Matrix notation for efficient development of first‐principles models within PAT applications: Integrated modeling of antibiotic production with Streptomyces coelicolor

Abstract

A matrix notation coupled to macroscopic principles is introduced as a means to develop first- principles models in an efficient and structured way within PAT applications. The notation was evaluated for developing an integrated biological, chemical (pH modeling) and physical (gas-liquid exchange) model for describing antibiotic production with Streptomyces coelicolor in batch fermentations. The model provided statistically adequate fits to all the monitored macroscopic biological, chemical and physical data of the process, except the phosphate uptake dynamics. This phosphate discrepancy is hypothesized to result from the internal storage of phosphate as polyphosphate prior to the exponential growth phase. The antibiotic production was associated with the stationary phase and its kinetics was adequately described using a modified Luedeking-Piret equation. Further, the maintenance was best described by employing a combination of Pirt and Herbert models, a result that was supported by a model-based hypothesis testing. Overall the process knowledge currently incorporated in the model is believed to be useful both for process optimization purposes and for further testing of hypotheses aiming at improving the mechanistic understanding of antibiotic production with S. coelicolor. Last but not least, the matrix notation is believed to be a promising supporting tool for efficient development and communication of complex dynamic models within a PAT framework.

Process analytical technology (PAT) for biopharmaceuticals

“…In this respect, mechanistic modeling has gained renewed attention because a mechanistic model can be considered as a structured representation of the available process knowledge. Indeed, during the model-building procedure, the process knowledge is coded in a mechanistic model using appropriate mathematical expressions [18][19][20][21]. Such a model therefore incorporates process-relevant input (critical process variables) -output (product concentration and product quality attributes) relationships, which can be used to establish a proper design space.…”

“…A systematic model development methodology addresses this drawback [26] and is beneficial for a number of reasons: (i) model development is more efficient (i.e., less time and resources required), and (ii) communication and knowledge transfer among the various members of the multidisciplinary team (i.e., researchers, engineers, operators, managers) typically involved in the development and implementation of a PAT system are facilitated. To this end, the matrix notation is commonly used because it allows a compact and visually appealing description of a complex mathematical model [20,27].…”

“…GMoP comprises the application of a set of mathematical and statistical techniques that allow improvements in the use and the reliability of the model. Examples include the calculation of correlation coefficients and confidence intervals for estimated parameters to verify sufficient data quality and quantity to allow reliable parameter estimation [20]. Additional examples include uncertainty analysis and sensitivity analysis [28][29][30].…”

Application of modeling and simulation tools for the evaluation of biocatalytic processes: A future perspective

“…Such a study is needed to theoretically establish whether biocatalysis models can in principle be identified reliably from the typical set of available measurements. For example, in case one could provide evidencefollowing a formal identifiability analysis 41,42 -that the biocatalysis models are unidentifiable, then this means the estimated-parameter values may not be interpreted as unique (the values themselves become arbitrary while the model fit remains equally good 41,42 ). In such a case, one needs to analyze the implications of parameter identifiability on model predictions which calls for uncertainty analysis.…”

Good modeling practice for PAT applications: Propagation of input uncertainty and sensitivity analysis

“…This activity is frequently used in life sciences for developing an improved understanding of microbiological processes. [1][2][3][4] The resulting mechanistic model can be considered as a summary of available process knowledge and understanding of a system. Process understanding is precisely what is asked for in the recent Process Analytical Technology (PAT) initiative introduced in the pharmaceutical industry.…”