Curve Fitting & Nonlinear Regression

Fit nonlinear curves, estimate binding parameters, and analyze dose-response assays in Excel with Python and SciPy.

Excel provides built-in tools for linear regression (LINEST) and simple trendlines, but laboratory and engineering datasets frequently follow nonlinear physical and biochemical laws. Estimating parameters from dose-response assays, enzyme kinetics, or degradation studies requires nonlinear optimization algorithms (such as Levenberg-Marquardt or trust-region methods) that Excel formulas cannot compute directly.

Boardflare integrates Python’s scientific ecosystem (scipy.optimize, lmfit) directly inside your workbook, giving you nonlinear regression without exporting data or managing external scripts.

Supported Models and Methods

Curve fitting templates provide ready-to-run models, parameter estimation with confidence intervals, and residual diagnostics:

  • Four-Parameter Logistic (4PL): Standard model for pharmacological inhibition and stimulation assays, reporting IC50/EC50, Hill slope, and upper/lower plateaus.
  • Analytical Calibration Curves: Weighted linear and quadratic fits with matrix effects and inverse prediction for unknown samples.
  • Enzyme Kinetics: Michaelis-Menten, Lineweaver-Burk, and competitive inhibition models estimating \(V_{\max}\) and \(K_m\).
  • Adsorption Isotherms: Langmuir and Freundlich surface adsorption models for chemical and environmental engineering.
  • Degradation & Stability Kinetics: First-order and Arrhenius temperature-dependent degradation equations.

How it Works in Excel

  1. Paste your raw experimental data into the designated data sheet.
  2. Configure model parameters and bounds in the defaults table (fix baselines, constrain slopes, or set confidence levels).
  3. Review interactive results in the task pane and output sheets, including fitted values, residuals, and publication-quality plots.
  4. Adapt with AI: Use Microsoft Copilot or ChatGPT inside Excel to change mathematical formulas, add replicates, or customize plotting styles.

Available Templates

Free
Adsorption isotherm (Langmuir, Freundlich)
Fit nonlinear Langmuir and Freundlich adsorption isotherms to equilibrium batch data, compare models by AICc, and determine capacity and separation factors.

Free
Calibration curve (linear, with unknowns)
Fit a linear instrument calibration curve with optional internal standard ratio, LOD/LOQ estimated with the ICH Q2(R2) approach (3.3 and 10 times the residual standard deviation divided by the slope), and QC recovery for unknown samples.

Free
Curve fitting (any x-y table)
Fit nonlinear and linear models to arbitrary x-y data, evaluate parameter uncertainties and confidence bands, and compare candidate models by AICc.

Free
Degradation kinetics (first-order decay)
Fit single first-order (SFO) degradation kinetics with replicates, half-life DT50, DT90, and log-linear cross-check.

Free
ELISA standard curve (4PL, 5PL)
Fit a 4-parameter or 5-parameter logistic (4PL/5PL) standard curve to ELISA optical densities, evaluate standard recovery and duplicate %CV, and interpolate unknown concentrations.

Free
Enzyme kinetics (Michaelis-Menten)
Fit initial reaction rates to substrate concentrations using the Michaelis-Menten model to estimate Vmax and Km with confidence intervals and Lineweaver-Burk comparison.

Free
IC50 from a dose-response assay
Fit a four-parameter logistic curve to a concentration-indexed replicate series, normalize with plate controls, and report the IC50 with its confidence interval, Hill slope, and validation against published datasets.
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