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Performing non-linear curve fits using 4 & 5-parameter logistic regression

Learn how to apply 4 and 5 parameter logistic fits to your data in Synthace

Updated this week

This documentation provides a comprehensive guide on performing curve fitting using the Synthace platform within a Design of Experiments (DOE) context. It covers the setup of factors, data preparation, and the application of logistic fits to analyze dose-response curves.

Curve fitting in Synthace

Curve fitting in Synthace enables you to model complex dose–response relationships directly within your data preparation workflow.


This functionality integrates seamlessly with the Prepare Data app, so you can clean, transform, and fit your data in one place — without needing to export to external tools.

What you can do

  • Fit multiple dose–response curves simultaneously across quasi-replicates or experimental runs

  • Extract parameters such as minimum and maximum asymptotes, inflection points, slope factors, asymmetry, and EC50/IC50 values

  • Use derived parameters as responses for DOE (Design of Experiments) analysis within Synthace

  • Apply parameter constraints to improve calculation accuracy and reduce fit time

  • Keep all data processing, curve fitting, and analysis fully traceable within your workflow

Supported models

Model

Description

When to use

Four-Parameter Logistic (4PL)

Standard sigmoidal fit without asymmetry

Use when the curve is approximately symmetric; faster to calculate (around 20–30 seconds per curve)

Five-Parameter Logistic (5PL)

Adds an asymmetry factor for more flexible fitting

Use when curves show asymmetric entry or exit slopes; calculates all parameters, including asymmetry and EC50


Step-by-step guide

Prepare your data

  1. Open your workflow and switch to DOE mode.

  2. Launch the Prepare Data app from the workflow panel.

  3. Use the pivot function to reorganize your dataset against the relevant independent variable — for example, substrate concentration or compound dose.

Apply curve fitting

  1. Open the Calculate tab within the Prepare Data app.

  2. From the Transform dropdown, choose either:

    • Four-Parameter Logistic (4PL), or

    • Five-Parameter Logistic (5PL)

  3. Verify that:

    • The independent variable (e.g., concentration) is correctly identified

    • The dependent variable (e.g,. fluorescence signal or absorbance) is correctly selected

  4. Check for missing or duplicated values before proceeding — clean data leads to more stable curve fits

  5. Optionally, apply parameter constraints to guide the fitting process. You can define minimum and maximum bounds for:

    • Minimum and maximum asymptotes

    • Inflection point

    • Slope factor

    • Asymmetry factor (for 5PL only)

Note: 5PL fits include one extra parameter and may take slightly longer to compute than 4PL.

Review derived parameters

Once the calculation completes, Synthace adds new parameter columns directly to your dataset. Each row now includes both the fitted values and a metric indicating the quality of the fit.

Derived parameters include:

  • Minimum and maximum asymptotes: Start and plateau points of the sigmoidal curve

  • Inflection point: Concentration at maximal slope (midpoint). In the case of 4-PL fits the inflection point is equal to the XC50 (e.g. EC50/IC50), the concentration producing a half-maximal effect.

  • Slope factor: Steepness of the curve

  • RMSE: Root mean squared error — a measure of fit quality

  • Asymmetry factor (5PL only): Degree of non-uniformity between entry and exit slopes

These derived parameters are automatically available as responses for DOE model analysis.
You can now proceed to fit DOE surfaces, run optimizations, or export fitted parameters for downstream work.


Visualize curve fits

  1. Use the graph view within the Prepare Data app to inspect fitted curves.

  2. Select or deselect runs in the data table to update which curves appear on the graph.

  3. The visualization highlights:

    • Best fits — lowest RMSE values, indicating strong agreement between data and model

    • Worst fits — higher RMSE values, often signaling noisy data or mis-specified constraints

  4. Review any outliers or poorly fitted curves:

    • Check if data points are mislabelled or missing

    • Adjust parameter constraints to stabilize the fit

    • Recalculate to confirm improvement

Note: For clarity, the curve visualization panel can show a maximum of 8 curves at once. If additional curves are selected for visualization, it will replace another curve in the plot.


Best practices

  • Start simple: use 4PL first — it’s faster and suitable for most sigmoidal curves

  • Use constraints: setting sensible bounds helps the model converge and avoids biologically implausible results

  • Check fit quality: always review RMSE and plotted curves before using fitted parameters in further analysis

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