CHEMICAL ENGINEERING TRANSACTIONS VOL. 79, 2020 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Enrico Bardone, Antonio Marzocchella, Marco Bravi Copyright © 2020, AIDIC Servizi S.r.l. ISBN 978-88-95608-77-8; ISSN 2283-9216 Microorganisms Growth in Gel Volume: Process Dynamics in Limiting Mass Transfer Conditions Boris G. Pokusaeva, Andrey V. Vyazminb,*, Dmitry A. Nekrasovb, Nikolay S. Zakharova, Dmitry P. Khramtsovb, Nadezhda V. Shumovab, Daria A. Belovab aDepartment of Chemistry and Biotehnology, Moscow Polytechnic University, Avtozavodskaya str., 16, Moscow, Russia bDepartment of Chemical Engineering, MIREA – Russian Technological University, Vernadskogo ave., 86, Moscow, Russia av1958@list.ru The work purpose is to find ways to effectively cultivate living microorganisms not near the outer surface, but inside the gel matrix volume by internal channels using, when the delivery of nutrients to the gel volume is carried out by a convective-diffusion mechanism. Immobilized cells development dynamics in gel under limited mass transfer conditions of nutrient across the surface was considered. The penetration depth of the nutrient from surface into the gel volume for providing a stable life of microorganisms has been estimated at 3.0 – 4.0 mm. The forming time-stable linear and branched channels possibility within the gel matrix volume has been experimentally confirmed and it usage for convective nutrient supply to the volume was tested. The qualitative nutrients diffusion regularities from the channels into the gel volume with immobilized cells are described. 1. Introduction Currently, a new scientific direction is being formed, which is called bioprinting (Murphy and Atala, 2014). The ideas of growing human organs from stem cells no longer seems impossible and even the first successes in this direction are known (see for example, Melchels et al., 2012). The bioprinting idea is implemented in the bio-printers. They are filled with cellular spheroids, which are applied in a certain order to a framework (scaffold) and thus form the basis for growing the organ (Rodrigues et al., 2011). However, it is not yet an organ, but rather an engineering construction that has a form of an organ. It can be called an organ when stem cells begin to grow, divide and differentiate. For this reason, the cells must be in suitable conditions to enable their immobilization. In particular, they must be provided with the necessary amount of nutrients for normal life. Promising materials for usage in bioprinting are hydrogels (Wang et al., 2015). There is a formal analogy between the mass transfer in gels with living cells and filtration with the formation of deposits in the pores (Taran et al., 2019). Gels capillary network is able to supply living cells with nutrients and oxygen, as well as remove metabolic products. This property depends on the capillaries size and the diffusion coefficient, which decrease with increasing concentration of the dispersed phase gel (Pokusaev et al., 2015; Pokusaev et al., 2019). It was found that the diffusion rate mass transfer in gels does not exceed the maximum possible for the pure dispersion phase (Pokusaev et al., 2018). It is obvious that the transfer of nutrients through the outer boundary of the formed organ due to its large size only due to diffusion will not be able to provide living cells with the necessary amount of nutrients and oxygen. For industrial biotechnology, the microorganisms growth problem in the gel volume is not fundamentally important, since the processes of cultivation of microorganisms in bioreactors are more convenient to carry out the deep method in the liquid phase, when there is no diffusion resistance to the mass transfer of nutrients to the cells. However, when growing tissues from stem cells in a gel, providing them with nutrients and oxygen becomes essential. In recent years, this causes an increase of interest in research related to additive methods creation (and not only) analogues of circulatory systems that provide a solution to the mass exchange problem of living cells with the environment (see, for example, Richards et al., 2017; Sasmal et al., 2018). Further, the experimental results for determine the possibility for providing nutrition and oxygen immobilized in the gel volume of living cells directly by mass transfer through the capillary network inside the gel from the DOI: 10.3303/CET2079003 Paper Received: 3 July 2019; Revised: 9 January 2020; Accepted: 10 March 2020 Please cite this article as: Pokusaev B.G., Vyazmin A.V., Nekrasov D.A., Zakharov N.S., Khramtsov D.P., Shumova N.V., 2020, Microorganisms Growth in Gel Volume: Process Dynamics in Limiting Mass Transfer Conditions, Chemical Engineering Transactions, 79, 13-18 DOI:10.3303/CET2079003 13 surface contacting with the nutrient medium will considered. Also, some results on the creation of artificial time-stable microchannels in the gel and data on modeling the nutrient medium delivery through them to living cells directly into the gel volume will presented. 2. Materials and methods In the experiments, both pure gels based on agarose "Chemapol" and gels with the addition of yeast culture with a nutrient solution were used. The concentration of agarose in the gels is varied in the range of 0.6 – 1.5 % by weight. At such concentrations, agarose gels are optically transparent, which makes it possible to study the growth kinetics of yeast culture by non-contact optical methods, without violating the conditions of its metabolism. Pichia polymorpha Y-314 culture was chosen as a model for experiments with living cells, since it is close to human somatic regarding the cell size (20 – 25 microns – the size of yeast cells and 25 microns – the size of human liver parenchyma hepatocytes) and life conditions. The culture is capable of glucose fermentation as the only source of carbon and grows well at temperatures from 30 to 42 °C. To visualize the mass transfer processes and measure the diffusion rate from the channels to the volume of agarose gels in the experiments, a 1.0 % aqueous fuchsin solution was used, which is sometimes added to nutrient media. Fuchsin (hydrochloric acid rosaniline) C20H20N3Cl is a substance with a high molecular weight, aqueous solutions of which has a purple-red color and has a high contrast against the gel. To study the unsteady mass transfer processes in agarose gels containing, among other things, biological cultures, an experimental setup was created that allows to register the diffusion of the substance into the samples under study (see Figure 1). For this purpose, a two-beam spectrophotometer UV-1280 manufactured by "Shimadzu" was included in the previously developed setup based on the spectrometric method. The technical capabilities of such equipment ensured the possibility for measurements in these studies by light transmission and absorption spectra at several wavelengths in the range of 190 – 1100 nm in automatic mode. In addition to the working area, a special system for measuring the position of the test sample in space was installed. For mass transfer processes registration in gel systems with artificial microchannels the working site including the photo-registering device of high resolution was used. Figure 1: Scheme of the experimental setup: 1– working area 1: 2 – optical cell with gel, 3 – level indicator, 4 – working area of scanning, 5 – scale of height measurement, 6 – cell holder, 7 – Shimadzu spectrophotometer, 8 – working area 2: 9 – system of connecting channels, 10 – optical cell with gel with channels, 11 – tank with nutrient medium, 12 – collection tank, 13 – camera, 14 – computer 3. Results and discussions 3.1 Preliminary comments Research using stem cells is a complex problem that requires the fulfillment of sterility conditions and the creation of multifactorial comfortable conditions for cell growth. The selection of suitable gels is also a difficult task related to materials science (see, for example, Lin et al., 2011). Obtaining concrete practical results will require taking into account and implementing the conditions associated with the specifics of the selected biological objects and gels. However, for the purposes of primary basic research, many exhibited qualities by different living cells and the properties of different gels have similar features. Therefore, at the first stage, it is 14 possible to perform experiments on simpler and more convenient objects in order to obtain results that allow to clarify the directions of research. When performing experiments with microbiological objects, analyzing their results and creating mathematical models of mass transfer, it is necessary to take into account that the consumption rate of various nutrient medium components by yeast is different. However, the rate of consumption of each component is proportional to the concentration of cells. The accumulation of biomass of microorganisms in a periodic process of growth without any additional components has the following stages: cells adaptation period to the environment without increasing their numbers (for the using yeast culture at the optimum temperature 2 - 6 h); exponential phase, characterized by a maximum growth rate of the number of cells (4 - 8 h), stationary phase in which growth rate and death equal to (2 - 4 h) and stage of death (with the exhaustion of the nutrient medium). The level of biomass accumulation for each strain of microorganisms is determined experimentally and depends on the initial number of seeded cells, the nutrient medium amount and temperature. The maximum rate of consumption of the nutrient medium at the carbon source, as it is the main structural component used for intracellular synthesis of all biopolymers. The rate of carbon consumption is directly proportional to the concentration of cells and is characterized by a carbon-to-biomass conversion rate. Following the abovementioned, to describe the temporal and spatial dynamics of concentration fields for the nutrient and the number of living yeast cells in the gel, models such as population dynamics with a delay should be used (Polyanin et al., 2018). They include at least two equations. The first is a non-stationary diffusion equation describes the material balance of the nutrient taking into account its absorption by cells. The second equation is an ordinary differential equation with a delay, describing the change in the concentration of yeast over time, taking into account their reproduction by cell division. The delay is associated with the presence of cells adaptation period due to which the microorganisms growth rate at the current time will be determined by their concentration at earlier times and the duration of adaptation. When modeling the growth of microorganisms in the gel volume under feeding through the surface, the kinetic model based on an ordinary differential equation with a delay is the most physically justified. In this case, the delay has a clear physical meaning, as the duration of the time adaptation interval of microorganisms to the environment before the beginning of division. Among the factors hindering the growth in the number of cells, consider the following: a lack of the nutrient medium during transport to the cells through diffusion, the gel mechanical resistance under increase the volume occupied by microorganisms, excretion by cells of metabolic products that inhibit their growth. 3.2 Cells reproduction kinetics under condition of diffusion limitation The influence of mass transfer diffusion restriction on the kinetics of living cells reproduction in the volume of layered gel systems is determined. Layered samples were prepared in a spectrometric cuvette with a size of 10×10×40 mm. Initially, a lower layer of gel was formed, after stabilization of which, the next layer was applied on top. Yeast cells were seeded in the top layer of the gel, and the bottom layer remained clean. The height of the lower layer was 10 mm, and the top layer of gel with cells was 4 mm. After the formation 1.0 ml nutrient medium with small concentration was poured onto the top layer. Further, the optical permeability of the test sample was measured at a wavelength of light of 540 nm. Studies were carried out at a temperature of 30 °C. Figure 2: Dependence from depth (x, mm) at different times of the relative (to distilled water) intensity of light absorption (D, %) in 0.6 % by weight agarose gel. Notation on the horizontal x axis: 0 – the interface of pure gel and gel with cells, values with a minus - a gel layer with cells, plus - pure agarose gel. Notation of curves: 1 – 30 min after the feeding of the nutrient medium, 2 – 6 h, 3 – 24 h 15 Figure 2 shows the results of measurements of light absorption intensity by height of a two-layer gel sample with agarose concentration for each layer equal to 0.6 % by weight. The zero point in the height of the cell corresponds to the boundary between the interface of the pure gel and the gel with cells. Positive values of the coordinate are counted into deep the pure gel, and negative values are counted into deep the gel with cells. Dependencies are presented for different times of the process. It can be seen that in the area of the cells height -4