OVERVIEW OF THE CURRENT YEAR’S PROJECT
With the goal of achieving economic viability for our synthetic cannabidiol (CBD), the USP-EEL-BRAZIL team identified the scale up of the CBDynamics project as one of its primary objectives for this year. However, this raises the question: how can this expansion be effectively implemented out of the laboratory? That is possible through, well, engineering! There are some benefits of having a team made of 16 engineering students, after all.
With that in mind, our 2024 modeling team divided itself into several projects in order to achieve this objective, them being:
- Kinetic Modeling, where we went after all the kinetic parameters of the 5 enzymes we modeled last year (which you can check in our recap section);
- Optimization cassettes, where we drew biological circuits to 1) induce the olivetolic acid pathway in S. cerevisiae; 2) accumulate and overexpress the terpenoid geranyl-diphosphate (GPP), the most important precursor to CBDA, in the yeast’s cell via interference RNA (RNAi) and the enzyme ERG20, respectively;
- Bioreactor Modeling: where we devised a logistical mathematical model to create an optimal feeding system for S. cerevisiae, in order to successfully scale-up the project.
OPTIMIZATION CASSETTES
In order to produce the cassettes to increase the production of CBD by the means provided by our project in 2023, we had to search through different methods to optimize and increase the production of our enzymes. It was of utmost importance that we interfered as much as we could with the genetic coding of the yeast whilst maintaining our metabolic pathway intact. For that, our main idea was to model cassettes so that GPP - a substance formed through the condensation of isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP) by geranyl pyrophosphate synthase (GPPS) that, once produced, combines with olivetolic acid to form cannabigerolic acid (CBGA), the central precursor for the synthesis of various cannabinoids, including CBD (Gagne et al., 2012) -, was kept in the cell at larger quantities so that the production of our substance of interest would be favored.
As a result, we believe to have found two different manners in which to achieve what we set up: to accumulate as much GPP as we could in the cell, we could either minimize its translation into products that would not be useful to our production or we could make it be “overproduced” (Luo et al., 2019). In both of the strategies, we would have a higher concentration of GPP in the cell, making so that the end results would be more favorable for our interests.
Additionally, all cassettes constructed in 2024 are mediated by homology sites - sites that are portions of the yeast genome inserted into the 5’UTR and the 3’UTR of the cassettes that will be recognized and adhered into its genome. For that, we searched for regions in the yeast that could be silenced and not damage the functionality of the cell (Chia et al., 2018). Our findings made it so that we used knockout protein sites differentiated in each of the cassettes.
For the RNAi, we had to find a site where we could meddle without the complete silencing of our gene. For that, we decided to use the site directly after the ERG20 location. We believe that, by adding our homology sites there we can only subside the amount of production of our gene, whilst not completely silencing it.
In the case of the RISC system, we were able to find a specific protease present in the gene of our enzymes that could be silenced without damaging its metabolism. This protease is pep4 - a protease that, when silenced, does not show significant variability in growth (Schoborg, Clark, Choudhury, C. Eric Hodgman, & Jewett, 2016). As can be seen in Table 1, it is the most similar in growth to the wild type (wt) of our yeast. Therefore, we can conclude that, by stopping its production completely, we are not going to interfere in the mechanism of the cell, making it the perfect site to locate our homology site.
Figure 1: Growth of the strains used in the study.
In the case of our SuperExpression cassette, we decided to silence the HXK2 enzyme that, when deleted, allowed for increased expression in the HXK1 enzyme - which can possibly be attributed to the fact that the “deletion of one HXK isoenzyme might trigger a marked increase in the expression of the other, causing reinforcement of the glycolysis flux to the MVA pathway” (Sun et al., 2014). Therefore, proving that by silencing the HXK2 enzyme using our homology sites will not hinder the function of our enzymes. The full cassettes will be shown in the course of our text.
To create a build-up of GPP in our cell, we used the following:
RNAi and the RISC system
The initial optimization that we utilized was based on interference RNA (RNAi), that consists of a RNA strand that will be produced but not read by the ribosomes that won’t, as a result, produce the protein transcribed there. This phenomenon occurs because the process of production of this specific strand creates a “hairpin”, a handle unrecognizable to the ribosomes. This process is often referred to as “silencing”, since it stops the expression of an enzyme (Chen, Guo, Zhang, & Si, 2020).
The silencing procedure happens initially by an enzyme known as Dicer that recognizes and cuts RNA strands in small fragments of about 21 base pairs. Next, these fragments are identified by the RNA-Induced Silencing Complex (RISC) that includes many enzymes such as the Slicer, a protein of the argonauts group. The RISC connects to one of the RNA strands and goes through the cytoplasm in search of complementary fragments that, when found, are cut and, consequently, not able to be translated and turned into protein (Chen, Guo, Zhang, & Si, 2020). The RNAi will be constructed for the enzyme ERG20, responsible for the conversion of GPP into FPP.
Figure 2: ERG20 pathway
However, it is important to understand that, because the pathway we are using is still important for cell growth, we can’t completely silence it. Therefore, our intention is not to completely stop its expression, only to diminish it.
Since the RISC system is essential to our strategy and not naturally present in S. cerevisiae, we also had to induce the production of the enzymes present in the system. This way, it’s clear we had to build two cassettes: one for the ERG20 and one for the RISC enzymes (Pratt & MacRae, 2009).
Figure 3: RNAi cassette
Source: Authors, 2024
Figure 4: RISC system cassette
In the making of the cassettes, additional information is important. Firstly, Tet is a promoter inducible by the antibiotic tetracycline - in the RNAi cassette, the second one is imputed to complete the inverse of the first one to create the hairpin. Secondly, URA3 is a selection mark, so that there is no need to add supplements to the environment and the yeast is capable of producing its compounds independently. Lastly, IRES is an internal site in the ribosome entryway (RBS in the middle of the circuit) (See more in parts).
GPPS super expression
The super expression cassette happens through the GPPS enzyme that converts GPP in FPP. In this case, our super expression will make it so that there is a lot more conversion of IPP into GPP, following the process in which IPP is transformed into GPP through the action of GPPS, setting the stage for the synthesis of cannabinoids like CBD.
Figure 5: Biosynthetic Pathway of Cannabinoids in C. sativa.
For that, we created the following cassette - finalized with the homologous recombination site:
Figure 6: SuperExpression cassette
In which the HXK2 is the hexokinase promotor, that will generate more GPPS transcripts and, consequently, more proteins and GPPS is the CDS of the enzyme that makes the conversion of IPP into GPP.
Lastly, in both the RNAi and SuperExpression cassettes, we added polylinkers: restriction enzymes that are able to cut sites in strategic locations to facilitate lab work in future modifications on our part. In our case, we realized that, while we could reasonably see that our research and plan could work and be the primary mean that we would use in biomanufacturing CBD, we also wanted to be able to modify our previous plan in case any of our strategies didn’t pan out. For that, our efforts led us to restrictions enzymes. Therefore, we added zero-cutter poli-linker enzymes before the 5’UTR region, after the 3’UTR region and between the CDS (ERG20 and GPPS) with the goal of being able to modify the genetic coding in these regions if necessary.
Our finalized cassettes, visualized through SnapGene are:
Figure 7: RNAi finalized cassette
Figure 8: RISC finalized cassette
Figure 9: SuperExpression finalized cassette
KINETIC MODELING
To enhance the efficiency and cost-effectiveness of cannabidiol (CBD) production utilizing the methodologies employed by the team in 2023, we concentrated this year on optimizing the enzymatic reactions integral to the CBD synthesis pathway. A critical component of this process is the determination of the optimal concentration of hexanoic acid, the substrate to be supplied to the cells, with the objective of maximizing the production of cannabidiolic acid (CBDA) while maintaining the activity of the enzymes involved. To address this challenge, kinetic modeling was employed, facilitating an understanding of the performance of each enzyme in the production process and allowing for the quantification of the effects of substrate and product concentrations on enzymatic activity. This study encompassed data collection, advanced modeling techniques, and phylogenetic analysis, all aimed at identifying the ideal conditions for enhanced CBD production.
Kinetic Data Collection
To derive the kinetic velocity equations for the enzymes under analysis, data collection was conducted utilizing the Brenda Enzyme and KEGG databases, both of which are well-established online resources. The KEGG database was employed to identify enzyme codes through the Cannabidiol (CBD) pathway available on the platform. These codes enabled the identification of the enzymes previously studied: Cannabidiolic Acid Synthase (CBDAS), Olivetolic Acid Cyclase (OAC), Prenyltransferase 4 (CsaPT4/PT4), Hexanoyl-CoA Synthase (CsHCS1), and Olivetol Synthase (OLS). Subsequently, the obtained codes were used to consult the kinetic profiles of these enzymes in the Brenda database, which also provided access to pertinent literature on enzyme kinetics (Wiles et al., 2022).
A notable finding was that the enzymes Olivetol Synthase (OLS), Prenyltransferase 4 (CsaPT4/PT4), and Cannabidiolic Acid Synthase (CBDAS) adhered to the Michaelis-Menten kinetic model. In contrast, the velocity profile of Hexanoyl-CoA Synthase (CsHCS1) exhibited inhibition at elevated concentrations of the substrate CoA (Stout et al., 2022). To calculate the velocity profiles for each enzyme, the following assumptions were made: all other reagents involved in the reactions, excluding the substrates, were maintained in excess; the conversion of reagents to products occurred without significant losses; and all cannabigerolic acid was fully converted to cannabidiolic acid.
Figure 10: Structural and functional properties of cannabinoid biosynthetic enzymes
| Enzyme | Mol. Wt (kDa) | Protein Family | Catalytic Reaction | Substrate | Kinetic Parameters | Additional Information |
|---|---|---|---|---|---|---|
| CBDAS | 62.237 | oxygen-dependent FAD-linked oxidoreductase family | stereoselective oxidative cyclisation of CBGA | CBGA | KM =0.137 mM Vmax = 2.57 nmol/ s/mg | CsHCS1 |
| AAE (Acyl-Activating Enzyme) | 79.715 | AAE (Acyl-Activating Enzyme), a class of acyl-CoA synthetases | Activation of hexanoate to form Hexanoyl-CoA | Hexanoate (hexanoic acid) | Km=3.7mM, 𝑉𝑚𝑎𝑥=6.8𝑝𝐾𝑡 | PT4 |
| PT4 | 44.928 | Belongs to the transferase family (geranyltransferases) | Transfer of geranyl to olivetolic acid, forming cannabigerolic acid | Olivetolic acid and geranyl pyrophosphate (GPP) | Km=5.7μM, 𝑉𝑚𝑎𝑥=0.1𝜇𝑚𝑜𝑙/𝑔/𝑚𝑖𝑛 | Olivetol synthase (OLS) |
The Michaelis-Menten model represents a foundational principle in biochemistry for characterizing the kinetics of enzymatic reactions. This model elucidates the relationship between the rate of a reaction catalyzed by an enzyme and the concentration of the substrate. The Michaelis-Menten equation, which expresses the initial reaction rate \( v_0 \) as a function of the substrate concentration \([S]\), is articulated by the following formula (Leow & Chan, 2019):
In this equation, Vmax denotes the maximum reaction rate, attained when the enzyme is fully saturated with substrate, while Km represents the Michaelis constant, which indicates the substrate concentration at which the reaction rate is half of the maximum rate. The Km value is particularly significant as it serves as a measure of the substrate's affinity for the active catalytic site of the enzyme, thereby reflecting the efficiency with which the enzyme converts the substrate into product.
The Km and Vmax values for the enzyme cannabidiolic acid synthase (CBDAS) were obtained from the Brenda Enzyme and UniProt databases, as well as from the study by Wiles et al. (2022). As previously mentioned, this enzyme adheres to the Michaelis-Menten model. Consequently, the equation that describes the initial reaction rate for the CBDAS enzyme is expressed as follows:
The Km and Vmax values for the enzyme are 0.137 mM and 2.57 nmol/sec/mg, respectively. The substrate concentration, cannabigerolic acid (CBGA), is 200 μM, while the enzyme concentration is 0.00132 g/L (equivalent to 0.66 μg of purified enzyme per 500 μl of standard solution) (Taura et al., 1996). The calculation of Vmax for the specified enzyme concentration was conducted as follows:
The calculation of the initial reaction rate was carried out using the following procedure:
Figure 11: CBDAS enzyme kinetic velocity profile graph
Although a Km value for the enzyme prenyltransferase 4 (CsaPT4) was identified in the literature, the lack of a corresponding Vmax value necessitated the adoption of an alternative approach for its determination. A BLAST alignment was conducted using the NCBI database to identify 14 enzymes exhibiting at least 40% similarity to CsaPT4, which had reported Km values and were not specific to Cannabis sativa.
The enzymes selected for this analysis included: Humulus lupulus 2-acylphloroglucinol 4-prenyltransferase, Humulus lupulus isolate HlPT1L aromatic prenyltransferase, Humulus lupulus mRNA for aromatic prenyltransferase, Pelargonium citronellum AT3G11945-like protein mRNA, Aquilaria malaccensis homogentisate solanesyltransferase (HST1), various mRNA proteins of the Pelargonium genus (such as AT3G11945-like), as well as Arabidopsis thaliana homogentisate prenyltransferase (HST) and homogentisate phytyltransferase VTE2-2.
Following the selection of these enzymes, their corresponding sequences were retrieved, and a phylogenetic analysis was conducted using T-Coffee Muscle software, employing a ClustalW alignment that maintained 90% conservation. This analysis aimed to compare the alignments of the catalytic sites of the selected enzymes with that of CsaPT4, with the objective of identifying conserved regions among them, as detailed below:
Figure 12: CsaPT4 phylogenetic analysis
Upon confirming the similarity among the enzymes, a phylogenetic tree was constructed to assess the homology of each enzyme in relation to CsaPT4. Based on the similarity values obtained, the mean and standard deviation of the Km and Vmax values for the comparable enzymes were calculated. These statistical metrics were subsequently utilized as estimates for CsaPT4.
Figure 13: CsaPT4 phylogenetic tree
The extrapolated values for Km and Vmax were determined to be 5.7 µM and 0.1 µmol/g/min, respectively. The determination of the substrate concentration was conducted based on the stoichiometry of the reaction involved in the production of cannabigerolic acid, as illustrated below.
Figure 14: Cannabigerolic acid production reaction
Considering that the concentration of cannabigerolic acid used was 200 μM and that the stoichiometric ratio between cannabigerolic acid and olivetolic acid is 1:1, it follows that the concentration of olivetolic acid, the substrate for the enzymatic reaction, is also 200 μM. As previously mentioned, this enzyme adheres to the Michaelis-Menten model. The equation that describes the initial reaction rate for the enzyme CsaPT4 is expressed as follows:
The calculation of the specific initial velocity of CsaPT4 was conducted using the following procedure:
Figure 15: CsaPT4 enzyme kinetic velocity profile graph
For the enzyme olivetolic acid cyclase (OAC), no Km or Vmax values were identified in the literature or in the BRENDA and UniProt databases. To address this gap, a procedure analogous to that employed for the enzyme prenyltransferase 4 (CsaPT4) was undertaken. However, it proved challenging to identify enzymes exhibiting at least 40% similarity to OAC that were not specific to Cannabis sativa and for which Km and Vmax values were available.
In light of this challenge, a literature review was undertaken to compare olivetolic acid cyclase (OAC) with two distinct enzyme families: DABB (α+β barrel-type polyketide cyclases) and chalcone isomerase. Studies indicate that OAC is a functionally characterized polyketide cyclase that catalyzes the C2-C7 aldol cyclization of linear pentyl tetra-β-ketide CoA as its substrate, leading to the formation of olivetolic acid (OA) (Yang et al., 2016; Gagne et al., 2012).
Considering that olivetol synthase (OLS) catalyzes the conversion of hexanoyl-CoA and malonyl-CoA into olivetol, which is subsequently transferred to the catalytic pocket of olivetolic acid cyclase (OAC) for immediate conversion into olivetolic acid, it can be concluded that the kinetics of the two enzymes can be effectively summarized by the kinetics of OLS. This enzyme represents the bottleneck and the limiting step in the sequence of reactions. Consequently, the initial velocity for OAC will not be calculated, as the efficiency of the catalytic process is predominantly determined by the activity of OLS.
However, it was essential to determine the concentration of the substrate 3,5,7-trioxododecanoyl-CoA, as this compound will be the product of the enzymatic reaction catalyzed by olivetol synthase (OLS). To achieve this, a stoichiometric analysis of the reaction was conducted, as detailed below:
Figure 16: Olivetolic acid production reaction
Given the 1:1 stoichiometric ratio and considering that the concentration of olivetolic acid is 200 μM, the concentration of the substrate 3,5,7-trioxododecanoyl-CoA is likewise established at 200 μM. Olivetol synthase (OLS), along with Cannabidiolic Acid Synthase (CBDAS) and Prenyltransferase 4 (CsaPT4), exhibits Km and Kcat values obtained from the UniProt database and the study by Wiles et al. (2022). The determined values for Km and Kcat are 60.8 µM and 2.96 1/min, respectively. To ascertain the concentration of the substrate hexanoyl-CoA, a stoichiometric analysis of the enzymatic reaction was conducted, as illustrated below. Based on the 1:1 ratio with the product 3,5,7-trioxododecanoyl-CoA, the concentration of hexanoyl-CoA was also established at 200 μM.
Figure 17: 3,5,7-trioxododecanoyl-CoA production reaction
The enzyme concentration was set at 0.005 g/L, corresponding to 5 mg in 1000 mL of buffer (Taura et al., 2009). The calculation of the enzyme concentration in mol/L was performed using the enzyme's mass in daltons (g/mol):
The Kcat constant, commonly referred to as the turnover number, is a critical kinetic parameter in enzymology that quantifies the efficiency of an enzyme in catalyzing the conversion of substrates into products. Specifically, Kcat represents the number of substrate molecules converted to product by a single enzyme molecule per unit of time, under the assumption that the enzyme is saturated with substrate.
The value of Vmax can be determined using the following relationship:
By substituting the known values, the following results are obtained:
Once the Vmax value for olivetol synthase (OLS) has been obtained, it is possible to proceed with the calculation of the initial reaction rate utilizing the Michaelis-Menten equation:
By substituting the relevant values, we arrive at:
The enzyme Hexanoyl-CoA Synthase (CsHCS1) exhibited Vmax and Km values for the substrate hexanoic acid, which were obtained from the UniProt database. This enzyme follows a kinetic model that accounts for substrate inhibition, described by a modified Michaelis-Menten equation suitable for such inhibition conditions (Stout et al., 2022). It was noted that, at elevated concentrations of the substrate CoA, the enzyme's velocity profile displays inhibitory characteristics. To effectively model this behavior, the following kinetic equation is employed (Leow & Chan, 2019):
In this equation, the parameters are defined as follows: Vmax = 6.8 pmol/sec/g, Km = 3.7 µM e Ki = 5.101 mM. The enzyme concentration in mol/L was calculated based on the knowledge that 0.1 μg of recombinant AAE was present in a 20 μL solution (Stout et al., 2022).
The calculation of Vmax for the specified enzyme concentration was conducted using the following method:
To ascertain the concentration of the substrate supplied to the cells for the production of cannabidiol (CBD), specifically hexanoic acid, a stoichiometric analysis of the enzymatic reaction was conducted, as illustrated below:
Figure 19: Hexanoyl-CoA production reaction
Considering a 1:1 stoichiometric ratio and a hexanoyl-CoA concentration of 200 μM, it can be concluded that the optimal theoretical substrate concentration to be supplied to the cell, in alignment with the previously discussed assumptions, should also be 200 μM. The calculation of the specific initial velocity of CsHCS1 was conducted using the following methodology:
Figure 20: CsHCS1 enzyme kinetic velocity profile graph.
To enhance clarity in the graphical representation, the initial velocity values for CsHCS1, which were on the order of 10e-19, were converted to the aKat unit of measurement, defined as 1x10e-18. This adjustment facilitates a more comprehensible visualization of the data.
Kinetic modeling facilitated a comprehensive understanding of the kinetic profiles of each enzyme involved in the production of cannabidiolic acid (CBDA). Furthermore, this approach enabled the determination of the concentration of hexanoic acid to be supplied to the cells, thereby establishing an acceptable range for substrate concentrations to be utilized in future laboratory experiments conducted by the research team.
BIOREACTOR MODELING
As previously discussed in the context of cassette and gene expression modeling, this year’s focus centers on geranyl diphosphate (GPP), the primary precursor of cannabidiolic acid (CBDA). The metabolite GPP, present in yeast, is part of the terpenoids pathway (Ignea et al, 2011). This pathway is of vital importance to the growth of baker’s yeast, producing hormones, fats, among other components (Yongshuo et al, 2022). Because of that, our logic was to make it grow to the best of our capabilities and then induce it to produce CBD via our inducible promoters. Thus, the transformed yeast will produce CBD during its stationary phase, without affecting its growth or our final yield. This phase is determined by microbial growth modeling conducted in the laboratory, as it varies according to the microorganism’s strain.
The biological circuits responsible for 1) the expression of the five enzymes involved in the olivetolic acid pathway and 2) the RNAi have promoters inducible by galactose and tetracycline, respectively. This allows for the control of their expression by adding these compounds to the culture medium of a bioreactor, ideally after the yeast enters the stationary growth phase.
Mathematical Modeling
The objective of a bioreactor in CBDynamics is to produce a large amount of biomass in order to increase our yield. As described by Borowiak et al. (2012), a methodology must be developed so that it maximizes yeast growth without diverting its metabolism towards ethanol production, which reduces the total biomass yield—whether due to a lack of oxygen in the medium or the microorganism’s positive Crabtree effect (Belo; Pinheiro; Mota et al., 2003 apud van Hoek et al., 2000).
Our modeling process followed in the footsteps of the model proposed by Borowiak et al, 2012. We wanted to see if the model the authors described could be successfully applied to our yeast, even though they are from different strains - that is, we wanted to verify if their model could successfully make our S. cerevisiae grow to a satisfactory degree.
In a fed-batch reactor, the goals of increased growth and high biomass yield can be achieved by controlling the nutrient medium supplied to the reactor (Borowiak et al., 2012), making it an ideal approach. The feeding of the nutrient medium over time can be modeled as a logistic equation (1), with a (g), b and c (h-1) as its parameters.
(1)
As demonstrated by Miskiewicz and Borowiak (2005), the logistic model fits very well with the time profile of glucose feeding during the growth of S. cerevisiae when using dissolved oxygen tension (percentage of saturation, DOT) as a control parameter. The initial definition of the logistic model’s parameters, which will be used as a basis, were done by the authors in triplicate and using DOT as the parameter controlling the inflow of the glucose medium and keeping aeration, pH, and temperature conditions constant. The parameters obtained can be seen in Table 2. In this first experiment, the authors had an initial biomass concentration in the culture medium of X(0)=2,1 g/L and a total amount of glucose of G(0)=0,36 g. Those results were applied to (1), which allowed them to determine an ideal logistic model for the glucose concentration that supplies the medium we’re working with (2).
Table 2: Parameters of the initial logistic model.
(2)
A technique was created to adjust the parameters of the original model in order to derive a formula that optimizes the inflow of the nutrient medium, maximizing the criterion K (where K = Yμ). In this expression, Y represents the yield of yeast biomass, and μ signifies the specific growth rate. The parameters of this modified model were influenced by the initial biomass concentration (Borowiak et al, 2012).
When we studied this model, it seemed reasonable to assume that this initial data in (2) could be extended to our yeast strain. We understood that, if we kept our conditions as similar as possible to those of the authors, we could test the consistency of this initial estimation.
How did we do that? Well, we took the authors’ optimized parameters in the concentration that seemed appropriate to the bioreactor we had available (3 g/L) (Table 3) in order to find both the supply time for the nutrient medium (that follows equation 3) and, finally, our nutrient medium volume (L).
Table 3: Optimized parameters of a,b and c for the initial concentration of 3g/L of cells
(3)
In (3), we have ton: delivery time for nutrient medium (h); g(t): glucose medium supply term as a function; Gc: glucose concentration in the nutrient medium (g/L) and W: rate of delivery of nutrient-dosing peristaltic pump (0.96 L/h).
Our results based on the methodology described above can be found in Table 3.
Table 4: Concentration and Supply Time for 10 hours of testing.| t [min] | g(t) [g] | ton [min] | Volume [mL] | |
| Added volume [mL] | Accumulated volume (samples) [mL] | |||
| 0 | 3,0954 | |||
| 5 | 3,1823 | 0,0543 | 0,8693 | |
| 10 | 3,2716 | 0,0558 | 0,8932 | |
| 15 | 3,3634 | 0,0574 | 0,9176 | |
| 20 | 3,4577 | 0,0589 | 0,9427 | |
| 25 | 3,5545 | 0,0605 | 0,9684 | |
| 30 | 3,6540 | 0,0622 | 0,9948 | 5,5860 |
| 35 | 3,7562 | 0,0639 | 1,0219 | |
| 40 | 3,8611 | 0,0656 | 1,0497 | |
| 45 | 3,9690 | 0,0674 | 1,0781 | |
| 50 | 4,0797 | 0,0692 | 1,1074 | |
| 55 | 4,1934 | 0,0711 | 1,1373 | |
| 60 | 4,3102 | 0,0730 | 1,1680 | 6,5624 |
| 65 | 4,4302 | 0,0750 | 1,1995 | |
| 70 | 4,5533 | 0,0770 | 1,2317 | |
| 75 | 4,6798 | 0,0790 | 1,2648 | |
| 80 | 4,8097 | 0,0812 | 1,2987 | |
| 85 | 4,9430 | 0,0833 | 1,3334 | |
| 90 | 5,0799 | 0,0856 | 1,3690 | 7,6970 |
| 95 | 5,2205 | 0,0878 | 1,4054 | |
| 100 | 5,3647 | 0,0902 | 1,4427 | |
| 105 | 5,5128 | 0,0926 | 1,4810 | |
| 110 | 5,6648 | 0,0950 | 1,5201 | |
| 115 | 5,8209 | 0,0975 | 1,5602 | |
| 120 | 5,9810 | 0,1001 | 1,6013 | 9,0108 |
| 125 | 6,1453 | 0,1027 | 1,6433 | |
| 130 | 6,3140 | 0,1054 | 1,6864 | |
| 135 | 6,4870 | 0,1081 | 1,7304 | |
| 140 | 6,6646 | 0,1110 | 1,7754 | |
| 145 | 6,8467 | 0,1138 | 1,8215 | |
| 150 | 7,0336 | 0,1168 | 1,8687 | 10,5258 |
| 155 | 7,2253 | 0,1198 | 1,9169 | |
| 160 | 7,4219 | 0,1229 | 1,9663 | |
| 165 | 7,6236 | 0,1260 | 2,0167 | |
| 170 | 7,8304 | 0,1293 | 2,0683 | |
| 175 | 8,0425 | 0,1326 | 2,1210 | |
| 180 | 8,2600 | 0,1359 | 2,1748 | 12,2639 |
| 185 | 8,4830 | 0,1394 | 2,2298 | |
| 190 | 8,7116 | 0,1429 | 2,2860 | |
| 195 | 8,9459 | 0,1465 | 2,3435 | |
| 200 | 9,1861 | 0,1501 | 2,4021 | |
| 205 | 9,4323 | 0,1539 | 2,4619 | |
| 210 | 9,6846 | 0,1577 | 2,5230 | 14,2464 |
| 215 | 9,9431 | 0,1616 | 2,5854 | |
| 220 | 10,2080 | 0,1656 | 2,6490 | |
| 225 | 10,4794 | 0,1696 | 2,7139 | |
| 230 | 10,7574 | 0,1737 | 2,7800 | |
| 235 | 11,0422 | 0,1780 | 2,8475 | |
| 240 | 11,3338 | 0,1823 | 2,9162 | 16,4919 |
| 245 | 11,6324 | 0,1866 | 2,9863 | |
| 250 | 11,9382 | 0,1911 | 3,0577 | |
| 255 | 12,2512 | 0,1956 | 3,1304 | |
| 260 | 12,5717 | 0,2003 | 3,2044 | |
| 265 | 12,8997 | 0,2050 | 3,2797 | |
| 270 | 13,2353 | 0,2098 | 3,3564 | 19,0149 |
| 275 | 13,5787 | 0,2147 | 3,4344 | |
| 280 | 13,9301 | 0,2196 | 3,5137 | |
| 285 | 14,2895 | 0,2247 | 3,5944 | |
| 290 | 14,6572 | 0,2298 | 3,6763 | |
| 295 | 15,0331 | 0,2350 | 3,7596 | |
| 300 | 15,4175 | 0,2403 | 3,8441 | 21,8225 |
| 305 | 15,8105 | 0,2456 | 3,9299 | |
| 310 | 16,2122 | 0,2511 | 4,0171 | |
| 315 | 16,6228 | 0,2566 | 4,1055 | |
| 320 | 17,0423 | 0,2622 | 4,1951 | |
| 325 | 17,4709 | 0,2679 | 4,2860 | |
| 330 | 17,9087 | 0,2736 | 4,3781 | 24,9117 |
| 335 | 18,3558 | 0,2795 | 4,4713 | |
| 340 | 18,8124 | 0,2854 | 4,5658 | |
| 345 | 19,2786 | 0,2913 | 4,6613 | |
| 350 | 19,7543 | 0,2974 | 4,7579 | |
| 355 | 20,2399 | 0,3035 | 4,8557 | |
| 360 | 20,7354 | 0,3097 | 4,9544 | 28,2664 |
| 365 | 21,2408 | 0,3159 | 5,0541 | |
| 370 | 21,7563 | 0,3222 | 5,1549 | |
| 375 | 22,2819 | 0,3285 | 5,2564 | |
| 380 | 22,8178 | 0,3349 | 5,3590 | |
| 385 | 23,3640 | 0,3414 | 5,4622 | |
| 390 | 23,9206 | 0,3479 | 5,5662 | 31,8528 |
| 395 | 24,4877 | 0,3544 | 5,6710 | |
| 400 | 25,0654 | 0,3610 | 5,7764 | |
| 405 | 25,6536 | 0,3676 | 5,8823 | |
| 410 | 26,2525 | 0,3743 | 5,9888 | |
| 415 | 26,8621 | 0,3810 | 6,0958 | |
| 420 | 27,4824 | 0,3877 | 6,2030 | 35,6173 |
| 425 | 28,1134 | 0,3944 | 6,3107 | |
| 430 | 28,7553 | 0,4012 | 6,4185 | |
| 435 | 29,4079 | 0,4079 | 6,5265 | |
| 440 | 30,0714 | 0,4147 | 6,6345 | |
| 445 | 30,7456 | 0,4214 | 6,7425 | |
| 450 | 31,4307 | 0,4282 | 6,8505 | 39,4832 |
| 455 | 32,1265 | 0,4349 | 6,9581 | |
| 460 | 32,8331 | 0,4416 | 7,0656 | |
| 465 | 33,5503 | 0,4483 | 7,1726 | |
| 470 | 34,2782 | 0,4549 | 7,2791 | |
| 475 | 35,0167 | 0,4616 | 7,3850 | |
| 480 | 35,7657 | 0,4681 | 7,4902 | 43,3506 |
| 485 | 36,5252 | 0,4747 | 7,5946 | |
| 490 | 37,2950 | 0,4811 | 7,6982 | |
| 495 | 38,0751 | 0,4875 | 7,8006 | |
| 500 | 38,8653 | 0,4939 | 7,9019 | |
| 505 | 39,6655 | 0,5001 | 8,0021 | |
| 510 | 40,4756 | 0,5063 | 8,1008 | 47,0982 |
| 515 | 41,2954 | 0,5124 | 8,1980 | |
| 520 | 42,1247 | 0,5184 | 8,2938 | |
| 525 | 42,9635 | 0,5242 | 8,3877 | |
| 530 | 43,8115 | 0,5300 | 8,4799 | |
| 535 | 44,6685 | 0,5356 | 8,5701 | |
| 540 | 45,5343 | 0,5411 | 8,6583 | 50,5878 |
| 545 | 46,4088 | 0,5465 | 8,7443 | |
| 550 | 47,2916 | 0,5518 | 8,8281 | |
| 555 | 48,1825 | 0,5568 | 8,9094 | |
| 560 | 49,0814 | 0,5618 | 8,9883 | |
| 565 | 49,9878 | 0,5665 | 9,0646 | |
| 570 | 50,9016 | 0,5711 | 9,1381 | 53,6728 |
| 575 | 51,8225 | 0,5756 | 9,2089 | |
| 580 | 52,7502 | 0,5798 | 9,2768 | |
| 585 | 53,6843 | 0,5838 | 9,3415 | |
| 590 | 54,6247 | 0,5877 | 9,4032 | |
| 595 | 55,5708 | 0,5914 | 9,4618 | |
| 600 | 56,5225 | 0,5948 | 9,5170 | 56,2092 |
| Total volume: | 534,2716 | |||
Bioreactor Scaling
Our bioreactor is a Minifors 2, from INFORS MT®. It is a stirred tank reactor (STR) with dimensions as shown in Table 4 and design as shown in Figure 20.
Table 5: Bioreactor’s dimensions
Figure 21: Bioreactor’s design
The reactor’s dimensions are relevant because they allow us to calculate the number of impellers we need in it through equation 4 (Schmidell, 2021). With our numbers, we evaluated the need for just one impeller to aerate and agitate our medium.
(4)
We also opted for using a Rushton turbine, with six flat blades. According to Schmidell, 2021, Rushton turbines are commonly used in fermentation processes because they provide excellent air distribution throughout the medium. This is crucial for aerobic organisms like yeast, which require efficient oxygen transfer for optimal growth. Additionally, the design of the Rushton turbine minimizes shear stress on the yeast cells, preventing damage that could impair cell function or reduce biomass yield.
Results
- Feeding time and Volume
Our team calculated the volume of glucose we would inject into the bioreactor via the flow proposed by Borowiak et al, 2012. As we can see in figure 39, our medium was fed batch during our process every thirty minutes - which is why the mass maintains itself in fairly high values. Our samples were taken with one hour intervals, at a rate of 2 mL. The ideal scenario for our test would be that the remaining glucose followed a profile close to ideal - Figure 21 shows that the numbers don’t, at any point, drop closer to it; that is, glucose in the medium is always very high. That is explained due to the low concentration of yeast into the reactor (our discussion and justification can be seen in our Engineering Success part). The insufficient yeast population was unable to consume the available glucose efficiently, leading to elevated levels throughout the process.
Figure 22: Comparison between fed, remaining and ideal glucose in medium.
- Cell mass X Glucose mass
Now, when we analyze cell mass and glucose mass, we have a very interesting discussion. Figure 22 shows that the cell mass curve obtained in this experiment is similar to an ideal microbial growth curve. This is shown by the phases it displays: lag, exponential, stationary and decline. Therefore, the model proposed by Borowiak et al, 2012 can be adjusted to our yeast successfully - that is, we can use it to predict cell mass in a quantitative way and then know exactly when we can induce CBD production without affecting its yield.
It is also clear that we have coherent results: when we compare the aforementioned glucose mass curve against the cell mass curve in figure 41, we can see that as our cell mass grew, their nutritive medium decreased in a fairly proportionate way. Table 6 was used to make all of our calculations.
Table 6: Comparison of cell mass and glucose mass.
Source: Authors, 2024.
Figure 23: Glucose mass during the experiments.
Figure 24: Comparison between consumed glucose and cell mass during the experiments
It is finally concluded that understanding the balance between nutrient availability and cell growth is key, particularly when planning the ideal moment to trigger CBD production in our transformed yeast without negatively impacting yield. The proportional relationship between cell mass increase and glucose consumption observed in the experiment supports the reliability of our findings and strengthens their relevance for optimizing biotechnological workflows.
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