right end of the curve in units of Y
Center 1= EC50_1 the concentration that gives half-maximal stimulatory or inhibitory effects in phase 1 in units of X).
Center 2= EC50_2 the concentration that gives half-maximal stimulatory or inhibitory effects in phase 2 in units of X).
Slope 1= unitless slope factors or Hill slopes.
Slope 2= unitless slope factors or Hill slopes.
Frac= the proportion of maximal response due to the more potent phase.
The following parameters will automatically be calculated by CDD Vault for this plot type:
- Area under the curve
- Frac
- Center 1 (EC50)
- Center 2 (EC50)
- Maximum measured
- Minimum measured
- N
- Plateau 1
- Plateau 2
- R squared
- Slope 1
- Slope 2
Area under the curve:
- The CDD Vault AUC is calculated as the (positive area - negative area) under the curve where:
- The curve is defined as straight line connections between responses, not the fitted curve (Linear Trapezoidal Non-uniform grid method)
- Units are (response units * log10(dose_units))
- The baseline is set at the negative control mean or 0 if control data is not available
Please note that all auto-calculated parameters listed above can be used in custom calculations as separate readouts. These parameters can be accessed within our robust formula editor