Bioprocess Engineering Aspects of the Cultivation of a Lovastatin Producer Aspergillus terreus

Abstract

The aim of this work is to review bioprocess engineering aspects of lovastatin (antihypercholesterolemia drug) production by Aspergillus terreus in the submerged culture in the bioreactors of various scale presented in the scientific literature since the nineties of the twentieth century. The key factor influencing the cultivation of any filamentous species is fungal morphology and that is why this aspect was treated as the starting point for further considerations. Fungal morphology is known to have an impact on the following issues connected with the cultivation of A. terreus reviewed in this article. These are broth viscosity in conjunction with non-Newtonian behaviour of the cultivation broths, and multistage oxygen transfer processes: from gas phase (air) to liquid phase (broth) and diffusion in the fungal agglomerates. The latest achievements concerning the controlling A. terreus morphology during lovastatin biosynthesis with the use of morphological engineering techniques were also reviewed. Last but not least, some attention was paid to the type of a bioreactor, its operational mode and kinetic modelling of lovastatin production by A. terreus.

Graphical Abstract

1 Introduction

Lovastatin is a polyketide secondary metabolite from filamentous fungi of high industrial importance as a drug lowering the level of endogenous cholesterol in the human blood serum. It acts as a competitive inhibitor of (S)-3-hydroxy-3-methylglutaryl-CoA reductase. Its chemical (IUPAC) name is [8-[2-(4-hydroxy-6-oxooxan-2-yl)ethyl]-3,7-dimethyl-1,2,3,7,8,8a-hexahydronaphthalen-1-yl] 2-methylbutanoate. Lovastatin is a lactone, water insoluble compound formed during the extraction from the cultivation media of the actual metabolite: mevinolinic acid, which is, from the chemical point of view, a β-hydroxy acid. The biosynthesis of lovastatin and its action in the human organism is visualized in a condensed form for the purpose of introduction in Fig. 1.

Fig. 1

Aspergillus terreus important metabolite lovastatin (mevinolinic acid) and its action in the human organism

There are several fungal species capable of producing of this metabolite such as Aspergillus terreus, Monascus ruber and Penicillium citrinum; nevertheless, it is A. terreus that became the industrial producer of this metabolite. A. terreus produces lovastatin with good efficiency and, if cultivated under proper conditions, a few other secondary metabolites (by-products) are formed. Much more by-products can be found in P. citrinum and M. ruber, e.g. mycotoxin citrinin and red pigments, respectively.

The quest to discover the inhibitors of (S)-3-hydroxy-3-methylglutaryl-CoA reductase, later called statins, started in the early 1970s in two international pharmaceutical companies Sankyo in Japan and Merck in the USA. This history was described in detail by Endo [24]. Finally, it was Merck, who succeeded and introduced lovastatin onto the market under the trade name Mevacor^® in 1986. At present, A. terreus mutant strains are employed to produce this metabolite on the industrial scale and the most efficient mutant, about which some public data are revealed comes from Metkinnen OY (Finland). It is capable of producing over 10 g lovastatin per litre. Not only lovastatin but also the variety of semi-synthetic and fully synthetic statins has been produced [65]. The leading global companies are Pfizer Inc., AstraZeneca PLC, Merck & Co Inc. and Novartis AG. The value of the global market for statins was estimated to 20.5 × 10⁹ dollars in 2011 with the forecast to decline to 12.2 × 10⁹ dollars in 2018 because of the expiry of the patents (Source Research and Markets).

The basic strain of A. terreus has been denounced in American Type Culture Collection as ATCC20542. In the scientific literature, often this strain, a recombinant ATCC74135 or other locally (in the lab of the research team) obtained mutants and local strains are the objects of research.

The research on lovastatin production by A. terreus was conducted in several universities all over the world. With regard to number of scientific papers published in the last two decades, the team from University of Almeria (Andalusia, Spain) is the leader (inter alia: [15, 62]). Fairly many publications come from Poland, from Lodz University of Technology (inter alia: [8–11, 28, 58]). In Asia, Chaoyang University of Technology in Taiwan leads (inter alia: [39–41]). Older but important papers were published by the Italian team from University of Milan (inter alia: [13, 44, 45]). Few papers were also published in the 1990s by scientists from Technical University of Budapest [66] and University of Ljubljana [52]. Various teams from India (inter alia: [30, 31, 38]) also joined to the research on lovastatin production.

Out of all these teams, the research on lovastatin production is still continued in Poland and recently appeared the Mexican team from two universities of Mexico City specializing in solid-state cultivation for lovastatin production by filamentous fungi (inter alia: 4, 5, 48]).

All the works published so far connected with lovastatin biosynthesis by A. terreus can be, in our opinion, subjectively divided into four groups: (1) the earliest works, including patents, focused on the newly discovered substance, i.e. lovastatin (or mevinolin or monacolin K, as this metabolite had more names in its history) from the 1980s (inter alia: [1, 2, 49]), (2) the works on genetic and biochemical mechanisms ruling the formation of lovastatin being a polyketide metabolite (inter alia: [3, 36, 68, 71]) (3) microbiologically focused publications mainly connected with media optimization and influence of media composition or any other substances on lovastatin formation (inter alia: [7, 12–16, 32, 39, 40, 44, 45, 66, 67]) and (4) the works with bioprocess engineering approach. The latter group is the subject of this review and the works belonging to it are collected and shortly described in Table 1.

Table 1 Publications with bioprocess engineering approach concerning lovastatin production by A. terreus in the chronological order

Lovastatin biosynthesis in the submerged culture consists of several steps, which are each time applied by the scientists studying this process. For the sake of clarity and better understanding of the further sections of the review, they are schematically presented in Fig. 2.

Fig. 2

General flow chart to biosynthesize lovastatin by A. terreus in the submerged culture

2 Fungal Morphology and Lovastatin Formation

Although the issues of fungal morphology do not seem to be, at first glance, closely connected with bioprocess engineering but with mycology or, more generally, microbiology, they are going to be discussed at the beginning. It is a common knowledge that fungal morphology is one of the strongest factors influencing any metabolite formation by filamentous fungi [55], so it is the case of lovastatin production by A. terreus too. Furthermore, apart from a strong impact on lovastatin formation, also other parameters and features of the culture, its viscosity and oxygen transfer are extremely influenced by A. terreus morphology. Morphology of A. terreus, as of any other filamentous fungi, can be affected by the hydrodynamic conditions in the bioreactor and also can be controlled by means of the novel morphological engineering techniques (see Sect. 5). There is no doubt that all aforementioned issues are in the domain of bioprocess engineering.

In the submerged cultures of filamentous fungi, two morphological forms are usually found, i.e. either hyphal aggregates (pellets) or dispersed hyphae (free hyphae). It is connected with the mechanisms and stages of filamentous fungi growth, i.e. spore swelling, hyphal tip extension, branching and finally mycelial aggregation. All these mechanisms were thoroughly described by Papagianni [55]. The aggregation process may occur at different stages of fungal evolution and it results with the formation of fungal aggregates (pellets). Different mechanisms of mycelial aggregation are known. These are the agglomeration of spores in Aspergillus sp. and hyphal aggregation, which is characteristic for Penicillium sp. Non-agglomerative mechanism (agglomerates formed from an individual spore) is found in prokaryotic Streptomyces [47, 51].

With regard to the growth of A. terreus mycelium, all researchers dealt with the agglomerates, namely fungal pellets. Thus, at the beginning, the quantitative parameters concerning the pelleted morphology of A. terreus are going to be presented. These, who more or less thoroughly referred to A. terreus morphology in their works, used above all the simplest parameter to describe it, i.e. pellet diameter. [11, 17, 26, 28, 30, 34, 60, 62, 63]. This selection is fully justified as fungal pellets are the most frequently of spherical shape.

Nevertheless, apart from the shape, a macroscopic structure of A. terreus pellets may differ dependent on the conditions, under which they grow. The most often used classification of fungal pellets comes from the review of Metz and Kossen [47]. It distinguishes fluffy loose pellets (with a compact centre and a much looser outer zone), compact smooth pellets (the whole pellet is compact, the surface of the pellet is smooth) and hollow smooth pellets (the centre of the pellet is empty, due to autolysis of hyphae and its surface is smooth). It can be without any doubts applied to A. terreus.

The quantitative measure of the filamentous growth in the A. terreus pellets, describing their hairiness was proposed by Rodriguez Porcel et al. [62] and Casas Lopez et al. [17]. Their concept was based upon the work of Cui et al. [18] and comprised two measures. First, they used the diameter corresponding to a circular area equivalent to the total pellet-projected area, as a one-dimensional measurement of the pellet size. Second, they measured the mean projected area of the whole pellet and the area of the hairy region. Upon this, they introduced the filament ratio that can be upon their description defined as:

$$ {\text{filament}}\,{\text{ratio}} = \frac{{A_{Z} }}{{A_{Z} + A_{C} }} $$

(2.1)

where A _Z —projected area of the core of pellet kernel, A _C —projected area of filaments. The definition of filament ratio is presented in Fig. 3 too.

Fig. 3

Definition of filament ratio (upon the description from [62])

All these above-described morphological parameters, being the quantitative measure of A. terreus morphology, should be connected with lovastatin formation. Unfortunately, the study of literature revealed that most of the authors did not do this explicitly.

Gbewonyo et al. [26] were the first who noticed the fact of lovastatin production by dispersed (it is not a frequent case) and pelleted hyphae of A. terreus without making any detailed morphological measurements. They only wrote that they had pellets of 100–300 μm. No data on lovastatin concentration were given in this paper.

Relatively large amount of data about A. terreus morphology were published by the research team from University of Almeria (Andalusia, Spain). Nevertheless, most of them are only the presentation of the data (no doubt that valuable) concerning the change of morphological parameters in time for various process conditions and bioreactors. Upon them hardly can any direct quantitative correlation between A. terreus morphology and lovastatin production be found as the quantitation of A. terreus morphology was not the main aim of most of these works.

Casas Lopez et al. [17] studied the influence of agitation speed on lovastatin production and thereby showed the difference between pellets formed under high (800 rpm) and low (300 rpm) agitation conditions in a 5-L stirred tank bioreactor (STB). In the first case, pellet diameters were below 1,500 μm and in the second one they achieved even 2,500 μm. Interestingly, they found that filament ratio is not so strongly influenced by the agitation. In all cases it decreased from about 0.9 at the beginning of the process to about 0.4 after 100 h. Casas Lopez et al. [17] did not show any direct mathematical correlation between pellet diameter and lovastatin formation. Nevertheless, they obtained higher titres of lovastatin for lower agitation speed, i.e. in the system with bigger pellets. Quantitative data concerning the mechanical properties of the formed A. terreus pellets, for example the correlation between specific energy dissipation rate and fungal morphology, as it had been done for A. awamori by Cui et al. [18], were not presented either.

Another work from this team by Rodriguez Porcel et al. [62] did not bring many new data. That time a different bioreactor, i.e. a 17-L fluidized bed bioreactor (FBB), was used. Its application led to obtaining bigger pellets compared to the STB. Their diameter was in the range from 2,000 to 3,000 μm. But filament ratio remained insensitive to the change of bioreactor. Similar findings were reported in Rodriguez Porcel et al. [63]. Here, the effect of various aeration gas compositions and organic nitrogen source concentration was studied. In the article concerning various feeding strategies for lovastatin production in a FBB [60], no new findings concerning A. terreus morphology, compared to the previous articles, can be found again.

There are also some data concerning A. terreus morphology from other research teams. Lai et al. [40] showed several distributions of pellet diameter in the optimum media (obtained by means of statistical medium design) for lovastatin production. Lai et al. [42] made the classification of the hyphal objects and presented pellet size distribution in two types of cultures: shake flasks and a 5-L STB. The pellets from shake flask culture were bigger and their diameter ranged from 750 to 1,600 μm with the maximum frequency for 1,200 μm pellets, while in the bioreactor, from 650 to 1,350 μm with the maximum frequency for 1,000 μm pellets. They claimed that stirring velocity is the strong factor influencing pellet size; however, lower shearing stress and consecutively bigger pellets are more useful for lovastatin formation. They also concluded that A. terreus pellets with a uniform size distribution (950 μm in average) aided lovastatin production largely. In the earlier work, Lai et al. [39, 41] observed the effect of addition of water-immiscible organic oxygen carrier (n-dodecane) on A. terreus morphology. Above all, it decreased pellet diameters (from 1,200 to 800 μm at 2.5 % n-dodecane) and changed their size distribution. Also the structure of pellets was altered. The pellets became less hairy. It increased lovastatin production. In the experiment made in a 5-L STB with the organic solvent added, the star-shape (diffused) pellets were undesirably formed, namely there was a transformation from compact pellets to extremely fluffy loose pellets. To this morphology, together with the elevated oxygen concentration, undesired pH effects and organic solvent droplet formation the aggravation of lovastatin production was attributed [41].

Gupta et al. [30] also traced the changes of A. terreus morphology in time in a 2-L STB. Describing methods, they declared the complex quantification of fungal morphology, including the measurement of mean projected area, diameter and circularity. Unfortunately, they did not show these data. They only observed the growth in pellet diameter within the 10-day cultivation from 3,500 μm (on average) in 3rd day up to 5,650 μm (on average) in 10th day. They postulated the deceleration of the process after 8th day to be connected with the breakage of the pellets formed. They also claimed, although they did not show any correlation, that neither very small pellets nor large hollow pellets are suitable for lovastatin production. Only medium-sized pellets 1,800–2,000 μm with the high ratio of filaments to core, actually they can be called fluffy pellets, optimally produced lovastatin at high oxygenation conditions. This study contains the interesting images from the electron microscopy to visualize the destruction of pellets in the late stages of lovastatin production.

Jia et al. [34] characterized A. terreus morphology during lovastatin production in shake flasks in terms of pellet core diameter (i.e. the equivalent diameter of the measured core area) and the width of the hairy zone in relation to the used carbon source. In their opinion, regular and compact pellets with slender spongy of outer hyphae and sporangia on the tips of pellet outer hyphae, (the latter is quite unusual opinion, not found in any other sources) were beneficial for A. terreus secondary metabolism. Larger pellets were formed on fast utilizable substrates (glucose or sucrose), while smaller ones on lactose, glycerol or starch assuring higher lovastatin titres.

The effect of fungal pellet size and the differentiation of hyphae in A. terreus pellets on lovastatin production were studied by Bizukojc and Ledakowicz [11] in the 150-mL shake flask culture. They confirmed the agglomerative mechanism of pellet formation in the 24-h preculture of A. terreus. Using various numbers of spores 1.39 × 10⁹ to 2.56 × 10¹⁰ L⁻¹ in the preculture, and using these precultures for the inoculation of the production medium, they generated smooth pellets of various sizes from about 1,000 to 3,500 μm in the production medium. About 10,400 spores capable of germination were found to form an individual pellet of A. terreus. Pellets once formed were not very prone to divide or agglomerate in the later stages of cultivation and their number remained more or less constant with the cultivation [11]. What is the most important, these authors directly found that the smallest pellets occurred to be the most efficient for lovastatin production, while the largest one effectively biosynthesized (+)-geodin, an octaketide by-product of A. terreus. Above all, only in this article, the differentiation of hyphae was visualized, quantified and associated with lovastatin formation (Fig. 4). Using microscopic stained slides and, if required, thin cross sections of pellets, two zones of various metabolic activity were distinguished: external active and internal less active or dead.

Fig. 4

Visualization of A. terreus pellets evolution from spore aggregation to the growth and differentiation of pellets of pellets (from a to m) and (n) changes of fractions of zones Z ₁ (active) and Z ₂ in time; negative values of time indicate the time of preculture in the reversed order and t = 0 h is the inoculation time [11]; reproduced with permission granted from Springer

The specific lovastatin formation rate π _LOV was proved to be dependent on the fraction of the active hyphae in the external regions of pellets in accordance with the equation:

$$ \pi_{\text{LOV}} = 0. 1 1 7\cdot{\text{Z}}_{ 1} + 0.0 4 7 $$

(2.2)

where Z ₁ is active external zone fraction and π _LOV is specific lovastatin formation rate (related to biomass concentration expressed in mg LOV g X⁻¹ h⁻¹).

In Table 2, the most important issues concerning A. terreus morphology and lovastatin formation are summarized.

Table 2 A. terreus morphology versus lovastatin formation

Although there is insufficient amount of data aiming at finding of the direct correlations between A. terreus morphology and lovastatin production in the submerged culture, the importance of fungal morphology in these cultivations shall be confirmed in the next sections. Almost all engineering aspects concerning lovastatin production in bioreactors, e.g. broth viscosity and its rheological properties, oxygen transfer in the system, operational parameters of the bioreactor and even its type are stronger or weaker affected and/or correlated with the morphological form of A. terreus. Thus, it is not an accident that the articles mentioned in this section will be cited again, as all these engineering aspects were almost always studied and discussed together with the morphology of A. terreus mycelium.

3 Rheology of A. terreus Cultivation Broths

At the beginning, it is worth mentioning that all data which concern rheology of A. terreus broths available in literature are the time changes of rheological parameters of the broth in time.

In one of the earliest works containing information on hydrodynamic properties of A. terreus broths, Gbewonyo et al. [26] showed the changes of apparent viscosity of the broth in relation to the morphological form of the fungus evolved during the cultivation in a pilot-scale 500-L STB. In the case of filamentous suspension (no pellets formed), apparent viscosity changed from about 50 cP (0.05 Pa s) at the beginning of the cultivation to about 700 cP (0.7 Pa s) for the dispersed morphology and 300 cP (0.3 Pa s) for the pelleted morphology after 100 h of the process. Furthermore, the increase in the apparent viscosity had a permanently increasing trend for the dispersed morphology, while in the case of pellets it stabilized on the aforementioned level after about 40 h. No rheological model was proposed in this study.

The more detailed research on the rheological properties of A. terreus broths was only conducted by the team from University of Almeria, whose works dominate in the scientific literature with regard to this subject. Nevertheless, only a few of these works were more directly aimed at the testing of the rheological properties of A. terreus broths. In most of them, the measurements of the rheological parameters were only the additional data included in these works.

Generally, in all these works it was assumed that A. terreus broth rheology can be described by the power law, i.e. Ostwald-de Waele equation. Using this law, the apparent viscosity of the broth can be expressed as

$$ \mu_{\text{app}} = \frac{\tau }{{\dot{\gamma }}} = K \cdot \dot{\gamma }^{n - 1} $$

(3.1)

where K—consistency (N m⁻² sⁿ); n—flow behaviour index (−); $\dot{\gamma }$—shear rate (s⁻¹) and τ—shear stress (N m⁻²).

In the light of the common knowledge on fungal suspensions, the use of the power law was justified as these suspensions satisfy this law being usually shear thinning liquids. These authors did not make any deeper insight into rheology of A. terreus cultivation broth than the determination of the parameters for Ostwald-de Waele law throughout the whole duration of the process, namely at various sampling times. No yield stress was described either. They always used the same rheometric measurement device, i.e. rotational viscometer with standard vane spindle of 21.67 mm diameter and 43.33 mm height.

The work from by Casas Lopez et al. [17] was the most detailed and comprised the determination of the rheological parameters satisfying Ostwald-de Waele equation for A. terreus broth cultivated in a 5-L STB agitated with Rushton turbines at various speeds, i.e. 300 and 800 rpm at various aeration conditions: with air and oxygen-enriched air. The values of consistency K and flow behaviour index n were determined within cultivation time and, irrespective of the aeration gas, consistency remained unchanged (0.01 N m⁻² sⁿ) within the time of cultivation, if the higher rotation speed of the impeller was used. At the lower rotation speed of the impeller (300 rpm), the increase in consistency from the initial 0.01 to 0.5 N m⁻² sⁿ was observed. Changes of flow index were different starting from about 1 (Newtonian fluid): at the beginning of the cultivation, it went towards 1.5 for the higher rotation speed of the impeller (shear thickening fluid) or towards 0.5 (shear thinning fluid) for the lower rotation speed of the impeller. It was also reflected in the apparent viscosities, which were higher for the strongly agitated broth (0.03–0.065 Pa s) and lower for the weaker agitated broth (0.01–0.035 Pa s). Cultivation broths aerated with oxygen-enriched air were usually more viscous. It is the only work, in which the changes of apparent viscosity along the culture time were graphically presented. In all studied runs, the increase of apparent viscosity in time by 0.01–0.03 Pa s within 200 h of the experiment was observed.

The untypical effect of the formation of shear thickening broth the authors explained by the formation of very small pellets (between 500 and 1,500 μm, as shown in the graphs) at the higher rotation speeds of the impeller. Taking the size of the pellets into account, this explanation seems not to be probable as these pellets are not extremely small, compared to other literature data. No correlation between lovastatin formation and broth rheology was explicitly shown. Any positive or negative effects regarding lovastatin yield were rather attributed to the varying process conditions.

Rodriguez Porcel et al. [62] made a comparative study on A. terreus broth rheology for two types of bioreactors: a 5-L STB and 17-L FBB. The interesting in this study was that the flow behaviour of the broth in the fluidized bed bioreactor was shear thickening with flow behaviour index value of around 1.2 throughout the whole duration of the cultivation (initially declined from 1.7 to 1.4), despite fairly large pellets (up to 1,500 μm). The reference data for the STB were the same as in Casas Lopez et al. [17]. The consistency index for FBB was more than one magnitude lower (0.005–0.025 Pa sⁿ) than for STB agitated at 300 rpm (up to 0.5 Pa sⁿ). In the opinion of the authors, the various values of flow behaviour index were associated to biomass concentration and fungal morphology, namely pellets diameter and, to the lesser extent, fluffiness of pellets. The correlation between lovastatin concentration and broth rheology was here again indirect, via fungal morphology.

Rodriguez Porcel et al. [63] continued their study in the FBB. They again tried to find the correlation between broth rheology and biomass concentration together with pellet size. The experiments were made in the media with varied organic nitrogen concentration. The clear correlation between nitrogen concentration and consistency was then described. Nitrogen-limited conditions (nitrogen initial level 0.15 g N L⁻¹) led to aggravated biomass formation (less than 5 g L⁻¹), which contributed to lower K values around 0.05 Pa sⁿ. Generally, consistency increased with time of the cultivation until the moment, when pellets ceased growing and retained the same diameter, which happened around 100 h. Consistency was found to be insensitive to the increase in the concentration of pellets of a fixed diameter. As both pellets and filaments were observed in the broths, the correlation between these two morphological forms of biomass and rheological properties was also noted. The filament-rich culture broth was more viscous (K > 0.5 Pa sⁿ) than in the case of pelleted growth (K = 0.2–0.4 Pa sⁿ dependent on the hour of the run). In these cultures, they observed the varying flowing pattern, indicating the change in the properties of the broth from shear thickening (n = 1.2–1.8) in the initial stages of the cultivation to strongly shear thinning liquid (n = 0.5–0.6) around 100 h of the run. It took place in the nitrogen-rich system, with high amount of biomass. In nitrogen-limited conditions, flow index was usually close to 1. No clear explanations about higher than 1 flow indices were given. Lovastatin yield was to the high extent correlated with high biomass concentration and fungal morphology, but again no direct correlation between the rheological properties of the broth and lovastatin titre was found.

Another work by Rodriguez Porcel et al. [60] was generally focused on establishing a complicated cultivation strategy (batch and semi-continuous operational mode bioreactor in the FBB). The rheological measurements were only the additional data. Here, the broth from the initial shear thickening became shear thinning together with the growth of biomass (n = 0.4–0.9) and the consistency index K was of similar level as for the slowly stirred STB as shown in Casas Lopez et al. [17]. Nevertheless, it was lower for the semi-continuous runs (around 0.05). In these runs, 90 % of biomass existed as fluffy small pellets (the rest were filaments) and this value decreased to 70 % in the end of the cultivation. In the work by Rodriguez Porcel et al. [61], a novel bioreactor strategy was proposed and rheological data actually confirmed the previous findings.

The only source, which may allow for the critical comparison of the above-presented data, is the publication of Gupta et al. [30]. They also used Ostwald-de Waele model to describe the rheology of A. terreus broths. They showed the changes of apparent viscosity¹ in time. It increased from the value of about 0.01 Pa s at 24 h to 0.06 Pa s at 144 h and subsequently decreased down to 0.035 Pa s. Consistency increased from 0.00978 to 0.06685 Pa sⁿ (its maximum) and flow behaviour index n changed from 0.694 to 0.48. These authors also correlated the flow behaviour index with biomass concentration introducing an exponent of biomass denounced as α, whose value was actually constant to 2.0. They presented this correlation only in the form of a graph, giving no equation.

All most important data concerning the rheology of A. terreus broths for lovastatin production were collected in Table 3.

Table 3 Rheological parameters of cultivation broth with A. terreus in lovastatin biosynthesis

Despite many data available, it would be still useful to seek for the quantitative correlations between lovastatin titre and rheological properties of the broth and fungal morphology. Probably a kind of the multivariate correlation would be useful for this purpose. In our subjective opinion, also the existence of the range, in which A. terreus broth is shear thickening, requires the confirmation from the other scientific teams.

4 Role of Oxygen Transfer in Lovastatin Biosynthesis

The main operational parameter that reflects the presence and influence of oxygen in the bioreactor process is dissolved oxygen saturation level, usually denounced as DO or pO₂. Holding its level constant is a convenient and very practical way to assure the required amount of this electron acceptor to the fungal culture. However, the varying composition of the cultivation broth and, above all, the varying fungal morphology in conjunction with broth rheology does not allow for detailed conclusions to be exclusively drawn from its levels. Thereby, the effect of oxygen on fungal culture has to be more thoroughly investigated, especially with regard to its transfer.

Due to the variety of morphological forms in filamentous fungi, the study of mass transfer in the bioreactors, in which filamentous fungi grow, is far more complicated than in the case of such microorganisms as yeasts or bacteria. Its main reason is the formation of macroscopic agglomerates, namely pellets (see Sect. 2), in which several stages of oxygen transfer might be potentially limiting (Fig. 5). Normally, oxygen transfer in biological systems is limited in the liquid film surrounding the air bubbles (stage 3 in Fig. 5). If pellets are formed, both the liquid film surrounding the pellets and diffusion in the pellets alone should be considered. There are three physical parameters to quantify these potentially limiting mass transfer processes, i.e. convective mass transfer coefficients, k _L a and k _S a, and effective diffusion coefficient, D _eff. However, not all these steps of oxygen transfer in the fungal cultures were studied with same engagement. It is clearly seen in the detailed review by Garcia-Ochoa and Gomez [25]. At the beginning, they presented all these steps, but further the review dealt with the gas-liquid phase transfer (k _L a), about which the literature is really rich.

Fig. 5

Oxygen transfer stages in the bioreactor during the cultivation a filamentous fungus: 1 convection in the turbulent bulk gas of the air bubble, 2 diffusion through gas–liquid interface, 3 convection in the liquid film, 4 convection in the turbulent bulk liquid 5 convection through the liquid film surrounding the fungal cells (filaments) or agglomerates (pellets) 6 diffusion through the liquid–solid interface 7 diffusion inside the pellet 8 biological reaction site (inspired and based upon Doran [19])

Similarly, with regard to lovastatin-producing A. terreus, the values of k _L a were presented in several papers, while the process of oxygen diffusion inside A. terreus pellets has been rarely studied. Nowhere can any data concerning the values of convective mass transfer coefficient in the liquid film surrounding the pellet k _S a be found.

4.1 Impact of Oxygen Saturation

There are few studies concerning directly the impact of oxygen saturation on lovastatin formation by A. terreus. The most detailed study was made by Lai et al. [42] in a 5-L STB. They tested four levels of pO₂, i.e. 10, 20, 30 and 40 % concluding that the optimum level was 20 %. Higher pO₂ level was in their opinion not favourable for lovastatin formation. This finding is to a certain extent in the contradiction with some works from University of Almeria. These researchers used in their several works the oxygen-enriched (80 % O₂) air for the aeration of A. terreus broths. It allowed for holding the oxygen saturation level at 400 % with vvm between 0.5 and 1.5 L_air L^–1 min^–1 [17, 60, 63]. On the other hand, Bizukojc and Ledakowicz [10] claimed that high constant aeration rate (above 1 L_airL⁻¹min⁻¹) led to (+)-geodin formation (an octaketide by-product) rather than to lovastatin. Earlier works concerning lovastatin formation were less focused on the issue of oxygen. Only Novak et al. [52], testing the following three levels of oxygen saturation, i.e. 35, 70 and 80 %, found that pO₂ = 70 % assured the highest lovastatin titres (in this publication lovastatin concentrations are not openly given in mg L⁻¹ but in “units”). Analysing all these data, it is also important to check what the initial carbon source concentration in the culture was. It is the common biochemical knowledge that more carbon source requires more final electron acceptor for its catabolism. That is why the conclusions about the optimum oxygen saturation level were different. In the works cited above, lactose (C-source concentration) varied from 20 g L⁻¹ [10], via 70 g L⁻¹ [42] up to 114 g L⁻¹ [17, 60, 63]. It certainly influenced the conclusions drawn by all these authors.

The most interesting idea of oxygen supply facilitation in A. terreus cultivation was proposed in the earlier mentioned work of Lai et al. [39, 41]. They used a water non-miscible organic oxygen carrier (n-dodecane) to increase lovastatin titre. They succeeded in shake flask culture, while in the bioreactor, the results were not satisfactory mainly due to undesired morphology of mycelium (see Sect. 2) and too high, in their opinion, oxygen saturation level in the broth.

4.2 Convective Mass Transfer Coefficients in Various Bioreactor Systems

The issue of mass transfer from the bubbles into the broth in A. terreus cultivation was the object of studies already in the early 1990s. Nevertheless, these data are usually scarce and, as it was with regard to broth rheology, no explicit correlation between k _L a and lovastatin production were given. The aforementioned Gbewonyo et al. [26] studied in the limited range the interactions between A. terreus morphology (pelleted and dispersed) and mass transfer (k _L a) during lovastatin biosynthesis. These measurements concerned the behaviour of their fungal system in response to the changes in agitation (between 100 and 250 rpm) in a STB. Convective mass transfer coefficient was usually lower for the systems with dispersed morphology (Table 4).

Table 4 Values of convective mass transfer coefficient for A. terreus cultivations

Casas Lopez et al. [17] also determined oxygen mass transfer coefficients in their culture. These values are given in Table 4 too. In their STB, pelleted growth of A. terreus dominated and they studied the time changes of k _L a dependent on the rotation speed of the impeller.

Casas Lopez et al. [17], using a classical chemical engineering approach, showed the experimental correlation for the A. terreus lovastatin-producing system between energy dissipation/circulation function EDCF (kW m⁻³ s⁻¹) defined as:

$$ {\text{EDCF}} = \frac{{P_{g} }}{{k_{c} D^{3} t_{c} }} $$

(4.1)

where P _g is gassed power input (kW m⁻³), k _c —geometric constant, D—impeller diameter (m), t _c —gassed circulation time (s), and convective mass transfer coefficient k _L a, achieving the following equation:

$$ k_{L} a\,(s^{ - 1} ) = 7.0 \times 10^{ - 4} \cdot \left( {\text{ECDF}} \right)^{0.76} $$

(4.2)

For P _g /V _L ratio (V _L —broth volume), the similar correlation was as follows:

$$ k_{L} a\,(s^{ - 1} ) = 2.24 \times 10^{ - 2} \cdot \left( {P_{g} /V_{L} } \right)^{0.92} $$

(4.3)

Rodriguez Porcel et al. [63] determined k _L a values (Table 4) in a 17-L fluidized bed bioreactor and determined experimentally the exponents and constants of the following correlation for k _L a in the function of broth viscosity and biomass concentration:

$$ k_{L} a = a \cdot U_{g}^{b} \cdot \mu_{\text{eff}}^{c} \cdot c_{\text{b}}^{d} $$

(4.4)

where U _g —superficial gas velocity (m s⁻¹), μ _eff—apparent broth viscosity (Pa s) and c _b—biomass concentration (kg m⁻³). As it was in the case of broth rheology, neither direct correlation between k _L a and lovastatin titre was given nor any explicit conclusions drawn. Only general comment confirming that higher aeration is profitable for lovastatin formation and more biomass in the system results in higher lovastatin titre was given.

Kumar et al. [38] determined several values of k _L a in a large 1,000-L bioreactor operating in the discontinuous fed-batch mode. It was maximally 280 h⁻¹ (0.0778 s⁻¹) in 24 h of the run. It gradually decreased in time achieving the minimum values below 100 h⁻¹ (0.0278 s⁻¹) in 288 h of the run (Table 4).

4.3 Effective Diffusivities in A. terreus Pellets

The determination of the effective diffusivities in the immobilized biocatalysts, as fungal pellets can be treated as a form of immobilized biocatalyst, is not an easy task. Precise measurements of oxygen profile in the pellet are required and the tools for this purpose are available since the 1980s [69]. Nevertheless, it must be remembered that these measurements can never be made directly in the bioreactor. Pellets must be withdrawn from the bioreactor or located in the special measuring tube connected to the bioreactor. It is the strong experimental limitation that has an impact on the number and quality of the obtained results.

A very good and detailed analysis how to measure and determine D _eff in the individual fungal pellet under various flow conditions was described by Hille et al. [33] for another fungal species A. niger AB.1.13 (α-amylase producer). For this purpose, the second Fick’s law was used:

$$ \frac{{{\text{d}}c_{{{\text{O}}_{2} }} }}{{{\text{d}}t}} = D_{\text{eff}} \cdot \frac{{{\text{d}}^{2} c_{{{\text{O}}_{2} }} }}{{{\text{d}}r^{2} }} $$

(4.5)

where r is pellet radius and D _eff-effective diffusivity.

The scarce data, as this paper generally concerned morphological engineering techniques to maximize lovastatin production, on the values of effective diffusivities in A. terreus pellets were only obtained by Gonciarz and Bizukojc [28]. Under quiescent flow conditions, the oxygen profiles in at least three A. terreus pellets of various diameters in each sampling time from the shake flask culture were made in this work. Effective diffusivities were found from the following oxygen balance (so-called shell model for a biocatalyst) with the assumed Michaelis-Menten kinetics for oxygen utilization $r_{{{\text{O}}_{ 2} }}$ in the pellets.

$$ \frac{{{\text{d}}^{2} c_{{{\text{O}}_{2} }} \left( r \right)}}{{{\text{d}}r^{2} }} \cdot r^{2} + 2 \cdot r \cdot \frac{{{\text{d}}c_{{{\text{O}}_{2} }} \left( r \right)}}{{{\text{d}}r}} - \frac{1}{{D_{eff} }} \cdot r_{{{\text{O}}_{2} }} \cdot r^{2} = 0 $$

(4.6)

Some exemplary data, i.e. an oxygen profile and the values of effective diffusivities, are shown in Fig. 6.

Fig. 6

Diffusion of oxygen inside A. terreus pellets: a measurement of oxygen profile in an individual pellet; solid line represents the solution of Eq. 4.6 (selected data from [28]) and b the effect of pellet diameter on effective diffusivity in A. terreus pellets (upon tabularized data from [28])

The determined values for A. terreus pellets from about 1,700 to 500 μm² s⁻¹ were similar to the ones as in other fungal systems, although they were found as the parameters of model equation and determined in the stationary pellets motionlessly submerged in the cultivation broth. To compare, the relative D _eff for A. niger pellets ranged from 1,960 to 2,799 μm² s⁻¹. Dependent on pellet density, it decreased even down to 1,120 μm² s⁻¹ [33].

5 Controlling Fungal Morphology: Application of Morphological Engineering Tools

5.1 Morphological Engineering with Regard to Filamentous Organisms

There are several techniques to influence fungal morphology in the cultivation of filamentous organisms (both fungi and prokaryotic Streptomyces). They can be divided into the classical approach and morphological engineering techniques [37] The classical approach covers the following methods: spore suspension preparation (manipulating with number of spores), changing of process parameters (e.g. pH and pO₂ shifting), changing of medium compositions (varying carbon and/or nitrogen source) and, above all, changing of hydrodynamic conditions in the bioreactor (shear stress induced by the impeller and aeration). The newer morphological engineering approach seems to be more subtle with regard to microorganisms as it acts on the level of the formation of pellets.

Filamentous fungi (and Streptomyces) cultures are evolved from spores. It often leads to obtaining various morphological forms of them. The importance of the morphological form of the filamentous fungi was already discussed in Sects. 2, 3 and 4 and strongly emphasized in the review by MacIntyre et al. [46]. What is the most important, in this work, the phrase “morphological engineering” is used as a keyword for the first time and defined as “tailoring morphologies for specific bioprocesses” [46].

The controversy, which morphological form is more useful for the formation of the given metabolic product, is always the matter of many discussions. Here, a good example was citric acid produced by A. niger. Never was it unequivocally said, which form is better [54].

There are two mechanisms of spore agglomeration in filamentous fungi dependent on their genera. In Penicilli, one observes the agglomeration of filaments and in Aspergilli the agglomeration of spores. In the case of prokaryotic Streptomyces, the pellet is formed from the individual spore [47, 51, 55].

In filamentous fungi, the size of pellets to be formed is the issue of the number of spores used. The higher number of spores is introduced to the preculture medium, the smaller pellets are formed. It is also possible that the dispersed mycelium occurs, if the number of spores is high enough [47]. This observation most likely became the foundation of morphological engineering. Various methods can be then applied to influence the process of spores agglomeration and this way to change the fungal morphology. There are several morphological engineering tools that can be used to act on the formation of fungal agglomerates. These are the following: (1) addition of mineral microparticles to the broth at the various stages of cultivation [20–23, 28, 29], called a microparticle-enhanced cultivation (MPEC) by [35], (2) change of broth osmolality [70] and (3) change of broth viscosity [53]. The applications of morphological engineering techniques to the filamentous microorganisms are collected in Table 5.

Table 5 Selected most important approaches to use morphological engineering tools in the cultivation of filamentous organisms

In all cases, the authors declared better productivity of the desired metabolite owing to the application of the morphological engineering technique. Generally, the mechanism of action was similar in all cases. The agglomerates of biomass obtained in the submerged culture, namely fungal pellets, had their structure changed because of the undertaken actions. The pellets got smaller and looser, what must have facilitated transport of nutrients into the cells and it was reflected in the productivity of a given metabolite.

5.2 Morphological Engineering for Lovastatin Production

The studies concerning the application of morphological engineering techniques for lovastatin production by A. terreus are limited (see Table 5). Actually, there are two publications, in which this issue was studied [28, 29] and all the conclusions were drawn upon shake flask culture of A. terreus (Table 3). The authors tested the addition of microparticles: talc and aluminium oxide. It was a two-stage cultivation: 24-h preculture and main culture. Talc powder occurred to be more efficient in A. terreus cultivation system. Also due to the fact that the microparticles act on the level of spore agglomeration, they had to be added to the preculture. It was the most important finding of these works, i.e. the stage, at which the microparticles should be added to the process. Only then, both the size and structure of A. terreus pellets were significantly changed and the positive effect on lovastatin titre was observed. Pellets once formed are not quite sensitive towards the action of microparticles, and in the case of A. terreus, the process of pellet formation was actually finished within 24 h in the preculture as earlier claimed by Bizukojc and Ledakowicz [11]. The increase of lovastatin titre with the decrease of fungal pellets diameter in the morphologically engineered culture confirmed the previous findings dealing with the relation of pellet diameter and lovastatin production [11]. The level of 12 g L⁻¹ talc powder in the preculture occurred to be optimum for further evolution of the mycelium and lovastatin production in the shake flask culture (even a 50 % increase of its titre) [28]. The experiments are being continued by these authors and their preliminary results indicate that the scale-up of lovastatin production by A. terreus with the use of talc microparticles to the 5.3-L working volume bioreactor was easy. It is due to the fact that the action of the microparticles takes place in the shake flask preculture step. Thereby, the inoculum was somewhat modified and further evolution of the fungus in the production medium either in shake flask or STB was influenced by its physiological and morphological state. In the bioreactor, the increase of lovastatin titre occurred to be even higher than that in shake flasks. Comparing to the control runs, it was doubled in the batch mode and even 2.5-fold increase was observed in the glycerol-fed fed-batch mode (publication in preparation).

It can be concluded from the statements above that MPEC of the lovastatin producer A. terreus is effective and future prospects are very promising.

6 Various Types and Operational Modes of Bioreactors to Produce Lovastatin

A bioreactor is the basic tool for bioprocess engineering research and the equipment without which there would not be any industrial production of useful metabolites. With regard to lovastatin biosynthesis by A. terreus in the submerged culture, there are quite many works, in which the experiments were conducted in bioreactors. Referring to the construction, actually type of bioreactor, mainly STBs of various working volume were used. A fluidized bed bioreactor was applied by only one research team [60–63]. One publication deals with an internal loop airlift bioreactor [31].

The majority of experiments were conducted in two operational modes of bioreactors, i.e. batch mode and various fed-batch modes. In the latter ones, higher metabolite titres are usually obtained. As there are several fed-batch modes of bioreactor operation and sometimes various names are used for it, here the classification of Moser [50] is going to be used irrespective of the fact how the authors of the given publication named it. In almost all cases of lovastatin production, two fed-batch modes have been used so far: either discontinuous fed-batch (feeding as an impulse flow in the set intervals) or continuous fed-batch mode, in which the feeding solution is pumped continuously with a constant or not constant rate to the bioreactor.

One of the earliest scientific works, in which lovastatin biosynthesis was studied in the bioreactor, was performed by Novak et al. [52]. They used a 15-L STB and two operational modes of the bioreactor: batch and discontinuous fed-batch at the initial glucose concentration of 100 g L⁻¹. Their lovastatin titres in the batch mode were different dependent on the set oxygen saturation but fast glucose utilization and its deficiency (below 10 g L⁻¹) signalized by dissolved oxygen level made these authors to apply discontinuous feeding with glucose solution at 150 h. The authors called their process as repeated fed-batch, but they did not write, whether during the feeding event a portion of broth was pumped out of bioreactor. Feeding allowed for regaining the activity of the fungus and higher lovastatin titre compared to the batch run. Next feeding step at 250 h occurred to be ineffective.

The work of Hajjaj et al. [32] was only aimed at testing various types of media, complex and synthetic ones, for lovastatin production by A. terreus ATCC 74135, but they applied 7- and 15-L STBs in the batch mode. They used constant aeration rate (vvm = 1 L_air L⁻¹ min⁻¹) and agitation (400 rpm). In the discussion, they did not refer to process conditions in the bioreactor.

The experiments of Kumar et al. [38] were made in the largest bioreactor of all discussed here. They cultivated a mutant originated from A. terreus ATCC20541 in an indigenously designed 1,000-L STB. It was equipped with four baffles, and three six-bladed Rushton turbines (tank diameter was 780 mm and impeller diameter 320 mm). Due to the scale of the bioreactor, they had to use a two-stage preculture preparation (the second stage in a smaller bioreactor). Using a highly complex media (containing three carbon sources: glucose, maltodextrin, starch and three nitrogen sources: corn steep liquor, yeast extract and peptonized milk), they carried out the batch and discontinuous fed-batch experiments (they actually named it repeated batch, although no medium was withdrawn from the bioreactor) fed with maltodextrin solution. They claimed the increase in lovastatin titre from 1,270 to 2,000 mg L⁻¹ in the fed-batch run.

Two types of bioreactors and various operational modes can be found in the publications from University of Almeria [17, 60, 61, 63].

Casas Lopez et al. [17] applied a 5-L STB in the batch mode for A. terreus ATCC20542. They studied the influence of various agitation speed (300, 600, 800 rpm) on the run of lovastatin formation in conjunction with the issues of fungal morphology, broth rheology and aeration of the broth (see Sects. 2, 3 and 4). Various aeration gases were used by them, i.e. air and oxygen-enriched air. They concluded that the highest speed of impeller 800 rpm irrespective of the aeration gas led to smaller pellets and worse lovastatin titre (below 40 mg L⁻¹). In their next work, a 17-L FBB (bubble column) for lovastatin production in the batch mode was applied [63]. Here, they studied the effect of various organic nitrogen levels and aeration for the process. In 2007, the same authors proposed a three-stage operational mode of the same FBB. The process started with the batch mode lasting from 4 to 7 days; next, it was fed with a fresh medium (2.4 L), and after 24 h, the semi-continuous phase occurred, in which the filtered broth was pumped in and out of the bioreactor (biomass was retained in the system). Batch runs were used to get reference data; nevertheless, the positive effect of the new strategy was not very significant. This strategy was repeated in another publication [61], but this time, the fed-batch stage was omitted and the feeding media in the semi-continuous mode were different. These were the complete initial medium, the medium without nitrogen source and the medium without carbon and nitrogen source. Feeding with the complete medium gave the worst results. The positive effects of the other two feeding strategies for lovastatin production were similar. All the works from this team are difficult to evaluate with regard to the positive effects of fed-batch or semi-continuous strategies, as theses authors never supplied data concerning carbon source (lactose) utilization.

Bizukojc and Ledakowicz [10] studied lovastatin formation by A. terreus ATCC20542 in a 2-L STB in batch and discontinuous fed-batch mode. What is interesting, apart from lovastatin, they traced for the first time the formation of (+)-geodin in the bioreactor. Their important finding concerning the operation of the bioreactor for lovastatin production in the batch mode was the introduction of pH control, never suggested in the previous works, with concentrated carbonates solution at the levels 7.6 and 7.8. It depressed by-product (+)-geodin formation and enhanced lovastatin production. They also confirmed that feeding of the batch culture with a carbon substrate led to the increase in lovastatin titre as lovastatin is believed to be strongly dependent on carbon substrate availability. There it was the discontinuous fed-batch mode and the bioreactor was fed with concentrated lactose solution. The solution was added when lactose concentration in the broth started to be deficient.

The work of Gupta et al. [31] is to a highest extent different from all the works presented above and below. They used strain A. terreus NRLL255. The authors proposed the continuous mode of bioreactor operation for lovastatin production. The biomass was either in the form of fungal pellets or immobilized hyphae on siran particles. They used an internal loop airlift bioreactor of 5-L working volume. On the contrary to the previous works (Rodriguez Porcel et al. [60, 61]), biomass was not retained in the bioreactor, but continuously withdrawn from the bioreactor. The continuous mode started after 72 h of the batch process, and the effect of varied of dilution rates from 0.01 to 0.05 h⁻¹ was studied. The optimum value of dilution rate at about 0.02 h⁻¹ and wash-out rate at 0.045 h⁻¹ was found. The authors claimed that they obtained steady states at each studied dilution rate. It may be discussible as fungal species differentiate and their cells are never identical. The most important achievement of this work is that these researchers successfully ran their continuous cultivation system for 45 days. Lovastatin productivity (volumetric formation rate) in the continuous mode was equal to 0.022 g L h⁻¹ and 0.0255 g L⁻¹ h⁻¹ (at the most optimum vvm = 0.6 L_air L⁻¹ min⁻¹) for pellets and immobilized biomass, respectively, and its concentration between 1.1 and 1.2 g L⁻¹ [31]. It is clearly seen that immobilized system did not occur much better.

The only work that focused on the impact of bioreactor scale on lovastatin production was reported by Pawlak et al. [59]. The variety of cultivation data is presented there. They come from 150-mL shake flasks, 2-L and 5-L STBs. At first glance, it seemed that shake flasks were generally a better “bioreactor” for lovastatin production by A. terreus than a “real” bioreactor, even when the same medium composition was used. Thus, there was a need to tune cautiously the conditions of the cultivation in the bioreactor to achieve similar titres as in shake flasks. To these factors belong the valid aeration to achieve comparable substrate utilization rate and pH control, which was previously applied by Bizukojc and Ledakowicz [10].

The latest work from Pawlak and Bizukojc [58] proved upon the continuous fed-batch experiment in a 5-L STB that feeding profile is not the sole factor that may influence lovastatin formation by A. terreus. No direct and clear correlation between the feeding profile, either constant or varied, nor feeding substrate (lactose and/or glycerol) was found and the hypothesis about the other factors influencing lovastatin formation in the bioreactor was proposed. Much attention in this article was for the first time devoted to the issue of redox potential of the culture broth and assimilation of bicarbonate ions from the pH correction solution. The authors concluded that the best lovastatin titres correlated with steep decrease of redox potential in the first hours of the process and high rate of inorganic carbon assimilation. These two process parameters were shown to have the association with the biochemical mechanism of lovastatin production [58].

7 Kinetic Modelling of Lovastatin Biosynthesis

7.1 Lovastatin Formation Kinetics

The issue of product formation kinetics is not an easy task, especially with regard to secondary metabolites as there is a plethora of kinetic expressions in literature to describe the formation of a metabolic product. In the most classical approach, product formation kinetics can be divided into four types upon the correlation between product specific formation rate and specific biomass growth rate. These are (1) growth-associated product formation, (2) mixed growth-associated product formation (two phase are then present growth-associated and non-growth-associated phase, described usually by Luedeking-Piret equation, (3) non-growth-associated product formation and (4) negative correlation between product formation and biomass growth [50]. Nevertheless, in some cases metabolite formation mechanism is complicated and none of these cases can be attributed to them.

With regard to lovastatin, this aspect was also considered; however, practically no articles were exclusively devoted to it. Various authors rather expressed their opinions about this fact discussing the other issues connected with lovastatin production by A. terreus. Furthermore, the opinions are to a certain extent divided. They are all collected in Table 6 (articles concerning kinetic models are not included).

Table 6 Types of association of lovastatin formation with biomass growth

The opinion that lovastatin formation is mixed associated with biomass growth dominates (Table 6). It is the most difficult to agree with the opinion of Hajjaj et al. [32] that starvation is required for lovastatin formation, as all other authors associate lovastatin production with the sufficient amount of carbon source in the culture (see Sect. 6 too).

Quantitative data concerning lovastatin formation kinetics, e.g. the values of specific lovastatin formation rate, are not frequently met in literature. Hajjaj et al. [32] found that in the late phase of cultivation, when the complex medium was used, it was equal to 0.034 mg LOV g X⁻¹ h⁻¹, while in the chemically defined medium (with sodium glutamate as the N-source) it was higher reaching 0.093 mg LOV g X⁻¹ h⁻¹). In the articles coming from Lodz University of Technology team several times, lovastatin formation rate was estimated and it reached even 0.25 mg LOV g X⁻¹ h⁻¹ in the medium with lactose and yeast extract (Bizukojc and Ledakowicz [9, 11]. It was twice higher (up to 0.5 mg LOV g X⁻¹ h⁻¹), when the mixture of glycerol and lactose was used as the carbon sources in the discontinuous fed-batch system [56]. In this work, the changes of specific lovastatin formation rate in time were also shown and its highest values were always observed in the trophophase.

7.2 Mathematical Models to Describe Lovastatin Production by A. terreus

In this section, a critical review of the so-far-published mathematical model for lovastatin biosynthesis is going to be presented. The advantages and drawbacks of these models are going to be discussed.

The oldest model for lovastatin formation by A. terreus can be found in Liu et al. [43]. This model belongs to the class of morphologically structured models. It means that the hyphae were divided into compartments of various morphological and physiological properties. The differentiation of hyphae was also taken into account. Nevertheless, this model is not fully original as these authors adopted the model for penicillin production by Penicillium chrysogenum. At the same time, they also used several model parameters for P. chrysogenum, especially the part of the model concerning the differentiation of hyphae was directly taken from P. chrysogenum model. It can be regarded as a certain drawback as Liu et al. [43] did not show any evidence that the differentiation process in Penicilli and Aspergilli is the same. Furthermore, the morphology of these two genera can be different due to mechanism of pellet formation (see Sects. 2 and 5).

Some parameters were estimated upon their own experimental data from a 10-L bioreactor. Finally, they verified it upon the experimental data from an industrial scale 1,000-L bioreactor. The main assumptions and equations of the model are as follows. There were three zones of the mycelium distinguished, i.e. zone M (z_M) to denounce actively growing hyphae, zone N (z_N) to denounce non-growing hyphae and zone D (z_D) of deactivated cells. Zone M could be transformed with rate r _N into zone N in accordance with the equation:

$$ r_{\text{N}} = \frac{{{\text{k}}_{{{\text{D}}1}} }}{{{\text{c}}_{\text{S}} + {\text{K}}_{{{\text{D}}1}} }} \cdot {\text{z}}_{\text{M}} $$

(7.1)

where k_D1 and K_D1 are the constants, and zone N with rate r _D into zone D in accordance with equation:

$$ r_{\text{D}} = {\text{k}}_{{{\text{D}}2}} \cdot {\text{z}}_{\text{N}} $$

(7.2)

where k_D1 and k_D2 are rate constants of this process and K_D1 is the saturation constant.

Carbon substrate (hydrolysed starch denounced as c_S) was assimilated by zone M for growth

$$ r_{\text{M}} = \mu_{{\hbox{max} {\text{AT}}}} \frac{{{\text{c}}_{\text{S}} }}{{{\text{c}}_{\text{S}} + {\text{K}}_{\text{S}} }} \cdot {\text{z}}_{\text{M}} $$

(7.3)

where μ _maxAT—maximum specific biomass growth rate and K_S is Monod constant.

Nitrogen substrate was not taken into account, which can be regarded as another drawback due to its inhibitive action with regard to lovastatin formation [16].

The most important equation for lovastatin production (c _P) with rate r _P was presented in the form:

$$ r_{\text{P}} = k_{\text{P}} \cdot \frac{{c_{S} }}{{K_{\text{P}} + c_{S} \cdot \left( {1 + \frac{{c_{S} }}{{K_{1} }}} \right)}} \cdot \left( {{\text{z}}_{\text{N}} + \gamma \cdot {\text{z}}_{\text{M}} } \right) - k_{\text{D}} \cdot c_{\text{P}} $$

(7.4)

where k _P is product (lovastatin) formation rate constant, k _D lovastatin decay rate and γ takes the participation of zone M in product formation into account.

The participation of both growing and non-growing hyphae in lovastatin formation indicates that these authors assumed mixed growth-associated product formation. It is here not understandable why glucose is regarded to be inhibitive in this system, as actually no other authors ever postulated it. The term of lovastatin decay is a good idea to describe frequently observed phenomenon of decreasing lovastatin concentration.

Substrate was assumed to be consumed by the actively growing zone to form biomass (X_AT) in accordance with Eq. 7.5, in which also the maintenance term (m) was included.

$$ r_{\text{SC}} = - \frac{1}{{Y_{{{\text{M}}/{\text{S}}}} }} \cdot \mu_{\text{maxAT}} \cdot \frac{{c_{S} }}{{K_{S} + c_{S} }} \cdot {\text{z}}_{\text{M}} - m \cdot {\text{X}}_{\text{AT}} $$

(7.5)

where Y_M/S is a yield of actively growing zone on substrate.

The fit of this model to the experimental data occurred to be very good.

The other model was proposed by Bizukojc and Ledakowicz [8]. This model was unstructured. It was formulated for the growth of A. terreus on an individual carbon substrate, lactose (LAC). Apart from lactose, organic nitrogen (N), lovastatin (LOV) and biomass (X) were balanced. It made four equations to describe both batch and fed-batch bioreactor.

The assumptions of this model were as follows. Lactose was regarded as a sole carbon source in the studied system. Amino acids originated from yeast extract were not utilized as a carbon source irrespective of lactose and yeast extract concentrations. Contois model (saturation constants K _LAC and K _N) which takes the amount of biomass into account was used as the limitation term in all rate expressions. Yeast extract was the sole nitrogen source. The excess of nitrogen exerted an inhibitive effect (K _I,N and $K_{{{\text{I}},{\text{N}}}}^{\text{LOV}}$) on lovastatin biosynthesis and lactose uptake. Mevinolinic acid (lovastatin) biosynthesis was mixed growth-associated. Lactose was both utilized for biomass formation (yield coefficient Y _X/LAC) and biosynthesis of lovastatin (yield coefficient Y _LOV/LAC). Therefore, two terms for these phenomena (growth-associated $q_{\hbox{max} }^{\text{LOV}}$ and non-growth-associated k _LOV product formation and substrate utilization) were applied in lactose and lovastatin balance. All that resulted in the following forms of equations to express the specific rates of lactose uptake (σ _LAC), nitrogen uptake (σ _N)_,, lovastatin formation (π _LOV) and biomass growth (μ):

$$ \begin{aligned} \sigma_{\text{LAC}} & = - \frac{1}{{Y_{{{\text{X}}/{\text{LAC}}}} }} \cdot \mu_{\hbox{max} } \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}} \cdot c_{\text{X}} }} \cdot \frac{{K_{{1,{\text{N}}}} }}{{K_{{1,{\text{N}}}} + c_{\text{N}} }} \\ & \quad - \frac{1}{{Y_{{{\text{LOV}}/{\text{LAC}}}} }} \cdot q_{\hbox{max} }^{\text{LOV}} \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}}^{\text{LOV}} \cdot c_{\text{X}} }} \cdot \frac{{K_{{1,{\text{N}}}}^{\text{LOV}} }}{{K_{{1,{\text{N}}}}^{\text{LOV}} + c_{\text{N}} }} \\ \end{aligned} $$

(7.6)

$$ \sigma_{\text{N}} = - \frac{1}{{Y_{{{\text{X}}/{\text{N}}}} }} \cdot \mu_{\hbox{max} } \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}} \cdot c_{\text{X}} }} $$

(7.7)

$$ \pi_{\text{LOV}} = q_{\hbox{max} }^{\text{LOV}} \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}}^{\text{LOV}} \cdot c_{\text{X}} }} \cdot \frac{{K_{{1,{\text{N}}}}^{\text{LOV}} }}{{K_{{1,{\text{N}}}}^{\text{LOV}} + c_{\text{N}} }} + k_{\text{LOV}} \cdot c_{\text{LAC}} $$

(7.8)

$$ \mu = \mu_{\hbox{max} } \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}} \cdot c_{\text{X}} }} $$

(7.9)

where K _LAC, K _N and $K_{\text{LAC}}^{\text{LOV}}$ are Contois-type saturation constants and c _LAC, c _N, c _LOV and c _X are concentrations of lactose, organic nitrogen, lovastatin and biomass, respectively.

The parameters of the model were either directly determined from the experimental data, namely μ _max and yield coefficients, or identified with the use of the optimization algorithm. The data from shake flask experiments (of 150 mL working volume) performed at various concentrations of carbon and nitrogen were used to find all model parameters. A separate set of data (also from shake flask culture) was used for its verification. Additionally, the model was tested on the set of experimental data coming from the discontinuous fed-batch process (in shake flask). Ultimately, another verification of this model with the use of the experimental data from the bioreactor runs was later published by Bizukojc [6]. The main drawback of this model is its simplicity, which hardly represent the biological phenomenon during A. terreus growth, moderately good fit of the simulated curves with experimental data. It especially concerned the character of biomass curve.

This model was later extended by Pawlak and Bizukojc [57] for a two carbon substrates system. Most symbols used in it are the same as above. The assumptions of the model were very similar. The main difference was that two carbon sources were used, i.e. lactose and glycerol (GLC). Due to the experimental observations that these substrates were utilized consecutively, first glycerol (with yield Y _X/GLC), then lactose, it was assumed that glycerol inhibits lactose uptake. Lovastatin formation was assumed to be mixed growth-associated (expressed by yields Y _LOV/X, Y _LOV/LAC and rate constant $q_{\hbox{max} }^{\text{LOV}}$). The equations of this model, expressed as above, in the forms of specific rates σ _LAC, σ _GLC, σ _N, π _LOV and μ, were as follows:

$$ \begin{aligned} \sigma_{\text{LAC}} & = - \frac{1}{{Y_{{{\text{X}}/{\text{LAC}}}} }} \cdot \mu_{\hbox{max} } \cdot \frac{{c_{\text{GLC}} }}{{c_{\text{GLC}} + K_{\text{GLY}}^{\text{X}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}}^{\text{X}} \cdot c_{\text{X}} }} \cdot \frac{{K_{{{\text{I}},{\text{GLC}},1}} }}{{K_{{{\text{I}},{\text{GLC}}.1}} + c_{\text{GLC}} }} \\ & \quad - \frac{1}{{Y_{{{\text{LOV}}/{\text{LAC}}}} }} \cdot q_{\hbox{max} }^{\text{LOV}} \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}}^{\text{LOV}} \cdot c_{\text{X}} }} \cdot \frac{{K_{{{\text{I}},{\text{N}}}}^{\text{LOV}} }}{{K_{{{\text{I}},{\text{N}}}}^{\text{LOV}} + c_{\text{N}} }} \cdot \frac{{K_{{{\text{I}},{\text{GLC}},2}} }}{{K_{{{\text{I}},{\text{GLC}},2}} + c_{\text{GLC}} }} \\ \end{aligned} $$

(7.10)

$$ \begin{aligned} \sigma_{\text{GLC}} & = - \frac{1}{{Y_{{{\text{X}}/{\text{GLC}}}} }} \cdot \mu_{\hbox{max} } \cdot \frac{{c_{\text{GLC}} }}{{c_{\text{GLC}} + K_{\text{GLY}}^{\text{X}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}}^{\text{X}} \cdot c_{\text{X}} }} \\ & \quad - \frac{1}{{Y_{{{\text{LOV}}/{\text{GLC}}}} }} \cdot q_{\hbox{max} }^{\text{LOV}} \cdot \frac{{c_{\text{GLC}} }}{{c_{\text{GLC}} + K_{\text{GLC}}^{\text{LOV}} \cdot c_{\text{X}} }} + \frac{{K_{{{\text{I}},{\text{N}}}}^{\text{LOV}} }}{{K_{{{\text{I}},{\text{N}}}}^{\text{LOV}} + c_{\text{N}} }} \\ \end{aligned} $$

(7.11)

$$ \sigma_{\text{N}} = - \frac{1}{{Y_{{{\text{X}}/{\text{N}}}} }} \cdot \mu_{\hbox{max} } \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}}^{\text{X}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}}^{\text{X}} \cdot c_{\text{X}} }} $$

(7.12)

$$ \begin{aligned} \pi_{\text{LOV}} & = Y_{{{\text{LOV}}/{\text{X}}}} \cdot \mu_{\hbox{max} } \cdot \frac{{c_{\text{GLC}} }}{{c_{\text{GLC}} + K_{\text{GLY}}^{\text{X}} \cdot c_{\text{X}} }} \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}}^{\text{X}} \cdot c_{\text{X}} }} \\ & \quad + q_{\hbox{max} }^{\text{LOV}} \cdot \frac{{c_{\text{LAC}} }}{{c_{\text{LAC}} + K_{\text{LAC}}^{\text{LOV}} \cdot c_{\text{X}} }} \cdot \frac{{K_{I,N}^{LOV} }}{{K_{{{\text{I}},{\text{N}}}}^{\text{LOV}} + c_{\text{N}} }} \\ \end{aligned} $$

(7.13)

$$ \mu = \mu_{\hbox{max} } \cdot \frac{{c_{\text{N}} }}{{c_{\text{N}} + K_{\text{N}}^{\text{X}} \cdot c_{\text{X}} }} $$

(7.14)

where $K_{\text{LAC}}^{\text{X}} ,K_{\text{GLY}}^{\text{X}} ,K_{\text{LAC}}^{\text{LOV}}$ and $K_{\text{N}}^{\text{X}}$ are Contois-type saturation constants, and K _I,GLC,1 and K _I,GLC,2 are inhibition constants referring to glycerol.

It is important to notice here that in this model, several limitation Contois terms were eliminated. It was done for the sake of better robustness of this model [57].

The latest approach to modelling of lovastatin production, but with the participation of another microorganism A. flavipes was shown by Gomes et al. [27]. Although it was not A. terreus, few comments should be added about it. First of all, this model was formulated for the fed-batch system with glucose, lactose (C-sources) and sodium glutamate (N-source). Also lovastatin, biomass, oxygen were balanced. The expressions for the reaction rates were as follows. Biomass growth on glucose was assumed to be influenced by dissolved oxygen level and expressed as

$$ \mu_{1} = \mu_{\text{M}} \frac{g}{{K_{\text{G}} + g}} \cdot \frac{{c_{L} }}{{c_{L}^{*} }} $$

(7.15)

where μ _M is maximum biomass growth rate, g—glucose concentration, and c _L and $c_{L}^{*}$ oxygen concentration, actual and saturation, respectively.

Biomass growth on lactose was expressed by Eq. (7.16)

$$ \mu_{2} = \mu_{\text{M}} \frac{l}{{K_{L} + l}} \cdot \left( {1 - \kappa } \right) $$

(7.16)

and product formation on lactose by Eq. (7.17)

$$ \pi = \pi_{\text{M}} \frac{l}{{K_{L} + l}} \cdot \kappa $$

(7.17)

where π _M—maximum lovastatin formation rate and l—lactose concentration, and at the same time, dependent on ratio κ

$$ \kappa = \frac{n}{n + g} $$

(7.18)

which expressed the presence of sodium glutamate n (N-source) in the medium. The interesting thing is that the structure of this model was checked with the use of control theory methods for its correctness. The authors also claimed that it was found to be suitable for process control applications [27]. Its undoubtful advantage is taking of the oxygen level in the culture broth into account.

7.3 Linear Growth of Biomass in A. terreus. Returning to Fungal Morphology

One of the most important issues connected with A. terreus growth kinetics is usually its untypical growth curve. It can be found in the variety of publications. In the growth phase, namely trophophase, as it is traditionally named for filamentous fungi, the character of growth is hardly exponential (inter alia: [27, 42]).

Some authors, like Casas Lopez et al. [17], did not show biomass concentration points from the beginning of the process but after 50 h of the cultivation. All in all, it is unlikely to find in literature the exponential growth curve for A. terreus. A linear biomass growth observed also by Bizukojc and Ledakowicz [8–10] and Pawlak and Bizukojc [57] seems to be untypical. Lack of typical exponential phase may make it difficult to model A. terreus growth as the existence of this phase is often assumed in the kinetic models, including the ones described above. A closer look to this phenomenon was made by Pawlak and Bizukojc [57]. They thoroughly studied the very early stages of A. terreus growth in the shake flask culture and found that the exponential growth phase lasted not longer than 12 h since the inoculation with the 24-h preculture (Fig. 7).

Fig. 7

Untypical biomass growth during lovastatin biosynthesis by A. terreus on lactose as a sole carbon source a linear growth phase between 12 and 96 h of the experiment, b determination of μ _max upon the data from the first twelve hours of the run c experimental data versus simulation made for the 12-h exponential growth (graph prepared upon the experimental data from [57])

Later, it changed into the linear growth phase. This change was easily correlated with the size of pellets formed, as they were usually not bigger that 500 μm in the exponential growth phase. As long as the pellets remained small enough, no additional growth limitations were present in the system and the sine qua non condition, evolving from the definition of exponential growth phase about unlimited growth was fulfilled. Further increase in pellet diameter and change of its structure led probably to the decrease of oxygen effective diffusivities (see Sect. 4.2) in the pellets and oxygen limitation. These findings remain also in agreement with the observation of Pawlak and Bizukojc [58]. A strong peak of oxygen utilization (increasing air flow rate in the bioreactor to hold the set 20 % dissolved oxygen level) was observed within the first 12 h of cultivation in the 5-L STB.

To conclude, the linear growth of A. terreus shows how important for the investigations of lovastatin biosynthesis is to take the issue of fungal morphology into account.

8 Future Prospects

The bioprocess engineering aspects of lovastatin biosynthesis by A. terreus were studied, in our subjective opinion, at the various levels of details. There are many studies in literature concerning lovastatin production in bioreactors of various types, sizes and, what is the most important, of various operational modes (from batch, through the variety of fed-batch, up to continuous). The fairly clear image of the most optimum bioreactor set-up to produce lovastatin by A. terreus can be drawn upon them. Also a lot of rheometric and viscosity data for A. terreus broths obtained at various process conditions and bioreactors supply the sufficient knowledge to associate the run of lovastatin production process with varying rheological properties of the fungal broth. Also there are numerous data concerning A. terreus morphology.

However, there are several engineering issues with regard to lovastatin biosynthesis by A. terreus that in our opinion still require thorough studies. These are (1) issue of culture aeration with regard to mass transfer, (2) application of morphological engineering techniques for enhancing of lovastatin production and (3) lovastatin formation kinetics.

The first point should be studied at the following three levels, i.e. oxygen transfer from gas to liquid phase, from liquid phase to solid (mycelium) phase and at the level of oxygen diffusion inside fungal agglomerates (pellets). The issues connected with oxygen transfer from gas to liquid phase seemed to be studied in detail in many papers as the values of convective mass transfer coefficients for A. terreus broths were determined and a variety of aeration strategies to hold the desired pO₂ levels were applied. Nevertheless, lack of direct correlations and clear conclusions associating the amount of carbon substrate introduced to the culture with oxygen concentration levels and lack of the correlations between oxygen uptake rate (OUR), k _L a and lovastatin formation makes this area of knowledge still incomplete. Also the changes of apparent viscosity and rheological parameters of the cultivation broth may have their contribution in these correlations. Furthermore, due to the strong experimental limitations, the studies on oxygen transfer into fungal pellets (film surrounding the pellet and intrapellet diffusion) were just began. In our opinion, the hypothesis can be propounded that these steps of oxygen transfer in A. terreus culture may have the predominant influence on the overall efficiency of the lovastatin biosynthetic system. It awaits the verification.

With regard to the second point, i.e. the application of morphological engineering techniques for enhancing of lovastatin production, there are very limited data. As generally, the application of morphological techniques is extremely promising upon the example of other filamentous fungi species and metabolites and at the same time the application of these techniques is not expensive even in the large scale, the research regarding lovastatin production by A. terreus should be directed into this route. Analysing literature data and own experiences the most significant factor that undoubtedly influence lovastatin production to the highest extent is fungal morphology. It cannot but have the effect on oxygen supply to the fungus, which connects this point with the issues above. That is why morphological engineering techniques shall prove successful in increasing the productivity of A. terreus for lovastatin biosynthesis.

Referring to the third point, it is known that the association of product formation kinetics with biomass growth can be fairly complicated. But it does not exclude thorough studies on this subject, although the elegant kinetic correlation would not be found. But the discrepancy in the opinions about lovastatin formation kinetics is at least anxious. It can be supposed that it is more dependent on growth conditions than one expects and the changes in medium composition or bioreactor processes conditions influence on it. It should be verified too.