Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany.

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

PyMC: a modern, and comprehensive probabilistic programming framework in Python.

PyMC is a probabilistic programming library for Python that provides tools for constructing and fitting Bayesian models. It offers an intuitive, readable syntax that is close to the natural syntax statisticians use to describe models. PyMC leverages the symbolic computation library PyTensor, allowing it to be compiled into a variety of computational backends, such as C, JAX, and Numba, which in turn offer access to different computational architectures including CPU, GPU, and TPU. Being a general modeling framework, PyMC supports a variety of models including generalized hierarchical linear regression and classification, time series, ordinary differential equations (ODEs), and non-parametric models such as Gaussian processes (GPs). We demonstrate PyMC's versatility and ease of use with examples spanning a range of common statistical models. Additionally, we discuss the positive role of PyMC in the development of the open-source ecosystem for probabilistic programming.

Experimental kS estimation: A comparison of methods for Corynebacterium glutamicum from lab to microfluidic scale.

Knowledge about the specific affinity of whole cells toward a substrate, commonly referred to as kS , is a crucial parameter for characterizing growth within bioreactors. State-of-the-art methodologies measure either uptake or consumption rates at different initial substrate concentrations. Alternatively, cell dry weight or respiratory data like online oxygen and carbon dioxide transfer rates can be used to estimate kS . In this work, a recently developed substrate-limited microfluidic single-cell cultivation (sl-MSCC) method is applied for the estimation of kS values under defined environmental conditions. This method is benchmarked with two alternative microtiter plate methods, namely high-frequency biomass measurement (HFB) and substrate-limited respiratory activity monitoring (sl-RA). As a model system, the substrate affinity kS of Corynebacterium glutamicum ATCC 13032 regarding glucose was investigated assuming a Monod-type growth response. A kS of <70.7 mg/L (with 95% probability) with HFB, 8.55 ± 1.38 mg/L with sl-RA, and 2.66 ± 0.99 mg/L with sl-MSCC was obtained. Whereas HFB and sl-RA are suitable for a fast initial kS estimation, sl-MSCC allows an affinity estimation by determining tD at concentrations less or equal to the kS value. Thus, sl-MSCC lays the foundation for strain-specific kS estimations under defined environmental conditions with additional insights into cell-to-cell heterogeneity.

Explore or exploit? A model-based screening strategy for PETase secretion by Corynebacterium glutamicum.

Extracellular production of target proteins simplifies downstream processing due to obsolete cell disruption. However, optimal combinations of a heterologous protein, suitable signal peptide, and secretion host can currently not be predicted, resulting in large strain libraries that need to be tested. On the experimental side, this challenge can be tackled by miniaturization, parallelization, and automation, which provide high-throughput screening data. These data need to be condensed into a candidate ranking for decision-making to focus bioprocess development on the most promising candidates. We screened for Bacillus subtilis signal peptides mediating Sec secretion of two polyethylene terephthalate degrading enzymes (PETases), leaf-branch compost cutinase (LCC) and polyester hydrolase mutants, by Corynebacterium glutamicum. We developed a fully automated screening process and constructed an accompanying Bayesian statistical modeling framework, which we applied in screenings for highest activity in 4-nitrophenyl palmitate degradation. In contrast to classical evaluation methods, batch effects and biological errors are taken into account and their uncertainty is quantified. Within only two rounds of screening, the most suitable signal peptide was identified for each PETase. Results from LCC secretion in microliter-scale cultivation were shown to be scalable to laboratory-scale bioreactors. This work demonstrates an experiment-modeling loop that can accelerate early-stage screening in a way that experimental capacities are focused to the most promising strain candidates. Combined with high-throughput cloning, this paves the way for using large strain libraries of several hundreds of strains in a Design-Build-Test-Learn approach.

Control of parallelized bioreactors II: probabilistic quantification of carboxylic acid reductase activity for bioprocess optimization.

Autonomously operated parallelized mL-scale bioreactors are considered the key to reduce bioprocess development cost and time. However, their application is often limited to products with very simple analytics. In this study, we investigated enhanced protein expression conditions of a carboxyl reductase from Nocardia otitidiscaviarum in E. coli. Cells were produced with exponential feeding in a L-scale bioreactor. After the desired cell density for protein expression was reached, the cells were automatically transferred to 48 mL-scale bioreactors operated by a liquid handling station where protein expression studies were conducted. During protein expression, the feed rate and the inducer concentration was varied. At the end of the protein expression phase, the enzymatic activity was estimated by performing automated whole-cell biotransformations in a deep-well-plate. The results were analyzed with hierarchical Bayesian modelling methods to account for the biomass growth during the biotransformation, biomass interference on the subsequent product assay, and to predict absolute and specific enzyme activities at optimal expression conditions. Lower feed rates seemed to be beneficial for high specific and absolute activities. At the optimal investigated expression conditions an activity of [Formula: see text] was estimated with a [Formula: see text] credible interval of [Formula: see text]. This is about 40-fold higher than the highest published data for the enzyme under investigation. With the proposed setup, 192 protein expression conditions were studied during four experimental runs with minimal manual workload, showing the reliability and potential of automated and digitalized bioreactor systems.

bletl - A Python package for integrating BioLector microcultivation devices in the Design-Build-Test-Learn cycle.

Microbioreactor (MBR) devices have emerged as powerful cultivation tools for tasks of microbial phenotyping and bioprocess characterization and provide a wealth of online process data in a highly parallelized manner. Such datasets are difficult to interpret in short time by manual workflows. In this study, we present the Python package bletl and show how it enables robust data analyses and the application of machine learning techniques without tedious data parsing and preprocessing. bletl reads raw result files from BioLector I, II and Pro devices to make all the contained information available to Python-based data analysis workflows. Together with standard tooling from the Python scientific computing ecosystem, interactive visualizations and spline-based derivative calculations can be performed. Additionally, we present a new method for unbiased quantification of time-variable specific growth rate µ ⃗ t based on unsupervised switchpoint detection with Student-t distributed random walks. With an adequate calibration model, this method enables practitioners to quantify time-variable growth rate with Bayesian uncertainty quantification and automatically detect switch-points that indicate relevant metabolic changes. Finally, we show how time series feature extraction enables the application of machine learning methods to MBR data, resulting in unsupervised phenotype characterization. As an example, Neighbor Embedding (t-SNE) is performed to visualize datasets comprising a variety of growth/DO/pH phenotypes.

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.