Modelling concentration gradients in fed‐batch cultivations of E. coli – towards the flexible design of scale‐down experiments

TLDR: Results indicate that the combination of a pulse‐based scale‐down approach with mechanistic models is a very suitable method to test strain robustness and physiological constraints at the early stages of bioprocess development.

Abstract: BACKGROUND: The impact of concentration gradients in large industrial‐scale bioreactors on microbial physiology can be studied in scale‐down bioreactors. However, scale‐down systems pose several challenges in construction, operation and footprint. Therefore, it is challenging to implement them in emerging technologies for bioprocess development, such as in high throughput cultivation platforms. In this study, a mechanistic model of a two‐compartment scale‐down bioreactor is developed. Simulations from this model are then used as bases for a pulse‐based scale‐down bioreactor suitable for application in parallel cultivation systems. RESULTS: As an application, the pulse‐based system model was used to study the misincorporation of non‐canonical branched‐chain amino acids into recombinant pre‐proinsulin expressed in Escherichia coli, as a response to oscillations in glucose and dissolved oxygen concentrations. The results show significant accumulation of overflow metabolites, up to 18.3% loss in product yield and up to 10‐fold accumulation of the non‐canonical amino acids norvaline and norleucine in the product in the pulse‐based cultivation, compared with a reference cultivation. CONCLUSIONS: Results indicate that the combination of a pulse‐based scale‐down approach with mechanistic models is a very suitable method to test strain robustness and physiological constraints at the early stages of bioprocess development. © 2018 Society of Chemical Industry

Figures

Figure 3 Schematic diagram of (A) the reference cultivation showing the constant agitation rate (lower curve) and the smooth glucose feed in two phases: exponential feed followed by constant feeding (upper curve), (B) the pulse-based cultivation showing the intermittent supply of glucose feed as pulses in both the exponential and constant feeding phases. The glucose pulses coincide with rpm shifts to achieve the desired gradients; (C) overall cultivation scheme.

Table 1. Results of model fitting for pulse-based scale-down experiments

Figure 1 (A) Schematic diagram of two-compartment bioreactor consisting of a stirred tank reactor and a plug-flow reactor. (B) Profiles of dissolved oxygen, biomass, glucose and acetate after running the 2CR for 10 hours with feed injection into the PFR (C ) top: Cascade configuration of 2CR and toroidal conversion for calculation of cell trajectories; middle: Gradient profiles of glucose showing the trajectory of a single cell and the glucose concentrations it encounters as it circulates between the STR and PFR; bottom: pulse representation of glucose gradients experienced by one cell (Glucose in feed = 250 g L-1,

Figure 4 Model fitting of fed-batch phase of the pulse-based scale down cultivation (experimental data , model — ). The dashed line represents the time of induction (3h). The Matlab code for the model fitting is available as a Supplementary Material.

Figure 5 (Left) Growth profiles and metabolic activity of E. coli during the fed-batch phase

Figure 2 Effect of recycling rate on (A) pulse frequency and (B) pulse size. High recycling rates result in high frequency of exposure, but at lower gradient sizes, and vice versa.

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This is the peer reviewed version of the following article:
Anane, E., Sawatzki, A., Neubauer, P., & Cruz-Bournazou, M. N. (2018). Modelling concentration
gradients in fed-batch cultivations of E. coli - towards the flexible design of scale-down experiments.
Journal of Chemical Technology & Biotechnology, 94(2), 516–526. https://doi.org/10.1002/jctb.5798
which has been published in final form at https://doi.org/10.1002/jctb.5798. This article may be used for
non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived
Versions.
Emmanuel Anane, Annina Sawatzki, Peter Neubauer, Mariano Nicolas
Cruz-Bournazou
Modelling concentration gradients in fed‐
batch cultivations of E. coli – towards the
flexible design of scale‐down experiments
Accepted manuscript (Postprint)Journal article |

1
Modelling concentration gradients in fed-batch cultivations of E. coli —towards the
flexible design of scale-down experiments
Emmanuel Anane
Annina Sawatzki
Peter Neubauer
Mariano Nicolas Cruz-Bournazou
Chair of Bioprocess Engineering, Institute of Biotechnology, Technische Universität Berlin,
Berlin, Germany
Correspondence: Dr.-Ing. Mariano Nicolas Cruz Bournazou, Chair of Bioprocess
Engineering, Institute of Biotechnology, Technische Universität Berlin, Ackerstraße 76,
ACK24, 13355 Berlin, Germany.
E-mail: mariano.n.cruzbournazou@tu-berlin.de
Keywords: E. coli, scale-down, glucose gradients, oxygen gradients, modelling,
inclusion bodies

2
Abstract
BACKGROUND: The impact of concentration gradients in large industrial-scale bioreactors
on microbial physiology can be studied in scale-down bioreactors. However, scale-down
systems pose several challenges in construction, operation and footprint. Therefore, it is
challenging to implement them in emerging technologies for bioprocess development,
such as in high throughput cultivation platforms. In this study, a mechanistic model of a
two-compartment scale-down bioreactor is developed. Simulations from this model are
then used as bases for a pulse-based scale-down bioreactor suitable for application in
parallel cultivation systems.
RESULTS: As an application, the pulse-based system model was used to study the
misincorporation of non-canonical branched-chain amino acids into recombinant pre-
proinsulin expressed in Escherichia coli, as a response to oscillations in glucose and
dissolved oxygen concentrations. The results show significant accumulation of overflow
metabolites, up to 18.3 % loss in product yield and up to 10 fold accumulation of the non-
canonical amino acids norvaline and norleucine in the product in the pulse-based
cultivation, compared to a reference cultivation.
CONCLUSIONS: Our results indicate that the combination of a pulse-based scale-down
approach with mechanistic models is a very suitable method to test strain robustness and
physiological constraints at the early stages of bioprocess development.

3
INTRODUCTION
Inadequate mixing and the associated concentration gradients in large-scale microbial
bioprocesses have significant impacts on both cell physiology and recombinant protein
quality. In these processes, cells are constantly exposed to oscillating concentrations of
substrate, metabolites, dissolved oxygen and carbon dioxide. Hence, the study of
performance under conditions similar to industrial scale process is essential to increase
scale-up reliability and speed up process development.
1,2
The effects of oscillating
cultivation conditions on microbial physiology and product yields have been studied in the
laboratory by applying scale-down techniques, either in the form of scale-down
bioreactors
3–6
or as pulse-based methods.
7–10
A scale-down system is a laboratory scale bioreactor designed to mimic the environmental
conditions in large-scale bioreactors. In multi-compartment scale-down bioreactors, a
perfectly mixed stirred tank reactor (STR) is connected to one or more STRs
11
or to one or
more plug flow reactors (PFR)
11,12
, through which the culture is circulated at a rate
equivalent to a specified residence time (Figure 1A). A stress inducing agent (e.g. highly
concentrated substrate, base or acid) is injected into one of the sections, which is
eventually mixed with the bulk of the culture in the other sections.
13
In a pulsing system,
the stress inducer is injected into the bioreactor intermittently, at specified intervals
7
or
randomly
14
. These operation mechanisms produce zones similar to feeding and starvation
zones in large-scale bioreactors and result in periodic exposure of the culture to varying
stresses.
15
Scale-down techniques have been applied for the successful study of the impact
of large-scale gradients for most industrially relevant organisms, with significant
differences in process behaviour compared to standard small scale cultivations.
1,12,16,17
The most recent advances in the development of scale-down concepts include the coupling
of computational fluid dynamics (CFD) models of bioreactors with cellular growth kinetics
(cellular reaction dynamics, CRD)
18–21
and the mechanistic description of population
groups in heterogeneous environments.
22,23
The CFD-CRD models have been used to
define specific stress exposure times that are assumed to occur at the larger scale, based
on mixing characteristics (CFD simulations) and the dynamics of cellular responses
18
.
However, the evaluation of the detailed physiological adaptation to oscillations and their
incorporation into CRD models can be an enormous amount of work, as is obvious from
the works of Vanrolleghem and Canelas.
24,25
In our opinion, the development of such
models and especially their parametrisation could benefit from the parallelization of scale-
down systems. Although some authors have applied pulse-based feeding profiles in
parallel mini-bioreactor systems
26
, mostly due to the difficulty that continuous feeding

4
was technically not possible, real scale-down approaches have not been published in
parallel systems, to our knowledge.
The objective of this work was to develop a mechanistic model of a typical pulse-based
scale-down bioreactor, suitable for application in high throughput parallel cultivation
platforms. The mechanistic model of the pulse-based system was developed from
simulations of a two-compartment scale-down bioreactor (2CR), which had been used in
many studies before. Thus, the principles of two different scale-down concepts (multi-
compartment and pulse-based systems) were combined in a mechanistic model to flexibly
design the exposure time of the culture to either high or low glucose and oxygen
concentrations. The pulse-based system was used to study the influence of model-derived
glucose and dissolved oxygen perturbations on the misincorporation of non-canonical
amino acids into pre-proinsulin expressed in E. coli. The mechanistic modelling concept
has the potential to facilitate the incorporation of scale-down studies into experimental
set-ups that would already consider scale-up effects at the early stages of bioprocess
development. The big benefit is that cellular reaction models which consider the response
to oscillations can be developed and parametrised with a much lower effort. Additionally,
the run of such experiments in efficient parallel robotic experimental facilities would
allow for a rapid phenotyping of large number of candidates under process relevant
conditions in short times.
26–29
MATERIALS AND METHODS
Mechanistic Model of Two-compartment Scale-down Bioreactor
The 2CR system that is modelled in this study has been thoroughly described by
Junne et al.
30
It consists of a 12 L (working volume) stirred tank bioreactor
connected to a 1.2 L plug flow reactor. Using the ratio of the volumes of the
PFR:STR and the feed and recycling rates, it is estimated that a cell, on average,
spends about 5 min in the STR before going through one cycle in the PFR, if the
residence time in the PFR is set to 30 seconds.
30
The mathematical model used to
describe the macro-kinetic dynamics of the culture has been presented elsewhere,
31
but a summarized version is presented in the Appendix. This model is a
nonlinear Ordinary Differential Equation (ODE) system given as:

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Modelling concentration gradients in fed‐ batch cultivations of e. coli – towards the flexible design of scale‐down experiments" ?

In this paper, the authors developed a mechanistic model of a typical pulse-based scale-down bioreactor, suitable for application in high throughput parallel cultivation platforms. 

Q2. What future works have the authors mentioned in the paper "Modelling concentration gradients in fed‐ batch cultivations of e. coli – towards the flexible design of scale‐down experiments" ?

Such experimental set-ups could be used to study the effects of scale-up stresses on the efficiency of bioprocesses at the early stages of process development. As demonstrated by Cruz et al. 26, model-based automation can be used to achieve faster bioprocess characterization. Therefore, incorporating scale-up effects into such platforms through modelling provides further opportunities to facilitate bioprocess development with scaleup in mind. 

Q3. What is the effect of the intermittent exposure of the culture to anaerobic conditions?

in the pulse-based cultivation, the intermittent exposure of the culture to anaerobic conditions can lead to the formation of formate and lactate which should have aninfluence on the cumulative degree of reduction of the metabolites. 

Q4. What are the effects of inadequate mixing in large-scale bioprocesses?

Inadequate mixing and the associated concentration gradients in large-scale microbial bioprocesses have significant impacts on both cell physiology and recombinant protein quality. 

Q5. What is the potential of the mechanistic modelling concept?

The mechanistic modelling concept has the potential to facilitate the incorporation of scale-down studies into experimental set-ups that would already consider scale-up effects at the early stages of bioprocess development. 

Q6. What is the recent development in the development of scale down concepts?

The most recent advances in the development of scale-down concepts include the coupling of computational fluid dynamics (CFD) models of bioreactors with cellular growth kinetics (cellular reaction dynamics, CRD) 18–21 and the mechanistic description of population groups in heterogeneous environments. 

Q7. How can the model be used to design simple scale-down experimental setups?

The model can then be used to design simple scale-down experimental setups, which is a step in simplifying scale-down bioreactor systems for application in parallelization. 

Q8. How is the effect of scale-down bioreactors studied in the laboratory?

1,2 The effects of oscillating cultivation conditions on microbial physiology and product yields have been studied in the laboratory by applying scale-down techniques, either in the form of scale-down bioreactors 3–6 or as pulse-based methods. 

Q9. Why haven't some authors applied pulse-based feeding profiles in parallel systems?

Although some authors have applied pulse-based feeding profiles in parallel mini-bioreactor systems 26, mostly due to the difficulty that continuous feedingwas technically not possible, real scale-down approaches have not been published in parallel systems, to their knowledge. 

Q10. What is the RQ of E. coli cultures grown on glucose?

In the analysis of E. coli cultures growing on glucose, the RQ value is unaffected by overflow metabolism due to the fact that the substrate (glucose), the major overflow product (acetate) and the biomass all have the same degree of reduction of approximately 4. 14,34 

Q11. What was the model parameter estimated by solving the optimization problem?

The model parameters were estimated by solving the optimization problem ̂ ( ) (5)where the nonlinear least-square objective function ( ) was calculated as( )( ( ) ) ( ( ) ) (6)In equation 6, ( ) represents the model predictions whereas represents the experimental data. 

Q12. What is the effect of the scale-down bioreactor?

15,43 In effect, the exposure time in the scale-down bioreactor should be a flexible parameter that can be changed easily, to suit a specific large-scale bioreactor. 

Q13. How long did the acetate re-assimilation take?

After the change to constant feeding, acetate was immediately re-assimilatedin the reference cultivation, but acetate re-assimilation in the pulse-based system was delayed up to 1 hour after protein induction (Figure 5B). 

Q14. What is the simplest way to transfer the characteristics of the 2CR to a pure glucose?

to transfer these characteristics to a pure glucose pulsing scheme, simulations were done todetermine the , µset and feed concentrations at which there would be a glucose carry over from the PFR into the STR.