Bayesian calibration, process modeling and uncertainty quantification in biotechnology.

High-throughput experimentation has revolutionized data-driven experimental sciences and opened the door to the application of machine learning techniques. Nevertheless, the quality of any data analysis strongly depends on the quality of the data and specifically the degree to which random effects in the experimental data-generating process are quantified and accounted for. Accordingly calibration, i.e. the quantitative association between observed quantities and measurement responses, is a core element of many workflows in experimental sciences. Particularly in life sciences, univariate calibration, often involving non-linear saturation effects, must be performed to extract quantitative information from measured data. At the same time, the estimation of uncertainty is inseparably connected to quantitative experimentation. Adequate calibration models that describe not only the input/output relationship in a measurement system but also its inherent measurement noise are required. Due to its mathematical nature, statistically robust calibration modeling remains a challenge for many practitioners, at the same time being extremely beneficial for machine learning applications. In this work, we present a bottom-up conceptual and computational approach that solves many problems of understanding and implementing non-linear, empirical calibration modeling for quantification of analytes and process modeling. The methodology is first applied to the optical measurement of biomass concentrations in a high-throughput cultivation system, then to the quantification of glucose by an automated enzymatic assay. We implemented the conceptual framework in two Python packages, calibr8 and murefi, with which we demonstrate how to make uncertainty quantification for various calibration tasks more accessible. Our software packages enable more reproducible and automatable data analysis routines compared to commonly observed workflows in life sciences. Subsequently, we combine the previously established calibration models with a hierarchical Monod-like ordinary differential equation model of microbial growth to describe multiple replicates of Corynebacterium glutamicum batch cultures. Key process model parameters are learned by both maximum likelihood estimation and Bayesian inference, highlighting the flexibility of the statistical and computational framework.

Complex Evolution of Light-Dependent Protochlorophyllide Oxidoreductases in Aerobic Anoxygenic Phototrophs: Origin, Phylogeny, and Function.

Light-dependent protochlorophyllide oxidoreductase (LPOR) and dark-operative protochlorophyllide oxidoreductase are evolutionary and structurally distinct enzymes that are essential for the synthesis of (bacterio)chlorophyll, the primary pigment needed for both anoxygenic and oxygenic photosynthesis. In contrast to the long-held hypothesis that LPORs are only present in oxygenic phototrophs, we recently identified a functional LPOR in the aerobic anoxygenic phototrophic bacterium (AAPB) Dinoroseobacter shibae and attributed its presence to a single horizontal gene transfer event from cyanobacteria. Here, we provide evidence for the more widespread presence of genuine LPOR enzymes in AAPBs. An exhaustive bioinformatics search identified 36 putative LPORs outside of oxygenic phototrophic bacteria (cyanobacteria) with the majority being AAPBs. Using in vitro and in vivo assays, we show that the large majority of the tested AAPB enzymes are genuine LPORs. Solution structural analyses, performed for two of the AAPB LPORs, revealed a globally conserved structure when compared with a well-characterized cyanobacterial LPOR. Phylogenetic analyses suggest that LPORs were transferred not only from cyanobacteria but also subsequently between proteobacteria and from proteobacteria to Gemmatimonadetes. Our study thus provides another interesting example for the complex evolutionary processes that govern the evolution of bacteria, involving multiple horizontal gene transfer events that likely occurred at different time points and involved different donors.

Development and application of a cultivation platform for mammalian suspension cell lines with single-cell resolution.

In bioproduction processes, cellular heterogeneity can cause unpredictable process outcomes or even provoke process failure. Still, cellular heterogeneity is not examined systematically in bioprocess research and development. One reason for this shortcoming is the applied average bulk analyses, which are not able to detect cell-to-cell differences. In this study, we present a microfluidic tool for mammalian single-cell cultivation (MaSC) of suspension cells. The design of our platform allows cultivation in highly controllable environments. As a model system, Chinese hamster ovary cells (CHO-K1) were cultivated over 150 h. Growth behavior was analyzed on a single-cell level and resulted in growth rates between 0.85 and 1.16 day-1 . At the same time, heterogeneous growth and division behavior, for example, unequal division time, as well as rare cellular events like polynucleation or reversed mitosis were observed, which would have remained undetected in a standard population analysis based on average measurements. Therefore, MaSC will open the door for systematic single-cell analysis of mammalian suspension cells. Possible fields of application represent basic research topics like cell-to-cell heterogeneity, clonal stability, pharmaceutical drug screening, and stem cell research, as well as bioprocess related topics such as media development and novel scale-down approaches.

Dynamic Environmental Control in Microfluidic Single-Cell Cultivations: From Concepts to Applications.

Microfluidic single-cell cultivation (MSCC) is an emerging field within fundamental as well as applied biology. During the last years, most MSCCs were performed at constant environmental conditions. Recently, MSCC at oscillating and dynamic environmental conditions has started to gain significant interest in the research community for the investigation of cellular behavior. Herein, an overview of this topic is given and microfluidic concepts that enable oscillating and dynamic control of environmental conditions with a focus on medium conditions are discussed, and their application in single-cell research for the cultivation of both mammalian and microbial cell systems is demonstrated. Furthermore, perspectives for performing MSCC at complex dynamic environmental profiles of single parameters and multiparameters (e.g., pH and O2 ) in amplitude and time are discussed. The technical progress in this field provides completely new experimental approaches and lays the foundation for systematic analysis of cellular metabolism at fluctuating environments.

Toward in silico CMC: An industrial collaborative approach to model-based process development.

The Third Modeling Workshop focusing on bioprocess modeling was held in Kenilworth, NJ in May 2019. A summary of these Workshop proceedings is captured in this manuscript. Modeling is an active area of research within the biotechnology community, and there is a critical need to assess the current state and opportunities for continued investment to realize the full potential of models, including resource and time savings. Beyond individual presentations and topics of novel interest, a substantial portion of the Workshop was devoted toward group discussions of current states and future directions in modeling fields. All scales of modeling, from biophysical models at the molecular level and up through large scale facility and plant modeling, were considered in these discussions and are summarized in the manuscript. Model life cycle management from model development to implementation and sustainment are also considered for different stages of clinical development and commercial production. The manuscript provides a comprehensive overview of bioprocess modeling while suggesting an ideal future state with standardized approaches aligned across the industry.

Multiscale dynamic modeling and simulation of a biorefinery.

A biorefinery comprises a variety of process steps to synthesize products from sustainable natural resources. Dynamic plant-wide simulation enhances the process understanding, leads to improved cost efficiency and enables model-based operation and control. It is thereby important for an increased competitiveness to conventional processes. To this end, we developed a Modelica library with replaceable building blocks that allow dynamic modeling of an entire biorefinery. For the microbial conversion step, we built on the dynamic flux balance analysis (DFBA) approach to formulate process models for the simulation of cellular metabolism under changing environmental conditions. The resulting system of differential-algebraic equations with embedded optimization criteria (DAEO) is solved by a tailor-made toolbox. In summary, our modeling framework comprises three major pillars: A Modelica library of dynamic unit operations, an easy-to-use interface to formulate DFBA process models and a DAEO toolbox that allows simulation with standard environments based on the Modelica modeling language. A biorefinery model for dynamic simulation of the OrganoCat pretreatment process and microbial conversion of the resulting feedstock by Corynebacterium glutamicum serves as case study to demonstrate its practical relevance.

Discrete-continuous reaction-diffusion model with mobile point-like sources and sinks.

In many applications in soft and biological physics, there are multiple time and length scales involved but often with a distinct separation between them. For instance, in enzyme kinetics, enzymes are relatively large, move slowly and their copy numbers are typically small, while the metabolites (being transformed by these enzymes) are often present in abundance, are small in size and diffuse fast. It seems thus natural to apply different techniques to different time and length levels and couple them. Here we explore this possibility by constructing a stochastic-deterministic discrete-continuous reaction-diffusion model with mobile sources and sinks. Such an approach allows in particular to separate different sources of stochasticity. We demonstrate its application by modelling enzyme-catalysed reactions with freely diffusing enzymes and a heterogeneous source of metabolites. Our calculations suggest that using a higher amount of less active enzymes, as compared to fewer more active enzymes, reduces the metabolite pool size and correspondingly the lag time, giving rise to a faster response to external stimuli. The methodology presented can be extended to more complex systems and offers exciting possibilities for studying problems where spatial heterogeneities, stochasticity or discreteness play a role.

Spatiotemporal microbial single-cell analysis using a high-throughput microfluidics cultivation platform.

Cell-to-cell heterogeneity typically evolves due to a manifold of biological and environmental factors and special phenotypes are often relevant for the fate of the whole population but challenging to detect during conventional analysis. We demonstrate a microfluidic single-cell cultivation platform that incorporates several hundred growth chambers, in which isogenic bacteria microcolonies growing in cell monolayers are tracked by automated time-lapse microscopy with spatiotemporal resolution. The device was not explicitly developed for a specific organism, but has a very generic configuration suitable for various different microbial organisms. In the present study, we analyzed Corynebacterium glutamicum microcolonies, thereby generating complete lineage trees and detailed single-cell data on division behavior and morphology in order to demonstrate the platform's overall capabilities. Furthermore, the occurrence of spontaneously induced stress in individual C. glutamicum cells was investigated by analyzing strains with genetically encoded reporter systems and optically visualizing SOS response. The experiments revealed spontaneous SOS induction in the absence of any external trigger comparable to results obtained by flow cytometry (FC) analyzing cell samples from conventional shake flask cultivation. Our microfluidic setup delivers detailed single-cell data with spatial and temporal resolution; complementary information to conventional FC results.

The effect of composition on diffusion of macromolecules in a crowded environment.

We study diffusion of macromolecules in a crowded cytoplasm-like environment, focusing on its dependence on composition and its crossover to the anomalous subdiffusion. The crossover and the diffusion itself depend on both the volume fraction and the relative concentration of macromolecules. In accordance with previous theoretical and experimental studies, diffusion slows down when the volume fraction increases. Contrary to expectations, however, the diffusion is also strongly dependent on the molecular composition. The crossover time decreases and diffusion slows down when the smaller macromolecules start to dominate. Interestingly, diffusion is faster in a cytoplasm-like (more polydisperse) system than it is in a two-component system, at comparable packing fractions, or even when the cytoplasm packing fraction is larger.

A new mixed-mode model for interpreting and predicting protein elution during isoelectric chromatofocusing.

Experimental data are combined with classic theories describing electrolytes in solution and at surfaces to define the primary mechanisms influencing protein retention and elution during isoelectric chromatofocusing (ICF) of proteins and protein mixtures. Those fundamental findings are used to derive a new model to understand and predict elution times of proteins during ICF. The model uses a modified form of the steric mass action (SMA) isotherm to account for both ion exchange and isoelectric focusing contributions to protein partitioning. The dependence of partitioning on pH is accounted for through the characteristic charge parameter m of the SMA isotherm and the application of Gouy-Chapman theory to define the dependence of the equilibrium binding constant Kbi on both m and ionic strength. Finally, the effects of changes in matrix surface pH on protein retention are quantified through a Donnan equilibrium type model. By accounting for isoelectric focusing, ion binding and exchange, and surface pH contributions to protein retention and elution, the model is shown to accurately capture the dependence of protein elution times on column operating conditions.

Zonal rate model for axial and radial flow membrane chromatography, part II: model-based scale-up.

Membrane chromatography (MC) systems are finding increasing use in downstream processing trains for therapeutic proteins due to the unique mass-transfer characteristics they provide. As a result, there is increased need for model-based methods to scale-up MC units using data collected on a scaled-down unit. Here, a strategy is presented for MC unit scale-up using the zonal rate model (ZRM). The ZRM partitions an MC unit into virtual flow zones to account for deviations from ideal plug-flow behavior. To permit scale-up, it is first configured for the specific device geometry and flow profiles within the scaled-down unit so as to achieve decoupling of flow and binding related non-idealities. The ZRM is then configured for the preparative-scale unit, which typically utilizes markedly different flow manifolds and membrane architecture. Breakthrough is first analyzed in both units under non-binding conditions using an inexpensive tracer to independently determine unit geometry related parameters of the ZRM. Binding related parameters are then determined from breakthrough data on the scaled-down MC capsule to minimize sample requirements. Model-based scale-up may then be performed to predict band broadening and breakthrough curves on the preparative-scale unit. Here, the approach is shown to be valid when the Pall XT140 and XT5 capsules serve as the preparative and scaled-down units, respectively. In this case, scale-up is facilitated by our finding that the distribution of linear velocities through the membrane in the XT140 capsule is independent of the feed flow rate and the type of protein transmitted. Introduction of this finding into the ZRM permits quantitative predictions of breakthrough over a range of industrially relevant operating conditions.

A class of compartmental models for long-distance tracer transport in plants.

Studies of long-distance tracer transport in plants result in spatio-temporal data sets. Compartmental tracer transport models can be used to quantitatively characterize or compare such data sets derived from different experiments. Depending on the specific experimental situation it might be necessary to apply different models. Here, we present a general class of compartmental tracer transport models which allows a systematic comparison of different models regarding the quality of fitting to the experimental data. This model class is defined by a system of partial differential equations (PDEs) for an arbitrary number of parallel compartments with individual transport velocities and numerous lateral exchange connections. A large number of model instances with adjustable complexity can be derived from this model class by permitting only certain model parameters such as flux velocities or exchange rates between compartments to be non-zero. Since some of these models are either inconsistent or redundant we designed a model filter using combinatory rules in order to keep only valid and unique models. A numerical solver for the PDEs was implemented using finite volumes and a weighted essentially non-oscillatory (WENO) scheme. Several candidate models were fitted to experimental data using a Monte Carlo multi-start strategy to approximate the global optimum within a certain parameter space. Analysis of exemplary tracer transport experiments on sugar beet, radish and maize root resulted in different best models depending on the respective data and the required fit quality.

Quantification of nisin concentration from fluorescence-based antimicrobial activity assay using Bayesian calibration.

Bacteriocins are ribosomally synthesized peptides with the innate ability to kill or inhibit growth of other bacteria. In recent years, bacteriocins have received increased interest, as their antimicrobial activity enhances food safety and shelf life by combatting pathogens such as Listeria monocytogenes. They also have application potential as an active pharmaceutical compound to combat multidrug-resistant pathogens. As new bacteriocins continue to be discovered, accelerated workflows for screening, identification, and process development have been developed. However, antimicrobial activity measurement is often still limited with regards to quantification and throughput. Here, we present the use of a non-linear calibration model to infer nisin concentrations in cultivation supernatants of Lactococcus lactis ssp. lactis B1629 using readouts of pHluorin2 fluorescence-based antimicrobial activity assays.

Zonal rate model for axial and radial flow membrane chromatography. Part I: knowledge transfer across operating conditions and scales.

The zonal rate model (ZRM) has previously been applied for analyzing the performance of axial flow membrane chromatography capsules by independently determining the impacts of flow and binding related non-idealities on measured breakthrough curves. In the present study, the ZRM is extended to radial flow configurations, which are commonly used at larger scales. The axial flow XT5 capsule and the radial flow XT140 capsule from Pall are rigorously analyzed under binding and non-binding conditions with bovine serum albumin (BSA) as test molecule. The binding data of this molecule is much better reproduced by the spreading model, which hypothesizes different binding orientations, than by the well-known Langmuir model. Moreover, a revised cleaning protocol with NaCl instead of NaOH and minimizing the storage time has been identified as most critical for quantitatively reproducing the measured breakthrough curves. The internal geometry of both capsules is visualized by magnetic resonance imaging (MRI). The flow in the external hold-up volumes of the XT140 capsule was found to be more homogeneous as in the previously studied XT5 capsule. An attempt for model-based scale-up was apparently impeded by irregular pleat structures in the used XT140 capsule, which might lead to local variations in the linear velocity through the membrane stack. However, the presented approach is universal and can be applied to different capsules. The ZRM is shown to potentially help save valuable material and time, as the experiments required for model calibration are much cheaper than the predicted large-scale experiment at binding conditions.

Machine learning in bioprocess development: from promise to practice.

Fostered by novel analytical techniques, digitalization, and automation, modern bioprocess development provides large amounts of heterogeneous experimental data, containing valuable process information. In this context, data-driven methods like machine learning (ML) approaches have great potential to rationally explore large design spaces while exploiting experimental facilities most efficiently. Herein we demonstrate how ML methods have been applied so far in bioprocess development, especially in strain engineering and selection, bioprocess optimization, scale-up, monitoring, and control of bioprocesses. For each topic, we will highlight successful application cases, current challenges, and point out domains that can potentially benefit from technology transfer and further progress in the field of ML.

Advanced error modeling and Bayesian uncertainty quantification in mechanistic liquid chromatography modeling.

Current mechanistic chromatography process modeling methods lack the ability to account for the impact of experimental errors beyond detector noise (e.g. pump delays and variable feed composition) on the uncertainty in calibrated model parameters and the resulting model-predicted chromatograms. This paper presents an uncertainty quantification method that addresses this limitation by determining the probability distribution of parameters in calibrated models, taking into consideration multiple realistic sources of experimental error. The method, which is based on Bayes' theorem and utilizes Markov chain Monte Carlo with an ensemble sampler, is demonstrated to be robust and extensible using synthetic and industrial data. The corresponding software is freely available as open-source code at https://github.com/modsim/CADET-Match.

Reliable cell retention of mammalian suspension cells in microfluidic cultivation chambers.

Microfluidic cultivation, with its high level of environmental control and spatio-temporal resolution of cellular behavior, is a well-established tool in today's microfluidics. Yet, reliable retention of (randomly) motile cells inside designated cultivation compartments still represents a limitation, which prohibits systematic single-cell growth studies. To overcome this obstacle, current approaches rely on complex multilayer chips or on-chip valves, which makes their application for a broad community of users infeasible. Here, we present an easy-to-implement cell retention concept to withhold cells inside microfluidic cultivation chambers. By introducing a blocking structure into a cultivation chamber's entrance and nearly closing it, cells can be manually pushed into the chamber during loading procedures but are unable to leave it autonomously in subsequent long-term cultivation. CFD simulations as well as trace substance experiments confirm sufficient nutrient supply within the chamber. Through preventing recurring cell loss, growth data obtained from Chinese hamster ovary cultivation on colony level perfectly match data determined from single-cell data, which eventually allows reliable high throughput studies of single-cell growth. Due to its transferability to other chamber-based approaches, we strongly believe that our concept is also applicable for a broad range of cellular taxis studies or analyses of directed migration in basic or biomedical research.

Zonal rate model for stacked membrane chromatography part II: characterizing ion-exchange membrane chromatography under protein retention conditions.

The Zonal Rate Model (ZRM) has previously been shown to accurately account for contributions to elution band broadening, including external flow nonidealities and radial concentration gradients, in ion-exchange membrane (IEXM) chromatography systems operated under nonbinding conditions. Here, we extend the ZRM to analyze and model the behavior of retained proteins by introducing terms for intra-column mass transfer resistances and intrinsic binding kinetics. Breakthrough curve (BTC) data from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min(-1). Through its careful accounting of transport nonidealities within and external to the membrane stack, the ZRM is shown to provide a useful framework for characterizing putative protein binding mechanisms and models, for predicting BTCs and complex elution behavior, including the common observation that the dynamic binding capacity can increase with linear velocity in IEXM systems, and for simulating and scaling separations using IEXM chromatography. Global fitting of model parameters is used to evaluate the performance of the Langmuir, bi-Langmuir, steric mass action (SMA), and spreading-type protein binding models in either correlating or fundamentally describing BTC data. When combined with the ZRM, the bi-Langmuir, and SMA models match the chromatography data, but require physically unrealistic regressed model parameters to do so. In contrast, for this system a spreading-type model is shown to accurately predict column performance while also providing a realistic fundamental explanation for observed trends, including an observed increase in dynamic binding capacity with flow rate.

Influence of Organic Solvents on Enzymatic Asymmetric Carboligations.

The asymmetric mixed carboligation of aldehydes with thiamine diphosphate (ThDP)-dependent enzymes is an excellent example where activity as well as changes in chemo- and stereoselectivity can be followed sensitively. To elucidate the influence of organic additives in enzymatic carboligation reactions of mixed 2-hydroxy ketones, we present a comparative study of six ThDP-dependent enzymes in 13 water-miscible organic solvents under equivalent reaction conditions. The influence of the additives on the stereoselectivity is most pronounced and follows a general trend. If the enzyme stereoselectivity in aqueous buffer is already >99.9% ee, none of the solvents reduces this high selectivity. In contrast, both stereoselectivity and chemoselectivity are strongly influenced if the enzyme is rather unselective in aqueous buffer. For the S-selective enzyme with the largest active site, we were able to prove a general correlation of the solvent-excluded volume of the additives with the effect on selectivity changes: the smaller the organic solvent molecule, the higher the impact of this additive. Further, a correlation to log P of the additives on selectivity was detected if two additives have almost the same solvent-excluded volume. The observed results are discussed in terms of structural, biochemical and energetic effects. This work demonstrates the potential of medium engineering as a powerful additional tool for varying enzyme selectivity and thus engineering the product range of biotransformations. It further demonstrates that the use of cosolvents should be carefully planned, as the solvents may compete with the substrate(s) for binding sites in the enzyme active site.

Mechanisms and Effects of Substrate Channelling in Enzymatic Cascades.

Substrate or metabolite channelling is a transfer of intermediates produced by one enzyme to the sequential enzyme of a reaction cascade or metabolic pathway, without releasing them entirely into bulk. Despite an enormous effort and more than three decades of research, substrate channelling remains the subject of continuing debates and active investigation. Herein, we review the benefits and mechanisms of substrate channelling in vivo and in vitro. We discuss critically the effects that substrate channelling can have on enzymatic cascades, including speeding up or slowing down reaction cascades and protecting intermediates from sequestration and enzymes' surroundings from toxic or otherwise detrimental intermediates. We also discuss how macromolecular crowding affects substrate channelling and point out the galore of open questions.