Parameter-wise predictions and sensitivity analysis for random walk models in the life sciences.

Area of Science:

• Computational Biology
• Mathematical Modeling
• Systems Biology

Background:

• Sensitivity analysis is crucial for understanding mathematical models but less developed for stochastic models, especially spatial ones like random walk models (RWMs).
• Analyzing computationally expensive stochastic simulations directly poses significant challenges.

Purpose of the Study:

• To develop a novel sensitivity analysis method, parameter-wise prediction, for computationally expensive, spatio-temporal stochastic models.
• To apply this method to two biologically relevant classes of lattice-based RWMs.

Main Methods:

• Employed continuum-limit partial differential equation (PDE) descriptions as surrogate models for RWMs.
• Linked surrogate PDE models to RWMs using biophysically-motivated measurement error models.
• Utilized a likelihood-based framework for parameter estimation, identifiability, and sensitivity analysis.

Main Results:

• Demonstrated the application of parameter-wise prediction to both classical RWMs (neglecting crowding) and exclusion process RWMs (incorporating crowding).
• Showcased how combining different process and measurement error models reveals parameter-specific impacts on simulation outcomes.
• Provided open-access software for reproducibility.

Conclusions:

• Parameter-wise prediction offers an efficient and robust approach for sensitivity analysis in complex stochastic models.
• The likelihood-based framework facilitates comprehensive model understanding, including parameter estimation and identifiability.
• This methodology advances the analysis of spatio-temporal stochastic processes in computational biology.