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Intensification of bacterial cellulose production process with sequential electromagnetic field exposure aided by dynamic modelling

Biochemical Engineering Journal 182 (2022) 108432
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Biochemical Engineering Journal
journal homepage: www.elsevier.com/locate/bej
Intensification of bacterial cellulose production process with sequential
electromagnetic field exposure aided by dynamic modelling
Maciej Konopacki a, b, *, Bartłomiej Grygorcewicz a, b, Marian Kordas a,
Paula Ossowicz-Rupniewska c, Anna Nowak d, Magdalena Perużyńska e, Rafał Rakoczy a
West Pomeranian University of Technology in Szczecin, Faculty of Chemical Technology and Engineering, Department of Chemical and Process Engineering, Piastów
Avenue 42, 71-065 Szczecin, Poland
Pomeranian Medical University in Szczecin, Chair of Microbiology, Immunology and Laboratory Medicine, Department of Laboratory Medicine, Powstańców
Wielkopolskich Avenue 72, 70-111 Szczecin, Poland
West Pomeranian University of Technology in Szczecin, Faculty of Chemical Technology and Engineering, Department of Chemical Organic Technology and Polymeric
Materials, Piastów Avenue 42, 71-065 Szczecin, Poland
Pomeranian Medical University in Szczecin, Department of Cosmetic and Pharmaceutical Chemistry, Powstańców Wielkopolskich Avenue 72, 70-111 Szczecin, Poland
Pomeranian Medical University in Szczecin, Department of Experimental and Clinical Pharmacology, Powstańców Wielkopolskich Avenue 72, 70-111 Szczecin, Poland
Bacterial cellulose
Rotating magnetic field
Magnetically assisted bioreactor
Bacterial cellulose (BC) is a natural polymer produced by acetic acid bacteria, e.g. Komagataeibacter xylinus. BC is
often preferred over plant cellulose and finds many medicinal and environmental protection applications thanks
to its high purity, water holding capacity, tensile strength, and biocompatibility. This work is aimed to test the
sequential exposure of the rotating magnetic field (RMF) on the BC static production process, aimed to reduce the
energetic cost of production. The increased values of optical density, metabolic activity, fructose, ethanol, citric
acid uptake, and wet and dry mass of produced BC were observed after seven days of processing under the action
of RMF compared to the control conditions (without RMF). Also, it was found that the RMF exposure altered the
acetic acid production. Results proved that this approach could be successfully utilised to stimulate BC pro­
duction. A mathematical model connecting BC production with cell growth was created using Laplace transform
approach. Such a model was built using a block structure in Matlab Simulink. Data suggested that a properly
selected forcing function can accurately predict BC production, even for various cultivation conditions, by
employing a created dynamic model.
1. Introduction
In recent years, there has been an increasing interest in the appli­
cation of cellulose. This biopolymer is commonly produced by means of
plants and microbes. However, a major problem with the application of
plant cellulose is contamination with the other polymers (i.e. hemicel­
lulose, lignin, etc.). There is increasing concern that the plant cellulose is
being disadvantaged because its composition may reduce its use in
medicine. Recent developments in the process production of cellulose
showed an increasing interest in the usage of microbes. Komagataeibacter
(former Gluconacetobacter) is one the most widely used group of bacteria
species to produce bacterial cellulose (BC) [1]. This material has high
purity, water retention capacity, tensile strength, biocompatibility [2].
This biopolymer may be successfully applied as an innovative material
for medical applications [3]. Especially, BC-based cost-effective drug
delivery systems, wound healing materials, regenerative medicine
application, and tissue engineering poses interesting properties [4,5].
It should be noted that the different forms of BC are produced under
static, agitated, or stirred conditions [6]. The culture and process con­
ditions have a crucial influence on the quality of the obtained BC. It has
been demonstrated that the faster method of production of BC is based
on agitated fermentation [7]. However, the BC produced with agitated
or stirred conditions revealed worse material properties (eg. purity,
tensile strength) than the BC produced under static conditions [8]. In
contrast to cellulose spheres produced in agitated culture, static cultures
conditions allow obtaining BC as a pellicle, while fibres, pellets.
* Corresponding author at: West Pomeranian University of Technology in Szczecin, Faculty of Chemical Technology and Engineering, Department of Chemical and
Process Engineering, Piastów Avenue 42, 71-065 Szczecin, Poland.
E-mail address: mkonopacki@zut.edu.pl (M. Konopacki).
Received 24 February 2022; Received in revised form 25 March 2022; Accepted 3 April 2022
Available online 6 April 2022
1369-703X/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
M. Konopacki et al.
Biochemical Engineering Journal 182 (2022) 108432
Although both of these BC bioprocessing methods are used in various
target productions, the medicine or cosmetic industry applications
require a defined shape of BC with the appropriate properties [9].
Therefore, it has been suggested that the only cultivation of BC in static
conditions meets these requirements [10]. On the other hand, BC pro­
duction under static conditions results in low efficiency, which is the
main problem. Thus, novel methods of processing or improving the
properties of BC are currently being sought.
One of the promising possibilities to improve BC production in static
conditions is an application of external electromagnetic fields (EMF).
The EMF was reported to have an impact on bacteria and can stimulate
their growth [11]. One of the specific kinds of EMF is a rotating magnetic
field (RMF) which occurs as a superposition of 3-phase electromagnetic
fields. Our previous works showed that the application of RMF can
stimulate the growth of certain bacterial strains [12] and improve the
mass oxygen transfer to the culture medium [13]. Recent studies found
that after 3 days of continuous exposure of the RMF produced BC
showed increased yield and altered properties (higher absorption, lower
density, different morphology) [6]. It has also been shown that this kind
of magnetic field was influenced by the nano- and microscale structure
of the BC [8]. In addition, the valuable properties of BC (e.g. crystallinity
index) may be improved by applying the RMF [14].
One of the most significant current discussions in bioprocessing is the
application of mathematical modelling to increase the efficiency of
process production with the usage of microbes (such as BC production).
For example, Raganati et al. [15] showed that the kinetic dynamic
model described the effect of the carbon source on the
acetone-butanol-ethanol production by Clostridium acetobutylicum. The
dynamic model also describes interactions between channel activity and
the intercellular Ca2+ concentration during T cell activation [16].
Moreover, previous studies have reported that the dynamic model of
photosynthesis can give accurate predictions in photobioreactors [17].
The proposed dynamic model can also describe the efficient use of light
in this type of bioreactor or optimise the productivity of strains based on
their photosynthetic parameters. The dynamic reaction kinetics using a
Monod equation modified to include the limiting effects were applied to
describe the process production of xylitol by Candida tropicalis [18]. It
should be noticed that the dynamic mechanistic modelling of cell culture
is a critical tool in biotechnology, and this approach might be used to
support the optimisation [19]. No previous studies have investigated the
application of mathematical model to describe process production of BC
under the electromagnetic field conditions.
This paper aims to present a comprehensive framework for the
analysis of the BC process production under the action of the RMF. This
study evaluated whether the BC production process and activity of
K. xylinus cells may be influenced by the RMF, especially with the
discontinuous exposure mode. The RMF sequential exposure mode was
performed for seven days, and every day the field was active for 12 h and
then deactivated (12/24 h). This kind of exposure can highly reduce the
energetic cost of the process, but the whole procedure’s effectiveness
should be studied first. Moreover, the objective of this study is to
establish a dynamic model of the BC process production. The mathe­
matical relation between the input (the biomass concertation) and
output of the process production of BC (the BC wet mass) is defined by
using the transfer function (based on the Laplace transform). The
transfer functions are commonly used to determine the input-output
relationships of the system in control theory that can be used to
describe the dynamic characteristics of the BC production fully. The
proposed approach allows creating a method of analysis for complex
process production of BC without the information concerning the sys­
tem’s physical structure.
2. Materials and methods
2.1. Cells cultivation
The reference bacteria strain Komagataeibacter xylinus ATCC 53524
was employed in the current study. Bacteria cells were cultivated using
modified Herstin-Schramm (HS) medium composed of fructose 2.2 w/v
%, yeast extract 0.5 w/v%, peptone 0.5 w/v%, citric acid 0.115 w/v%,
Na2HPO4 0.27 w/v%, MgSO4.7 H2O 0.05 w/v% and ethanol 1 w/o%. It
should be noted that ethanol was added after sterilising the medium to
prevent its thermal decomposition. The cultivation process was con­
ducted inside sterile plastic probes CELLSTAR® CELLreactor™ (Greiner,
USA) of 50 ml working volume. The probe’s cap was equipped with a
filter that allowed gas exchange but at the same time prevented
contamination of the probe. The inoculum was prepared through the
shaking of a 7-days bacteria culture. At first, 1.6 ml of bacteria inoculum
was transferred to the glass container with 400 ml of modified HS me­
dium and vigorously shaken. Prepared cells suspension was then split
into probes (25 ml of suspension each). Such prepared probes (8 for each
bioreactor and 1 additional with the clear medium) were placed inside
magnetically assisted bioreactor and control bioreactor (without elec­
tromagnetic field) for a 7-days cultivation process at a constant tem­
perature of 28 ◦ C [8].
2.2. Rotating magnetic field exposure
Experiments were conducted using a novel, self-designed system
containing a magnetically assisted bioreactor. The system includes two
identical bioreactors that can be used at the same time independently
(one with the action of a rotating magnetic field and the second without
the activity of this kind of magnetic field). The pictures of bioreactors
and schematic of a single bioreactor set-up are presented in Fig. 1.
The rotating magnetic field (RMF) is generated by the set of 3-phase
internal windings (1) powered by the AC through the phase inverter (2)
connected with PC (3), which allows control of the current parameters.
The voltage was equal to 150 V, and the current frequency was 50 Hz,
resulting in maximum RMF induction of Bmax = 34 mT. The RMF
generator was placed inside a cylindrical-shaped stainless-steel tank (4)
(that screens the field keeping it inside a bioreactor) filled with silicon
oil. The tank centre was placed in a second container (5) made of
transparent polycarbonate. Inside the inner container filled with water
(to improve heat capacity) were placed probes with bacteria suspension
The temperature of the inner bath was measured by the CX-701
multimeter (6) equipped with the Pt-1000 temperature probe (7). The
external cooling/heating loop controlled the cultivation temperature
inside the bioreactor. In this loop, the flow of silicon oil was forced by
the circulation pump (8) through the plate heat exchanger (9) powered
by tap water or through the bypass parallel to the heat exchanger. The
direction of oil flow was controlled by the 3-way automatic valve (10)
equipped with an electronic controller (11) with a temperature sensor.
The heat inside the system was generated by the wires of the generator’s
windings powered by AC. The heat from windings was transported by
the silicon oil through the heat exchanger (cooling it) or through the
bypass back to the main tank, depending on the oil temperature. For
cases without powered winding (so without internal heat source), the
plate heat exchanger was supplied with hot water (e.g. in the control
process). This system maintained cultivation temperature very precisely
in the range ± 0.1 ◦ C from the demanded temperature level.
In this study, probes with the cells suspension were exposed to RMF
(f = 50 Hz, Bmax ≈ 34 mT) in 12 h per day cycles (12 h on and 12 h off).
The control process was conducted in the second bioreactor without the
RMF action. During the process, probes were collected for analysis every
24 h up to day seven, and all experiments were triplicated.
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Biochemical Engineering Journal 182 (2022) 108432
Fig. 1. View of employed bioreactors set-up: a) front view, b) top view, c) experimental set-up schematic. 1 – RMF generator, 2 – phase inverter, 3 – PC, 4 – generator
tank, 5 – inner container, 6 – CX-701 multimeter, 7 – temperature probe, 8 – circulation pump, 9 – plate heat exchanger, 10 – three-way valve, 11 – valve controller,
12 – plastic probe (with cells suspension).
2.3. Biomass harvest
2.6. Fructose concentration
The biomass concentration was measured for the cells inside of
produced cellulose. The cellulose sample was digested, releasing bac­
teria cells into the medium. For that reason, BC was washed in distilled
water and placed inside 5 ml of cellulase (Sigma-Aldrich, Germany)
solution in 0.05 M citrate buffer (pH=4.8) and then incubated with
shaking for 24 h in 35 ◦ C. The obtained cells suspension was centrifuged
for 20 min in 3.3 G. The received sediment was washed in PBS (SigmaAldrich, Germany), again centrifuged for 20 min in 3.3 G, and finally
dissolved in the original volume PBS. Such prepared cells suspension
was introduced to further analysis.
Fructose concentration in the medium was measured using a com­
mercial kit (Megazyme, USA). The detailed procedure has been
described in the supplementary materials section.
2.7. Ethanol concentration
Ethanol concentration in the medium was measured using a com­
mercial kit (Megazyme, USA). Detailed The detailed procedure has been
described in the supplementary materials section.
2.8. Citric acid concertation
2.4. Optical density
The citric acid concentration in the medium was measured using a
commercial kit (Megazyme, USA). The detailed procedure has been
described in the supplementary materials section.
The optical density measurement was conducted by the spectro­
photometric microplate reader Synergy H1 (Biotek, USA). For the
analysis, 100 µl of cell suspension was transferred into the 96-wells
plate, both from exposed and control samples and from a clear me­
dium, in five repetitions. The absorbance was read at the 600 nm
2.9. Acetic acid concentration
The acetic acid concentration in the medium was measured using a
commercial kit (Megazyme, USA). The detailed procedure has been
described in the supplementary materials section.
2.5. Metabolic activity
2.10. Amount of bacterial cellulose
The metabolic activity of bacteria cells was measured using a com­
mercial Alamar Blue kit (Life Technologies, USA). The detailed pro­
cedure has been described in the supplementary materials section.
Harvested bacterial cellulose was weighted using analytical balance
XA-52/X (Radwag, Poland). The result was marked as the mass of wet
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cellulose. Moreover, BC was cleaned in 0.1 M solution of NaOH at 80 ◦ C
for 30 min and washed in distilled water. This procedure was triplicated
to remove the remaining cells or medium components. Next, the BC
pellicles were dried overnight in an EV-50 oven (Trade Raypa, Spain).
After drying, BC was again weighted, and the result was marked as the
mass of dry cellulose.
operational method of expressing the differential equation related to the
output variable. This function is a property of a system itself (in this case,
the process production of BC is treated as the system), independent of
the magnitude and nature of the input or driving function. The transfer
function is the relation between the input and the system’s output, but it
does not provide any information connecting with the system’s physical
structure. The output can be obtained for various inputs if the system’s
transfer function is known. This approach allows one to understand the
nature of the system. From the practical point of view, if the system’s
transfer function is unknown, it may be established experimentally by
introducing known inputs and analysing the system’s output. It should
be emphasised that the transfer function offers a complete description of
the dynamic characteristics of the systems.
2.11. Statistical analysis
Experimental results are presented as the average value ± standard
errors calculated from the measurements of three different samples. All
statistical calculations were performed with Statistica version 13.3
software (Statsoft, USA). Statistical differences between the RMF expo­
sure and the control samples were analysed through the Student’s t-test.
Differences were considered statistically significant when the p-value
was less than 0.05.
3. Results and discussion
3.1. Impact of the electromagnetic field on the BC production
2.12. Transfer function
The BC production process was conducted for 7 days, as was
mentioned previously. This process was performed without mechanical
mixing (in stationary form). In such a case, the bacteria formed BC on
the interphase surface (between gas and liquid) in the form of pellicles.
The optical density (OD) of bacteria suspension was measured first.
Changes of OD during the process are illustrated in Fig. 2.
The results presented in Fig. 2 demonstrate that under RMF expo­
sure, the medium OD (proportional to the amount of biomass) increases
up to 68% after 7 days. The significant differences between the exposed
and control processes occur after 3 days. Nevertheless, the OD shows
also dead cells, so in the next step, the metabolic activity was controlled.
The changes in metabolic activity ratio are presented in Fig. 3.
Obtained data indicate that RMF influences the cell’s metabolic ac­
tivity stimulating the inter-cellular processes. The metabolic activity
was increased up to 77% after 7 days of the process. The first two days
show only a slight rise of metabolic activity (less than 20%) when after 3
days, the stimulation was much more significant.
During experiments, the biomass concentration was also measured.
The results are presented in Fig. 4.
In Fig. 4, it can be observed that the magnetic field alters the biomass
growth under RMF exposure. The first three days show almost no
The transfer function of the system (in this work, the process pro­
duction of BC is treated as the system) is the ratio of the Laplace
transformed output to the Laplace transformed input when the initial
conditions are zero:
G(s) =
G (s)- transfer function,
L- Laplace transform of output or input.
For suitable function k, the Laplace transform is integral:
L{k} =
k(t) e− st dt
It should be noticed that the concept of the transfer function is
allowed to represent system dynamics by algebraic equations in s. The
transfer function of a system is a mathematical model. It is an
Fig. 2. Changes of OD during the process. An asterisk * means statistically significant difference at p < 0.05 between exposed and control samples.
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Fig. 3. Changes in metabolic activity ratio during the process.
Fig. 4. Changes in biomass concentration during the process. An asterisk * means statistically significant difference at p < 0.05 between exposed and con­
trol samples.
differences. However, from day four, statistically significant differences
to the end of the process could be noticed when more than 50% higher
biomass concentrations were observed in relation to the control process.
In the next step, the fructose concentration in the medium was
measured. Changes in fructose concentration are presented in Fig. 5.
The fructose concentration decreases through the process due to its
consumption by the bacteria. The RMF exposure causes higher fructose
uptake, but the differences are slight and are not higher than a few per
cent (about 3%, so about 0.5 g⋅dm− 3 after 7 days). Carbohydrates up­
take is connected mainly with the production of BC. Thus, higher uptake
should produce more cellulose [20].
The concentration of ethanol, which is the main carbon source for
K. xylinus, was measured in the next step. The changes in ethanol con­
centration in the medium are presented in Fig. 6.
The bacteria cells under the action of RMF show increasing ethanol
uptake from day 1 to day 6, but on the last day of the process, the level of
ethanol was the same in both cases. The highest differences were
observed for 3 days (about 21%).
The following analysed parameter was the concentration of citric
acid in the medium. Changes in citric acid concentration are illustrated
in Fig. 7.
Obtained data showed that during the first 3 days concentration of
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Fig. 5. Changes of fructose concentration in the medium during the process. An asterisk * means statistically significant difference at p < 0.05 between exposed and
control samples.
Fig. 6. Changes of ethanol concentration during process. An asterisk * means statistically significant difference at p < 0.05 between exposed and control samples.
citric acid was decreasing rapidly in both cases, and from 4 days, its
concentration remained almost at the same level. Nevertheless, uptake
under RMF exposure was higher (max. about 14%).
The acetic acid concentration was also measured as the main
K. xylinus metabolic product. The acetic acid concentration changes
during the process are presented in Fig. 8.
Presented data revealed different behaviour of acetic acid production
under RMF exposure in correlation with the control process. After three
days, the concentration of acetic acid increased by about 50%. However,
the concentration decreased in the next four days, when in the control
process amount of acetic acid was still improved. This situation may
suggest that in RMF exposure, due to higher metabolic activity and
depletion of the main carbon source (ethanol), bacteria cells use some
part of produced acetic acid as a nutrient employing a new metabolic
pathway to convert acetic acid. At the end of the process (day 7), the
acetic acid concentration was lowered in the magnetically assisted
process by 26%.
The key parameter of this study is the amount of produced BC. The
changes of wet cellulose mass during the process are illustrated in Fig. 9.
The BC production given by wet mass under action of RMF was
increased by 35% after 7 days of the process. However, the significant
differences were observed after 3 days, and each process’s speed
remained almost the same until the last day. This situation could suggest
that the RMF exposure stimulates mainly the first phase of cellulose
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Fig. 7. Changes of citric acid concentration during process. An asterisk * means statistically significant difference at p < 0.05 between exposed and control samples.
Fig. 8. Changes of acetic acid concentration during process. An asterisk * means statistically significant difference at p < 0.05 between exposed and control samples.
production, thus forming the BC membrane. Moreover, the mass of
cellulose after drying was measured. The changes of BC dry mass during
the process are presented in Fig. 10.
The highest differences between both runs were observed in the last
three days. The RMF exposure increased the mass of dry BC after 7 days
of the process by 33%, concerning the control process results in almost
40 mg of dry cellulose from a single probe. It should be noticed that
cellulose produced after 3 days had about 15% higher dry mass and
almost three times higher wet mass relating to the control process. Thus,
the young cellulose produced under RMF exposure can pose a much
bigger water capacity. For that reason, the cellulose water capacity as
the difference between wet and dry mass was calculated. The results are
presented as the ratio between RMF exposure and control process using
the following equation:
Wcr =
mBC,wC − mBC,dC
mBC,wRMF – mass of wet BC produced with RMF [g],
mBC,dRMF – mass of dry BC produced with RMF [g],
mBC,wC – mass of wet BC produced without RMF [g],
mBC,dC – mass of dry BC produced without RMF [g].
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Fig. 9. Changes of wet BC mass during process. An asterisk * means statistically significant difference at p < 0,05 between exposed and control samples.
Fig. 10. Changes of BC dry mass during process. An asterisk * means statistically significant difference at p < 0,05 between exposed and control samples.
Changes in water content ratio calculated using Eq. (3) during the
process are presented in Fig. 11.
The water content ratio confirms that the BC produced at the first
four days under RMF exposure possessed the highest water capacity
(over 250% increase at day 3 about the control process). However, water
content has been significantly lower in the last three days. This result
suggests that young cellulose created under the action of the electro­
magnetic field had a more loose structure which became more tightened
after the third day.
The measured amounts of products (wet and dry mass of cellulose)
and uptake of substrates (fructose, ethanol, and citric acid) allowed us to
evaluate efficiency coefficients Xps defined as the mass of obtained
product per mass of used substrate using the following equation:
Xps =
mp – obtained mass of product [g],
ms – mass of used substrate [g].
The results from the control and magnetically assisted process were
calculated as the ratio using the following equation:
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Fig. 11. Changes in water content ratio during the process. At the beginning and first day (t = 0 and 1 day) were no cellulose membranes to measure.
Xps,r =
bioreactor system can be a promising alternative to perform BC
Based on the presented experimental results, the RMF exposition on
bacteria cells altered the BC production. There are a few ways that RMF
can influence this process. Firstly, it should be noticed that many dis­
solved ions derive from nutrients inside the liquid cultivation medium,
e.g. Na+, K+, Ca2+. As known, every charged particle is forced to move in
the electromagnetic field, and the direction of this move is consistent
with the magnetic field (MF) lines [21]. The RMF creates round-shape
MF lines, thus particles travelling around the central axis.
Moreover, the alternate MF generates the eddy currents within the
cultivation medium [22,23]. These eddy currents produce local MFs
causing the presence of external MF to spin the ions around its axis,
which have been called the microlevel dynamo concept [24]. The syn­
ergistic effect of both movements (global rotation and local spin of
Xps,RMF – Xps coefficient for process with RMF exposure,
Xps,C – Xps coefficient for process without RMF exposure.
The Xps,r coefficient defined by Eq. (5) has been calculated for every
substrate-product pair. The results are presented in Fig. 12.
Data presented in Fig. 12 show that RMF exposure stimulates the BC
production process efficiency by over 30% in every case (compared to
the control process). Furthermore, the efficiency of fructose conversion
to the wet and dry mass of BC was increased markedly – up to almost
50%. These results show that the proposed magnetically assisted
Fig. 12. Xps,r coefficients calculated for fructose, ethanol, and citric acid as substrates in relation to cellulose’s wet and dry mass as a product.
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particles) powered by the Lorentz force evokes a micro-mixing effect
that agitates elements of cultivation liquid [25]. This kind of agitation
stimulates the growth of cells and bacteria metabolic activity thanks to
the enhancement of transport phenomena and relative small shear stress
(with mechanical agitators) that could be harmful to cells and BC
structure [12].
The RMF also affects the inter-cellular transport process, especially
for the Gram-negative bacteria (like K. xylinus) that pose a much thinner
cell wall than the Gram-positive bacteria [12]. In addition, EMF can
create an electroporation phenomenon increasing conductivity and
permeability of the cell membrane [26]. The electroporation causes the
creation of the electropores, which are hydrophilic spaces that helps
penetration of the hydrophilic particles through the membrane (e.g.
Ca2+ ions) that are important in the metabolic processes [27]. Due to the
enhancement of the inter-cellular transport, the metabolic processes
could occur faster, thus increasing metabolic activity, which was
observed during this experiment.
The K. xylinus strain employed in this study is a bacteria of acetic
fermentation that is an aerobic process. During this process, ethanol (as
the preferred carbon source) is converted to acetic acid by the bacteria
assimilating the surrounding oxygen. Additionally, carbon sources such
as glucose, fructose, mannitol, and glycerol allow the microorganisms to
convert substrate into BC [20]. During experiments, enhanced acetic
acid production under RMF action was observed due to increased
metabolic activity in the first three days. After that, due to ethanol
depletion, stimulated bacteria started to uptake acetic acid and oxidise it
to carbon dioxide and water. Thus, oxygen demand was high during the
whole process. For that reason, the BC in static conditions (without
mechanical mixing) is produced only at the liquid-gas interface [28],
and the insufficient content of oxygen in the cultivation medium leads to
inhibition of the BC production [29]. It has been proved that RMF can
alter the gas exchange, resulting in enhanced mass transfer (given in
volumetric mass transfer coefficient) proportionally to the MF induction
[13]. The increased gas transport from the atmosphere to the cultivation
medium under RMF exposure helps meet the raised oxygen needs of
stimulated cellulose-synthesising bacteria. Furthermore, some re­
searchers speculate that water particles (which are dipoles) inside EMF
have lowered surface tension and disturbed the creation of the hydrogen
bonds, which facilitate the stabilisation of the crystalline structure and
the establishment of the BC membranes at the cultivation medium sur­
face [30–32].
In the present study, the changes of the BC structure given by the
water content were also observed under RMF exposure. Increased water
content suggests more space between the BC fibrils than the water
particles. The increased porosity of BC is also connected with the
extension of the surface area [33,34]. Observed results show that RMF
may alter the arrangement of the BC fibrils creating a more loose
H(s) =
H(s) =
mathematical model of the BC process production, respectively. This
approach shows that the relationship between these two process pa­
rameters may be expressed by using mathematical descriptions.
The biomass concentration (Fig. 4) and the BC wet mass (Fig. 9)
might be described by means of the second-order response to an input
step-change disturbance:
T1 exp −
− T2 exp −
g(t) = K 1 −
T1 − T2
K – gain factor [-],
T1, T2 – time constants [s].
The above function described the obtained experimental results
(biomass concentration and the BC wet mass). These functions are
defined as follows:
x(t) = K 1 −
T1X exp −
− T2X exp −
T1X − T2X
y(t) = K 1 −
− T2Y
T1Y exp −
− T2Y exp −
x(t)- the variation of biomass concentration at time (input
y(t)- the variation of BC wet mass at time (output parameter).
The Laplace transform of the above functions is given as follows:
X(s) =
T1X T2X s2 + (T1X + T2X )s + 1
T1Y T2Y s2 + (T1Y + T2Y )s + 1
Y(s) =
Kx, T1x, T2x – constants of biomass concentration model,
Ky, T1y, T2y – constants of the BC wet mass model.
It should be noticed that the BC process production can be described
by using the following transfer function:
T1Y T2Y s2 + (T1Y + T2Y )s + 1 T1X T2X s2 + (T1X + T2X )s + 1
structure [8,35] (highest at the first few days), and similarly to the
bacteria intercellular transport, the RMF exposure may facilitate pene­
tration of water particles through the BC pores and capillaries, creating
more distance between the BC fibrils.
H(s) =
KY T1X T2X s2 + KY (T1X + T2X )s + KY
KX T1Y T2Y s2 + KX (T1Y + T2Y )s + KX
Eq. (12) has a form of polynomial equations ratio of the general form:
3.2. Dynamic modelling of the BC production
H(s) =
The bacteria growth connected with the BC production process can
be treated as a dynamic system. Therefore, the biomass concentration
and the BC wet mass are treated as the input and output to the
n2 s2 + n1 s + n0
d2 s2 + d1 s + d0
M. Konopacki et al.
Biochemical Engineering Journal 182 (2022) 108432
n2 , n1 , n0 - numerator parameters,
d2 , d1 , d0 - denominator parameters.
x(t) =
Y(s) = H(s)X(s)
y(t) = L− 1 [Y(s)] ⇒
y(t) = L− 1 [H(s)X(s)]
L− 1 [Y(s)]- inversed Laplace transform of Y(s) function.
Therefore, in order to make numerical simulation, a proper growth
model as forcing function is needed. In the literature, there are many
mathematical models describing bacteria growth. In the current study,
two forms of forcing function were used. First (model 1), a very common
growth model combines biomass concentration with the maximal spe­
cific growth rate. The initial and the final biomass concentration was
employed, defined as follows [28]:
x(t) =
X0 exp(μmax t)
1 − (Xr )(1 − exp(μmax t))
t− x0
) + y0
Both biomass growth models from Eqs. (15) and (16) fit the experi­
mental data of bacteria growth, presented in Fig. 13.
In Fig. 13, it can be noticed that model 2 better fits the experimental
data than model 1, which still has a good agreement with the last three
time points. Therefore, at this point, it was decided to proceed with the
modelling using those two growth models.
In the next step, block models of both forcing functions were created
using MATLAB 2021a Simulink (MathWorks, USA). Then, both were
connected to the transfer function block, where Eq. (13) parameters
were defined. Finally, the transformed curve and the initial one were
observed through the scope block. The schematic of the Simulink block
model is presented in Fig. 14.
The initial signal was set as time with linear and constant growth up
to 7 days. Therefore, the left side of the block structure before the
transfer function block strictly represents the growth curves of each
model presented previously in Fig. 13. Then, using those input functions,
we simulate the BC production associated with the bacteria growth
process to verify the correctness of the Simulink model. The result of this
simulation is presented in Fig. 15.
Data presented in Fig. 15 shows that simulation performed using the
second model as the forcing function better adjusts to the experimental
data from the control process. Both models create over-estimated values
for the middle region of the process. However, the error level of the
second model is more acceptable. Moreover, these results strongly
correspond with the accuracy of the growth curve fitting presented in
Fig. 13, where the second model also indicated better precision.
These results also proved that the created transform function works
well in the studied case, predicting the experimental data of produced
BC wet mass. However, the response is very sensitive to the accuracy of
the initial signal.
The same dynamic model created in Simulink was tested using data
for the BC production process under RMF exposure in the next step. It
was assumed that because the BC production is strongly associated with
bacteria growth, the impact of the magnetic field observed on growth
changes would allow estimating BC production rate using the same
previously created model. Therefore, the growth curves from the process
Receiving transfer function H(s) allows to model system response (in
the form of wet BC mass production curve) through introducing various
forms of the forcing function (biomass growth curve) x(t). First, such
function should be transformed to the Laplace domain, giving the
function X(s). Then knowing the system transfer function H(s), it is
possible to simulate its output y(t) using the following relations:
H(s) =
1 + exp −
X0 – initial biomass concentration,
Xmax – final biomass concentration,
µmax – maximal specific growth rate,
t – time,
Xr = X0 /Xmax .
The second mathematical model of biomass concentration growth
(model 2) is a sigmoidal growth curve, presented previously [36]:
Fig. 13. Biomass growth models fitted to the experimental data.
M. Konopacki et al.
Biochemical Engineering Journal 182 (2022) 108432
Fig. 14. Simulink block model of the analysed dynamic system for two different forcing functions.
Fig. 15. Result of BC production process simulated in Simulink.
under RMF exposure were fitted to the experimental data using Eqs. (15)
and (16), which was presented in Fig. 16.
In Fig. 16, both models agree with the experimental data, but the
second model still has better adjustment.
Like in the previous case, the same Simulink block model was used to
simulate BC production (again for the 7 days), now using the new
forcing functions obtained for the bacteria growth under RMF exposure,
presented in Fig. 16. It should be highlighted that the transform function
(Eq. 13) parameters remain unchanged. The results of the simulation are
illustrated in Fig. 17.
The obtained results confirmed that this dynamic model accuracy is
sensitive to the model’s growth curve fitting introduced as the forcing
function. Moreover, it can be observed that the simulation results are in
excellent agreement with the experimental data. This suggests that a
developed dynamic model can precisely predict the BC production
process in an analysed set-up using a well-fitted bacteria growth curve as
the input signal. This result gives a possibility to study the response of
the BC production process on different modes of RMF exposure using
only knowledge about bacteria growth. This could be easily done by
introducing a new forcing function describing the bacteria growth in
new conditions to the Simulink model.
M. Konopacki et al.
Biochemical Engineering Journal 182 (2022) 108432
Fig. 16. Growth curves fitted to the experimental data (under RMF exposure).
Fig. 17. Results of Simulink modelling for the new forcing functions (case with RMF exposure).
4. Conclusions
sequential exposure that was applied, besides it being less energyconsuming, allowed to produce the more loose structure of BC (given
by the higher water content in the range 130–250%), which could be
essential in the medical applications, e.g. for the after-burn wound
treatment to produce soaked bandages.
The second aim of this study was to develop a dynamic model that
can predict the production of BC, assuming it is associated with the
growth of the cells. Using the Laplace transform method, it was possible
to design a block structure model and solve it using Matlab Simulink. It
was found that results are susceptible to adjusting the input forcing
function. However, it is possible to achieve accurate model results,
which predicts the BC production rate for various cultivation conditions
under RMF exposure.
The BC production under static conditions (without mixing) results
in a material with desired properties but is less efficient than the mixed
process. Thus, new intensification factors need to be developed, e.g.
electromagnetic field. The first aim of this study was to analyse the RMF
influence on BC production under sequential exposure. In conclusion,
the current work confirmed that the RMF could alter the cells’ metabolic
processes and impact the productivity of the BC. Due to the increased
metabolic activity, higher uptake of substrates (fructose, ethanol, citric
acid) was observed under the RMF exposure.
Moreover, the amount of biomass was also raised. Furthermore, it
was shown that the amount of produced BC was increased by over 30%,
with higher process efficiency than the control process. Additionally, the
M. Konopacki et al.
Biochemical Engineering Journal 182 (2022) 108432
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Maciej Konopacki: Conceptualization, Methodology, Formal anal­
ysis, Investigation, Writing − original draft, Writing − review & editing,
Visualization. Bartłomiej Grygorcewicz: Investigation, Writing − re­
view & editing. Marian Kordas: Investigation, Visualization. Paula
Ossowicz-Rupniewska: Investigation, Writing − review & editing.
Anna Nowak: Investigation, Writing − review & editing. Magdalena
Perużyńska: Investigation, Writing − review & editing. Rafał Rakoczy:
Writing − original draft, Writing − review & editing, Supervision,
Funding acquisition.
Declaration of Competing Interest
The authors declare the following financial interests/personal re­
lationships which may be considered as potential competing interests.
Rafal Rakoczy reports financial support was provided by National Sci­
ence Centre Poland.
This study was supported by the National Science Centre, Poland
[OPUS 16, Project No. UMO-2018/31/B/ST8/03170, granted to Rafał
Appendix A. Supporting information
Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.bej.2022.108432.
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