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A novel approach based on supervised machine-learning is proposed to predict the solubility of drugs and drug-like molecules in mixtures of organic solvents. Similar to quantitative structure-property relationship (QSPR) models, different solvent types are identified by molecular descriptors, which, in this study, are considered as UNIFAC subgroups. To overcome the potential lack of UNIFAC subgroups for the complex Active Pharmaceutical Ingredients (APIs) currently developed in the pharmaceutical industry, the API molecule is considered as a unique entity in the proposed modelling approach. Therefore, API solubility is predicted as a function of temperature, functional subgroups of the solvents and composition of the solvent mixture; in turn, regressors' correlation is handled through Partial Least-Squares (PLS) regression. The method is developed and tested with experimental data of a real API and 14 organic solvents that are industrially employed for crystallisation. Solubility predictions are accurate and precise for single solvents, binary mixtures and ternary mixtures of organic solvents at different compositions and temperatures, with a determination coefficient R2 ≥ 0.90. To further test the applicability of the model, the proposed approach is applied to 9 literature organic solubility datasets of drugs and drug-like compounds and compared to benchmark solubility models in the literature. Results show that the proposed approach provides satisfactory predictions: the majority of validation and calibration data have R2 = 0.95-0.99; the ratio between RMSE (root mean squared error) of the proposed method and the range of measured solubility values is from 1 to 3 orders of magnitude smaller than the RMSE ratio obtained by the benchmark models.

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The identification of process Design Space (DS) is of high interest in highly regulated industrial sectors, such as pharmaceutical industry, where assurance of manufacturability and product quality is key for process development and decision-making. If the process can be controlled by a set of manipulated variables, the DS can be expanded in comparison to an open-loop scenario, where there are no controls in place. Determining the benefits of control strategies may be challenging, particularly when the available model is complex and computationally expensive - which is typically the case of pharmaceutical manufacturing. In this study, we exploit surrogate-based feasibility analysis to determine whether the process satisfies all process constraints by manipulating the process inputs and reduce the effect of uncertainty. The proposed approach is successfully tested on two simulated pharmaceutical case studies of increasing complexity, i.e., considering (i) a single pharmaceutical unit operation, and (ii) a pharmaceutical manufacturing line comprised of a sequence of connected unit operations. Results demonstrate that different control actions can be effectively exploited to operate the process in a wider range of inputs and mitigate uncertainty.

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To disclose the net effect of light on microalgal growth in photobioreactors, self-shading and mixing-induced light-dark cycles must be minimized and discerned from the transient phenomena of acclimation. In this work, we performed experiments of continuous microalgal cultivation in small-scale photobioreactors with different thicknesses (from 2 to 35 mm): working at a steady state allowed us to describe the effect of light after acclimation, while the geometry of the reactor was adjusted to find the threshold light path that can discriminate different phenomena. Experiments showed an increased inhibition under smaller culture light paths, suggesting a strong shading effect at thicknesses higher than 8 mm where mixing-induced light-dark cycles may occur. A Haldane-like model was applied and kinetic parameters retrieved, showing possible issues in the scalability of experimental results at different light paths if mixing-induced light-dark cycles are not considered. To further highlight the influence of mixing cycles, we proposed an analogy between small-scale operations with continuous light and PBR operations with pulsed light, with the computation of characteristic parameters from pulsed-light microalgae growth mathematical modeling.

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The classification of high dimensional gene expression data is key to the development of effective diagnostic and prognostic tools. Feature selection involves finding the best subset with the highest power in predicting class labels. Here, we conducted a comparative study focused on different combinations of feature selectors (Chi-Squared, mRMR, Relief-F, and Genetic Algorithms) and classification learning algorithms (Random Forests, PLS-DA, SVM, Regularized Logistic/Multinomial Regression, and kNN) to identify those with the best predictive capacity. The performance of each combination is evaluated through an empirical study on three benchmark cancer-related microarray datasets. Our results first suggest that the quality of the data relevant to the target classes is key for the successful classification of cancer phenotypes. We also proved that, for a given classification learning algorithm and dataset, all filters have a similar performance. Interestingly, filters achieve comparable or even better results with respect to the GA-based wrappers, while also being easier and faster to implement. Taken together, our findings suggest that simple, well-established feature selectors in combination with optimized classifiers guarantee good performances, with no need for complicated and computationally demanding methodologies.

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The successful development of mammalian cell culture for the production of therapeutic antibodies is a resource-intensive and multistage process which requires the selection of high performing and stable cell lines at different scale-up stages. Accordingly, science-based approaches exploiting biological information, such as metabolomics, can support and accelerate the selection of promising cell lines to progress. In fact, the integration of dynamic biological information with process data can provide valuable insights on the cell physiological changes as a consequence of the cultivation process. This work studies the industrial development of monoclonal antibodies at micro-bioreactor scale (Ambr®15) and aims at accelerating the selection of the better performing cell lines. To that end, we apply a machine learning approach to integrate time-varying process and biological information (i.e., metabolomics), explicitly exploiting their dynamics. Strikingly, cell line performance during the cultivation can be predicted from early process timepoints by exploiting the gradual temporal evolution of metabolic phenotypes. Furthermore, product titer is estimated with good accuracy at late process timepoints, providing insights into its relationship with underlying metabolic mechanisms and enabling the identification of biomarkers to be further investigated. The biological insights obtained through the proposed machine learning approach provide data-driven metabolic understanding allowing early identification of high performing cell lines. Additionally, this analysis offers the opportunity to identify key metabolites which could be used as biomarkers for industrially relevant phenotypes and onward fit into our commercial manufacturing platforms.

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In the pharmaceutical industry, lyophilization is typically adopted to extend long-time stability of valuable thermolabile medicines and vaccines. Primary drying is the most time-consuming and energy-intensive step of the entire process; thus, accelerating and optimizing the primary drying recipe is a key process development goal. To that purpose, mathematical models have been proposed and successfully validated. However, models typically require invasive experiments and/or sensors (e.g. product temperatures) for parameter estimation, which are rarely available in good manufacturing practice (GMP) environment. This represents a severe limitation when leveraging the model to transfer operation recipes across different facilities and for scale-up. In this study, we assess the possibility to exploit limited industrial data for model parameter estimation, namely pressure measurements and gravimetric tests, by defining a calibration protocol that is tested on two different pieces of equipment. Results are verified on a recently proposed model, and show that statistically meaningful estimates can be obtained without the need of product temperature measurements. Model predictions and optimal inputs trajectories are comparable to those obtained from the model calibrated using the full set of temperature and pressure data.

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In oral solid dosage production through direct compression powder lubrication must be carefully selected to facilitate the manufacturing of tablets without degrading product manufacturability and quality (e.g. dissolution). To do so, several semi-empirical models relating compression performance to process operating conditions have been developed. Among them, we consider an extension of the Kushner and Moore model (Kushner and Moore, 2010, International Journal Pharmaceutics, 399:19) that is useful for the purpose, but requires an extensive experimental campaign for parameters identification. This implies the preparation and compression of multiple powder blends, each one with a different lubrication extent. In turn, this translates into a considerable consumption of Active Pharmaceutical Ingredient (API), and into time-consuming experiments. We tackled this issue by proposing a novel model-based design of experiments (MBDoE) approach, which minimizes the number of optimal blends for model calibration, while obtaining statistically sound parameters estimates and model predictions. Both sequential and parallel MBDoE configurations were compared. Experimental results involving two placebo blends with different lubrication sensitivity showed that this methodology is able to reduce the experimental effort by 60-70% with respect to the standard industrial practice independently of the formulation considered and configuration (i.e. parallel vs. sequential) adopted.

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In continuous solid-dosage form manufacturing, the powder feeding system is responsible for supplying downstream the correct formulation of the drug product ingredients. The composition of the powder delivered by the feeding system is inferred from the measurements of powder mass flow from the system feeders. The mass flows are, in turn, inferred from the loss in weight measured in the feeder hoppers. Most loss-in-weight feeders post-process the mass flow signal to deliver a smoothed value to the user. However, such estimated mass flows can exhibit a low signal-to-noise ratio. As the feeders are critical elements of the control strategy of the manufacturing line, better instantaneous estimates of mass flow are desirable for improving the quality assurance. In this study, we propose a model-based approach for monitoring the composition of the powder fed to a continuous solid-dosage line. The monitoring system is based on a moving-horizon state estimator, which carries out model-based reconciliation of the feeder mass measurements, thus enabling accurate composition estimation of the powder mixture. Experimental datasets from a direct compression line are used to validate the methodology. Results demonstrate improvement with respect to current industrial solutions.

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The massive increase in carbon dioxide concentration in the atmosphere driven by human activities is causing huge negative consequences and new sustainable sources of energy, food and materials are highly needed. Algae are unicellular photosynthetic microorganisms that can provide a highly strategic contribution to this challenge as alternative source of biomass to complement crops cultivation. Algae industrial cultures are commonly limited by light availability, and biomass accumulation is strongly dependent on their photon-to-biomass conversion efficiency. Investigation of algae photosynthetic metabolism is thus strategic for the generation of more efficient strains with higher productivity. Algae are cultivated at industrial scale in conditions highly different from the natural niches they adapted to and strains development efforts must fully consider the seminal influence on productivity of regulatory mechanism of photosynthesis as well as of cultivation parameters like cells concentration, light distribution in the culture, mixing, nutrients and carbon dioxide availability. In this review we will focus in particular on how mathematical models can account for the complex influence of all environmental parameters and can be exploited for development of improved algae strains.

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A reduced von Willebrand factor (VWF) synthesis or survival, or its increased proteolysis, alone or in combination, contributes to the development of von Willebrand disease (VWD).We describe a new, simple mechanistic model for exploring how VWF behaves in well-defined forms of VWD after its 1-desamino-8-D-arginine vasopressin (DDAVP)-induced release from endothelial cells. We aimed to ascertain whether the model can consistently predict VWF kinetic changes. The study involved 9 patients with VWD types Vicenza (a paradigmatic form with a reduced VWF survival), 8 type 2B, 2 type 2A-I, 1 type 2A-II (associated with an increased VWF proteolysis), and 42 normal controls, whose VWF levels were measured after a 24-hour-long DDAVP test. The rate constants considered were: k0, associated with the VWF release phase; k1, illustrating the phase of conversion from high- to low-molecular-weight VWF multimers; and ke, associated with the VWF elimination phase. The amount of VWF released (D) was also measured. ke and D were significantly higher in O than in non-O blood group controls; k1 was also higher, but less markedly so. All the parameters were accelerated in type Vicenza, especially ke (p < 0.0001), which explains the significant reduction in VWF half-life. In types 2B and 2A-II, k1 was one order of magnitude higher than in controls, which explains their loss of large VWF multimers. All parameters except ke were lower in type 2A-I.The proposed mechanistic model clearly describes the altered biochemical pathways in well-characterized VWD, prompting us to suggest that it might help clarify elusive forms of VWD too.

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The optimization of algae biomass productivity in industrial cultivation systems requires genetic improvement of wild type strains isolated from nature. One of the main factors affecting algae productivity is their efficiency in converting light into chemical energy and this has been a major target of recent genetic efforts. However, photosynthetic productivity in algae cultures depends on many environmental parameters, making the identification of advantageous genotypes complex and the achievement of concrete improvements slow. In this work, we developed a mathematical model to describe the key factors influencing algae photosynthetic productivity in a photobioreactor, using experimental measurements for the WT strain of Nannochloropsis gaditana. The model was then exploited to predict the effect of potential genetic modifications on algae performances in an industrial context, showing the ability to predict the productivity of mutants with specific photosynthetic phenotypes. These results show that a quantitative model can be exploited to identify the genetic modifications with the highest impact on productivity taking into full account the complex influence of environmental conditions, efficiently guiding engineering efforts.

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The development of mathematical models capable of accurate predictions of the photosynthetic productivity of microalgae under variable light conditions is paramount to the development of large-scale production systems. The process of photoacclimation is particularly important in outdoor cultivation systems, whereby seasonal variation of the light irradiance can greatly influence microalgae growth. This paper presents a dynamic model that captures the effect of photoacclimation on the photosynthetic production. It builds upon an existing semi-empirical model describing the processes of photoproduction, photoregulation and photoinhibition via the introduction of acclimation rules for key parameters. The model is calibrated against a dataset comprising pulsed amplitude modulation fluorescence, photosynthesis rate, and antenna size measurements for the microalga Nannochloropsis gaditana in several acclimation states. It is shown that the calibrated model is capable of accurate predictions of fluorescence and respirometry data, both in interpolation and in extrapolation.

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PURPOSE: The purpose of this study is to develop a new pharmacokinetic-pharmacodynamic (PK-PD) model to characterise the contribution of (S)- and (R)-warfarin to the anticoagulant effect on patients in treatment with rac-warfarin. METHODS: Fifty-seven patients starting warfarin (W) therapy were studied, from the first dose and during chronic treatment at INR stabilization. Plasma concentrations of (S)- and (R)-W and INRs were measured 12, 36 and 60 h after the first dose and at steady state 12-14 h after dosing. Patients were also genotyped for the G>A VKORC1 polymorphism. The PK-PD model assumed a linear relationship between W enantiomer concentration and INR and included a scaling factor k to account for a different potency of (R)-W. Two parallel compartment chains with different transit times (MTT1 and MTT2) were used to model the delay in the W effect. PD parameters were estimated with the maximum likelihood approach. RESULTS: The model satisfactorily described the mean time-course of INR, both after the initial dose and during long-term treatment. (R)-W contributed to the rac-W anticoagulant effect with a potency of about 27% that of (S)-W. This effect was independent of VKORC1 genotype. As expected, the slope of the PK/PD linear correlation increased stepwise from GG to GA and from GA to AA VKORC1 genotype (0.71, 0.90 and 1.49, respectively). CONCLUSIONS: Our PK-PD linear model can quantify the partial pharmacodynamic activity of (R)-W in patients contemporaneously exposed to therapeutic (S)-W plasma levels. This concept may be useful in improving the performance of future algorithms aiming at identifying the most appropriate W maintenance dose.

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[This corrects the article DOI: 10.1371/journal.pone.0152387.].

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Reliable quantitative description of light-limited growth in microalgae is key to improving the design and operation of industrial production systems. This article shows how the capability to predict photosynthetic processes can benefit from a synergy between mathematical modelling and lab-scale experiments using systematic design of experiment techniques. A model of chlorophyll fluorescence developed by the authors [Nikolaou et al., J Biotechnol 194:91-99, 2015] is used as starting point, whereby the representation of non-photochemical-quenching (NPQ) process is refined for biological consistency. This model spans multiple time scales ranging from milliseconds to hours, thus calling for a combination of various experimental techniques in order to arrive at a sufficiently rich data set and determine statistically meaningful estimates for the model parameters. The methodology is demonstrated for the microalga Nannochloropsis gaditana by combining pulse amplitude modulation (PAM) fluorescence, photosynthesis rate and antenna size measurements. The results show that the calibrated model is capable of accurate quantitative predictions under a wide range of transient light conditions. Moreover, this work provides an experimental validation of the link between fluorescence and photosynthesis-irradiance (PI) curves which had been theoricized.

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In this proof-of-concept study, a methodology is proposed to systematically analyze large data historians of secondary pharmaceutical manufacturing systems using data mining techniques. The objective is to develop an approach enabling to automatically retrieve operation-relevant information that can assist the management in the periodic review of a manufactory system. The proposed methodology allows one to automatically perform three tasks: the identification of single batches within the entire data-sequence of the historical dataset, the identification of distinct operating phases within each batch, and the characterization of a batch with respect to an assigned multivariate set of operating characteristics. The approach is tested on a six-month dataset of a commercial-scale granulation/drying system, where several millions of data entries are recorded. The quality of results and the generality of the approach indicate that there is a strong potential for extending the method to even larger historical datasets and to different operations, thus making it an advanced PAT tool that can assist the implementation of continual improvement paradigms within a quality-by-design framework.

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Monitoring batch bioreactors is a complex task, due to the fact that several sources of variability can affect a running batch and impact on the final product quality. Additionally, the product quality itself may not be measurable on line, but requires sampling and lab analysis taking several days to be completed. In this study we show that, by using appropriate process analytical technology tools, the operation of an industrial batch bioreactor used in avian vaccine manufacturing can be effectively monitored as the batch progresses. Multivariate statistical models are built from historical databases of batches already completed, and they are used to enable the real time identification of the variability sources, to reliably predict the final product quality, and to improve process understanding, paving the way to a reduction of final product rejections, as well as to a reduction of the product cycle time. It is also shown that the product quality "builds up" mainly during the first half of a batch, suggesting on the one side that reducing the variability during this period is crucial, and on the other side that the batch length can possibly be shortened. Overall, the study demonstrates that, by using a Quality-by-Design approach centered on the appropriate use of mathematical modeling, quality can indeed be built "by design" into the final product, whereas the role of end-point product testing can progressively reduce its importance in product manufacturing.

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This paper presents a mathematical model capable of quantitative prediction of the state of the photosynthetic apparatus of microalgae in terms of their open, closed and damaged reaction centers under variable light conditions. This model combines the processes of photoproduction and photoinhibition in the Han model with a novel mathematical representation of photoprotective mechanisms, including qE-quenching and qI-quenching. For calibration and validation purposes, the model can be used to simulate fluorescence fluxes, such as those measured in PAM fluorometry, as well as classical fluorescence indexes. A calibration is carried out for the microalga Nannochloropsis gaditana, whereby 9 out of the 13 model parameters are estimated with good statistical significance using the realized, minimal and maximal fluorescence fluxes measured from a typical PAM protocol. The model is further validated by considering a more challenging PAM protocol alternating periods of intense light and dark, showing a good ability to provide quantitative predictions of the fluorescence fluxes even though it was calibrated for a different and somewhat simpler PAM protocol. A promising application of the model is for the prediction of PI-response curves based on PAM fluorometry, together with the long-term prospect of combining it with hydrodynamic and light attenuation models for high-fidelity simulation and optimization of full-scale microalgae production systems.

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The introduction of the Quality-by-Design (QbD) initiative and of the Process Analytical Technology (PAT) framework by the Food and Drug Administration has opened the route to the use of systematic and science-based approaches to support pharmaceutical development and manufacturing activities. In this review we discuss the role that latent variable models (LVMs) can play in the practical implementation of QbD paradigms in the pharmaceutical industry, and the potential they may have in assisting the development and manufacturing of new products. The ultimate scope is to provide practitioners with a perspective on the effectiveness of the use of LVMs in any phase of the development of a pharmaceutical product, from its design up to its commercial production. After an overview of the main regulatory paradigms the QbD initiative is founded on, we show how LVMs can be feasibly used to support pharmaceutical development and manufacturing activities while matching the regulatory Agencies' requirements. Three main areas are identified, wherein the use of LVMs can provide significant benefits: (i) process understanding, (ii) product and process design, and (iii) process monitoring and control. For each of them, the main contributions recently appeared in the literature are reviewed. Issues open for further research are also identified.

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The use of pharmacokinetic (PK) and pharmacodynamic (PD) models is a common and widespread practice in the preliminary stages of drug development. However, PK-PD models may be affected by structural identifiability issues intrinsically related to their mathematical formulation. A preliminary structural identifiability analysis is usually carried out to check if the set of model parameters can be uniquely determined from experimental observations under the ideal assumptions of noise-free data and no model uncertainty. However, even for structurally identifiable models, real-life experimental conditions and model uncertainty may strongly affect the practical possibility to estimate the model parameters in a statistically sound way. A systematic procedure coupling the numerical assessment of structural identifiability with advanced model-based design of experiments formulations is presented in this paper. The objective is to propose a general approach to design experiments in an optimal way, detecting a proper set of experimental settings that ensure the practical identifiability of PK-PD models. Two simulated case studies based on in vitro bacterial growth and killing models are presented to demonstrate the applicability and generality of the methodology to tackle model identifiability issues effectively, through the design of feasible and highly informative experiments.

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