Comprehension of viscous morphology—Evaluation of fractal and conventional parameters for rheological characterization of Aspergillus niger culture broth

Journal of Biotechnology 163 (2013) 124–132

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Comprehension of viscous morphology—Evaluation of fractal and conventional parameters for rheological characterization of Aspergillus niger culture broth Thomas Wucherpfennig, Antonia Lakowitz, Rainer Krull ∗ Institute of Biochemical Engineering, Technische Universität Braunschweig, Gaußstraße 17, 38106 Braunschweig, Germany

a r t i c l e

i n f o

Article history: Received 15 February 2012 Received in revised form 1 August 2012 Accepted 6 August 2012 Available online 8 October 2012 Keywords: Filamentous fungi Aspergillus niger Image analysis Rheology Fractal analysis Lacunarity

a b s t r a c t The filamentous fungus Aspergillus niger is a widely used host in industrial processes from food, chemical to pharmaceutical industry. The most prominent feature of this filamentous microorganism in submerged cultivation is its complex morphology which comprises dense spherical pellets as well as viscous elongated filaments. Depending on culture conditions, the exhibited morphology has tremendous effect on the overall process, making a precise understanding of fungal growth and morphology indispensable. Morphology, however, is only industrially relevant as long as it can be linked to important cultivation characteristics of filamentous microorganisms such as culture broth flow behavior. In the present study, different conventional and fractal morphological parameters gained from automatic image analysis were tested for their eligibility to predict culture broth rheology from morphologic appearance. The introduced biomass independent rheological parameters KBDW and nBDW obtained by power law relationship were successfully estimated from morphology related fractal and conventional parameters. For improved characterization of morphologic appearance of filamentous fungi newly introduced fractal quotient and lacunarity were compared to conventional particle shape parameters in form of the earlier established Morphology number (MN). © 2012 Elsevier B.V. All rights reserved.

1. Introduction Filamentous fungi are of extraordinary industrial importance due to their ability to grow on rather simple and inexpensive substrates as well as their ability for production and secretion of commercially interesting products, such as organic acids, pharmaceuticals and proteins (Meyer, 2008; Wucherpfennig et al., 2010). Especially Aspergillus species stand out from other microbial cell factories of bacterial, yeast or even mammalian origin, because of their ability to tolerate extreme cultivation conditions (Meyer et al., 2011). Numerous solid-state or submerged cultivation protocols already exist. In submerged processes the morphology is of critical importance, as optimal production requires a distinct morphology, which is most often process specific (Driouch et al., 2011a). Filamentous organisms such as Aspergillus niger can grow either in dense, spherical pellets with a near Newtonian flow behavior or as disperse and viscous mycelia (Krull et al., 2010). The exhibited morphology herby influences not only culture broth viscosity but also productivity, substrate diffusion and downstream processing (Wucherpfennig et al., 2010). While

∗ Corresponding author. Tel.: +49 0 531 391 7653; fax: +49 0 531 391 7652. E-mail addresses: [email protected] (T. Wucherpfennig), [email protected] (A. Lakowitz), [email protected] (R. Krull). 0168-1656/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jbiotec.2012.08.027

a pellet morphology was favorable for the production of citric acid (Papagianni, 2004) and glucose-oxidase (El-Enshasy et al., 1999), mycelial morphology significantly increased fructofuranosidase production (Wucherpfennig et al., 2011). Recently a big step towards a customization of filamentous morphology as fungal morphology was reproducible created through addition of microparticles or increase of culture broth osmolality (Driouch et al., 2009, 2010, 2011a; Wucherpfennig et al., 2011). Through creation of high producing mycelial morphologies, however, other problems with process performance such as significant increase of culture broth viscosity and reduced mass transfer present itself. In such cultivations hyphal entanglement can result in significant changes in broth rheology (Metz et al., 1979). Filaments tend to grow uniquely to form three-dimensional networks by biomass accumulation at the growing tip of the hyphal network (Ruohang and Webb, 1995). The resulting highly branched network exhibits several fluid dynamic interactions, thus changing the properties of the cultivation broth from the initially Newtonian character to a non-Newtonian one (Gbewonyo and Wang, 1983). The increased culture broth viscosity leads to heterogeneous, stagnant, nonmixed zone formations within the bioreactor, which make the cultivation challenging and more expensive to operate (Metz and Kossen, 1977; Oncu et al., 2007). The strong negative influence of broth viscosity on oxygen transfer has been shown previously (Moo-Young et al., 1987). Some of these problems can be increased when the process is scaled up, due to increased mixing times and

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Nomenclature A BDW D d DBM DBM /DBS DBS K KBDW  MN n nBDW N(ε) S  ε app 

projected area biomass concentration fractal dimension maximal diameter box mass dimension fractal quotient box surface dimension consistency index (Ostwald–de Waele model) biomass independent consistency coefficient lacunarity Morphology number flow behavior index (Ostwald–de Waele model) biomass independent flow behavior coefficient number of overlapping boxes (fractal analysis, box counting method) solidity shear rate width of the grid (fractal analysis, box counting method) apparent viscosity shear stress

generally lower agitation rates (Riley et al., 2000). To control cultivation performance, it is essential to know how the operating conditions influence the rheological properties of the filamentous cultivation broth, as these depend on the morphology of the biological system. Consequently, the relationship between rheology and morphology is vitally important and has to be fully investigated (Wucherpfennig et al., 2010). Such knowledge can be very valuable in the optimization and design of common cultivation processes (Oncu et al., 2007; Papagianni, 2004). Numerous studies exist where viscosity is estimated on biomass and some kind of morphological information, mostly based upon image analysis methods (Olsvik et al., 1993; Riley and Thomas, 2010; Riley et al., 2000; Ruohang and Webb, 1995; Tucker, 1994; Tucker and Thomas, 1993). A general problem with most of these studies is the relatively low number of conducted cultivations, as rheological samples are usually extracted from few rather large scale cultivations. An advantage of these studies is that development of culture broth viscosity over time can be studied very easily. However, since different morphologic forms are created permanently through the process environment, this approach cannot generate sufficient samples for meaningful estimation of rheological parameters from fungal morphology. In the present study 100 mL shaking flasks were used to compare 45 different morphological forms, created through a permanent change of culture broth osmolality, through addition of sodium chloride previous to inoculation (Wucherpfennig et al., 2011). Through this approach it is possible to study a comparatively large number of samples with different morphology. Thereby the whole spectrum of A. niger morphology is used for a holistic estimation of rheology, based on the previously introduced dimensionless Morphology number and other fractal parameters. 2. Materials and methods 2.1. Microorganism and inoculum preparation The recombinant strain A. niger SKAn1015 used in this study, carried the suc1 (fructofuranosidase) gene to produce fructofuranosidase under the control of the constitutive pkiA (pyruvate kinase) promoter and was obtained from the protease deficient

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mutant A. niger AB1.13 by transformation (Zuccaro et al., 2008). The organism was maintained as frozen spore suspension at −80 ◦ C in 50% glycerol. To obtain spores, agar plates with the sporulation medium were plated out with spores from a frozen stock and incubated for five days at 30 ◦ C. The sporulation medium for A. niger SKAn1015 contained 30 g L−1 potato dextrose agar (Sigma–Aldrich) and 10 g L−1 agar (Sigma–Aldrich). After growth and sporulation, 30 mL sterile NaCl solution (0.9%, w/v) was added to each agar plate, which was scraped to release the aerial mycelium. The suspension was filtered through two layers of sterile Miracloth (pore size 22–25 ␮m, Merck) to prevent agar debris and conidiophores in the spore suspension. The optical density of the spore suspension was measured photometrically at 600 nm (SmartSpecTM 3000, BioRad) and converted to spore concentration (m L−1 ) by a predetermined calibration curve. 2.2. Media and cultivation conditions The cultivation medium of A. niger SKAn1015 contained per liter 20 g d-glucose as 20 mL salt solution (6 g L−1 NaNO3 , 0.5 g L−1 KCl, 1.5 g L−1 KH2 PO4 , 0.5 g L−1 MgSO4 ·7H2 O) and 1 mL trace element solution (10 mg L−1 EDTA, 4.4 mg L−1 ZnSO4 ·7H2 O, 1.01 mg L−1 MnCl2 ·4H2 O, 0.32 mg L−1 CuSO4 ·5H2 O, 1 mg L−1 FeSO4 ·7H2 O, 0.32 mg L−1 CoCl2 ·6H2 O, 1.47 mg L−1 CaCl2 ·2H2 O, and 0.22 mg L−1 (NH4 )6 Mo7 O24 ·4H2 O). Carbon source, salt, and trace element solutions were autoclaved separately at 121 ◦ C for 20 min and chilled to room temperature prior to mixing and use. The medium exhibited a standard osmolality of 0.35 osmol kg−1 . 250 mL shaking flasks with 4 baffles containing 100 mL medium were incubated for 72 h at 120 ± 1 min−1 on a rotary shaker (Certomat BS-1/50 mm, Sartorius, Göttingen, Germany). All cultivations were carried out at least in triplicate. The inoculation with a spore suspension was performed such, that spore concentration within the shaking flask was 106 spores mL−1 . Growth temperature was 37 ± 0.1 ◦ C. To prepare culture broth for the biomass viscosity correlations, batch cultivations were carried out in a 2 L stirred tank bioreactor (Applikon, Schiedam, The Netherlands) with two six-bladed disc turbine impellers. Bioreactors were inoculated with a suspension of freshly harvested conidia to give a spore concentration of 1 106 m L−1 after inoculation. Growth temperature was 37 ± 0.1 ◦ C. Aeration rate (1.0 L min−1 ), agitation speed (200 min−1 ) and pH value (pH 5.0) were automatically kept constant. An increase in osmolality by addition of sodium chloride was previously discovered to alter fungal morphology and improve productivity up to a certain point (Wucherpfennig et al., 2011). Following this procedure osmolality was permanently raised prior to inoculation. The first shaking flask contained standard medium, in shaking flask 2, sodium chloride was added to increase the osmolality to 0.4 osmol kg−1 . In the following flasks osmolality from the preceding flask was raised and additional 50 mosmol kg−1 respectively. The highest osmolality (2.55 osmol kg−1 ) was prepared in shaking flask 45. Osmolality was measured using an Osmometer (Osmomant 030, Gonotec, Germany). 2.3. Biomass concentration, sampling Biomass was determined after 72 h of cultivation. The biomass concentration was measured gravimetrically by filtering (Nalgene 300–4000) a 10 mL of biomass suspension through a pre-dried (48 h at 105 ◦ C) and pre-weighted suction filter (Filter Discs Grade 389, Sartorius, Germany). Prior to drying (48 h at 105 ◦ C), the filter was rinsed several times with deionized water to remove medium components from the biomass. The biomass dry weight concentration (g L−1 ) was calculated as the difference between the weight of the

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filter with and without dried biomass divided by the sample volume. 2.4. Microscopy, image analysis and Morphology number Fungal morphology was characterized using a semiautomatic system consisting of image acquisition by microscopy and a subsequent image analysis. For microscopy image acquisition approximately 2 mL culture broth sample was taken at the end of the cultivation and suspended in a petri dish containing cultivation medium. An all-inclusive all digital inverted microscope (EVOS xl, AMG, Bothell, WA, USA) was used in the process containing a 3.1 mega pixel color sensor. Pictures were taken with 2× magnification in the maximal resolution of 2048 × 1536 pixels (3.2 ␮m/pixel). Between 50 and 100 pictures were made for each shaking flask, containing a minimum of 100 fungal particles, either pellet or mycelial. Image analysis and characterization was carried out using the ImageJ 1.45 software (National Institute of Health, Bethesda, USA) that is available in the public domain. Each image was converted into an 8-bit grey-scale image. Subsequently a grey-level threshold, calculated by ImageJ using the Otsu algorithm, was applied, resulting in a binary image which was later analyzed using the inbuilt analyze particles function. Only macro morphological parameters were considered for image analysis. The morphological parameters evaluated were projected area A, maximal diameter d, the image analysis parameter solidity S, and aspect ratio (elongation) E for mycelial aggregates (clumps and pellets) of A. niger. These relevant parameters were combined to a previously introduced dimensionless Morphology number (MN) (Wucherpfennig et al., 2011) √ 2· A·S MN = √ (1) . ·d·E Perfectly round and smooth pellets exhibit an MN of 1, whereas small mycelial fragments have values close to zero. All other fungal particles will have a MN between these two extremes. 2.5. Fractal analysis and lacunarity The box-counting method as described by Obert et al. (1990) was used in this study to assess the fractal dimension of fungal morphology. A picture of the desired object is covered by a grid of the width ␧. Subsequently, the number of boxes N(ε) which overlap with the fungal particle is counted. The number of overlapping boxes N(ε) changes with the width of the grid ε. For a given picture several grid widths ε are tried out and related to N(ε). N(ε) is proportional to ε−D , where D is the fractal dimension and C is the proportionality constant. N(ε) = C · ε−D ,

(2)

Through sampling with various grid widths and grid positions an adequate number of ε/N(ε) values can be determined to calculate the fractal dimension D (Obert et al., 1990; Papagianni, 2006; Ryoo, 1999). Furthermore, there are boxes wholly contained by the fractal object and boxes which contain or adjoin at least one pixel of the object. N(ε) is the total number of boxes intersected by the fractal object. Mycelial structures can be mass fractals, where the whole mass of the particle is fractal, or surface fractals, where just the surface of the object is fractal (Obert et al., 1990; Papagianni, 2006). The method using all boxes for the calculation of the fractal dimension is called box mass (BM) method and the gained fractal dimension is called box mass dimension DBM (Papagianni, 2006). DBM describes the whole mass of the object, the space filling capacity and inner structure. The box surface dimension DBS is obtained by using only boxes covering the surface. DBS refers to the surface irregularity of an object. Objects for which DBM equals DBS are true mass fractals

with a high degree of self-similarity and can be described by a single fractal dimension (Papagianni, 2006). If DBM > DBS , the object is a surface fractal and therefore not a true fractal (Barry, 2009). Fractal dimensions can be applied for Euclidean figures as well. For a line applies DBM = DBS = 1, a circle or rectangle has a DBM of 2 and a DBS of 1 (Obert et al., 1990). A fractal based value, which so far has not been used for characterization of fungal morphology, is the so-called ‘lacunarity’ (from latin ‘lacuna’ for lack, gap or hole), although it has been recently applied for description of micro vascular systems, glia cells and identification of cancer cells (Borys et al., 2008; Gould et al., 2011). It describes heterogeneity of structure or the degree of structural variance within an object (Smith et al., 1996), which makes it an auspicious parameter for characterization of clump morphology. The box counting and lacunarity determination were conducted using the ImageJ plugin “Fractal Dimension and Lacunarity” (Karperien, 2011). Lacunarity () was determined based on data gathered during non-overlapping box counts using the following formula



ε,g =

ε,g ε,g

2

,

(3)

where  is the standard deviation of pixels per box, stands for mean pixels per box, the index ε is the grid width and the index g is the location of the box (Karperien, 2011). For determination of the surface fractal dimension, the outline function of ImageJ was used previous to analysis, which eliminates all pixels except for a halo of 1 pixel around the particle. Since selfsimilarity has its limitations for very large and very small objects (Obert et al., 1990) the grid width ε was set to be no smaller than a single hyphae and not larger than a large fungal pellet (Papagianni, 2006). 2.6. Measurement of culture broth rheology Mycelial cultivation broths generally have pronounced nonNewtonian rheological characteristics and exhibit shear thinning or most often pseudo plastic behavior (Olsvik and Kristiansen, 1994). Non-Newtonian viscosity is usually described using the apparent viscosity (app ) defined by app ≡

 

(4)

with the shear stress  and the shear rate . It is not always possible to have a complete knowledge of shear stress/shear rate relations and elastic properties of inhomogeneous mixtures such as cultivation broths. Therefore, several rheological models have been introduced which may be regarded as an empirical fit to the experimental data (Oolman et al., 1986). As in most studies (Olsvik and Kristiansen, 1994; Riley and Thomas, 2010; Riley et al., 2000; Ruohang and Webb, 1995; Ryoo, 1999) the Power law relationship of Ostwald–de Waele  = K · n

(5)

is used to describe the rheological behavior of the cultivation broth where K is the consistency index and n the flow behavior index. This relatively simple model is already demonstrated to be sufficient to describe the rheological properties of non-Newtonian cultivation broths (Allen and Campbell, 1991). The fitting parameters K and n are most often used as the sole indicator of viscosity of filamentous cultivations (Allen and Campbell, 1991; Casas López et al., 2005; Olsvik and Kristiansen, 1994; Petersen et al., 2008; Riley and Thomas, 2010; Riley et al., 2000). Rheological measurements in this study were performed using a Searle rotational viscosimeter (type Bohlin CS10, Malvern Instruments, UK), equipped with a four

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3. Results and discussion

in biomass, irrespective of the method which is used for manipulation of fungal morphology, which could be pH, micro particle supplementation, or as in the current study osmolality. Therefore, it is practically impossible to obtain samples with a different morphology but the same biomass. The second approach, chosen in the present study, is to exactly determine the link between biomass and viscosity and incorporate this knowledge in correlations aimed at predicting rheology from morphology. To investigate the influence of biomass concentration on culture broth viscosity, the method introduced by Riley et al. (2000) was applied. Three separate 2 L stirred tank bioreactor cultivations were conducted, one with pellet morphology, one with mycelial morphology and one with an intermediate clump morphology. After 65 h of cultivation samples with differing morphology were collected from the bioreactors. Through settling and gentle centrifugation (Variofuge 3.OR, Heraeus Centrifuges, UK) 9 subsamples with differing biomass, but identical morphology, were created through centrifugation and re-suspension as shown in other studies (Riley et al., 2000; Tucker, 1994; Tucker and Thomas, 1993). Biomass concentration was adjusted in the usual range of shaking flask and bioreactor cultivations with A. niger SKAn 1015 and the related strain A. niger AB1.13 between 0.3 and 9 g L−1 biomass concentration, which might be considered low compared to industrial cultivations of bulk products but was reasonable range for the used strain (Driouch et al., 2009, 2010, 2011a,b; Lin et al., 2010; Lu et al., 2010; Wucherpfennig et al., 2011). For each of the obtained 27 samples viscosity was measured. K (consistency index) and n (flow behavior index) were determined using the Ostwald–de Waele model and correlated with the biomass concentration (Fig. 2A and B). For the consistency index K (Fig. 2A) the following correlation between consistency index and biomass was found

3.1. Influence of biomass on rheological parameters

K(BDW) = 1.3 × 10−5 · BDW4.8 .

Fig. 1. Development of biomass concentration and consistency index (K) with increased medium osmolality prior to inoculation.

bladed vane tool (V25 Vane Tool, Malvern Instruments, UK). 100 mL sample was measured while the temperature was maintained at 37 ◦ C. Rheology was measured at a shear rate range of 10–400 s−1 . Below a shear rate of 10 s−1 settling was observed, beyond 400 s−1 conditions became turbulent preventing reliable measurements. A measurement incorporated 25 data points and took 5 min including 30 s of pre-shearing at 50 s−1 to counter sedimentation issues.

Biomass concentration has a significant influence on the viscosity of the culture broth (Casas López et al., 2005; Riley and Thomas, 2010; Riley et al., 2000; Ruohang and Webb, 1995). Ruohang and Webb (1995) found an exponential dependency between the consistency index (K) and biomass, and a polynomial relationship between the flow behavior index (n) and biomass for culture broth of Aspergillus awamori. This proves that the relationship between biomass and rheology has to be considered before morphologic characteristics can be correlated with rheology. Furthermore, the biomass concentration of A. niger SKAn 1015 samples with filamentous morphology was reasonably lower than that of samples with pellet morphology. Process parameters which influence fungal morphology usually do effect biomass concentration as well, so biomass has either to be incorporated in the correlations for prediction of rheology directly as practiced Riley and colleagues (Riley and Thomas, 2010; Riley et al., 2000) or considered beforehand. Fig. 1 shows the decline of biomass concentration with increasing medium osmolality. Meanwhile, the consistency index K stays approximately constant until 1600 mosmol kg−1 and increases at higher osmolalities. This change of the consistency index is concurrent with a change from pellet to a mycelial morphology. Culture broth viscosity is generally highly biomass dependent. The A. niger SKAn 1015 cultivation at 500 mosmol kg−1 exhibits a biomass concentration of 7.5 g L−1 , whereas the cultivation at 2500 mosmol kg−1 has a biomass concentration of only 1 g L−1 (Fig. 1). This large difference in biomass has great effect on the culture broth viscosity. In order to investigate the effect of fungal morphology on culture broth viscosity without the influence of biomass, there are two approaches. The first would be to compare samples of the same biomass with different morphological growth forms. However, for the strain A. niger SKAn 1015 used in this study, a more mycelial morphology goes hand in hand with a decrease

(6)

The correlation of the flow behavior index n with biomass (Fig. 2B) led to n(BDW) = 2.1 − 0.6 · BDW0.5 .

(7)

Very similar correlations for both rheological parameters were found in the study of Ruohang and Webb (1995). In Fig. 2A shear thickening is evident for very low biomass concentrations below 2 g L−1 . This rather rare property was reproduced several times and might be a common trait due to hyphal entanglement and agglomeration. From 2 to 4 g L−1 , the flow behavior is Newtonian and at higher biomass concentrations, it becomes pseudoplastic. Correlations (6) and (7) enable the calculation of a rheological parameter based on biomass exclusively, regardless of morphological growth form. The quotient of the measured consistency K divided by K(BDW) with equal biomass obtained by Eq. (6), results in the dimensionless consistency coefficient KBDW =

K . K(BDW)

(8)

The quotient of the flow behavior index n divided by n(BDW) with equal biomass deduced from Eq. (7) makes up the dimensionless flow coefficient n . (9) nBDW = n(BDW) These calculated parameters KBDW and nBDW are independent from biomass concentration and can help to characterize impact of morphology on rheology regardless of different biomass concentrations. To test for statistically significant differences between the biomass adjusted dimensionless consistency coefficient (KBDW ) and the flow behavior coefficient (nBDW ) in the 45 different samples, the Monte Carlo approach was applied (Caflisch, 1998). Sample

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Fig. 2. (A) shows the change of the consistency index (K) with increased biomass (R2 value of 0.98), (B) depicts the correlation of the flow behavior index (n) with a biomass concentration (R2 value of 0.91). Biomass for these correlations was gained from three 2 L bioreactor cultivations.

data, within the standard error previously determined by experimentation, was evaluated using Matlab (MathWorks, USA). The data sets were used in a paired t-test (p < 0.05) conducted with Origin (Originlab, USA) to test for statistical difference between rheological data of each cultivation experiment. 3.2. Correlation of morphological and rheological data While specific productivity most commonly is the parameter which is strived to be improved during process development, easy purification of the product is equally important. For filamentous microorganisms an increased culture broth viscosity leads to a more difficult and therefore economically unfavorable purification process. A further important aspect directly affecting process economics is the increased energy consumption for agitation of such cultivations. The flow behavior in turn is heavily dependent on fungal morphology. In the present study osmolality was used to specifically create 45 different morphologic forms in shaking flask culture, to investigate the influence of morphology on culture broth viscosity. The rheological behavior of pellets or mycelia in general was the issue of many studies (Casas López et al., 2005; Kim et al., 1983; Olsvik et al., 1993; Ruohang and Webb, 1995). The high variability of fungal morphology however was mostly ignored. It is not sufficient to describe the influence of either pellet or free mycelial morphology, rather should intermediate morphological forms, like small elongated and fluffy pellets be considered as well. The influence of pellet sizes and their surface morphology on rheological behavior of A. niger culture for instance was studied rarely (Mitard and Riba, 1986). While still being less viscous than mycelial growth forms, different morphological forms of pellets were found to differ significantly in terms of culture broth rheology (Mitard and Riba, 1986). The accurate characterization of fungal morphology therefore remains a key target for industrial biotechnology and image analysis methods are central for achieving this goal (Barry, 2010). Since the introduction of automatic image analysis, lots of quantified information enabled a detailed characterization of various morphological forms of filamentous fungi (Paul and Thomas, 1998; Thomas, 1992) and a quantitative characterization of the relationship between fungal morphology and productivity (Papagianni et al., 1998). The combination of relevant parameters image analytical parameters to the already introduced Morphology number (MN) provides a simple way to characterize filamentous morphology. Furthermore, consideration of fractal dimension seems a promising approach to describe, irregular structures of mycelial particles

and structures lying between the two extreme forms of pellet and mycelial morphology. Like many other natural structures mycelia are approximately fractal (Obert et al., 1990). The concept of fractals was first introduced by Mandelbrot (Mandelbrot, 1982) as an extension of the conventional (Euclidean) geometry. The fractal nature of mycelia has been studied at two distinct levels using the measures of the surface fractal dimension (DBS ) and the mass fractal dimension (DBM ), making it possible to discriminate between systems which are fractal only at their boundaries like pellets and true mass fractals like mycelia (Barry, 2009). In the present study the fractal quotient (DBM /DBS ) was introduced, which is an adaption from parameters used by Papagianni (2006), to relate the fractal nature of A. niger SKAn 1015 to culture broth viscosity. However, the computation of fractal dimensions cannot always provide unique or definite descriptions, same as size or weight are not sufficient for particle description. Due to this shortcoming a second fractal dimensional parameter, lacunarity, was considered to further differentiate between sets and textures that share the same fractal dimension values, but which still look different (Landini, 2011), as it is the case with A. niger SKAn 1015 pellet morphology. Lacunarity as a measure of how data fills space complements fractal dimension which basically measures how much space is filled (Tolle et al., 2003). This parameter takes into account that fungal pellets at higher osmolality are generally more heterogenic with a higher variance in room filling capacity of the particle, for example through gaps or uneven surface. Thus, already introduced parameters Morphology number (MN), the fractal quotient (DBM /DBS ) and Lacunarity are compared to assess the rheological parameters consistency coefficient KBDW and flow behavior coefficient nBDW (Fig. 3). KBDW varies from around 10−7 to 30. nBDW takes values between 0.3 and 3.5. Since the parameters take into account biomass dependency of rheological behavior, both values are not equal to the regular K and n from the Ostwald–de Waele model. These values should not be confused with each other. Textbook correlations and dependencies about the consistency index K and the flow behavior index n are not necessarily valid for the biomass independent values of KBDW and nBDW . Prior to correlating rheological parameters and fungal morphology, statistical significance of obtained rheological parameters had to be ensured. To this end a Monte Carlo approach was conducted and a paired t-test was used to check whether differences in rheological parameters of adjoining shaking flasks were statistically significant. The difference in the predominant majority of the rheological parameters was found to be statistically significant.

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Fig. 3. KBDW and nBDW are depicted over Morphology number (MN) (A, B), fractal quotient (DBM /DBS ) (C, D) and lacunarity (E, F). Rheological parameters are biomass normalized. Each dot represents morphology and rheology of a single 100 mL shaking flask cultivation after 72 h of cultivation. Each value is an absolute mean of at least 3 cultivations.

In Fig. 3A KBDW is depicted over fungal morphology displayed by MN. An exponential relationship between morphology and the KBDW is obvious (R2 = 0.95)

In Fig. 3B the flow behavior coefficient nBDW can been seen to increase exponentially (R2 = 0.78) with increasing MN nBDW = 0.13 · (2.44 × 102 )

KBDW = 4.12 × 105 · (2.5 × 10−25 )

MN

.

(10)

MN

.

(11)

A correlation of fractal quotient (DBM /DBS ) and KBDW is depicted in Fig. 3C. The exponential fit again shows a very good correlation

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Fig. 4. Actual and predicted values of biomass independent KBDW using correlations 10 (A), 12 (B) and 14 (C). Dots are means for at least three 100 mL shaking flask cultivations.

(R2 = 0.90) between fungal morphology and the rheological parameter KBDW KBDW = 3.10 × 1017 · (3.42 × 10−16 )

DBM /DBS

.

(12)

nBDW over fractal quotient (DBM /DBS ) in Fig. 3D shows an exponential correlation as well, although with a much poorer fit (R2 = 0.64) nBDW = 3.60 × 10−3 · 77.86DBM /DBS .

(13)

The morphological parameter lacunarity  can also be used to show the interrelation of rheology and morphology. A very good allometric correlation (R2 = 0.96) is reached when KBDW is plotted over  (Fig. 3E) KBDW = 4.11 × 10−4 · 2.99 .

(14)

The biomass independent rheological parameter nBDW is also depicted over  (Fig. 3F), although the correlation is fairly poor (R2 = 0.52) nBDW = 1.91 · −0.41 .

(15)

All three parameters introduced for characterization of fungal morphology are adequate to study the relationship between fungal morphology and culture broth flow behavior. The biomass rheology correlation was intentionally not directly included in these correlations to have a clearer approximation of the impact of fungal morphology and to increase the applicability for greater ranges of biomass or different microorganisms which might show other correlations between biomass and rheological parameters. A strong exponential correlation between fungal morphology and rheology is demonstrated. In general the classical flow behavior index n remains elusive in most rheology correlations. Thus almost all correlations in literature are based on the consistency index K assuming a constant flow behavior index n. Because n is an exponent, changes in n will have a larger effect on shear stress than a similar change in K, therefore limiting the use of K-values as single indicator of fluid viscosity to datasets where n is constant (Olsvik and Kristiansen, 1994). No simple relationship between n and the biomass concentration for P. chrysogenum and either A. oryzae or A. niger was discovered (Riley and Thomas, 2010; Riley et al., 2000). The inability to find any global value for this parameter was found disturbing by Riley and Thomas. The authors speculated that separate flow behavior and consistency index correlations will be needed for every species, and possibly for different strains (Riley and Thomas, 2010). In this study the flow behavior was shown to correlate well with biomass concentration BDW (Fig. 2), but only reasonably well with fungal morphology, depending on the examined fungal parameter (Fig. 3). In Fig. 4 predicted values of the consistency coefficient KBDW using correlations (Eq. (10) – Fig. 4A), (Eq. (12) – Fig. 4B) and

(Eq. (14) – Fig. 4C) are plotted over measured values showing the quality of the correlations. Here the Morphology number (MN) and the fractal quotient (DBM /DBS ) lead to reasonable results over the whole range of consistency coefficient values (Fig. 4A and B). All three models have problems predicting low values of KBDW but correlate well at higher values. This is especially true for KBDW predicted from Lacunarity (Fig. 4C). This morphological parameter is obviously unsuitable to describe differences in pellet morphology which are responsible for the low KBDW values. Moreover, the measuring system has to be taken into account, because the lowest concentrations of biomass had a viscosity which was on the lower limit of the rheological measuring system where the sensitivity of the used rheometer might be insufficient. In Fig. 5 predicted values using correlations (Eq. (11) – Fig. 5A), (Eq. (13) – Fig. 5B) and (Eq. (15) – Fig. 5C) and actual values of the nBDW are depicted. Here the same tendencies as in Fig. 4 are apparent. The models fail to predict large values of nBDW representing low viscosity values. Depending on the correlation used, 6–7 samples of low viscosity cannot be described by the majority of the correlations. After correction of the biomass influence samples with lowest viscosities exhibited pellets morphologies. Especially very large pellets of around 2000 ␮m, as common at standard conditions (Table 1), could also impair the rheological measurement, as they have a higher tendency to settle and also locally prevent laminar flow through formation of Taylor vortices, even if these could not be observed on a global scale. Correlation (11) gained by morphology characterization with the Morphology number (MN) shows the best agreement between predicted and measured values of nBDW (Fig. 5A). Evaluation of the data available shows that MN and (DBM /DBS ) are obviously the best morphological parameter for modeling of the KBDW , while the MN is preferable to predict the nBDW . The relationship between particle diameter, pellet concentration, and rheology is obvious to be increasingly nonlinear and very complex, especially when considering length and branching characteristics of single hyphae (Petersen et al., 2008). Hyphal entanglement is responsible for significant changes in broth rheology as found for dispersed growth forms (Metz et al., 1979). The degree of hyphal branching, however, seems to decrease culture broth viscosity, because highly branched mutants tended to be less viscous than wild type strains (Bocking et al., 1999). In most studies micro morphology was neglected because of the predominance of clumps even for pure mycelial morphology. Furthermore, broth rheology has been often shown to correlate better with clump morphological parameters than with those of free filaments (Olsvik et al., 1993; Tucker and Thomas, 1993). Clump projected area, for example, was the parameter correlating best with Penicillium chrysogenum broth rheology (Riley et al., 2000). In

T. Wucherpfennig et al. / Journal of Biotechnology 163 (2013) 124–132

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Fig. 5. Actual and predicted values of biomass independent nBDW using correlations 11 (A), 13 (B) and 15 (C). Dots are means for at least three 100 mL shaking flask cultivations of A. niger SKAn1015.

Table 1 Overview of A. niger SKAn 1015 morphology at key culture broth osmolality values. Error bars are means for at least 3 cultivations. Osmolality [mosmol/kg]

Morphology [−]

Maximal diameter [mm]

Morphology number [−]

DBM [−]

Fractal quotient [−]

500

1.94 ± 0.53

0.51 ± 0.11

1.71 ± 0.05

1.41 ± 0.14

1.20 ± 0.63

1000

1.25 ± 0.57

0.49 ± 0.08

1.71 ± 0.03

1.45 ± 0.06

3.07 ± 1.19

1500

1.02 ± 0.38

0.45 ± 0.07

1.69 ± 0.06

1.35 ± 0.07

4.33 ± 1.30

2000

0.71 ± 0.29

0.30 ± 0.05

1.53 ± 0.06

1.14 ± 0.06

10.80 ± 1.54

2500

0.27 ± 0.07

0.17 ± 0.04

1.31 ± 0.09

1.04 ± 0.04

38.63 ± 3.50

their major work Riley and colleagues came up with the following correlation K = BDW2 · [4 × 10−5 · d − 9 × 10−4 ],

(16)

where BDW2 is the biomass concentration as dry cell weight and d is the clump maximum diameter. The flow behavior index n was here either fixed or found from different correlations. The applicability of correlation (16) for A. niger or A. oryzae, however, was limited. A reasonable agreement was found between predicted and measured values for the consistency index for A. oryzae cultivations broth, not however for broths of A. niger (Riley and Thomas, 2010). In the present study the Riley-correlation was tested as well, but did not lead to any satisfactory results for the culture broth of A. niger SKAn 1015. This might be due to the rather large diameter difference of fungal particles between both strains, 100–300 ␮m (P. chrysogenum) and 250–2000 ␮m (A. niger, this study), respectively. Furthermore, the biomass concentration was distinctly different, as dry weight between 6 and 30 g L−1 of P. chrysogenum was considered in the Riley study (Riley and Thomas, 2010; Riley et al., 2000), whereas the highest biomass concentration reached in cultivations of A. niger SKAn 1015 was 9 g L−1 . More sensitive measurement techniques, however, allowed a determination of rheology beginning at biomass concentrations of 0.3 g L−1 . In contrast to correlations found by Riley et al. (2000) the correlations in this study are completely independent from magnification, because analysis was based on pixels which were converted to ␮m. A resolution of 2048 × 1536 pixels with 3.2 ␮m per pixel was sufficient to capture all fungal particles and avoid inaccuracies through conversion of units.

Lacunarity [−]

4. Conclusion There has been an impressive amount of research concerning the morphology of filamentous fungi. The implementation of these results in the industry, however, is rather limited (Kossen, 2000). This is partly due to economic pressure and industrial fixation on strain improvement, on the other hand there is a rather complex interrelationship between all factors involved in fungal growth such as morphology, physiology, rheology and productivity (Schügerl et al., 1998). Problems concerning fungal morphology are usually solved by empirical methods and experience (Kossen, 2000), because most models are too difficult to apply or lack industrial applicability. In the present study it was demonstrated that rheological properties of the culture broth in form of the biomass independent consistency coefficent KBDW and flow behavior coefficient nBDW can be successfully correlated to whole range of specific filamentous growth forms of A. niger SKAn 1015. Fractal and conventional parameters were obtained from image analysis. Fractal geometry provides formal mathematical foundations to better understand and characterize a variety of phenomena in complex morphological structures especially related to microscopy (Landini, 2011). The fractal quotient (DBM /DBS ) and Lacunarity  were suitable tools to predict culture broth viscosity from morphologic appearance, save for very low viscosities. However, both fractal values were not superior to the already introduced Morphology number (MN) based on conventional particle shape analysis. Comprehensive morphologic analysis can most likely be enhanced by combining strength of conventional parameters for describing pellet morphology and fractal parameters for describing filamentous morphology.

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