Model

Introduction

Modeling of biological systems is a scientific approach that involves creating simplified representations or simulations of complex biological processes, organisms, or ecosystems to gain a better understanding of how they function. These models can be based on mathematical equations, computer simulations, or conceptual frameworks, and they serve as tools to analyze, predict, and explain various aspects of the natural world.
Along with the modeling of the biological system and in-silico characterization of the parts that we are using, we have also simulated and proposed a model for a bioreactor in which the bacteria will be introduced. These mathematical simulations and computations are necessary, not only as a scientific endeavor but also as a practical necessity.

TccA gene regulation in E.coli

Gene regulation refers to controlling a particular gene expression in a cell. Gene regulation in Fig 1 depicts the TCC pathway in the bacteria and the simultaneous expression of the amidase gene using the T7 promoter(BBa_1719005). RBS(shine-dalgarno sequence) and PelB sequence have been integrated into our genetic circuit as part of our plasmid pET22b+ backbone. Modeling gene expression would help us accurately predict the rate at which our desired enzyme is being expressed in a cell under certain conditions and calculate our bacteria's degradation efficiency of triclocarban.

Parameter	Explanation	Units
K1	Transcription rate of T7 RNA polymerase	bps/sec(Base pairs per second)
K2	Translation rate of a ribosome in E.coli	AAs/sec(Amino acids per second)
d1	Degradation rate of mRNA	bps/sec(Base pairs per second)
d2	Degradation rate of protein	AAs/sec(Amino acids per second)

The genetic circuit represents the regulation of TccA gene in E.coli. In the presence of TCC, the T7 promoter is activated, and the T7 RNA polymerase binds to the promoter and starts the transcription. The transcription rate of T7 RNA polymerase is 250 bps/ sec. Our gene, including RBS, is 1562 bps long; assuming that the degradation of mRNA is negligible the time taken to transcribe our gene is 6.25 secs.
Generally, the translation rate of a ribosome in E.coli will range from 12 to 21, but here we are assuming the most extended translation rate, which is 12.1 AA/sec. Our protein sequence is about 515 AA long, so assuming that protein degradation is low and negligible the time taken to translate mRNA to protein is 42.56 secs.
We modeled the protein production in E.coli . However, in the future, we can study and model the protein production rate in our preferred chassis Acinetobacter baylyi.

Structure Modelling

Structure modeling was used in our project to identify the possible mechanism(s) to help determine the prediction outcomes. We could analyze the biological micromolecule's or macromolecule's three-dimensional structure through modeling. In our project, we wanted to identify the effect of how TCC binds to the amidase enzyme, as it hasn’t been elucidated in the literature. To do so, we had to predict the structure of the enzyme.

Structure Prediction

The structure of an enzyme is essential to determine the functions of the enzymes. The linear sequence of the polypeptide chain influences the chain's characteristic fold into a three-dimensional structure. Our enzyme of interest is an amidohydrolase enzyme (EC 3.5.1.4) produced by the TccA gene in Ochrobactrum spTCC-2. This amidohydrolase is responsible for the hydrolysis of the two amide bonds in Triclocarban (TCC), thereby converting it into more biodegradable byproducts like 4-chloroaniline [4CA], 3,4-Dichloroaniline [3,4DCA] and 4-Chlorocatechol [4CC], which are also toxic to the environment. We found that the TccA gene has the conserved catalytic triad of the amidase signature enzyme family and has low amino acid sequence similarity of about 27%-38% with other biochemically characterized amidase [1]. We proposed a model to improve the amidase enzyme efficiency but did not pursue it further due to time and resource constraints. As the amidase enzyme has yet to be characterized, we explored the possibility of directed evolution. The directed evolution method involves random mutagenesis to engineer the protein's active site to produce an enzyme with the required efficiency without in-depth knowledge of its structure. To carry this out, we need an initial understanding of the enzyme's activity and properties like Km and Vmax. To determine these parameters, we proposed drawing inferences from the enzymes of the family, which will target the carbon-nitrogen bonds, apart from the peptide bonds for linear amidase, the same as our enzyme[2][3].

Eventually, we dropped this idea as an in-silico study with only improved binding efficiency of the substrate to the enzyme will not be enough proof of concept to show that the enzyme efficiency has been increased. In contrast, an in-vitro study would not suit our timeline. Moreover, the amidase shows 76.92% efficiency in the absence of glucose, which mimics our system; thus, the scope of improvement will be negligible [1].

Catalytic Triad

The catalytic triad comprises a group of three amino acids found in the active sites of some enzymes like hydrolase and transferase. The catalytic triad provides a model for the chemical features and the structural properties of the enzyme, which allows them to facilitate reactions. Through a literature survey, we found the catalytic triad of the amidase family to be Ser-Ser-Lys. To identify exactly which triad (Ser-Ser-Lys) of the amidase family was involved, we used multiple alignments to identify it. In our amidase enzyme, we identified six lysine residues, namely L43, L79, L193, L271, L281, and L471, in the protein structure, of which 4, namely L43, L271, L281, and L471, lie on the surface. Among the remaining two lysines, L193 resulted in the formation of the ser-ser-lys triad; as this particular triad is stretched over 300 amino acids, we decided to rule it out as it is improbable to be involved in the binding. The final lysine was L79, surrounded by four probable serine residues around which it forms a catalytic triad, stretching over 100 amino acids [1].

AlphaFold [4,5]

SWISS-MODEL [7-11]

Conclusion:
We generated a Ramachandran plot for both the structures predicted by AlphaFold and SWISS-MODEL. The AlphaFold structure showed 93.5% residues in the favorable region, whereas the structure predicted using SWISS-MODEL showed 90% residues. Therefore, we chose the same because the AlphaFold predicted structure is more energetically favorable.

Since the structure of our amidase enzyme isn't well studied, we used software to predict its structure and binding sites. Models predicted by different software like SWISS-MODEL showed 35.6% sequence identity with 6-aminohexanoate cyclic dimer hydrolase. The binding site of all models was predicted using GRASP [12].

GRASP shows the amino acid residues that most probably form the binding pocket of the enzyme, out of which Ser 155 and Ser 179 showed 85% confidence scores showing that it interacts and Lys 79 with 59% confidence score showing it is not actively involved in bond cleavage but does help in stabilizing the interactions. The catalytic triad also shows a very high GC content, which is very common across all of the amidases having this triad. These glycines are also involved in stabilizing the structure. In the Ser-Ser-Lys catalytic triad, the lysine polarizes the serine in the middle, forming one strong hydrogen bond with the nucleophilic serine to activate it. Further, the lysine can stabilize the structure, which is crucial for its orientation inside the active site.

We used Clustal Omega [13] for multiple sequence alignment of p-nitro acetanilide hydrolase (Accession No. -K9NBS6), 6-aminohexanoate-cyclic-dimer hydrolase (Acc No.-P13397), linuron hydrolase(AEO20132),omega-lactams(BAI44731) and our Ochrobactrum sp. TCC-2 amidase. After aligning our amidase with several other biochemically similar amidases, which also have the Ser-Ser-Lys catalytic triad, it was observed that our predicted triad residues perfectly align with all the other ones. This further validates the hypothesis that the catalytic triad was a major active site involved in the interaction between TCC and TccA amidase.

Enzyme Efficiency

Two key methods for enhancing enzyme efficiency through site-directed mutagenesis are [14]: Replacing one amino acid with an isosteric residue of different function: This method investigates how changes in chemical properties affect enzyme function while keeping the enzyme's overall structure constant.
Replacing one amino acid with another of identical function but resulting in a different structure: This method explores the relationship between function and structural variation, focusing on how enzyme efficiency depends on structural diversity.

To further ensure our predicted binding site was accurate, we changed the Serine-Serine-Lysine (Ser-Ser-Lys) residues within the amidase enzyme's catalytic triad. Using PolyPhen software, we predicted that these mutations would harm the enzyme's function. This indicates that these specific residues are crucial for the enzyme's activity.

This finding highlights that the residues around the catalytic triad are essential. Altering the amino acids close to the catalytic triad requires a comprehensive understanding of each amino acid's functions. However, in contrast, previous directed evolution studies have demonstrated improved efficiency through modifications to amino acids situated at a distance from the binding site. This observation does represent the relationship between residue changes and enzymatic performance, showing that an iterative approach may not yield the desired goal.

The amidase enzyme possesses a high-efficiency rate portrayed by its ability to degrade 77% of initial TCC concentration (in 24 hours without glucose). This indicates that nature has optimized it to a significant degree, leaving limited room for improvement through evolutionary methods. The suggested maximum improvement achievable through directed evolution, approximately 3-4%, is quite modest. The effort required for such a marginal enhancement may not be justified. Resource constraints, including a lack of access to supercomputers, further impede the feasibility of exploring complex methods like modifying the enzyme's transient state at an atomic level. Given these factors, the project's original goal of substantially increasing the enzyme's efficiency may not be feasible using the chosen approaches. Therefore, exploring alternative strategies or objectives that align better with the available resources and constraints would be a better option.

Docking

We docked our amidase enzyme from the TccA gene of Ochrobactrum sp. TCC-2 to the TCC molecule using the following softwares: AutoDock [15] (Version 1.5.7) When we docked TCC to the amidase enzyme usingAutoDock for 50 docking runs, we got the best binding energy, -7.51 kcal/mol (a considerably good binding affinity score), where TCC was bound to the catalytic triad.

Binding energy	-7.51
Ligand efficiency	-0.4
Intermolecular energy	-8.11
Total internal energy	-0.38
Electrostatic energy	0.09
Torsional energy	0.6
Unbound energy	-0.38
cIRMSs	1.42
refRMSr	8.61

A web server SeamDock [16,17] as a confirmatory - Its docking protocol incorporates various powerful software tools, enhancing its capability for molecular docking simulations. These software tools include Dock 6, AutoDock4, EADock, AutoDock Vina, and rDock.

Workflow/Procedure of SeamDock: To generate results, we provided input files containing our ligand(UniProt ID: A0A167MNS0) and receptor [18] information to the system. Subsequently, we examined the output data and drew conclusions based on our analysis, as outlined in the study [19].

Results: The binding affinity was -4.7 kcal/mol, and the TCC molecule was binding to the Ser-Ser-Lys catalytic triad, which proves that it could further act upon TCC to degrade it.

Dock of TccA amidase with linuron

Linuron (3-(3,4-chlorophenyl)-1-methoxy-1-methylurea) is a phenyl urea herbicide that accumulates in the soil and controls the germination and new emergence of grasses and broad-leafed weeds. It inhibits the photosynthesis in plants.

Inference from the dock: ΔG values between -5.6 and -6.7 point to stable interactions between the amidase and the linuron, possibly leading to product degradation. This research was performed to see whether the TccA amidase enzyme can break down additional substances that are ideally broken down by other amidases. Linuron is one of the numerous compounds an enzyme from the amidase family has degraded. Amidohydrolases break it down into the carcinogenic byproduct 3,4-DCA. This by-product is also a by-product of TCC being broken down by the enzyme TccA amidase. According to the BLAST results shown in Fig. 11, the TccA amidase enzyme shares roughly 50% identity with other amidase enzymes. Hence, it is safe to assume that it may also degrade other substances broken down by the enzymes in the amidase family.

Inference from the docking studies: The catalytic triad has Ser-Ser-Lys. The nitrogen molecule of TCC showed H bond interactions with Ser 179 and Ser 155. The two Serines interact with TCC and are nearer to it in the docked structure. Being positively charged, Lysine is a bit far, helps bring a water molecule closer, and aids the Serine for the proper cleavage of TCC amide bonds. Hence, lysine doesn't actively interact with TCC but brings a water molecule for the hydrolytic reaction.

Molecular Dynamic Simulations

A Molecular Dynamics Simulation (MDS) is a computational method used to simulate and study the behavior of atoms and molecules over a period of time. It helps simulate the interactions between atoms or molecules using force fields. Force fields are mathematical models that describe forces acting on the sample to be studied due to factors like van der Waal interactions, hydrogen bonding, electrostatic interactions, etc, over a period of time. It helps record the positions and velocities of every atom or molecule while considering their interactions. MDS is often used to study protein folding, chemical and protein interaction reactions, and material properties. It is a powerful tool and requires significant computational resources. We conducted MDS studies for the TccA amidase and analyzed the results to check the overall stability of the enzyme.

MDS Results of the docked structure of TccA amidase with TCC
Specifics-

• pH - 7
• Temperature - 37°C
• Ionized water
• OPLS3 force field
• Software used - GROMACS v4.5.5
RMSF

Root Mean Square Fluctuation (RMSF) calculates how much each residue fluctuates inside a molecular structure. It sheds light on the system's adaptability and dynamics. Throughout the simulation track, RMSF determines the average deviation of atom positions from their average positions. It focuses on the positional variations of each specific residue for time in a given environment.


Most of the peaks in Fig.17 are less than 2 nm, an ideal range for a stable structure. The peaks around the 100th, 200th, and 275th residues are due to loops formed by the residues in that range. This can be seen in the Fig.18. The regions highlighted in pink, orange, and red are the residues forming turns and loops; they are generally more unstable than the rest of the structural residues. Hence, they contribute to the peaks. Apart from the highlighted residues, the rest are stable. Hence, we can say that the enzyme may retain its conformation despite getting docked with TCC and other environmental changes.


Orange- residue 95 to 105 residue Pink - residue 200 - 212 residue Red - residue 270 to 275 residue RMSD




Root Mean Square Deviation (RMSD) depicts the quality of the prediction over a period of time. It displays the Euclidean distance (the distance between two points in Euclidian space) between predicted values and measured actual values.



In our case, the deviation from the predicted value of the distance between the atoms is increasing very slightly with time; however, the structure is stable, and that stability extends up to 10 ns.
It reaches a plateau after 7(ns), beyond which it will have a constant fluctuation between 0.175 and 0.225.
The overall fluctuations are within 1Å. Hence, all data obtained from further experimentation will provide accurate results.


Hydrogen bonds depict the hydration of the enzyme. It shows the number of hydrogen atoms interacting with the amino acid residues in the enzyme over a period of time. The hydrogen bonds stabilize the transitional residues that occur as time progresses. Hence, the greater the hydrogen interactions, the more stable the enzyme. Hence, if certain hydrogen interactions are removed, especially from the residues involved in catalysis, there may be a change in the K_cat (catalytic constant) value. The effect the hydrogen bonds have on each residue will need to be tested by conducting experiments. One advantage of MDS over docking studies is in docking, the water molecules are removed for ease of operation. But this step becomes a huge issue for enzymes that actively use the hydrogen bonds from the surrounding water molecules for their catalytic reactions, which would be the case for our amidase enzyme.

In the Fig.20, the residues in the enzyme are bonding with 330 to 390 hydrogen atoms with fluctuations of 20 to 30 hydrogen atoms. This implies that the conformation of the enzyme after getting docked with TCC does not vary extensively over time. Hence, we can conclude that the docked structure is very stable and can be used for experimentation.




The radius of gyration (RoG) is used to monitor the structural formation process of a molecule. It represents the compactness of the molecule's structure and is calculated as the average distance between each atom and the molecule's center of mass.





It provides valuable information about the overall size and shape of the molecule during the simulation process. The radius of gyration decreases with time, and it becomes more compact showing that TCC is a natural substrate of our enzyme and forms a stable structure with TccA. The changes in the radius of gyration can tell us the conformational changes and dynamics of the docked molecule over time.
As shown in Fig 21, the radius of gyration (Rg) fluctuates between 2.15 and 2.1 (nm); this implies that the structure of the enzyme is very stable and can be used for further experimentation.


Solvent Accessible Surface (SAS) is the structure's surface area accessible to a solvent measured over a period of time. The TccA enzyme docked with TCC has an area fluctuating between 180 nm² and 205 nm² accessible to the solvent (water). This implies that the enzyme folding is very stable, and this structure can be used for further experiments.




Growth Modeling


Enzyme Kinetics






The next steps for us would be to model the degradation pathway of the toxic by-products of TCC by our amidase. We would then put it inside our chassis and predict the concentration of the by-products as time goes by.
Enzyme kinetics governing the degradation pathway from TCC to nontoxic by-products inside our chassis Acinetobacter baylyi:

Without product Inhibition Assumption taken here is the product formed doesn't have an inhibitory effect on the substrate. Hence the equations are formed without product inhibition.



With product Inhibition
When the product is formed during the process, it acts as an inhibitor and binds to the enzyme or enzyme-substrate complex, thus stopping product formation.




Bioreactor Modeling









Introduction



Bioreactors are tanks where raw materials are converted into biochemical products using microbial, human, plant, or animal cells. In wastewater treatment plants, bioreactors are designed to support an active biological climate, which helps the bacteria and protozoa to survive. The bioreactor we are proposing is a packed bed model. We have opted for a packed bed reactor as it helps establish better contact between the fluids and the solids. To determine the kinetics of the bioreactor, we had to come up with equations that could help us calculate the kinetics. To break down the calculation into different parts, we had to understand the different stages of our final degradation. The 3 stages that lead to the degradation of TCC are as follows:


1. Growth of our chassis
2. Adsorption of the TCC from sludge onto biochar, and then TCC goes into the cell by passive diffusion, given its hydrophobic nature,
3. Degradation kinetics come into play.



The bacteria uses TCC as a carbon source after the TccA amidase is introduced, and the bacteria itself breaks it down further into non-toxic byproducts.
Hence, we came to the conclusion to divide our design equation into the following three parts:


1. Based on microbial growth.
2. Based on the degradation kinetics of TCC.
3. Based on the adsorption kinetics.



To pick the right type of bioreactor, we went through literature and talked to experts. We have made a Bioreactor Handbook to make this process easier for future iGEM teams.
The common assumption taken into consideration for determining kinetics is that it is an ideal case with no regard for other compounds in the sludge.





Growth Kinetics



DESIGN EQUATION FOR THE GROWTH RATE:


Number of cells versus time called the Bacterial Growth Curve


1. Lag Phase - No cell division takes place. Change in the number of cells is 0.
2. Exponential (Log) phase- Cell division increases and then becomes constant. Change in the number of cells increases exponentially.
3. Stationary phase- No cell division takes place.
4. Death phase- All the nutrients are used up.



In all these phases, the phase that has the growth of cells (more cell division) is in the Log phase. To calculate the growth of the microorganisms, we used the Monod kinetic equation.

DESIGN EQUATION

The Monod kinetics equation is an empirical model suggested for the growth of microorganisms. It describes the complex process of development and biodegradation linked to growth involving multiple enzymes [3]. The Monod mathematical model is the most frequently and widely used method to describe the growth of microbes in pure and mixed cultures. Monod is used to model the growth of bacteria in the exponential (log) phase. In this phase, the bacteria divides rapidly and hence requires a lot of carbon sources, and TCC is actively used as a carbon source by our bacteria.

• μm - maximum specific growth rate
• S - Concentration of the growth limiting factor or substrate
• Ks - Saturation or Monod model

There are two main dominant constants, μmax and Ks, in Monod kinetics. The Ks values have been observed to vary concerning μmax, thereby implying that the two parameters are not entirely independent but come together during the fitting procedure [4]. We got the values of μmax and Ks from the growth curve data provided by wet-lab experimentation and assumed a few conditions to develop a design equation for our proposed bioreactor model.
The three main assumptions considered were as follows:


1.Balanced growth was assumed concerning OD (optical density). In the maximum growth phase, the cells have adjusted to a new environment and multiply rapidly at a maximum rate. This period of exponential growth with respect to time is referred to as balanced growth, where the cell components grow at the same rate (pseudo-steady state).
2.Cell suspension is homogeneous. The cell suspension in the form of a homogenous mixture was assumed to ensure that all components, mainly nutrients, oxygen, and other cellular byproducts.
3.In our calculations, we have considered TCC as the variable component and kept everything else constant.
Our main goal here is the check the growth of our chassis utilizing LB broth in the presence the TCC.

The above equation is the design equation for our ideal batch reactor. This equation calculates the time required for the exponential phase of growth of our bacteria in the presence of TCC in ppm levels in our ideal batch reactor.
where,




From Acinetobacter baylyi growth curve graph given above from wet lab we obtained the value of μmax

In batch, growth change in the biomass concentration with respect to time in the exponential phase is given by this equation.
The growth kinetics model has the following assumptions


1. A.baylyi is not transformed
2. A.baylyi is growing in a media like LB broth having a simple carbon source and in the presence of TCC concentration present in the sludge.
3. A.baylyi does not take in TCC as a carbon source as our amidase gene is not present in it (degradation kinetics of the transformed bacteria is done in the following sections).
4. The bacteria follows Monod, utilizing nutrients of LB broth and tolerating the TCC concentration until TCC concentration needs the maximum limit and the bacteria dies as shown in the graph below, obtained from the experiments carried out in wet lab.

To calculate the yield coefficient of our bacteria
*The values used in the calculation are obtained from the experiments carried out in wet lab. Refer to wet lab page for more information about the experiments and growth curve.
This is the amount of time required for the bacteria Acinetobacter baylyi to grow efficiently in the exponential phase utilizing LB broth and in the presence of TCC in ppm levels.






Adsorption Kinetics


DESIGN EQUATION FOR THE ADSORPTION:
Our goal is to achieve 90% adsorption efficiency as after 90% adsorption, the TCC concentration in the outlet sludge falls down to non toxic levels ; to do that, we are calculating the amount of biochar needed. For our bacteria to degrade TCC, TCC first needs to get adsorbed from sludge onto our biochar. Hence, adsorption kinetics(mass transfer) plays a very important role in modeling our bioreactor.
From the literature, we know that the adsorption kinetics of TCC onto biochar has been done only up to batch process in a shake flask where only 0.5g of biochar was used [34]. In our model, we have calculated and scaled up the adsorption kinetics of TCC onto the biochar from 0.5 g to a lab-scale packed bed bioreactor. According to our Raschig ring calculation mentioned below, the amount of biochar we need for our lab scale packed bioreactor of height 900mm and 5cm diameter is 1211g or 1.211 Kg, and we scaled up our calculation to fit the lab scale, including the treatment of 1.2L of sludge instead of 50 mL as mentioned in the literature. The calculations related to scaling up to lab-scale haven't been done before; by using our calculation on the scaling-up mechanism, we modeled our bioreactor to identify the number of cycles we need to run our packed bed through and determine the reusability of our packed bed before it is discharged. An immobilized packed bed bioreactor with biochar is used to treat harmful aniline and chloroaniline contaminants in the sludge, and the calculations ensuing it have been proposed for the first time.
A few assumptions taken are as follows:


1. Bacterial growth in the pores of biochar doesnt affect the adsorption.
2. Biofilm formation on the biochar wont be significant enough before the packed bed is replaced.
3. Hydrophobic Contaminants other than TCC will also get adsorbed onto biochar, which will be removed by the regeneration process (our chassis also degrades a huge number of other contaminants that might be adsorbed onto biochar). Hence, biochar will not get easily exhausted by other contaminants.



Material balance: TCC lost from sludge= TCC gained by biochar
This is the ideal design equation for adsorption kinetics in our packed bed. To optimize the method, we decided to do the calculations based on the highest(21 ppm), lowest (10 ppm), and average concentration (15 ppm) of TCC in sludge.
The pseudo-second-order model fit the data better, suggesting that TCC adsorption capacity increased as initial TCC concentrations increased. According to the pseudo-second-order estimation, the adsorption process was a rate-controlling phase of TCC removal by biochar. The kinetic model predicts activity over the entire spectrum of adsorption by assuming that the rate-limiting step is chemisorption. In this case, the adsorption rate was determined by adsorption capacity rather than adsorbate concentration (TCC).
Langmuir Isotherm: The adsorption equilibrium of TCC on biochar follows the Langmuir isotherm. A better fit with the Langmuir model results suggests that monolayer TCC adsorption occurred in BC(biochar) and BK1(biochar:KOH=1:1). The adsorbate (TCC) was attached to the biochar surface homogeneously.
Since TCC adsorption follows pseudo second order kinetics [34]: From pseudo 2nd order kinetics:



Equation (1) was validated by taking the data points from the literature, which matches the literature results. Hence, we went ahead with this equation for our scaled-up lab-scale studies [34].

Case 1: Taking yo as 21 ppm for n=1(Cycle 1)


n=2 (Cycle 2)
This is the mass balance of cycle 2 adsorption kinetics


Value of n = 46, where n is the number of cycles that can treat 21 ppm of TCC with 1211 g of biochar.

For 46 cycles, our packed bed can treat 46x1.2L of sludge = 55.2 L of sludge.

Each cycle is run for 2 days, so 46x2 = 92 days of run time. Hence, 55.2L of sludge can be treated in 92 days, after which our packing material needs to be replaced.
Case 2: Taking yo as 15 ppm

n=1(Cycle 1)


Value of n = 65, where n is the number of cycle that can treat 15 ppm of TCC with 1211 g of biochar.
For 65 cycles, our packed bed can treat 65x1.2L of sludge = 78 L of sludge.
Each cycle is run for 2 days, so 65x2 = 130 days of run time. Hence, 78L of sludge can be treated in 130 days, after which our packing material needs to be replaced.
Case 3: Taking yo as 10 ppm

Value of n = 96, where n is the number of cycles that can treat 10 ppm of TCC with 1211 g of biochar.
For 96 cycles, our packed bed can treat 96x1.2 L of sludge = 115.2 L.
Each cycle is run for 2 days, so 96x2 = 192 days of run time. Hence, 115.2L of sludge can be treated in 192 days, after which our packing material needs to be replaced.

Raschig ring calculation:
Raschig rings are tubular tubes for facilitating chemical processing and mass transfer packing material. They are porous, homogeneous, and have the same length and diameter [5].

L/D*=1, as it is the optimum ratio for Rashig ring.




Degradation Kinetics



DESIGN EQUATION BASED ON DEGRADATION KINETICS: The rate expression is related to the rate at which the Ochrobactrum cell can degrade TCC. One of the assumptions that we have taken is that since our chassis is Acinetobacter baylyi, which is also gram-negative like Ochrobactrum sp.TCC-2, the rate of transport or the passive diffusion of TCC into the cell will be similar in both the bacterias and hence the rate of degradation of the TCC inside the cell by our amidase inserted in our chassis will be very similar. The time calculated here for 21 ppm will be used to model the bioreactor.

In this study [33], we have used their values, as shown in the tabular column above. These values were used to calculate -rA, (the rate of reaction with respect to reactant A or in our case, TCC) using differential calculation.








Input = Output +Accumulation + Disappearance of TCC by the reaction —(1)
0 = 0 + accumulation + disappearance of TCC by the reaction.

Material balance is the starting point for designing any reactor; by using the above equation, we can derive the design equation or the performance equation for the batch, fed-batch, and continuous reactors.

For an ideal batch reactor:
1. Input = Output = 0; during the reaction, since it's an ideal batch reactor, there's no input and output.
2. Ideality in the batch reactor is defined with respect to the uniform concentration within the reactor.
3. Dead zones or dead pockets are the main reasons for the non-ideality in a batch reactor.


In an ideal batch reactor, concentration is uniform throughout the reactor, implying no spatial non-uniformity. Therefore, the entire batch reactor can be treated as a single element, and the material balance can be applied in the whole batch reactor, and the concentration is uniform. In the continuous reactor, one portion of the reactor is taken for material balance, and then it is integrated. A batch reactor is called an unsteady state operation as the concentration of product and substrate varies with time.

The above equation is the general design equation for our ideal batch reactor. This equation calculates the time required to degrade TCC in an ideal batch reactor.

Analytical method :
To optimize the method, we decided to do the calculations based on the highest (21 ppm), lowest (10 ppm), and average concentration (15 ppm) of TCC in sludge. We have gone with 90% degradation efficiency in each case.
To simplify our calculations, we have assumed that nothing interferes with the degradation of TCC.
For varying concentrations (ppm):

The time to degrade 90% of the initial TCC concentration is the same in all three cases(20.56 hrs), as it only considers the degradation kinetics and not the biomass needed in each case. To degrade 21 ppm of TCC, the amount of biomass required is much more than 10 ppm of TCC, which is not considered in the pure degradation kinetics but is considered in the growth kinetics. Unlike other models available, the time required for growth has also been considered along with the degradation kinetics.
The time calculated here for 21 ppm will be used to model the bioreactor.
This time is quite close to the data in one of the graphs in [33] in this paper. The data presented closely aligns with our assumptions and equations, further validating our model. This study found that 31.7muM (10 ppm) of TCC is degraded to approximately 2.1 muM (0.66 ppm) in 20 hours, achieving an impressive degradation efficiency of 93%. This outcome aligns with our initial assumption of 90% efficiency, reinforcing the accuracy of our calculations.

Conclusion:
After doing all the kinetic calculations, we concluded that the toggling time should be around 2 days for the bacteria to be effectively growing, considering both ideal and real-life conditions. To learn more about our bioreactor design and analysis, refer to our implementation page.







References


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