The Distance Between: An Algorithmic Approach to Comparing Stochastic Models to Time-Series Data.

Area of Science:

• Systems Biology
• Computational Biology
• Biophysics

Background:

• Macroscopic cellular processes are understood via mean-field models.
• Stochastic models offer molecular-level insights but require quantitative validation.
• Experimental biological data often feature small sample sizes and evolving distributions.

Purpose of the Study:

• To identify suitable distance metrics for comparing stochastic model outputs with time-evolving experimental data.
• To find metrics that facilitate parameter inference, model comparison, and model validation.
• To address challenges posed by small sample sizes and temporal dynamics in biological data.

Main Methods:

• Compared stochastic model outputs to synthetic data across multiple experimental scales.
• Evaluated discrete (Kolmogorov-Smirnov) and integrated (Wasserstein-1) distance metrics based on empirical cumulative distribution functions (ECDFs).
• Assessed metric sensitivity to parameter changes and robustness to added noise simulating experimental error.

Main Results:

• Integrated distance metrics exhibited smoother parameter transitions compared to discrete measures.
• Integrated metrics demonstrated robustness to noise, effectively replicating experimental error.
• Discrete measures showed high sensitivity only near true parameters, limiting their utility.

Conclusions:

• Integrated distance metrics are superior for fitting stochastic models to real-world biological data.
• These findings enable the design of algorithms for accurate stochastic model parameterization.
• The study provides a foundation for advancing molecular-scale understanding of cellular systems.