Investigation into struvite precipitation: A commonly encountered problem during fermentations on chemically defined media

Chemically defined mineral media are widely used in bioprocesses, as these show less batch to batch variation compared with complex media. Nonetheless, the recommended media formulations often lead to the formation of precipitants at elevated pH values. These precipitates are insoluble and reduce the availability of macronutrients to the cells, which can result in limiting growth rates and lower productivity. They can also damage equipment by clogging pipes, hoses, and spargers in stirred tank fermenters. In this study, the observed precipitate was analyzed via X‐ray fluorescence spectroscopy and identified as the magnesium ammonium phosphate salt struvite (MgNH4PO4 × 6H2O). The solubility of struvite crystals is known to be extremely low, causing the macronutrients magnesium, phosphate, and ammonium to be bound in the struvite crystals. Here, it was shown that struvite precipitates can be redissolved under common fermentation conditions. Furthermore, it was found that the struvite particle size distribution has a significant effect on the dissolution kinetics, which directly affects macronutrient availability. At a certain particle size, struvite crystals rapidly dissolved and provided unlimiting growth conditions. Therefore, struvite formation should be considered during media and bioprocess development, to ensure that the dissolution kinetics of struvite are faster than the growth kinetics.

The composition of the fermentation medium is crucial for the success of microbial fermentations.Raw material quality and quantity of the used components significantly affect product titer, yield, and volumetric productivity.Besides, the composition impacts medium costs that affect the overall process' economics, including downstream processing, as the used components can also impact the purification steps and product recovery (Kennedy & Krouse, 1999).
Chemically defined growth media are commonly used during protein production campaigns, as they allow greater batch-to-batch consistency, compared to complex media (Diederichs et al., 2014;Jose et al., 2011;Zhang et al., 2003).In Pichia pastoris processes, media composition is particularly important, because extreme cell densities of more than 200 g/L cell dry weight can be achieved (Heyland et al., 2010) alongside high protein production.Generally, to supply all nutrients required for unlimited growth, high cell density fermentations utilize concentrated culture media.These processes are usually performed in fed-batch operation mode, where the carbon source is gradually dosed into the fermenter.Usually, the feeding is performed at a rate that limits cellular growth by carbon limitation, but all other nutrients should not be growth limiting.
Most of the chemically defined media described for P. pastoris show slight deviations in their composition (Hyka et al., 2010;Invitrogen, 2010;Tolner et al., 2006), as several attempts to optimize the culture medium toward production of recombinant proteins have been made (Matthews et al., 2018).A widely used defined medium is derived from the Invitrogen fermentation protocol (Invitrogen, 2010).However, the concentrations of the media components in this protocol are very high, resulting in the formation of precipitates, as soon as the pH is adjusted towards neutral or alkaline conditions.Heavy precipitation is observed when the pH is greater than 5.0 (Cos et al., 2006;Zhang et al., 2000).
Moreover, Zhang et al. (2005) describe a cloudy appearance for another mineral medium named basal salts medium (BSM), when the pH is adjusted to 5.0.Other media for P. pastoris, such as the FM22 medium (Laroche et al., 1994), also lead to cloudiness at high pH values.
The formation of precipitates in mineral media is not exclusive to P. pastoris media.In several studies, precipitate formation is described for Escherichia coli and Arxula adeninivorans media formulations (Knabben et al., 2010;Knoll et al., 2007).Therefore, precipitate formation is a universal effect that can be observed in chemically defined mineral media.Curless et al. (1996) explain this observation by the low solubility of ortho-phosphate (HPO 4 − ) that derives from the potassium dihydrogen phosphate added to the medium.It forms a complex with Mg 2+ and Ca 2+   cations, especially at pH values greater than 5.5.Thus, it is very likely that the observed precipitation is magnesium ammonium phosphate hexahydrate (MgNH 4 PO × 6H 2 O), also known as struvite (Kennedy & Krouse, 1999).It is known that in the formation of the phosphate salt struvite, the divalent magnesium cation can also be substituted by manganese cations (Mn 2+ ) or calcium cations (Ca 2+ ).As a result, designing chemically defined mineral media becomes challenging, as most microorganisms require essential mineral nutrients, such as Mg 2+ , PO 4 3− , and NH 4 + (Kennedy & Krouse, 1999).
Struvite solubility mainly varies depending on the temperature and ionic strength of a solution.The most commonly used thermodynamic solubility product (pK sp ) for struvite has a value of 12.6 (Snoeyink & Jenkins, 1980;Stumm, 1981).A summary of different solubility products can be found in Bhuiyan et al. (2007).Furthermore, the equilibrium strongly depends on the availability of the actual ionic species (e.g. , slight variations in the pH result in more or less favorable conditions for struvite formation (Bhuiyan et al., 2007).
The formation of struvite in chemically defined media is unfavorable for microbial cultivations, as the formed particles are hardly soluble and resistant to shear (Kennedy & Krouse, 1999).Moreover, the precipitate can cause an unbalanced nutrient supply or nutrient starvation.This is particularly important in high cell density fermentations of P. pastoris, as nutrient starvation can lead to reduced growth rates and significantly reduce the productivity of heterologous protein production (Siegel & Brierley, 1989).This is also the case for other microbial hosts.Egli and Fiechter (1981)  Further disadvantages of the observed precipitation include difficulties during aliquoting and cell density measurements, because the cells sediment together with the precipitate during the centrifugation process (Zhang et al., 2000).Moreover, the handling of the equipment can be negatively affected, as hoses, pipes, and spargers can get clogged.Struvite also forms deposits on the surface of heat exchangers or in pipes, which can result in additional maintenance costs (Aage et al., 1997).If the medium is prepared in a separate vessel, transfer of all struvite is a challenge and can cause undefined medium compositions.
In this study, dried medium precipitates from P. pastoris defined medium were analyzed via X-ray fluorescence spectroscopy (XRF) to clarify the chemical nature of the observed precipitated salt.Growth limiting concentrations for Mg 2+ , PO 4 3− , and NH 4 + were determined from breathing activity measurements using the µRAMOS technology (Dinger et al., 2022)

| Strains
The P. pastoris host strain BSYBG11 (Mut S ), obtained from Bisy GmbH (Hofstaetten a. d.Raab, Austria), was used for all media testing experiments.

| Media
All chemicals applied for media preparation were of analytical grade and purchased from Carl Roth GmbH, if not stated otherwise.
For the experiments, the microorganisms were grown in mineral Syn6-MES medium.Syn6-MES medium had the following composition (Hellwig et al., 2005): glycerol and glucose were prepared each as a 500 g/L stock solution and autoclaved separately.dissolved in deionized water and the pH was titrated from 3.0 to 8.0 at an interval of 1 using ammonia solution (30% v/v).Then the media were immediately photographed.This titration procedure was additionally performed with Syn6-MES medium.A summary of main media components is given in Supporting Information S1: Table S1.

| Two stage preculture in shake flasks
Pre-cultures were grown in Syn6-MES medium using 10 g/L glycerol or 10 g/L glucose as carbon source.The liquid culture volume was 10 mL and 125 µL of a cryo-stock was added for inoculation.Cultivations were performed in 250 mL shake flasks at 30°C with a shaking frequency of 350 rpm at a shaking diameter of 50 mm for 10-14 h.To prevent carryover effects of medium components, such as magnesium, phosphate or ammonium ions from the pre-culture, a two-step preculture procedure was conducted.Therefore, the first pre-culture was set up in standard Syn6-MES medium.In the second pre-culture, magnesium, phosphate, ammonium, or all three components were left out, depending on the omitted component in the main culture.The corresponding concentrations are given in the caption of the respective experiment.

| MTP cultivations
For cultivations at 96-well MTP scale, a micro-scale Transfer rate Online Measurement device (µTOM) was used (Dinger et al., 2022).Cultivations were conducted in 96-deepwell MTP (riplate SW, 2.5 mL square deepwell plate; HJ-Bioanalytik GmbH), sealed with a gas-permeable sealing film (AeraSeal™-film; Sigma-Aldrich).The filling volume of each well was 0.6 mL, operated at a shaking speed of 350 rpm, a shaking diameter of 50 mm, at 30°C and a relative humidity higher than 85% in a Kühner Shaker.Initial OD 600 and number of replicates are specified in the caption of the corresponding experiment.

| Elemental component analysis
Two different P. pastoris biomass samples were analyzed, P1 was grown in mineral medium under non-limiting conditions and P2 was grown under phosphate limitation, using Syn6-MES medium (Hellwig et al., 2005).The analysis of the samples was carried out by ZEA-3 at Research Centre Jülich.The elemental composition (C, H, N, S) was determined using a vario cube EL (Elementar, Germany).This device facilitates a high temperature digestion, coupled with dynamic gas separation and detection.The other elements were determined by ZEA-3 using an inductively coupled plasma with optical emission spectroscopy (ICP-OES; Thermo Fisher Scientific Inc.) method (Nischwitz, 2022).

| Determination of precipitate composition
The analysis of the composition of the precipitate was performed by Budenheim (Chemische Fabrik Budenheim KG) using XRF.Commercial struvite from Alfa Aesar (CAS 13478-16-5) (Thermo Fisher Scientific Inc.) was used as reference sample.

| Determination of struvite particle size distribution
A commercial struvite sample from Alfa Aesar (CAS 13478-16-5) (Thermo Fischer Scientific Inc.) and a mortared sample were diluted in 20 mL Isoton II electrolyte from Beckman Coulter.The particle size distribution was measured in a Coulter Counter (A-Cuvette) with an aperture of 100 µm.The resulting distributions were fitted to a Gaussian distribution.

| Determination of maximal oxygen transfer rate and data fitting
The maximal achieved oxygen transfer rate (OTR) was determined for the first peak in the OTR (OTR peak ).If the culture was performed under unlimiting conditions, the observed OTR peak is regarded as OTR peak, unlimited .The resulting relation between the added nutrient amount and the maximal oxygen transfer rate was fitted by a Hill kinetic, given by the following Equation ( 1), with the concentration of the limiting nutrient c, the affinity constant K s and Hill exponent n: 3 | RESULTS AND DISCUSSION 3.1 | Investigating the impact of the pH on the formation of precipitates in commonly used mineral media Zhang et al. (2000) describe the development of medium cloudiness due to precipitate formation, as soon as the pH of mineral medium is adjusted to values larger than 5.0.Therefore, commonly used mineral media, Syn6-MES medium (Hellwig et al., 2005) for shake flasks, and bioreactor media according to Hyka et al. (2010) and Invitrogen (2010) were pH titrated and the results were photographed and summarized in Figure 1.
The Syn6-MES medium, with an initial pH ~5 prior pH adjustment, was titrated with phosphoric acid (85% w/v) or aqueous ammonia solution (25% v/v).The Hyka and Invitrogen media, with an initial pH ~2 before pH adjustment, were only titrated with aqueous ammonia solution (25% v/v).Figure 1 shows the Invitrogen medium is already cloudy at pH 3, whereas the other tested media remain clear.The Hyka medium, which corresponds in its composition to the Invitrogen medium, but with lower concentrations of all components, visualizes the impact of the pH value the best.The turbidity, that is, the amount of precipitate formed, increases with increasing pH value.In comparison, the Syn6-MES medium, which is usually applied in small-scale cultivations, only shows signs of precipitation at pH values larger than 7.The major difference between the investigated culture media is the overall salt concentration.
Additionally, Syn6-MES medium contains citrate, which has chelating properties.Therefore, the presence of bi-valet cations is further reduced, as they are chelated by citrate.Other substances could also affect precipitation.This includes organic acids that can potentially be formed during the cultivation process.The effect varies depending on the used microorganism and applied condition, as this affects the formation of organic acids.As a result, the impact on medium precipitation and medium design needs to be individually considered for every cultivation process.It can be concluded that the precipitation process is not only pH, but also concentration dependent.
To  In Table 1, the amount of measured components ( With the presented analysis method, the exact nature of the observed precipitate could be clarified.Struvite is known to be hardly soluble in water.Therefore, it is relevant to know, whether the salt can entirely resolubilize over time.This is of particular importance, as essential nutrients are bound in the struvite crystals and are no longer available to the cells.This can potentially lead to nutrient limitations that can have a negative effect on cell growth.This problem does not only affect P.
pastoris cultivations, as chemically defined mineral media are widely used for a broad variety of microbes.

| Nutrient limitation in Invitrogen medium due to struvite precipitation
The precipitation of struvite was investigated in the Invitrogen medium (Invitrogen, 2010).Figure 2a shows the total main ion (Mg 2+ , PO 4 3− , NH 4 + , K + , Ca 2+ ) concentrations in the medium in red and the calculated dissolved ion concentrations after struvite precipitation in blue.Struvite precipitation is calculated according to the theoretical thermodynamic solubility given in Supporting Information S1:  S2).A detailed view of Figure 2a for the Mg 2+ concentrations is plotted in Figure 2b.From the total concentration of 1.42 g/L Mg 2+ in the medium, 97.6% precipitates as struvite, leaving only a low dissolved Mg 2+ concentration of 34 mg/L in the medium (Supporting Information S1: Table S2).This could potentially lead to a growth limitation after struvite precipitation.
To estimate the impact of the struvite precipitation on P. pastoris, macronutrient (Mg, P, N) limitation experiments were performed.
Figure 3 shows the results of P. pastoris cultivations with varying Mg 2+ concentrations in the medium.In Figure 3a the course of the oxygen transfer rate OTR over time is depicted.The reference curve at 140 mg/L Mg 2+ for 5 g/L glucose (half concentrated Syn6-MES medium) shows a typical OTR curve for unlimited growth (Anderlei & Büchs, 2001).After a short lag phase of ~12 h, the OTR increases exponentially reaching a peak at about 7 mmol/L/h.After this peak, the OTR drops sharply, due to glucose depletion (Wollborn et al., 2020), ).The fifth row summarizes the analytical result for the precipitate formed during preparation of the medium, according to the Invitrogen protocol at pH = 6 (2nd row in Figure 1).Analysis was performed by Budenheim.
indicating total carbon source consumption, and the end of the cultivation.No further metabolic activity is observed.Reducing the Mg 2+ concentration in the cultivation medium to 14 mg/L does not influence the course of the OTR (Figure 3a).At 7 mg/L and 3.5 mg/L Mg 2+ , the height of the resulting OTR peak is reduced, but the shape of the curve stays invariant.At 1.4 mg/L Mg 2+ , the maximal OTR is significantly reduced to 2 mmol/L/h and no sharp drop can be seen in the OTR course, indicating a strong Mg-limitation.Similar results were obtained by Kottmeier et al. (2009), where 0-3 mg/L Mg 2+ lead to a similar OTR course and Mg-limitation in H. polymorpha cultivation.
Further reducing the Mg 2+ concentration in the medium reduces the maximal OTR.At 0.14 mg/L Mg 2+ no breathing activity can be observed.
In Figure 3b, the maximal oxygen transfer rates depicted in Figure 3a are plotted over the Mg 2+ concentration in the medium.The data is normalized to the added carbon source, which is 5 g/L glucose.The data is fitted according to Equation (1) using a Hill kinetic.Fit parameters are listed in Supporting Information S1: Table S3, line 1.
Struvite precipitation in the Invitrogen medium theoretically leads to a Mg 2+ concentration of 34 mg/L (Supporting Information S1: Table S2).At this concentration, no negative effect on growth is observed.It can be concluded, that the Mg 2+ concentration does not result in a limitation due to struvite precipitation.Therefore, the  S1.Solubility calculations were conducted for the Invitrogen medium (Invitrogen, 2010) with the struvite solubility data from Supporting Information S1: Table S2.Reference Mg 2+ concentration in half-concentrated Syn6-MES medium is 140 mg/L (see Supporting Information S1: Table S1).
Experiments were conducted using a μTOM device.X-axes in (B) normalized with added carbon source (5 g/L glucose).Data fitted to a Hill kinetic.Fit parameters are given in Supporting Information S1: Table S3, line 1.Cultivation conditions: half concentrated Syn6-MES medium (100 mM MES), c Glucose = 5 g/L, OD 600 (0 h) = 0.2, 96 deep square well plate, V = 2.4 mL, V L = 600 μL, T = 30°C, 85% r.  glucose in the medium (Wollborn et al., 2022).After the first OTR peak, two further peaks can be seen at 23 and 26 h, indicating the metabolization of some overflow metabolites (Anderlei & Büchs, 2001;Käppeli, 1986).Methylotrophic yeasts such as P. pastoris are classified as crabtree-negative organisms (Porro et al., 2005).Despite the categorization as crabtree-negative, the P. pastoris wildtype is also known to produce metabolites from the respiro-fermentative pathway including ethanol, pyruvate, acetaldehyde, acetate, and arabitol (Eck et al., 2018;Heyland et al., 2010;Inan & Meagher, 2001;Nocon et al., 2014).The amount of produced overflow metabolites is higher than for the reference in Figure 3a.This is a consequence of the increased glucose concentration from 5 g/L (in Figure 3) to 10 g/L (in Figure 4)., the first OTR peak is reduced, indicating a growth limitation (Kottmeier et al., 2009).Further reducing the PO 4 3− concentration, enhances the limitation.Therefore, Figure 4a shows, that a minimal concentration of 400 mg/L PO 4 3− is needed for unlimited growth at 10 g/L glucose (40 mg PO 4 3− per g glucose).
In Figure 4b the variation of the NH 4 + concentration is shown.A similar effect to the P-limitation in Figure 4a is observed.The results show that cell growth starts to be affected around concentrations of approximately 400-600 mg/L of NH 4 + .Therefore, a minimal concentration of 500 mg/L NH 4 + is needed to avoid a N-limitation at 10 g/L glucose (50 mg NH 4 + per g glucose).Furthermore, the shape of the OTR curves is distinctly different.In Figure 4b the cultures grow exponentially until the N-limitation is reached.This leads to a sharp "bend" in the OTR.In contrary, in Figure 4a, P-limited cultures do not show a sharp bend, when diverging from the unlimited reference.The OTR continues rising, but with a reduced slope, indicating a lower growth rate.Kottmeier et al. (2009) describe a similar behavior for H.
polymorpha.This behavior could be due to internal phosphate pools in the cells.Saccharomyces cerevisiae can store up to 28% phosphate in the form of polyphosphates in the cells (Christ & Blank, 2019).
Further, it has been shown, that Corynebacterium glutamicum continues to grow, even when phosphate is exhausted in the culture medium, by reducing the phosphorus content of the cells (Büchs et al., 1988).The results for the P-limitation are shown in Figure 4e and for the N-limitation in Figure 4f.Analogous to Figure 3, the data is fitted by a Hill kinetic.The evaluated parameters of the fit are given in Supporting Information S1: Table S3, lines 2-5.biomass yield Y X/S of 0.62 g/g is used for glycerol and 0.50 g/g for glucose (data not shown).This is consistent with previously reported values (Garcia-Ortega et al., 2013;Nieto-Taype et al., 2020).
Furthermore, the cultivations for biomass generation for elemental analysis were performed in batch mode in Syn6-MES medium with 10 g/L glucose as carbon source.Cells were grown under unlimited conditions and under P-limited conditions.For this aim, the P-source , or NH 4 + ) uptake rate of the applied microorganism.This may be the case, if nutrient solubilization is determined by surface diffusion from the struvite particles.Low surface to mass ratios for the struvite particle (large particles) may lead to stronger growth limitations than high surface to mass ratios of the particles (small particles).This is schematically illustrated in Supporting Information S1: Figure S3.
To analyze the influence of the solubilization kinetics, struvite particles with two different particle size distributions were generated.& Büchs, 2001).After about 6 h, the culture enters an exponential growth phase, reaching a maximal OTR of 30 ± 1 mmol/L/h after 16 h.This is 6 h earlier than the reference cultivation in Figure 4a and may be explained by variations in inoculation density, leading to varying lag-phases (Palmen et al., 2013).In Supporting Information  S4).Mg and N are not limiting.
Furthermore, the maximal OTR reached during cultivation is reduced and shifted to the right, leading to a longer total cultivation time.For 0.1 g/L struvite, the same trend can be observed.These cultures are limited more strongly than the cultures supplemented with 0.3 g/L struvite.Cultures without struvite show no breathing activity at all.
Due to the equimolar content of PO 4 3− and Mg 2+ in struvite and the significantly higher P content (2.5% w/w P vs. 0.29% w/w Mg) in the cells (see Supporting Information S1: Table S4 for elemental analysis), PO 4 3− can be identified as the limiting component.Furthermore, the growth limited cultures with 0.3 and 0.1 g/L struvite in Figure 7a show the same OTR course characteristic for a P-limited P. pastoris culture, as depicted in Figure 4a,c.This is in accordance with the higher N content of the cells compared with the P content (2.5% w/w P vs. 7.96% w/w N, see Supporting Information S1: Table S4 for elemental analysis).Similar to the P-limited cultures in Figure 7a, a supplementation with larger struvite crystals (d = 21 µm) leads to an earlier growth limitation and lower OTR in .This result matches the data for glucose for P-limited cultures (Figure 7a).For the N-limited culture on glycerol (Figure 7d), the limitation starts at a struvite concentration of 7 g/L (d = 8 µm and d = 21 µm).This result also matches the concentrations determined for cultures grown on glucose (Figure 7b).
To quantify the influence of the solubilization kinetics of the supplemented struvite on the described growth limitations, the height of the first OTR peak of the cultures in Figure 7a-d S3, lines 6-13. Figure 7e  for glycerol cultures reach 34.2 ± 3 mmol/L/h.Taking into account the substrate yields for glucose (Y X/S = 0.50 g/g) and glycerol (Y X/ S = 0.62 g/g), a biomass-specific oxygen demand for unlimited growth of 5.1-5.5 mmol/g/h was calculated.This data is consistent with Charoenrat et al. (2005).By these authors, a specific oxygen demand of 5 mmol/g/h was determined for P. pastoris at maximal growth rate.
For all four conditions (Figure 7e-h), the OTR peaks of the cultures without struvite, but with Mg 2+ , PO 4 3− , and NH 4 + (crossed symbols), reach the saturation at lower macronutrient concentrations than the struvite supplemented cultures (filled and empty symbols).Moreover, with increasing mean struvite crystal diameter from 8 µm (filled symbols) to 21 µm (empty symbols), the saturation is reached at higher macronutrient concentrations.S3, lines 6-13.First preculture was conducted in Syn6-MES medium, second preculture was conducted in Syn6-MES media without Mg, P, and N. Experiments were conducted using the μTOM device.Cultivation conditions: Syn6-MES medium (200 mM MES), c Glucose = 10 g/L or c Glycerol = 10 g/L, OD 600 (0 h) = 0.2, 96 deep square well plate V = 2.4 mL, V L = 600 μL, T = 30°C, 85% r.h., n = 350 rpm d 0 = 50 mm.The lines represent the average of four biological replicates.For clarity, only every 10th measured point is shown as a symbol.Partially st.dev. is barely visible, as it is smaller than data points.
Struvite solubilization is limited by diffusion through the boundary layer around the particles and the available surface area.
An equilibration at 30°C is achieved after 0.3-0.7 h, depending on the crystal structure (Ariyanto et al., 2017;Bouropoulos & Koutsoukos, 2000).A greater crystal surface area A (smaller mean particle size) leads to a linearly higher total diffusive nutrient flow j into the medium.Taking into account Equation (2), the nutrient flow is inversely proportional to the particle diameter (Equation 3) The affinity constant K S (the concentration at which the solubilization speed is half maximal) is inversely proportional to the diffusive nutrient flow j for a diffusion limited struvite solubilization.
This leads to a linear relation between the affinity constant K S and the particle diameter (Equation 4).
The increase in the affinity constant K S is three times stronger for the N-limitation, than for the P-limitation.This may result from the possibility of cells to reduce their phosphorus content (Büchs et al., 1988).

| CONCLUSION
When using mineral media for microbial cultivations, the formation of a precipitate is often observed.In this study, a commonly used medium recipe for P. pastoris cultivations was investigated.This host organism is known for reaching a very high cell density and, therefore, requires a rich mineral medium formulation (Heyland et al., 2010).Previous research has suggested that the observed precipitate appears due to the formation of struvite (MgNH 4 PO 4 × 6H 2 O) (Kennedy & Krouse, 1999).Here, it was proven by XRF that the observed precipitate in the P. pastoris medium recipe is in fact a MgNH 4 PO 4 × XH 2 O salt.
As struvite is quite insoluble, its formation binds macronutrients (Mg 2+ , PO 4 3− and NH 4 + ) that are essential for cell growth.Under thermodynamic equilibrium conditions, a concentration of only 34 mg/L Mg 2+ is available for the cells (see Figure 2).The limiting concentrations for magnesium, ammonium, and phosphate were determined using the µTOM technology (Dinger et al., 2022).The procedure to determine the limiting concentrations was demonstrated using P. pastoris cultivations with glucose as carbon source (Figure 3).It was shown that Mg 2+ becomes growth limiting at concentrations lower than 1.29 mg/g C .As a result, struvite formation had no negative effect on the growth of P. pastoris.The same was observed for phosphate, where the minimal required concentration was 40-49 mg/g C , while ammonia became limiting at 31-50 mg/g C (Figure 4).These concentrations are smaller than the concentrations present in the medium after precipitation and, therefore, are not growth limiting.The minimal required nutrient concentrations could also be confirmed via elemental analysis of P. pastoris biomass (Figure 5).The experiments showed that P. pastoris reacts differently to the introduced limitations.Under ammonia limited conditions (Figure 4b,d), there is a sharp kink visible in the OTR signals when ammonia becomes limiting.Compared to this, phosphate limiting conditions become apparent in the OTR signal as a smooth decrease deviating from the exponential growth (Figure 4a,c).These results hint towards the presence of internal phosphate storage depots in P. pastoris.
The availability of macronutrients bound in the struvite crystal is highly dependent on the solubilization kinetics.To prevent nutrient limitations, the solubilization of the crystal needs to occur faster than the uptake by the cells.Thus, not only the thermodynamic equilibrium for struvite needs to be considered, but also the actual solubilization kinetics of the struvite crystals, which vary depending on the particle size.Commercially available struvite, with an average particle diameter of 21 µm, was investigated and compared to its mortared version, which had an average particle size of 8 µm.The two different struvite fractions were varied in concentration, to achieve phosphate or ammonium limitations (Figure 7).These findings were then used to determine the particle size-dependent affinity constant (K S ) (Figure 8).
In conclusion, struvite was identified as the precipitate formed in commonly used chemically defined mineral media.It was shown that struvite can in principle resolubilize.However, depending on its particle size and its resolubilization kinetics, it may become cell growth limiting.Therefore, this phenomenon, and its putative effects on cell growth, need to be considered and quantified in culture medium formulations.The presented method may also be applied to determine minimal media compositions at variable conditions (e.g., | 1087 temperature, pH, presence of chelating agents) for a variety other microorganisms.In addition, precipitates can be a nuisance, when the media is prepared in a separate vessel, as a complete transfer of the precipitates is hardly guaranteed, which could subsequently lead to varying cell growth.
clarify the chemical composition of the observed precipitate, a sample of the precipitated media was collected through centrifugation, washed with deionized water and dried at 80°C.The obtained powder was sent to the external analytics laboratory Budenheim (Chemische Fabrik Budenheim KG).X-ray fluorescence (XRF) analysis revealed that the precipitate mainly consisted of ammonium magnesium phosphate F I G U R E 1 Precipitate formation in different mineral media at different pH values.Tested media were Syn6-MES(Hellwig et al., 2005), cultivation media for bioreactor cultivations, according to the Invitrogen protocol (Invitrogen, 2010) andHyka et al. (2010).All media were titrated with ammonia solution (25% v/v) or phosphoric acid (85% w/v) within a pH-range from 3 to 8 at an interval of 1 pH units and immediately photographed.
Calculated total concentration of ions in Invitrogen medium (Invitrogen, 2010) before (red) and after (blue) struvite precipitation.(a) Concentration of the main ions in the medium relevant for struvite formation.(b) Detailed evaluation of Mg 2+ ions.Total concentration of Mg 2+ (red) is split in the dissolved portion (blue) and the crystalline bound portion (hatched gray).Numbers are given in Supporting Information S1: Table U R E 3 (a) Variation of Mg 2+ concentration in Syn6-MES medium for Pichia pastoris cultivations.(b) Maximal oxygen transfer rate depending on the total amount of added Mg 2+ .First preculture was conducted in Syn6-MES medium, second preculture was conducted in Syn6-MES media without Mg, P, and N. Main culture was conducted in half-concentrated Syn6-MES medium with varying Mg 2+ concentrations.5 g/L glucose were used as carbon source.
h., n = 350 rpm d 0 = 50 mm.The lines represent the average of four biological replicates.For clarity, only every 12th measured point is shown as a symbol.Standard deviation is barely visible, as it is smaller than the size of the points.dissolution kinetic of struvite does not affect cell growth.Magnesium becomes growth limiting at much lower concentrations of 1.4 mg/L or 0.28 mg/g C .At this condition, the OTR Peak diverges from the OTR Peak, unlimited of the reference cultivation already at the beginning of the cultivation.

Figure 4
Figure 4 depicts the results of P. pastoris cultivations with varying PO 4 3− and NH 4 + concentrations in the growth medium.The cultivations were conducted using 10 g/L glucose (Figure 4a,b) and 10 g/L glycerol (Figure 4c,d).The course of the OTR is plotted over time.In Figure 4a, the PO 4 3− variation for the cultivation with 10 g/L glucose is shown.The reference with 700 mg/L PO 4 3− is shown in black.The OTR increases exponentially over time, reaching a maximum of 24 mmol/L/h after 21 h.This marks the depletion of Following the consumption of overflow metabolites, the metabolic activity decreases to near-zero levels.Reducing the PO 4 3− concentration in the medium from 700 to 400 mg/L does not significantly influence the course of the OTR.Starting at 300 mg/

Figure
Figure 4c and D show cultivations with varying PO 4 3− and NH 4 + concentrations with 10 g/L glycerol as C-source.The cultivations with glycerol led to similar results as the ones on glucose.The concentrations, which show the first signs of limitation are 210 mg/L PO 4 3− and 200 mg/L NH 4 + , respectively.The use of glycerol eliminates overflow production by P. pastoris (Macauley-Patrick et al., 2005; Wollborn et al., 2022).Similar to Figure 4a, in Figure 4c the effect of internal phosphate pools is obvious.Only discrete limiting concentrations could be determined from Figure 4a-d.Therefore, the maximal OTR of the first peak is correlated with the applied nutrient concentration.The nutrient concentration is normalized with the added carbon source of 10 g/L (glucose or glycerol).
Figure 4e,f show four saturation curves.The limiting concentration is defined by the value, where the maximal OTR falls below 90% of the maximal OTR of the unlimited culture.These concentrations are marked in Figure 4e,f by vertical dashed lines.For glucose, the limiting concentrations of 39.5 mg PO 4 3− per g glucose from Figure 4e match the previous value that were obtained by visual evaluation from Figure 4a (40 mg PO 4 3− per g glucose).In addition, the limiting concentrations of 50 mg NH 4 + per g glucose from Figure 4f match the values from Figure 4b (50 mg NH 4 + per g glucose).For glycerol, the limiting concentration from the Hill fit in Figure 4e is 132% higher precipitation for the Invitrogen medium and shown in Figure 2 (blue bars).The same can be concluded for the Hyka medium (Supporting Information S1: Figure S1).Therefore, for both carbon sources (glucose and glycerol) in the Invitrogen medium (Figure 2) or the Hyka medium (Supporting Information S1: Figure S1), no limitation of PO 4 3− or NH 4 + is expected after struvite precipitation at equilibrium, as long as the precipitate enters the cultivation vessel and is not separated during media preparation.The limiting concentrations of the secondary substrates Mg 2+ , PO 4 3− , and NH 4 + determined from Figure 4e,f were compared with an elemental analysis of the used P. pastoris strain.The results can be seen in Figure 5.The limiting concentrations of Mg 2+ , PO 4 3− , and NH 4 + for cultures on glucose are shown as blue bars and for cultures on glycerol as orange bars.To convert the carbon normalized data from Figure 4e,f to data relative to CDW, biomass yields for glycerol and glucose are considered.From previous experiments, a total

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Pichia pastoris cultivations in Syn6-MES media.First preculture was conducted in Syn6-MES medium, second preculture conducted in Syn6-MES media without Mg, P, and N. Main culture was conducted in Syn6-MES media with Mg 2+ concentration identical to Syn6-MES medium and varying P and N concentrations.Experiments were conducted using a μTOM device.(a) shows cultivation with glucose and P variation with Mg and N concentration identical to normal Syn6-MES medium, (b) with glucose and N variation with Mg and P concentration identical to normal Syn6-MES medium, (c) with glycerol and P variation with Mg and N concentration identical to normal Syn6-MES medium, (d) with glycerol and N variation with Mg and P concentration identical to normal Syn6-MES medium.Reference concentration in Syn6-MES medium of PO 4 3− is 700 mg/L and of NH 4 + is 1050 mg/L (see Supporting Information S1: TableS1).(e) shows maximal OTR from (a) and (c).(f) shows maximal OTR from (b) and (d).Concentration of PO 4 3− and NH 4 + normalized with carbon source.Data is fitted to a Hill kinetic.Fit parameters are given in Supporting Information S1: Table S3, lines 2-5.Concentration for 90% of maximal OTR are marked.Cultivation conditions: Syn6-MES Batch medium (200 mM MES), c Glucose = 10 g/L, c Glycerol = 10 g/L, OD 600 (0 h) = 0.2, 96 deep square well plate V = 2.4 mL, V L = 600 μL, T = 30°C, 85% r.h., n = 350 rpm d 0 = 50 mm.The lines represent the average of four biological replicates.For clarity, only every 12th measured point is shown as a symbol.Standard deviation is barely visible, as it is smaller than data points.in the medium was fully omitted and replaced by sulfate to not alter the osmotic pressure.The results of the elemental analysis are shown in Figure 5 as green bars.The full elemental analysis is given in Supporting Information S1: Table S4.The open green bars P and N content, respectively) of the unlimited cells, the hatched green bars show the composition of the P-limited cells.The results for the Mg 2+ and NH 4 + content of the cells does not vary significantly between the unlimited cells and the P-limited cells.For the PO 4 3− content, a significant reduction of phosphorus in the cells is seen for cells cultivated under PO 4 3− limitation.This supports the hypothesis of the presence of phosphate pools in P. pastoris cells in the form of polyphosphates, as it has previously been described for S. cerevisiae (Christ & Blank, 2019), allowing the cells to significantly reduce the P content of the cells under P-limitation.The data from the elemental analysis (Figure 5 open green bars) fits the previously determined relative limiting concentrations for Mg 2+ , PO 4 3− , and NH 4 + (Figure 5 blue and orange bars) well.The highest deviation of 51% between the elemental analysis (open green bar) and the determined limiting concentration from Figure 4f (orange bar) for the limiting concentration of NH 4 + in glycerol culture.The rest of the determined limiting concentrations deviate less than 10% from the elemental analysis.The data in Figure 5 validates the developed method for determination of limiting concentrations Influence of struvite solubilization kinetics on nutrient limitation It could be shown that no growth limitation has to be expected for nutrient concentrations of Mg 2+ , for struvite.However, this does not take into account the solubilization kinetics of the struvite crystals.Babić-Ivančić et al. (2002) and Roncal-Herrero and Oelkers (2011) described an extremely slow struvite solubilization.Therefore, a limitation can be expected, if the struvite solubilization is slower than the nutrient (Mg 2+ , PO 4 3−

Figure 6
Figure 6 shows the relative particle size distribution of commercial struvite crystals (squares) and mortared struvite crystals (circles), measured in a Coulter counter (Multisizer 4e Particle Analyzer; Beckman Coulter).The commercial struvite crystals show a mean particle diameter of 21 µm.Mortaring reduces the mean particle diameter to 8 µm.Microscopic images of the crystals can be found in Supporting Information S1: Figure S2.The source of the macronutrients Mg 2+ , PO 4 3− , and NH 4 + was completely replaced in Syn6-MES medium by varying concentrations of the analyzed struvite crystals (commercial and mortared).First, only PO 4 3− and Mg 2+ were replaced in the medium.NH 4 + was supplemented as (NH 4 ) 2 SO 4 .Then, Mg 2+ , PO 4 3− and NH 4 + were replaced by struvite.The media were used in P. pastoris cultivations.The cultivations were performed after a two-stage preculture with Syn6-MES medium without Mg 2+ , PO 4 3− , and NH 4 + .All main cultures were conducted in parallel to a reference cultivation, where struvite did not replace the analyzed nutrients (PO 4 3− or NH 4 + ), to compensate for varying lag phases amongst various, individual experiments.The results are shown in Figure 7.In Figure 7a the time course of the OTR during cultivation on glucose without PO 4 3− and Mg 2+ is depicted.The cultures with 7 and 3 g/L struvite (d = 8 µm and d = 21 µm), together with the reference, show a typical OTR curve for unlimited growth (Anderlei

S1:
Figure4a, the OTR course matches the OTR course of the rest of the reference cultivations with 10 g/L glucose.After the main OTR peak, two more peaks at around 16 and 18 h can be seen.These can be attributed to overflow metabolites produced during metabolization of glucose.Cultures with 0.3 g/L struvite terminate the exponential increase earlier (d = 8 µm and d = 21 µm).In the case of the smaller crystals (0.3 g/L struvite d = 8 µm), the exponential increase ceases after 13.6 h.For the larger crystals (0.3 g/L struvite d = 21 µm), it already ceases after 10 h, suggesting the larger particle size enhances the limitation.

Figure
Figure 7b shows the OTR course for cultivations on glucose without Mg 2+ , NH 4 + , and PO 4 3− source except by the supplemented struvite.The culture with 20 g/L struvite and the reference show the same unlimited growth as shown in Figure 7a.For a struvite concentration of 7 g/L (d = 8 µm and d = 21 µm), a slight, but significant, growth limitation can be observed.Since the culture without Mg 2+ and PO 4 3− supplemented with 7 g/L struvite (Figure 7a) showed no apparent limitations, a N-limitation can be expected for 7 g/L struvite (d = 8 µm and d = 21 µm) in Figure 7b.

Figure 7b .
Figure 7b.In Figure7c,d, struvite supplementation was analyzed for P. pastoris cultivations with glycerol.With the exchange of carbon source, a higher OTR peak is achieved, compared to Figure7a,b.As described for Figure4e,f).The results can be seen in Figure7e-h.The data is fitted by a Hill kinetic.Fit parameters are listed in Supporting Information S1: TableS3, lines 6-13.Figure7erepresents the maximum OTR data represents the maximum OTR data for the P-limited and Figure 7f the data for the N-limited culture on glucose.The saturation values of the OTR peak (OTR peak,unlimited ) for these cultures reach 25.4 ± 2 mmol/L/h.Figure 7g summarizes the data for the P-limited and Figure 7h the data for the N-limited culture on glycerol.The saturation values of the OTR peak (OTR peak,unlimited )

Figure 8
Figure8summarizes the kinetics from Figure7e-h by the affinity constant K S , obtained from the fit by a Hill kinetic.The data is normalized to cell dry weight using substrate yields for glucose (Y X/S = 0.50 g/g) and glycerol (Y X/S = 0.62 g/g).Generally, the affinity constant K S increases linearly with struvite particle size d, therefore, leading to a stronger limitation.For PO 4 3− (half-filled symbols and dashed fit line), the K S increases from 13.4 ± 0.7 mg/g CDW to 46.2 ± 4.6 mg/g CDW .For NH 4 + (filled symbols and solid fit line), the K S increases from 17.7 ± 0.7 mg/ g CDW to 121.1 ± 20.2 mg/g CDW .This increase can be explained by the smaller surface area A of struvite particles given in Equation (2) with density ρ available for solubilization at a given concentration c of NH 4 + or PO 4 3− in a liquid filling volume V L .
Pichia pastoris cultivations in magnesium, phosphate, and ammonium free Syn6-MES media with varying struvite concentration added.(a) Culture on glucose, ammonium, and struvite.NH 4 + concentration was identical to the normal Syn6-MES medium.(b) Culture on glucose and struvite.(c) Culture on glycerol, ammonium, and struvite.NH 4 + concentration was identical to the normal Syn6-MES medium.(d) Culture on glycerol and struvite.(e and f): Maximal OTR from a, c, and Figure 4e.(f and h) Maximal OTR from B, D, and Figure 4f.Cultivations with commercial struvite (d = 21 µm) are depicted with open symbols and continuous lines, while mortared struvite (d = 8 µm) are depicted with closed symbols and dashed lines.Cultivations from Figure 4e,f are depicted with crossed symbols and dotted lines.Nutrient concentration normalized with carbon source.Glucose cultures are shown in blue squares.Glycerol cultures are shown in orange circles.Data fitted to a Hill kinetic.Fit parameters are given in Supporting Information S1: Table

Table 1
, lines 4 and 5) is compared to theoretical values of suspected components (Table1, lines 1-3).Additionally, pure struvite was included as reference control (Table1, line 4).The chemical formula of struvite is MgNH 4 PO 4 × 6H 2 O.It is possible that during the drying process 2 O).On average, the cations in both components can be described for the monovalent species as [K 0.15 (NH 4 ) 0.85 ] + and for the bivalent cations as [Mg 0.90 Ca 0.10 ] 2+ .However, considerable amounts of calcium and potassium were also detected, which replaced the magnesium and ammonium in the crystalline structures, respectively.The mean composition of the sample can be described as follows: ~90% (w/v) of [K

Table S2 .
The theoretical struvite composition of MgNH 4 PO 4 × 6H 2 O is assumed for the calculation of the precipitation.Therefore, K + and Ca 2+ are freely available and not bound in struvite crystal.The concentration of the dissolved ion K + and Ca 2+ in the solution (Invitrogen, 2010).They are compared to the concentrations that remain solubilized, if struvite precipitates (in blue).Mg 2+ reaches a concentration of 34 mg/L at equilibrium (Supporting Information S1: Table precipitate measured by X-ray fluorescence spectroscopy (XRF).
Note:The first three rows show the composition of the tested commercial standard components.The fourth row summarizes the analytical result for the commercial reference struvite (MgNH 4 PO 4 × 6 H 2 O) from Alfa Aesar (CAS 13478-16-5 E 8 Affinity constant K s depending on struvite particle size.Affinity constant from Hill kinetic fit to maximal OTR.The fitted data is shown in Figure 7. Data points with PO 4 3− or NH 4 + without struvite are shown for d = 0 µm.Data for ammonium limitation are depicted with full symbols, for phosphate with half-empty symbols, for glucose in blue, and for glycerol in orange.Linear data fit for ammonium (line) y = 5.4 ± 1.6x + 36.26 ± 21.3, R 2 = 0.729.For phosphate (dashed line) y = 1.62 ± 0.19x + 12.53 ± 2.43, R 2 = 0.949.Standard deviation is depicted as error bars.