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Symbolic Regression (SR) is a Machine Learning method that seeks for a mathematical expression to find the best model given a dataset. This remains a really hard task as, unlike classic Machine Learning, both model parameters and model structure are unknown. Typically, algorithms for Symbolic Regression have been based on classical heuristic search algorithms as Genetic Programming, Simulated Annealing or Bayesian approaches. Nevertheless, in the last years a new movement trying to tackle the problem using Neural Networks has arisen. The results obtained show a promising research pathway but the usage of these networks for SR is still under-explored. In this thesis, we propose a data-dependent Transformer Model trained in two phases (supervised phase and Reinforcement Learning phase) to improve the state-of-the-art in Symbolic Regression. The performance of our model is compared to its direct predecessor, NeSymRes and, gplearn, a widely used algorithm based on Genetic Programming. The results obtained demonstrated that we have succeeded in building a model that is able to create high accurate and low complex equations given a dataset (X, Y) as an input. Our model outperforms the compared algorithms in terms of accuracy, recoverability rate, complexity and execution time. Most importantly, we help to settle the usage of Neural Networks for SR as a promising and interesting future line of research.

Nonreplicating rotavirus vaccine (NRRV) candidates are being developed with the aim of serving the needs of developing countries. A significant proportion of the cost of manufacturing such vaccines is the purification in multiple chromatography steps. Crystallization has the potential to reduce purification costs and provide new product storage modality, improved operational flexibility, and reduced facility footprints. This communication describes a systematic approach for the design of the crystallization of an NRRV candidate, VP8 subunit proteins fused to the P2 epitope of tetanus toxin, using first-principles models and preliminary experimental data. The first-principles models are applied to literature data to obtain feasible crystallization conditions and lower bounds for nucleation and growth rates. Crystallization is then performed in a hanging-drop vapor diffusion system, resulting in the nucleation and growth of NRRV crystals. The crystals obtained in a scaled-up evaporative crystallization contain proteins truncated in the P2 region, but have no significant differences with the original samples in terms of antibody binding and overall conformational stability. These results demonstrate the promise of evaporative crystallization of the NRRV.

Development of continuous biopharmaceutical manufacturing processes is an area of active research. This study considers the long-term transgene copy number stability of Pichia pastoris in continuous bioreactors. We propose a model of copy number loss that quantifies population heterogeneity. An analytical solution is derived and compared with existing experimental data. The model is then used to provide guidance for stable operating timescales. The model is extended to consider copy number dependent growth such as in the case of Zeocin supplementation. The model is also extended to analyze a continuous seeding strategy. This study is a critical step towards understanding the impact of continuous processing on the stability of Pichia pastoris and the resultant products.

© 2020 Elsevier B.V. The freezing step plays a key role in the overall economy of the vacuum freeze-drying of pharmaceuticals, since the nucleation and crystal growth kinetics determine the number and size distribution of the crystals formed. In this work, a new mathematical model of the freezing step of a (bio)pharmaceutical solution is developed and validated. Both nucleation and crystal growth kinetics are modeled and included in a one-dimensional population balance (1D-PBM) that describes, given the product temperature measurement, the evolution of the pore size distribution during freezing. The developed model is coupled with the real-time measurements obtained from an infrared video camera. The ending time of the primary drying stage, and the maximum temperature inside the material, simulated through a simplified model of the process and the pore distribution forecast, resulted in good agreement with experimental values. The resulting Process Analytical Technology (PAT) has the potential to boost the development and optimization of a freeze-drying cycle and the implementation of a physically grounded Quality-by-Design approach in the manufacturing of pharmaceuticals. A more general mathematical model, including the aforementioned population balance, of a vial filled with a solution of sucrose was also developed and used to further validate the approach.

The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern formation to learn the functional forms of the nonlinear and nonlocal constitutive relations in the governing equation. We use PDE-constrained optimization to infer the governing dynamics and constitutive relations and use Bayesian inference and linearization to quantify their uncertainties in different systems, operating conditions, and imaging conditions. We discuss the conditions to reduce the uncertainty of the inferred functions and the correlation between them, such as state-dependent free energy and reaction kinetics (or diffusivity). We present the inversion algorithm and illustrate its robustness and uncertainties under limited spatiotemporal resolution, unknown boundary conditions, blurry initial conditions, and other non-ideal situations. Under certain situations, prior physical knowledge can be included to constrain the result. Phase-field, reaction-diffusion, and phase-field-crystal models are used as model systems. The approach developed here can find applications in inferring unknown physical properties of complex pattern-forming systems and in guiding their experimental design.

Redox flow batteries are a nascent, yet promising, energy storage technology for which widespread deployment is hampered by technical and economic challenges. A performance-determining component in the reactor, present-day electrodes are often borrowed from adjacent electrochemical technologies rather than specifically designed for use in flow batteries. A lack of structural diversity in commercial offerings, coupled with the time constraints of wet-lab experiments, render broad electrode screening infeasible without a modeling complement. Herein, an experimentally validated model of a vanadium redox flow cell is used to generate polarization data for electrodes with different macrohomogeneous properties (thickness, porosity, volumetric surface area, and kinetic rate constant). Using these data sets, we then build and train a neural network with minimal average root-mean squared testing error (17.9 ± 1.8 mA cm−2) to compute individual parameter sweeps along the cell polarization curve. Finally, we employ a genetic algorithm with the neural network to identify electrode property values for improving cell power density. While the developed framework does not supplant experimentation, it is generalizable to different redox chemistries and may inform future electrode design strategies.

An augmented Bayesian optimization approach is presented for materials discovery with noisy and unreliable measurements.

Batch low-pH hold is a common processing step to inactivate enveloped viruses for biologics derived from mammalian sources. Increased interest in the transition of biopharmaceutical manufacturing from batch to continuous operation resulted in numerous attempts to adapt batch low-pH hold to continuous processing. However, control challenges with operating this system have not been directly addressed. This article describes a low-cost, column-based continuous viral inactivation system constructed with off-the-shelf components. Model-based, reaction-invariant pH controller is implemented to account for the nonlinearities with Bayesian estimation addressing variations in the operation. The residence time distribution is modeled as a plug flow reactor with axial dispersion in series with a continuously stirred tank reactor, and is periodically estimated during operation through inverse tracer experiments. The estimated residence time distribution quantifies the minimum residence time, which is used to adjust feed flow rates. Controller validation experiments demonstrate that pH and minimum residence time setpoint tracking and disturbance rejection are achieved with fast and accurate response and no instability. Viral inactivation testing demonstrates tight control of logarithmic reduction values over extended operation. This study provides tools for the design and operation of continuous viral inactivation systems in service of increasing productivity, improving product quality, and enhancing patient safety.

Under appropriate buffer and pH conditions, the magnitude and dispersion of the product protein crystals were reproducibly manipulated by controlling the spatial temperature along the tube in a continuous tubular crystallizer.

Manufacturing of recombinant adeno-associated virus (rAAV) viral vectors remains challenging, with low yields and low full:empty capsid ratios in the harvest. To elucidate the dynamics of recombinant viral production, we develop a mechanistic model for the synthesis of rAAV viral vectors by triple plasmid transfection based on the underlying biological processes derived from wild-type AAV. The model covers major steps starting from exogenous DNA delivery to the reaction cascade that forms viral proteins and DNA, which subsequently result in filled capsids, and the complex functions of the Rep protein as a regulator of the packaging plasmid gene expression and a catalyst for viral DNA packaging. We estimate kinetic parameters using dynamic data from literature and in-house triple transient transfection experiments. Model predictions of productivity changes as a result of the varied input plasmid ratio are benchmarked against transfection data from the literature. Sensitivity analysis suggests that (1) the poorly coordinated timeline of capsid synthesis and viral DNA replication results in a low ratio of full virions in harvest, and (2) repressive function of the Rep protein could be impeding capsid production at a later phase. The analyses from the mathematical model provide testable hypotheses for evaluation and reveal potential process bottlenecks that can be investigated.