The presented models combine microscopic and macroscopic descriptions of pellet development.
There are still some assumptions in the model which are difficult to verify
experimentally like the inactivation of the biomass as a consequence of mechanical damage.
However, we presented a novel approach which allows to study influences on the overall
process such as substrate limitations within the pellets, hyphal morphology or mechanical
forces

Bellgardt, K.-H.

Meyerhoff, J.

English

Periodica Polytechnica (Budapest University of Technology and Economics)

PERIODICA POLYTECHNICA SER. CHEM. ENG. VOL. 38, NOS. 1-2, PP. 111-117 (199~) MORPHOLOGY-BASED MODELLING OF PENICILLIUM CHRYSOGENUM FED-BATCH CULTIVATIONS J. MEYERHOFF and K.-H. BELLGARDT Institut fur Technische Chemie U niversitat Hannover CallinstraBe 3, 30167 Hannover, Germany Fax: (0)511/762-3004; E-Mail: nhchpelt@rrzn-user.uni-hannover.de Received: July 20, 1994 Abstract The presented models combine microscopic and macroscopic descriptions of pellet de-velopment. There are still some assumptions in the model which are difficult to verify experimentally like the inactivation of the biomass as a consequence of mechanical damage. However, we presented a novel approach which allows to study influences on the overall process such as substrate limitations within the pellets, hyphal morphology or mechanical forces. Keywords: penicillium chrysogenum fed-batch cultivations 1. Introduction The cultivation of pellet-forming microorganisms is advantageous com-pared to filamentous morphologies because of a lower cultivation broth vis-cosity the facilitation of the biomass separation. On the other hand, nutri-ents and oxygen can enter the inner parts of a pellet only diffusively. Thus, large pellets (> 400 /-Lm diameter) often become hollow in the centre due to oxygen or nutrient starvation CWITTLER et al., 1986). The first comprehensive theoretical study on modelling pellet-con-taining bioprocesses was published by METZ (1976). His models, however, had some serious restrictions, for example, the assumption of a constant biomass density within the pellet. A model which primarily considers the mycelial growth was presented by YANG et al. (1992a, b). This model is capable of describing early pellet development in detail but does not consider internal substrate limitations. BUSCHULTE (1991) expressed the pellet development by a set of partial differential equations. None of these models was applied for process simulations. It was the aim of our work to build a statistical model which not only describes the morphology of single pellets but also an ensemble of pellets to represent the biomass in a process. 112 J. MEYERHOFF and K.·H. BELLGARDT 2. Mathematical Models The model is subdivided into three parts: a morphologically detailed model considering each hyphal subunit of the pellet, a simplified model for pellet development, and finally a pellet ensemble representing the pellet popula-tion in a fed-batch fermentor. 1 2.1. Single Hyphae Model This part of the model is largely adopted from YANG et al. (1992a, b). It describes growth, septation and branching of single hyphae. The growth of the hyphal network is simulated in three dimensions. We added expressions for oxygen and glucose diffusion into the pellet. As soon as one of the substrates in the pellet centre drops below a critical concentration, the biomass is inactivated and lyses. Furthermore, the model describes the chipping of hyphae from the pellet surface. 2.2. Simplified Layer Model Since the detailed model makes great demands on the computer capacity, the detailed model for single pellets had to be simplified. The spherical space in which the pellet grows is subdivided into layers of equal thickness. Biomass density, the hyphal growth unit, concentrations of substrates and tips are averaged within a layer. The model avoids partial differential equa-tions; all calculations are discretisized in time and space. Some of the ex-pressions were empirically modified in order to make the correspondence to the single hyphae model as close as possible. Except for the detailed de-scription of the mycelial structure, the features of layer model are equiva-lent to the single hyphae model. 2. 3. Model for Pellet-Containing Bioprocesses The simulations of the layer model are extended to an ensemble of 100 or more pellets, each of which represents a subpopulation of the biomass. Balances were set up for a Penicillium chrysogenum fed-batch process and compared to experimental data. Spore germination at different times (PAUL etal., 1993) and pellet breakup by mechanical forces were included 1 In order to keep the text concise. all mathematical formulae were omitted. Further information is available upon request. MORPHOLOGY·BASED MODELLING 113 so as to explain pellet size distributions. Pellet disruption was assumed to cause cell damages which diminish the growth activity. Penicillin produc-tion was coupled to the morphology: In the model, all active hyphae except the first 20 /-Lm adjacent to a tip produce penicillin with first order rate. 3. Results a~ ~ ~_ 300)lm ~ Fig. 1. Two·dimensional projection of the mycelial structure during pellet develop-ment without influence of shear force. a) 2 compartments/13 h, b) 10/32 hi c) 50/51 hi d) 250/69 hi e) 1250/84 hi f) 4000/96 hi g) 10000/103 hi h) 17000/110 h. Fig. 1 shows a two-dimensional projection of the developing hyphal struc-ture of a pellet. Abrasing of hyphae from the surface is not included in this simulation. Studies with the single hyphae model showed that the maximal hyphal growth rate is crucial in determining the maximum vol-ume density and the radius of the pellet. Glucose is not limiting unless the medium concentration drops below about 100 mg Z-I. The functional re-lation of the oxygen diffusion coefficients to the mycelial volume density is not as decisive for lysis as the oxygen concentration in the medium. Fig. 2 shows the simulated development of a single pellet represented by profiles of the local cell volume density. It also shows that both the single hyphae and the layer model yield similar results. The sharp edge in the inner parts of the older pellets is due to lysis which follows an all-or-nothing mechanism. 114 J. MEYBJUIOFF "",d K.-H. BELLGARDT ~.-r.-----------------------------------------------, o , , , o 50 100 150 200 250 300 Radius [~] , , , , , , , , 350 ~~ 400 Fig_ 2.. Comparison between results of simulations with the single hyphae model (dashed line) and the la.yer model (solid line). Cell volume densities a.fter a.) 90 hi b) 105 h; c) 115 h; d) 125 h; e) 135 hi f) 149 h. 0.1 0.15 0.2 0.25 0.3 Radius [mm] 3. Compruisoll between oxygen a.nd giucose profiles as obtained from microprobe measurements and simulations (dashed lines) with the layer model. The ceil volume density profile is obtained from digital image processing. Cs: concentration of glucose. c-.-CZl C Q) "0 Q) M e c:i ::l -0 > N - c:i Q) U N .... c:i / ......... o / . ., .. ./ 0.05 MORPHOLOGY-BASED MODELLING ./ ./ ./ / / ./ 0.1 .,.// ./ 0.15 0.2 Radius [mm] 0.25 115· 0.3 0.35 Fig. -4. De novo simulation of a pellet. (- - - - -) Simulation results of ceII 'YOIume density; (0) image processing density measurements connected by cubic spfine interpolation (- - - - -); ( - .. - - . - .. ) simulated oxygen profile. ~ 'Cl "" .:> cl M N ~ "l ,......., 3:: ,......., '" ,......., - - -Cl) "" Cl)"l Cl) Cl) '--' '--' <::> ~ '--' 0.. ~ CIJ U :::J U 0 ..,. 0 ] *0 0 '" 6. <=> , J I , J , , <=> 0 t Fig. 5. Time course of biomass, glucose and product concentrations of a p~~ chrysogenum fed-batch cultivation. Symbols refer to data. Cs, ex: concentrations of penicillin, glucose and oiomass, OUR: oxygen uptake rate. 116 J. MEYERHOFF and K.·H. BELLGARDT Experimental data from microprobe measurements and digital image processing were used to verify the layer model (CRONENBERG, 1994; CRO-NENBERG et al., 1994, POTTEL and BELLGARDT, 1992). The image pro-cessing method yielded cell volume density profiles after the pellets had been cut into thin slices and stained. Fig. 3 shows the comparison of sim-ulated and measured oxygen and glucose profiles using the experimentally measured cell density profiles. Fig. 4 shows that the cell volume density profiles can also be obtained by de novo simulation. The simulated time corresponds to the time of sampling the examined pellet. Experimental fed-batch cultivations of Penicillium chl'ysogenum were described by an ensemble of 80 pellets (Fig. 5). The same data were used in a conventional segr(fgated model by TILLER et al. (1994). The pellet model presented here achieves similar results. In addition, the pellet model explains the experimentally observed pellet size distribution. The inhibi-tion of growth caused by pellet breakage turned out to be most important for the development of the Ox-plateau after t = 80 h. This corresponds to the assumption of an inactive fraction of the biomass in the model by TILLER et al. (1994). A sensitivity analysis showed that the penicillin productivity is strongly dependent on the morphology since the number of tips per mycelial length determines the size of the fraction of producing biomass. 4. Conclusion The presented models combine microscopic and macroscopic descriptions of pellet development. There are still some assumptions in the model which are difficult to verify experimentally like the inactivation of the biomass as a consequence of mechanical damage. However, we presented a novel approach which allows to study influences on the overall process such as substrate limitations within the pellets, hyphal morphology or mechanical forces. References BUSCHULTE, T. K. (1991): Mathematische Modellbildung und Simulation von Zellwach-stum, Stofftransport und Stoffwechsel in Pellets aus Streptomyceten. (lvIathematical modelling and simulation of cell growth, substrate transport and metabolism in pellets of Streptomyces species) Ph. D. thesis, University of Stuttgart. CaoNENBERG, C. C. H. - OTTENGRAF, S. P. P. - VAC; DEC; HEUVEL, J. C. - POTTEL, F. SZIELE, D. SCHUGERL, K. BELLGARDT, K.-H. (1994): Influence of Age and Structure of Penicillium Chrysogenum Pellets on the Internal Concentration Profiles. Bioprocess Engineering, in print. MORPHOLOGY·BASED MODELLING 117 CRONENBERG, C. C. H. (1994): Biofilms Investigated with Needle-type Glucose Sensors. Ph. D. thesis, University of Amsterdam. METZ, B. (1976): From Pulp to Pellet. An Engineering Study on the Morphology of Moulds. Ph. D. thesis, Technical University of Delft. PAUL, G. C. - KENT, C. A. - THOMAS, C. R. (1993): Viability Testing and Characteri-zation of Germination of Fungal Spores by Automatic Image Analysis. Biotechnol-ogy Bioengineering, Vo!. 42, pp. 11-23. POTTEL, F. - BELLGARDT, K.-H. (1992): Investigation of Morphology of Pellets during Cultivations of Penicillium Chrysogenum by Digital Image Processing. DECHEMA Biotechnology Conferences, Vol. 5, Part A, pp. 381-386. TILLER, V. - MEYERHOFF, J. - SZIELE, D. SCHUGERL, K. BELLGARDT, K.-H. (1994): Segregated Mathematical Model for the Fed-batch Cultivation of a High-producing Strain of Penicillium Chrysogenum. Journal of Biotechnol. Vo!. 34, pp. 119-13l. WITTLER, R. - BAUMGARTL, H. - LUBBERS, D. W. SCHUGERL, K. (1986): Investi-gations of Oxygen Transfer into Penicillium Chrysogenum Pellets by Microprobe Measurements, Biotechnology Bioengineering, Vo!. 28, pp. 1024-1036. YANG, H. - KING, R. - REICHL, U. - GILLES, E. D. (1992a): Mathematical Model for Apical Growth, Septation and Branching of Mycelial Microorganisms. Biotechnology Bioengineering. Vol. 39, pp. 49-58. YANG, H. - REICHL, U. KING, R. - GILLES, E. D. (1992b): Measurement and Simu-lation of the Morphological Development of Filamentous Microorganisms. Biotech-nology Bioengineering, Vo!. 39, pp. 44-48. 

MORPHOLOGY-BASED MODELLING OF PENICILLIUM CHRYSOGENUM FED-BATCH CULTIVATIONS

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MORPHOLOGY-BASED MODELLING OF PENICILLIUM CHRYSOGENUM FED-BATCH CULTIVATIONS

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