Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design

Evolving Improved Sampling Protocols for Dose-Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Using design of experiments to guide genetic optimization of engineered metabolic pathways

Design of experiments (DoE) is a term used to describe the application of statistical approaches to interrogate the impact of many variables on the performance of a multivariate system. It is commonly used for process optimization in fields such as chemical engineering and material science. Recent advances in the ability to quantitatively control the expression of genes in biological systems open up the possibility to apply DoE for genetic optimization. In this review targeted to genetic and metabolic engineers, we introduce several approaches in DoE at a high level and describe instances wherein these were applied to interrogate or optimize engineered genetic systems. We discuss the challenges of applying DoE and propose strategies to mitigate these challenges.

ONE-SENTENCE SUMMARY

This is a review of literature related to applying Design of Experiments for genetic optimization.

Accurately summarizing an outbreak using epidemiological models takes time

Recent outbreaks of Mpox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The feasibility of this estimation task is known as the practical identifiability (PI) problem. Here, we investigate the PI of eight commonly reported statistics of the classic susceptible-infectious-recovered model using a new measure that shows how much a researcher can expect to learn in a model-based Bayesian analysis of prevalence data. Our findings show that the basic reproductive number and final outbreak size are often poorly identified, with learning exceeding that of individual model parameters only in the early stages of an outbreak. The peak intensity, peak timing and initial growth rate are better identified, being in expectation over 20 times more probable having seen the data by the time the underlying outbreak peaks. We then test PI for a variety of true parameter combinations and find that PI is especially problematic in slow-growing or less-severe outbreaks. These results add to the growing body of literature questioning the reliability of inferences from epidemiological models when limited data are available.

A plausible identifiable model of the canonical NF-κB signaling pathway

An overwhelming majority of mathematical models of regulatory pathways, including the intensively studied NF-κB pathway, remains non-identifiable, meaning that their parameters may not be determined by existing data. The existing NF-κB models that are capable of reproducing experimental data contain non-identifiable parameters, whereas simplified models with a smaller number of parameters exhibit dynamics that differs from that observed in experiments. Here, we reduced an existing model of the canonical NF-κB pathway by decreasing the number of equations from 15 to 6. The reduced model retains two negative feedback loops mediated by IκBα and A20, and in response to both tonic and pulsatile TNF stimulation exhibits dynamics that closely follow that of the original model. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is both structurally and practically identifiable given measurements of 5 model variables from a simple TNF stimulation protocol. The reduced model is capable of reproducing different types of responses that are characteristic to regulatory motifs controlled by negative feedback loops: nearly-perfect adaptation as well as damped and sustained oscillations. It can serve as a building block of more comprehensive models of the immune response and cancer, where NF-κB plays a decisive role. Our approach, although may not be automatically generalized, suggests that models of other regulatory pathways can be transformed to identifiable, while retaining their dynamical features.

Process Model Inversion in the Data-Driven Engineering Context for Improved Parameter Sensitivities

Industry 4.0 has embraced process models in recent years, and the use of model-based digital twins has become even more critical in process systems engineering, monitoring, and control. However, the reliability of these models depends on the model parameters available. The accuracy of the estimated parameters is, in turn, determined by the amount and quality of the measurement data and the algorithm used for parameter identification. For the definition of the parameter identification problem, the ordinary least squares framework is still state-of-the-art in the literature, and better parameter estimates are only possible with additional data. In this work, we present an alternative strategy to identify model parameters by incorporating differential flatness for model inversion and neural ordinary differential equations for surrogate modeling. The novel concept results in an input-least-squares-based parameter identification problem with significant parameter sensitivity changes. To study these sensitivity effects, we use a classic one-dimensional diffusion-type problem, i.e., an omnipresent equation in process systems engineering and transport phenomena. As shown, the proposed concept ensures higher parameter sensitivities for two relevant scenarios. Based on the results derived, we also discuss general implications for data-driven engineering concepts used to identify process model parameters in the recent literature.

Microbial technologies for biotherapeutics production: Key tools for advanced biopharmaceutical process development and control

Current trends in the biopharmaceutical market such as the diversification of therapies as well as the increasing time-to-market pressure will trigger the rethinking of bioprocess development and production approaches. Thereby, the importance of development time and manufacturing costs will increase, especially for microbial production. In the present review, we investigate three technological approaches which, to our opinion, will play a key role in the future of biopharmaceutical production. The first cornerstone of process development is the generation and effective utilization of platform knowledge. Building processes on well understood microbial and technological platforms allows to accelerate early-stage bioprocess development and to better condense this knowledge into multi-purpose technologies and applicable mathematical models. Second, the application of verified scale down systems and in silico models for process design and characterization will reduce the required number of large scale batches before dossier submission. Third, the broader availability of mathematical process models and the improvement of process analytical technologies will increase the applicability and acceptance of advanced control and process automation in the manufacturing scale. This will reduce process failure rates and subsequently cost of goods. Along these three aspects we give an overview of recently developed key tools and their potential integration into bioprocess development strategies.

Monte Carlo-Based Error Propagation for a More Reliable Regression Analysis across Specific Rates in Bioprocesses

During process development, bioprocess data need to be converted into applicable knowledge. Therefore, it is crucial to evaluate the obtained data under the usage of transparent and reliable data reduction and correlation techniques. Within this contribution, we show a generic Monte Carlo error propagation and regression approach applied to two different, industrially relevant cultivation processes. Based on measurement uncertainties, errors for cell-specific growth, uptake, and production rates were determined across an evaluation chain, with interlinked inputs and outputs. These uncertainties were subsequently included in regression analysis to derive the covariance of the regression coefficients and the confidence bounds for prediction. The usefulness of the approach is shown within two case studies, based on the relations across biomass-specific rate control limits to guarantee high productivities in E. coli, and low lactate formation in a CHO cell fed-batch could be established. Besides the possibility to determine realistic errors on the evaluated process data, the presented approach helps to differentiate between reliable and unreliable correlations and prevents the wrong interpretations of relations based on uncertain data.

Long-term stability predictions of therapeutic monoclonal antibodies in solution using Arrhenius-based kinetics

Long-term stability of monoclonal antibodies to be used as biologics is a key aspect in their development. Therefore, its possible early prediction from accelerated stability studies is of major interest, despite currently being regarded as not sufficiently robust. In this work, using a combination of accelerated stability studies (up to 6 months) and first order degradation kinetic model, we are able to predict the long-term stability (up to 3 years) of multiple monoclonal antibody formulations. More specifically, we can robustly predict the long-term stability behaviour of a protein at the intended storage condition (5 °C), based on up to six months of data obtained for multiple quality attributes from different temperatures, usually from intended (5 °C), accelerated (25 °C) and stress conditions (40 °C). We have performed stability studies and evaluated the stability data of several mAbs including IgG1, IgG2, and fusion proteins, and validated our model by overlaying the 95% prediction interval and experimental stability data from up to 36 months. We demonstrated improved robustness, speed and accuracy of kinetic long-term stability prediction as compared to classical linear extrapolation used today, which justifies long-term stability prediction and shelf-life extrapolation for some biologics such as monoclonal antibodies. This work aims to contribute towards further development and refinement of the regulatory landscape that could steer toward allowing extrapolation for biologics during the developmental phase, clinical phase, and also in marketing authorisation applications, as already established today for small molecules.

Towards the Experimentally-Informed In Silico Nozzle Design Optimization for Extrusion-Based Bioprinting of Shear-Thinning Hydrogels

Research in bioprinting is booming due to its potential in addressing several manufacturing challenges in regenerative medicine. However, there are still many hurdles to overcome to guarantee cell survival and good printability. For the 3D extrusion-based bioprinting, cell viability is amongst one of the lowest of all the bioprinting techniques and is strongly influenced by various factors including the shear stress in the print nozzle. The goal of this study is to quantify, by means of in silico modeling, the mechanical environment experienced by the bioink during the printing process. Two ubiquitous nozzle shapes, conical and blunted, were considered, as well as three common hydrogels with material properties spanning from almost Newtonian to highly shear-thinning materials following the power-law behavior: Alginate-Gelatin, Alginate and PF127. Comprehensive in silico testing of all combinations of nozzle geometry variations and hydrogels was achieved by combining a design of experiments approach (DoE) with a computational fluid dynamics (CFD) of the printing process, analyzed through a machine learning approach named Gaussian Process. Available experimental results were used to validate the CFD model and justify the use of shear stress as a surrogate for cell survival in this study. The lower and middle nozzle radius, lower nozzle length and the material properties, alone and combined, were identified as the major influencing factors affecting shear stress, and therefore cell viability, during printing. These results were successfully compared with those of reported experiments testing viability for different nozzle geometry parameters under constant flow rate or constant pressure. The in silico 3D bioprinting platform developed in this study offers the potential to assist and accelerate further development of 3D bioprinting.

Hybrid Process Models in Electrochemical Syntheses under Deep Uncertainty

Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities.

Automated Conditional Screening of Multiple Escherichia coli Strains in Parallel Adaptive Fed-Batch Cultivations

In bioprocess development, the host and the genetic construct for a new biomanufacturing process are selected in the early developmental stages. This decision, made at the screening scale with very limited information about the performance in larger reactors, has a major influence on the efficiency of the final process. To overcome this, scale-down approaches during screenings that show the real cell factory performance at industrial-like conditions are essential. We present a fully automated robotic facility with 24 parallel mini-bioreactors that is operated by a model-based adaptive input design framework for the characterization of clone libraries under scale-down conditions. The cultivation operation strategies are computed and continuously refined based on a macro-kinetic growth model that is continuously re-fitted to the available experimental data. The added value of the approach is demonstrated with 24 parallel fed-batch cultivations in a mini-bioreactor system with eight different Escherichia coli strains in triplicate. The 24 fed-batch cultivations were run under the desired conditions, generating sufficient information to define the fastest-growing strain in an environment with oscillating glucose concentrations similar to industrial-scale bioreactors.

Coupled metabolic-hydrodynamic modeling enabling rational scale-up of industrial bioprocesses

Metabolomics aims to address what and how regulatory mechanisms are coordinated to achieve flux optimality, different metabolic objectives as well as appropriate adaptations to dynamic nutrient availability. Recent decades have witnessed that the integration of metabolomics and fluxomics within the goal of synthetic biology has arrived at generating the desired bioproducts with improved bioconversion efficiency. Absolute metabolite quantification by isotope dilution mass spectrometry represents a functional readout of cellular biochemistry and contributes to the establishment of metabolic (structured) models required in systems metabolic engineering. In industrial practices, population heterogeneity arising from fluctuating nutrient availability frequently leads to performance losses, that is reduced commercial metrics (titer, rate, and yield). Hence, the development of more stable producers and more predictable bioprocesses can benefit from a quantitative understanding of spatial and temporal cell-to-cell heterogeneity within industrial bioprocesses. Quantitative metabolomics analysis and metabolic modeling applied in computational fluid dynamics (CFD)-assisted scale-down simulators that mimic industrial heterogeneity such as fluctuations in nutrients, dissolved gases, and other stresses can procure informative clues for coping with issues during bioprocessing scale-up. In previous studies, only limited insights into the hydrodynamic conditions inside the industrial-scale bioreactor have been obtained, which makes case-by-case scale-up far from straightforward. Tracking the flow paths of cells circulating in large-scale bioreactors is a highly valuable tool for evaluating cellular performance in production tanks. The "lifelines" or "trajectories" of cells in industrial-scale bioreactors can be captured using Euler-Lagrange CFD simulation. This novel methodology can be further coupled with metabolic (structured) models to provide not only a statistical analysis of cell lifelines triggered by the environmental fluctuations but also a global assessment of the metabolic response to heterogeneity inside an industrial bioreactor. For the future, the industrial design should be dependent on the computational framework, and this integration work will allow bioprocess scale-up to the industrial scale with an end in mind.

On the use of in-silico simulations to support experimental design: A case study in microbial inactivation of foods

The mathematical models used in predictive microbiology contain parameters that must be estimated based on experimental data. Due to experimental uncertainty and variability, they cannot be known exactly and must be reported with a measure of uncertainty (usually a standard deviation). In order to increase precision (i.e. reduce the standard deviation), it is usual to add extra sampling points. However, recent studies have shown that precision can also be increased without adding extra sampling points by using Optimal Experiment Design, which applies optimization and information theory to identify the most informative experiment under a set of constraints. Nevertheless, to date, there has been scarce contributions to know a priori whether an experimental design is likely to provide the desired precision in the parameter estimates. In this article, two complementary methodologies to predict the parameter precision for a given experimental design are proposed. Both approaches are based on in silico simulations, so they can be performed before any experimental work. The first one applies Monte Carlo simulations to estimate the standard deviation of the model parameters, whereas the second one applies the properties of the Fisher Information Matrix to estimate the volume of the confidence ellipsoids. The application of these methods to a case study of dynamic microbial inactivation, showing how they can be used to compare experimental designs and assess their precision, is illustrated. The results show that, as expected, the optimal experimental design is more accurate than the uniform design with the same number of data points. Furthermore, it is demonstrated that, for some heating profiles, the uniform design does not ensure that a higher number of sampling points increases precision. Therefore, optimal experimental designs are highly recommended in predictive microbiology.

Dynamic Modelling of Phosphorolytic Cleavage Catalyzed by Pyrimidine-Nucleoside Phosphorylase

Pyrimidine-nucleoside phosphorylases (Py-NPases) have a significant potential to contribute to the economic and ecological production of modified nucleosides. These can be produced via pentose-1-phosphates, an interesting but mostly labile and expensive precursor. Thus far, no dynamic model exists for the production process of pentose-1-phosphates, which involves the equilibrium state of the Py-NPase catalyzed reversible reaction. Previously developed enzymological models are based on the understanding of the structural principles of the enzyme and focus on the description of initial rates only. The model generation is further complicated, as Py-NPases accept two substrates which they convert to two products. To create a well-balanced model from accurate experimental data, we utilized an improved high-throughput spectroscopic assay to monitor reactions over the whole time course until equilibrium was reached. We examined the conversion of deoxythymidine and phosphate to deoxyribose-1-phosphate and thymine by a thermophilic Py-NPase from Geobacillus thermoglucosidasius. The developed process model described the reactant concentrations in excellent agreement with the experimental data. Our model is built from ordinary differential equations and structured in such a way that integration with other models is possible in the future. These could be the kinetics of other enzymes for enzymatic cascade reactions or reactor descriptions to generate integrated process models.