Overcoming the Limits of Traditional Rate Calculations from Sparse Concentration Data: A Probabilistic Framework for Bioprocess Modeling

Accurate estimation of growth and metabolic rates is essential for understanding and optimizing bioprocesses, yet traditional methods often fail when faced with sparse or noisy concentration data. We present a probabilistic framework based on Bayesian inference and Nested Sampling that addresses these challenges by integrating biological knowledge directly into the model structure. The approach transforms raw concentration measurements into pseudo-concentrations that account for distortions caused by bioreactor volume changes (e.g., feed additions, sample withdrawals), and models metabolic rates as linear combinations of basis functions to yield continuous rate profiles from discrete data. Using in-silico simulations, we evaluated the framework under a range of experimental conditions and compared its performance with a conventional rate calculation method. We further analyzed the influence of key experimental design parameters - sampling frequency, sample volume, and measurement noise - on both rate estimation accuracy and concentration reconstruction quality. Results demonstrate that the proposed framework delivers accurate, robust metabolic rate estimates even under severe data sparsity and noise, offering a powerful tool for improving bioprocess characterization and optimization.