Biochemical Engineering Journal 182 (2022) 108432 Contents lists available at ScienceDirect 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 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 c 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 d Pomeranian Medical University in Szczecin, Department of Cosmetic and Pharmaceutical Chemistry, Powstańców Wielkopolskich Avenue 72, 70-111 Szczecin, Poland e Pomeranian Medical University in Szczecin, Department of Experimental and Clinical Pharmacology, Powstańców Wielkopolskich Avenue 72, 70-111 Szczecin, Poland b A R T I C L E I N F O A B S T R A C T Keywords: 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). https://doi.org/10.1016/j.bej.2022.108432 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 (12). 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. 2 M. Konopacki et al. 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 wavelength. 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 3 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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) = L[output] L[input] (1) where: 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 0 (2) 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. 4 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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 5 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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 6 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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,wRMF − mBC,dRMF ⋅100% mBC,wC − mBC,dC where: 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]. 7 (3) M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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 ms (4) where: 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: 8 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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 = Xps,RMF Xps,C bioreactor system can be a promising alternative to perform BC production. 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 (5) where: 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. 9 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 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) = Y(s) X(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: ( ( ( ) ))] [ 1 t t T1 exp − − T2 exp − (6) g(t) = K 1 − T1 − T2 T1 T2 where: 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: [ ( ) ))] ( ( 1 t t x(t) = K 1 − T1X exp − − T2X exp − (7) T1X − T2X T1X T2X and [ y(t) = K 1 − T1Y 1 − T2Y ( ( T1Y exp − t T1Y ) ( − T2Y exp − t T2Y ))] (8) where: x(t)- the variation of biomass concentration at time (input parameter), 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) = KX T1X T2X s2 + (T1X + T2X )s + 1 (9) KY T1Y T2Y s2 + (T1Y + T2Y )s + 1 (10) and Y(s) = where: 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: [ ]− KY KX 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. 1 (11) then: H(s) = KY T1X T2X s2 + KY (T1X + T2X )s + KY KX T1Y T2Y s2 + KX (T1Y + T2Y )s + KX (12) 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 where: 10 n2 s2 + n1 s + n0 d2 s2 + d1 s + d0 (13) M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 n2 , n1 , n0 - numerator parameters, d2 , d1 , d0 - denominator parameters. x(t) = Y(s) X(s) ⇒ Y(s) = H(s)X(s) y(t) = L− 1 [Y(s)] ⇒ (14) y(t) = L− 1 [H(s)X(s)] where: 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 b ) + y0 (16) 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) = a ( 1 + exp − (15) where: 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. 11 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. 12 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 13 M. Konopacki et al. Biochemical Engineering Journal 182 (2022) 108432 CRediT authorship contribution statement [14] R. Drozd, R. Rakoczy, M. Konopacki, A. Frąckowiak, K. Fijałkowski, Evaluation of usefulness of 2DCorr technique in assessing physicochemical properties of bacterial cellulose, Carbohydr. Polym. (2017), https://doi.org/10.1016/j. carbpol.2016.12.063. [15] F. Raganati, A. Procentese, G. Olivieri, P. Götz, P. Salatino, A. Marzocchella, Kinetic study of butanol production from various sugars by Clostridium acetobutylicum using a dynamic model, Biochem. Eng. J. 99 (2015) 156–166, https://doi.org/10.1016/J.BEJ.2015.03.001. [16] P. Eichinger, A.M. Herrmann, T. Ruck, M. Herty, L. Gola, S. Kovac, T. Budde, S. G. Meuth, P. Hundehege, Human T cells in silico: Modelling dynamic intracellular calcium and its influence on cellular electrophysiology, J. Immunol. Methods 461 (2018) 78–84, https://doi.org/10.1016/J.JIM.2018.06.020. [17] C. Brindley, N. Jiménez-Ruíz, F.G. Acién, J.M. Fernández-Sevilla, Light regime optimization in photobioreactors using a dynamic photosynthesis model, Algal Res 16 (2016) 399–408, https://doi.org/10.1016/J.ALGAL.2016.03.033. [18] N.L. Mohamad, S.M. Mustapa Kamal, M.N. Mokhtar, S.A. Husain, N. Abdullah, Dynamic mathematical modelling of reaction kinetics for xylitol fermentation using Candida tropicalis, Biochem. Eng. J. 111 (2016) 10–17, https://doi.org/ 10.1016/J.BEJ.2016.02.017. [19] A.J. Stacey, E.A. Cheeseman, K.E. Glen, R.L.L. Moore, R.J. Thomas, Experimentally integrated dynamic modelling for intuitive optimisation of cell based processes and manufacture, Biochem. Eng. J. 132 (2018) 130–138, https://doi.org/10.1016/J. BEJ.2018.01.012. [20] I. de A.A. Fernandes, A.C. Pedro, V.R. Ribeiro, D.G. Bortolini, M.S.C. Ozaki, G. M. Maciel, C.W.I. Haminiuk, Bacterial cellulose: From production optimization to new applications, Int. J. Biol. Macromol. 164 (2020) 2598–2611, https://doi.org/ 10.1016/j.ijbiomac.2020.07.255. [21] S.M. Feynman RP, R.B. Leighton, The Feynman Lectures on Physics. Mainly Electromagnetism and Matter (Basic Books), N. Millenn. Ed. (2010) (Basic Books). [22] V. Anton-Leberre, E. Haanappel, N. Marsaud, L. Trouilh, L. Benbadis, H. Boucherie, S. Massou, J.M. François, Exposure to high static or pulsed magnetic fields does not affect cellular processes in the yeast Saccharomyces cerevisiae, Bioelectromagnetics (2010), https://doi.org/10.1002/bem.20523. [23] E.-S.A. Gaafar, M.S. Hanafy, E.Y. Tohamy, M.H. Ibrahim, The effect of electromagnetic field on protein molecular structure of E. coli and its pathogenesis, Rom. J. Biophys. (2008). [24] J. Hristov, Magnetic field assisted fluidization - A unified approach.Part 8. Mass transfer: Magnetically assisted bioprocesses, Rev. Chem. Eng. (2010), https://doi. org/10.1515/REVCE.2010.006. [25] K.S. Ryu, K. Shaikh, E. Goluch, Z. Fan, C. Liu, Micro magnetic stir-bar mixer integrated with parylene microfluidic channels, Lab Chip (2004), https://doi.org/ 10.1039/b403305a. [26] J.C. Weaver, Y.A. Chizmadzhev, Theory of electroporation: A review, Bioelectrochem. Bioenerg. 41 (1996) 135–160, https://doi.org/10.1016/S03024598(96)05062-3. [27] T.D. Xie, L. Sun, T.Y. Tsong, Study of mechanisms of electric field-induced DNA transfection. I. DNA entry by surface binding and diffusion through membrane pores, Biophys. J. (1990), https://doi.org/10.1016/S0006-3495(90)82349-3. [28] M. Hornung, M. Ludwig, A.M. Gerrard, H.P. Schmauder, Optimizing the production of bacterial cellulose in surface culture: Evaluation of substrate mass transfer influences on the bioreaction (Part 1), Eng. Life Sci. (2006), https://doi. org/10.1002/elsc.200620162. [29] K. Fijałkowski, A. Żywicka, R. Drozd, A.F. Junka, D. Peitler, M. Kordas, M. Konopacki, P. Szymczyk, R. Rakoczy, Increased water content in bacterial cellulose synthesized under rotating magnetic fields, Electromagn. Biol. Med. 36 (2017), https://doi.org/10.1080/15368378.2016.1243554. [30] X.F. Pang, D. Bo, The changes of macroscopic features and microscopic structures of water under influence of magnetic field, Phys. B Condens. Matter (2008), https://doi.org/10.1016/j.physb.2008.05.032. [31] A. Szcześ, E. Chibowski, L. Hołysz, P. Rafalski, Effects of static magnetic field on water at kinetic condition, Chem. Eng. Process. Process. Intensif. (2011), https:// doi.org/10.1016/j.cep.2010.12.005. [32] E.J.L. Toledo, T.C. Ramalho, Z.M. Magriotis, Influence of magnetic field on physical-chemical properties of the liquid water: Insights from experimental and theoretical models, J. Mol. Struct. (2008), https://doi.org/10.1016/j. molstruc.2008.01.010. [33] C. Gao, Y. Wan, C. Yang, K. Dai, T. Tang, H. Luo, J. Wang, Preparation and characterization of bacterial cellulose sponge with hierarchical pore structure as tissue engineering scaffold, J. Porous Mater. (2011), https://doi.org/10.1007/ s10934-010-9364-6. [34] J. Guo, J.M. Catchmark, Surface area and porosity of acid hydrolyzed cellulose nanowhiskers and cellulose produced by Gluconacetobacter xylinus, Carbohydr. Polym. (2012), https://doi.org/10.1016/j.carbpol.2011.07.060. [35] K. Fijałkowski, A. Żywicka, R. Drozd, A.F. Junka, D. Peitler, M. Kordas, M. Konopacki, P. Szymczyk, M. El Fray, R. Rakoczy, Increased yield and selected properties of bacterial cellulose exposed to different modes of a rotating magnetic field, Eng. Life Sci. 16 (2016), https://doi.org/10.1002/elsc.201500151. [36] M. Konopacki, A. Augustyniak, B. Grygorcewicz, B. Dołęgowska, M. Kordas, R. Rakoczy, Single mathematical parameter for evaluation of the microorganisms’ growth as the objective function in the optimization by the doe techniques, Microorganisms 8 (2020), https://doi.org/10.3390/microorganisms8111706. 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. Acknowledgements This study was supported by the National Science Centre, Poland [OPUS 16, Project No. UMO-2018/31/B/ST8/03170, granted to Rafał Rakoczy]. 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. References [1] U. Römling, M.Y. Galperin, Bacterial cellulose biosynthesis: Diversity of operons, subunits, products, and functions, Trends Microbiol (2015), https://doi.org/ 10.1016/j.tim.2015.05.005. [2] X. Wang, J. Tang, J. Huang, M. Hui, Production and characterization of bacterial cellulose membranes with hyaluronic acid and silk sericin, Colloids Surf. B Biointerfaces (2020), https://doi.org/10.1016/j.colsurfb.2020.111273. [3] T. Carvalho, G. Guedes, F.L. Sousa, C.S.R. Freire, H.A. Santos, Latest advances on bacterial cellulose-based materials for wound healing, delivery systems, and tissue engineering, Biotechnol. J. 14 (2019) 1–19, https://doi.org/10.1002/ biot.201900059. [4] L.K. Zhang, S. Du, X. Wang, Y. Jiao, L. Yin, Y. Zhang, Y.Q. Guan, Bacterial cellulose based composites enhanced transdermal drug targeting for breast cancer treatment, Chem. Eng. J. 370 (2019) 749–759, https://doi.org/10.1016/j. cej.2019.03.216. [5] J. Ahmed, M. Gultekinoglu, M. Edirisinghe, Bacterial cellulose micro-nano fibres for wound healing applications, Biotechnol. Adv. 41 (2020), 107549, https://doi. org/10.1016/j.biotechadv.2020.107549. [6] K. Fijałkowski, A. Zywicka, R. Drozd, A. Niemczyk, A.F. Junka, D. Peitler, M. Kordas, M. Konopacki, P. Szymczyk, M.E. Fray, R. Rakoczy, Modification of bacterial cellulose through exposure to the rotating magnetic field, Carbohydr. Polym. 133 (2015), https://doi.org/10.1016/j.carbpol.2015.07.011. [7] F. Esa, S.M. Tasirin, N.A. Rahman, Overview of bacterial cellulose production and application, Agric. Agric. Sci. Procedia 2 (2014) 113–119, https://doi.org/ 10.1016/j.aaspro.2014.11.017. [8] K. Fijałkowski, R. Rakoczy, A. Zywicka, R. Drozd, B. Zielińska, K. Wenelska, K. Cendrowski, D. Peitler, M. Kordas, M. Konopacki, E. Mijowska, Time dependent influence of rotating magnetic field on bacterial cellulose, Int. J. Polym. Sci. 2016 (2016), https://doi.org/10.1155/2016/7536397. [9] I. Cielecka, M. Ryngajłło, S. Bielecki, BNC biosynthesis with increased productivity in a newly designed surface air-flow bioreactor, Appl. Sci. 10 (2020), https://doi. org/10.3390/app10113850. [10] J.K. Park, J.Y. Jung, T. Khan, Bacterial cellulose, in: Handb. Hydrocoll. Second Ed., 2009. 〈https://doi.org/10.1533/9781845695873.724〉. [11] L.W.E. Tessaro, N.J. Murugan, M.A. Persinger, Bacterial growth rates are influenced by cellular characteristics of individual species when immersed in electromagnetic fields, Microbiol. Res. 172 (2015) 26–33, https://doi.org/ 10.1016/J.MICRES.2014.12.008. [12] M. Konopacki, R. Rakoczy, The analysis of rotating magnetic field as a trigger of Gram-positive and Gram-negative bacteria growth, Biochem. Eng. J. 141 (2019) 259–267, https://doi.org/10.1016/j.bej.2018.10.026. [13] R. Rakoczy, J. Lechowska, M. Kordas, M. Konopacki, K. Fijałkowski, R. Drozd, Effects of a rotating magnetic field on gas-liquid mass transfer coefficient, Chem. Eng. J. 327 (2017), https://doi.org/10.1016/j.cej.2017.06.132. 14