An all-in-one state-observer for protein refolding reactions using particle filters and delayed measurements

Proper monitoring as basis for process optimization and control of protein refolding reactions in real-time is difficult and currently available techniques are either expensive, not applicable in real-time or give only limited information about the ongoing process. Model-based methods such as particle filters (PFs) have been used in different biological systems for state-estimation to overcome difficulties arising from states that are hard or impossible to measure, often low measurement frequencies and high measurement delay. Since recent approaches had difficulties to overcome all these problems, a novel approach via a PF including a mechanistic model is used. The PF is calibrated and tuned with experimental data and its applicability validated with two additional experiments. It is shown how augmentation of model parameters can be used for state-estimation in real-time to better adapt to model inaccuracies, poor model calibration or application of the calibrated model to a new process. Furthermore, it is shown that the PF can deal with low measurement frequencies and high measurement delay, resulting in reliable tracking of the process with normalized root mean squared errors (NRMSE) of the native protein and folding intermediates between 3.44 and 6.62%, values in the range of 18 to 93% less compared to simple feed-forward simulation.