Non-Invasive Estimation of Acetates Using Off-Gas Information for Fed-Batch E. coli Bioprocess ^†

Abstract

Pharmaceutical industries widely use Escherichia coli cell strain to synthesize various target products. The main goal is to reach the highest possible product yield. However, the formation of by-products is inevitable throughout the cell growth stage. Metabolic compounds such as acetates cause inhibition, particularly in later bioprocess stages. Therefore, the acetate accumulation model is necessary for planning bioprocesses to maximize cell biomass growth. The decision tree method was in possession to replicate the approach. Specific biomass growth at induction, broth weight, oxygen uptake rate, and consumed substrate weight were the inputs of model training. Broth and consumed substrate weight had additional aging-related information incorporated as separate inputs to introduce the cumulative regularization.

1. Introduction

Bioprocess data monitoring and control is one of bioengineers’ problematic and time-consuming tasks. Bioprocesses have complex mathematical models, noisy, inconsistent data, and complicated control systems [1,2]. Offline measurements are time-delayed, require additional instruments, and are time-consuming. Developing soft sensors allows for improving and optimizing the process by facilitating real-time data collection. Process optimization leads to the primary goal of all pharmaceutical industries—to reach the highest possible product yield.

Metabolic compounds such as acetates interfere with target product synthesis by causing inhibition, particularly in later bioprocess stages. Furthermore, inhibition lengthens the lag phase, leading to loss of biomass production and growth rate [3]. By-product formation under aerobic conditions is mainly caused by the lack of dissolved oxygen and the imbalance between glucose uptake and its conversion to biomass [4]. To better understand these processes, real-time acetate estimation is necessary.

By-product estimation uses soft sensors that consist of numerous mathematical models [5]. These models vary from mechanistic and data-driven empirical models to hybrid models. Among the mechanistic models, the extended Kalman filter is one of the most popular approaches [6]. The EKF results are firmly related to the accuracy of the mathematical model. Therefore, hybrid models with data-driven subparts correct these inaccuracies [7,8].

This study gives an E. coli by-product estimation model based on gathered offline data with a black-box model. It discusses model inputs, their physical meanings, and the impact of incorporating age-related information. The novelty of this study is the proposition that off-gas analysis also carries information about the forming of by-products.

2. Materials and Methods

Data used for model training originates from fed-batch E. coli BL21(DE3) pET21-IFN-alfa-5 experiments. It consisted of 24 cultivation processes, some of which were with limited feeding. The cultivation medium throughout the experiments consisted of 46.55 g KH₂PO₄, 14 g (NH₄)₂HPO₄, 5.6 g C6H₈O₇·H₂O, 3 mL of concentrated antifoam, 35 g H₁₄MgO₁₁S, and 105 gD (+) glucose monohydrate. The pressure and temperature of the system remained constant. During the cultivation process, pure oxygen flow from 0 to 7.5 L/min was used to increase the oxygen transfer rate in the bioreactor.

3. Development of a Black-Box Model for Acetate Estimation

Decision trees serve for data classification and continuous data prediction [9]. Decision trees used in continuous data prediction are called regression trees. Later is used as a data-driven model in making this estimator. MATLAB software was the model development and data processing tool. Training and validation datasets were generated by dividing the sampled data from the experiments. The training dataset consisted of samples from 18 cultivation experiments and a validation dataset of 6.

3.1. Input Selection

Previous studies showed that specific growth rate μ is one of the best descriptors for estimating bioprocess parameters [10]. This parameter and oxygen uptake rate (OUR) carry much information about the growth and life of the cell [11,12]. The latter is estimated using a soft-sensor with off-gas information. The specific growth rate is expressed using OUR or offline-sampled biomass concentration X:

$$\mu =\frac{1}{OUR\left(t\right)}·\frac{\mathrm{d}OUR\left(t\right)}{\mathrm{dt}}-\frac{1}{\mu +\beta /\alpha }·\frac{\mathrm{d}\mu }{\mathrm{d}t},$$

(1)

$$\mu =\frac{\mathrm{d}X}{\mathrm{d}t}·\frac{1}{X\left(t\right)},$$

(2)

where $\alpha$—oxygen consumption parameter for biomass growth and the parameter $\beta$ for maintenance. As an input, the specific growth rate is used only during the induction phase of the process (${\mu }_{ind}$). The value (${\mu }_{ind})$ is calculated during the induction moment using Equation (2) formula shown above. After the induction, new biochemical reactions start, and the cells synthesize the target product [13]. During cultivations, substrate consumption affects cell development, and its inconsistent feeding may lead to cell conversion to metabolisms [14]. Substrate consumption and broth weight give model information about biomass growth, and broth weight also gives information about the dilution effect of substrate feeding. Additionally, broth and consumed substrate weight with supplementary aging-related information are separate inputs introducing the cumulative regularization [10]. The selected inputs were (

Table 1. Model inputs.

Time	h
The specific growth rate during induction ${\mu }_{ind}$	1/h
Broth weight	kg
Consumed substrate weight	g
Oxygen uptake rate OUR	g/(h·g)
Broth weight with age information	kg/h
Consumed substrate weight with age information	g/h

):

3.2. Model Errors

Model parameters fitting was based on minimizing the errors. Errors were based on measured and estimated acetates sums of squared residuals (RSS) and mean absolute error (MAE) results

$$RSS={{\displaystyle \sum }}_{i=1}^n{\left(A_i^{*}-A_i\right)}^2,$$

(3)

$$MAE=\frac{{{\displaystyle \sum }}_{i=1}^n\left|A_i^{*}- A_i\right|}{n},$$

(4)

where $A_i^{*}$ is acetate i-th observation, and the value ($A_i$) is a black-box model acetate estimate. The values RSS and MAE are shown with two different sets of inputs in

Table 2. Model errors with age-related info and without.

Inputs	MAE	RSS
Without age-related info	0.192	1.739
With age-related info	0.155	1.264

. The first set included time (${\mu }_{ind}$), the OUR, broth and consumed substrate weights, and the second set contained additional broth and consumed substrate weights with cumulative regularization. As shown in Table 2, these additional inputs improved the results.

4. Results and Discussion

Model results show that the regression tree model is applicable for estimating E. coli cell metabolic compounds in fed-batch cultivation. Figure 1 shows the difference between measured and estimated acetate values. By comparing results from inputs with age-related information (dark blue color) and inputs without age-related information (light blue color), it is clear that introducing cumulative regularization improved by-product estimation. These extra inputs resolved the errors in the first half of the bioprocess and smoothened the big spikes in the second half of the process. After bioreactor inoculation, sudden spikes in acetate estimation can be related to new biochemical processes. This phenomenon requires further, more in-depth data analysis.

On the other hand, comparing this model to the traditional EKF model’s lowest MAE, the black box model estimation lowered MAE by approximately 5% [6]. Also, this study used only two samples of biomass concentration, whereas EKF based model used biomass observed once every 5 s. Additionally, experiments used for this model validation and training contained data involving the induction. Such an event causes a disturbance for bioprocess dynamics, making it more challenging to estimate acetates.

In the future, the proposed model will serve as feedback that can potentially improve the quantity and quality of a synthesized product. Altering the main parameters responsible for metabolic pathways such as substrate feed or/and oxygen transfer rate enhances the growth and well-being of the cell. Bioprocess improvements lead to easier process control and managing, providing a better workspace for future optimizations.

5. Conclusions

This study proposed an acetate estimator using the regression tree method. The model training dataset consisted of eighteen cultivation experiments, and a dataset of six cultivation experiments validated the chosen inputs and model parameters. The regression tree model had the best results by using samples integrated with aging-related information, and it achieved satisfactory results estimating acetates reaching MAE of 0.155 and RSS of 1.264.