Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models

Area of Science:

• Mathematical Biology
• Computational Biology
• Biophysics

Background:

• Stochastic individual-based models capture biological variability but are computationally expensive.
• Coarse-graining stochastic models into continuum models reduces computational cost but can introduce bias.
• Accurate parameter inference requires addressing inaccuracies in continuum approximations.

Purpose of the Study:

• To develop a computationally efficient method for accurate parameter inference in cell biology models.
• To combine stochastic and continuum models by statistically correcting for continuum approximation discrepancies.
• To demonstrate the approach on cell proliferation and barrier assays.

Main Methods:

• Developed a statistical model for the discrepancy between stochastic and continuum models.
• Employed computer experiment design to select sampling points for the discrepancy model.
• Integrated the discrepancy model with continuum models (logistic ODE, Fisher-KPP) for corrected inference using maximum likelihood estimation.

Main Results:

• The combined approach accurately recovers parameters and provides reliable confidence intervals, unlike continuum models alone.
• Discrepancy correction significantly reduces bias in parameter estimation and improves confidence interval coverage.
• The method achieves this accuracy with minimal computational overhead compared to purely stochastic simulations.

Conclusions:

• Statistically modeling the discrepancy between stochastic and continuum models is an effective strategy for accurate computational biology simulations.
• This hybrid approach offers a balance between computational efficiency and the fidelity of stochastic models.
• The developed algorithms, implemented in Julia, enable robust parameter inference in complex biological systems.