Bayesian calibration, process modeling and uncertainty quantification in biotechnology

Abstract

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.

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

“…This model describes the data in a generative fashion by first discretizing time into many segments of exponential growth, followed by simulating the biomass curve resulting from a growth rate that drifts over time. For this it assumes an initial biomass concentration $$X_0$$ and a vector of growth rates $$\overrightarrow{\mu }$$, calculates biomass concentrations deterministically and compares them to the observed backscatter using a calibration model built with the calibr8 package [12]. Parameters $$X_0$$ and $$\overrightarrow{\mu }$$ can be obtained through optimization or MCMC.…”

“…Most importantly it describes the distribution of backscatter observations that can be expected from an underlying biomass concentration, thereby enabling uncertainty quantification that accounts for precision of the measurement method. A thorough introduction can be found in [12], but generally a calibration model can be constructed in three steps: 1. Acquisition of calibration data , preferably singular replicates at a high number of concentrations ranging three orders of magnitude up to 2−3× the biomass concentration expected in experiments. …”

“…For calibrations of biomass/backscatter relationships in the BioLector system we recommend the procedure described in the methods section of [12].…”

“…The dataset presented as an application example in this study was obtained in an automated cultivation workflow on the previously described microbial phenotyping platform. 48 cultures of Corynebacterium glutamicum ATCC 13032 harboring the pPBEx2[30]‐based plasmid pCMEx8‐NprE‐Cutinase (GenBank accession number OL456171) were cultivated in CGXII medium (recipe as in [12]) with different carbon sources. Carbon sources were prepared as C‐equimolar, random combinations of $$8\ \frac{g_{C}}{L}$$ glucose, fructose, maltose, sucrose, gluconate, lactate, glutamate or myo ‐inositol.…”

“…For example, we provide functions for data smoothing by cross‐validated spline approximation, growth rate analysis and time series feature extraction. Building on top of our recent work on uncertainty quantification and calibration modeling [12], we introduce a new method for Bayesian analysis of time‐variable specific growth rate and benchmark the objectivity of the method on a synthetic dataset in comparison with commonly used alternative growth rate calculation methods. In addition to an extensive documentation and automated software tests, we provide application examples on a dataset without biological surprises, such that it is well suited for method understanding.…”