Biomanufacturing innovation relies on an efficient Design of Experiments (DoEs) to optimize processes and product quality. Traditional DoE methods, ignoring the underlying bioprocessing mechanisms, often suffer from a lack of interpretability and sample efficiency. This limitation motivates us to create a new optimal learning approach for digital twin model calibration. In this study, we consider the cell culture process multi-scale mechanistic model, also known as Biological System-of-Systems (Bio-SoS). This model with a modular design, composed of sub-models, allows us to integrate data across various production processes. To calibrate the Bio-SoS digital twin, we evaluate the mean squared error of model prediction and develop a computational approach to quantify the impact of parameter estimation error of individual sub-models on the prediction accuracy of digital twin, which can guide sample-efficient and interpretable DoEs.