Team:Kyoto/Model
Modeling
Overview
Based on the human practice work for wastewater treatment plants, we decided to create a device that would precipitate and recover microplastics. In this section, we focus on the process in which Encapsulin (or in other words actual part where binds to PET, CBM/ Carbohydrate Binding Module;) adsorb to PET, then adsorb to other substances to cause precipitation. From a paper, we learned that cellulose is one of the most abundant substances in wastewater, and CBM binds specifically to not just PET but also to cellulose, so we have decided to simulate how much it would compete with cellulose instead [1]. From this approach, we can quantitatively measure how much PET and CBM adsorb ultimately in the presence of cellulose.
Background
Prepared an equation to represent the concentration of CBM, PET and cellulose.
In the present modeling, the adsorption of CBM and PET, and the adsorption of CBM and cellulose were regarded as secondary reversible reactions. Assuming that PET, CBM, and cellulose were uniformly present, the chemical formula was simplified as followed:
The time change in the chemical formula shown above is expressed by the following formula.
Equilibrium constants and rate constants were indispensable for studying the time development of adsorption, and it was necessary to examine the rate constants in the adsorption and dissociation of PET and CBM. However, there was no literature data available so we calculated it empirically.
According to the result of experiments, it was easily anticipated that CBM will remain in excess when the reaction is complete. Thus, the above reaction can be regarded as a first-order reversible reaction and we did as so.
The time change in the chemical formula shown above is expressed by the following formula.
Equilibrium constants and rate constants were indispensable for studying the time development of adsorption, and it was necessary to examine the rate constants in the adsorption and dissociation of PET and CBM. However, there was no literature data available so we calculated it empirically.
According to the result of experiments, it was easily anticipated that CBM will remain in excess when the reaction is complete. Thus, the above reaction can be regarded as a first-order reversible reaction and we did as so.
Method
We will describe the process of deriving equations used in modeling.
First, a rate constant was derived.
As mentioned before, chemical formula (1) in the above can be regarded as first-order reaction since the concentration of <CBM> is kept constant.
(1) has an equilibrium constant (Kd) of 25.4 (ug/L), [2] so the equilibrium constants (Ka) for (2) is
Moreover,
Kfa and Kba are rate constants related to the increase and decrease of CBM. <A>e and <B >e are the equilibrium values of <A >and <B>. The weight (g) of CBM-PET generated by CBM 1g is expressed as sm,
and this equation is established. <A>0 is the initial value of <A>. From equation (4), (6)
At equilibrium, the time change of x becomes zero,
Integrating the equation above,
Therefore,
From the above, the rate of constant Kf can be derived. This Kf is the amount of CBM reduced by the positive reaction. Adsorption between the device and PET is represented by the following equation.
Similarly, the time variation of the adsorption of the device and cellulose is expressed by the following equation.
Kon and Koff are values derived from literature [3]. Staff at wastewater treatment plant said (see HP gold). that the time for washing water to flow through the washing pipe was 1 hour, and the time for washing water to enter the wastewater treatment plant to the next stage was 2 hours. This treatment time is assumed to be for households around Kyoto University. In this project, the device is installed before the washing drainage enters the sewer. As for the cellulose concentration, it is assumed that the cellulose concentration increases at a constant rate from the moment it enters the plant and reaches the concentration of the wastewater treatment plant at equilibrium in tens minutes or so. The input (t) represents a constant increase in cellulose concentration. In this situation, we compare the two dimers.
As mentioned before, chemical formula (1) in the above can be regarded as first-order reaction since the concentration of <CBM> is kept constant.
(1) has an equilibrium constant (Kd) of 25.4 (ug/L), [2] so the equilibrium constants (Ka) for (2) is
Moreover,
Kfa and Kba are rate constants related to the increase and decrease of CBM. <A>e and <B >e are the equilibrium values of <A >and <B>. The weight (g) of CBM-PET generated by CBM 1g is expressed as sm,
and this equation is established. <A>0 is the initial value of <A>. From equation (4), (6)
At equilibrium, the time change of x becomes zero,
Integrating the equation above,
Therefore,
From the above, the rate of constant Kf can be derived. This Kf is the amount of CBM reduced by the positive reaction. Adsorption between the device and PET is represented by the following equation.
Similarly, the time variation of the adsorption of the device and cellulose is expressed by the following equation.
Kon and Koff are values derived from literature [3]. Staff at wastewater treatment plant said (see HP gold). that the time for washing water to flow through the washing pipe was 1 hour, and the time for washing water to enter the wastewater treatment plant to the next stage was 2 hours. This treatment time is assumed to be for households around Kyoto University. In this project, the device is installed before the washing drainage enters the sewer. As for the cellulose concentration, it is assumed that the cellulose concentration increases at a constant rate from the moment it enters the plant and reaches the concentration of the wastewater treatment plant at equilibrium in tens minutes or so. The input (t) represents a constant increase in cellulose concentration. In this situation, we compare the two dimers.
Result 1
We figured out that the binding of CBM to cellulose did not compete with that of microfiber.
The experimental data for Kf is as follows.
The weights of CBM is presented by <MF-CBM>. At equilibrium and 10 seconds later were 2.55 e + 04 and 2.54 e + 04, respectively (μg/litre). Since the initial values of <PET> and <CBM> were 1.73 e + 06 and 5.00 e + 05, respectively, sm = 68.6, Kf = 1.52 e-08 and Kb = 3.86 e-07 (1/s) were calculated.
Then, equations (14) and (15) were made to be the same conditions as in the wastewater treatment plant [1], and the ratio of devices bound to cellulose was examined by simulation in Matlab, and the following graph was obtained.
The Competing Rate is the percentage of the device in cellulose and the device dimers in the total of the device. This indicates the ratio of the input device adsorbed to cellulose.
The weights of CBM is presented by <MF-CBM>. At equilibrium and 10 seconds later were 2.55 e + 04 and 2.54 e + 04, respectively (μg/litre). Since the initial values of <PET> and <CBM> were 1.73 e + 06 and 5.00 e + 05, respectively, sm = 68.6, Kf = 1.52 e-08 and Kb = 3.86 e-07 (1/s) were calculated.
Then, equations (14) and (15) were made to be the same conditions as in the wastewater treatment plant [1], and the ratio of devices bound to cellulose was examined by simulation in Matlab, and the following graph was obtained.
The Competing Rate is the percentage of the device in cellulose and the device dimers in the total of the device. This indicates the ratio of the input device adsorbed to cellulose.
Result 2
We calculated how much microfibers can be recovered based on the quantity of the device we put in.
From the results of the simulation above, we thought that cellulose would be another substance to be adsorbed to Encapsulin in a wastewater treatment plant, and the following equation was obtained:
We considered PET adsorbs to the device as “captured PET”.The Capture Rate indicates the percentage of captured PET in the total of PET in the laundry wastewater.
If 6.20*10^4 (μg/liter) of our device are inserted, which can recover PET by about 80%, their values change with time as the following graph.
The amount of enzyme used in one wash is 2.8 ~ 3.0 g, assuming 45 L of washing water are used. Referring to [4] and the list price of general enzymatic detergents, the cost of the device is estimated at about 1 dollar per month. To calculate this cost we conducted an experiment to measure how much enzymes are contained in major household detergents [4].
We considered PET adsorbs to the device as “captured PET”.The Capture Rate indicates the percentage of captured PET in the total of PET in the laundry wastewater.
If 6.20*10^4 (μg/liter) of our device are inserted, which can recover PET by about 80%, their values change with time as the following graph.
The amount of enzyme used in one wash is 2.8 ~ 3.0 g, assuming 45 L of washing water are used. Referring to [4] and the list price of general enzymatic detergents, the cost of the device is estimated at about 1 dollar per month. To calculate this cost we conducted an experiment to measure how much enzymes are contained in major household detergents [4].
Conclusion
From the calculation results above, the following statement can be said:
・The binding reaction associated with the device is rapid relative to the reaction time at the wastewater treatment plant.
・The device generates many trimers in which two PET adsorb.
・Since the binding reaction is rapid, there is a high possibility that plastics other than microfibers such as scrub can be recovered.
・The device is estimated to cost around 1 dollar per month.
・The device generates many trimers in which two PET adsorb.
・Since the binding reaction is rapid, there is a high possibility that plastics other than microfibers such as scrub can be recovered.
・The device is estimated to cost around 1 dollar per month.
Future Application
Accurate Kf could be measured by performing an experiment that can accurately measure the time variation.
In result 2 section, it is estimated that about 30g of SONOBE for its reaction, but this is mainly due to Encapsulin weights way more than CBM. Moreover, in the simulation above, there are only 2 binding sites that can attach to the Encapsulin, but in reality, there are 60. If 60 CBMs were grown, a higher recovery rate could be expected due to the formation and precipitation of masses of PET-SONOBE-PET.
You can also grow something else. This may be used to increase the efficiency by generating a bond that adsorbs only to PET and another bond that adsorbs only to another substance at the ratio calculated by simulation.
There are a large number of devices that does not adsorb to either MF or cellulose after sedimentation treatment. However, it may be possible to recover easily if a hand corresponding to an activated sludge microorganism is developed from Encapsulin.
A Survey of Cellulose Profiles in Actual Wastewater Treatment Plants.
Japanese Journal of Water Treatment Biology 36, 9-14 2 Weber, J., Petrović, D., Strodel, B., Smits, S.H.J., Kolkenbrock, S., Leggewie, C., and Jaeger, K.E. (2019).
Interaction of carbohydrate-binding modules with poly(ethylene terephthalate).
Appl. Microbiol. Biotechnol. 103, 4801–4812. 3 Kari, J., Olsen, J., Borch, K., Cruys-Bagger, N., Jensen, K., and Westh, P. (2014).
Kinetics of cellobiohydrolase (Cel7A) variants with lowered substrate affinity.
J. Biol. Chem. 289, 32459–32468. 4 Chaplin, M. and Bucke, C. (1992).
Enzyme technology. 1st ed.
Cambridge: Cambridge University Press, pp.139-141.
In result 2 section, it is estimated that about 30g of SONOBE for its reaction, but this is mainly due to Encapsulin weights way more than CBM. Moreover, in the simulation above, there are only 2 binding sites that can attach to the Encapsulin, but in reality, there are 60. If 60 CBMs were grown, a higher recovery rate could be expected due to the formation and precipitation of masses of PET-SONOBE-PET.
You can also grow something else. This may be used to increase the efficiency by generating a bond that adsorbs only to PET and another bond that adsorbs only to another substance at the ratio calculated by simulation.
There are a large number of devices that does not adsorb to either MF or cellulose after sedimentation treatment. However, it may be possible to recover easily if a hand corresponding to an activated sludge microorganism is developed from Encapsulin.
References
1 Honda, S., Miyata, N., Iwahori, K. (2000).A Survey of Cellulose Profiles in Actual Wastewater Treatment Plants.
Japanese Journal of Water Treatment Biology 36, 9-14 2 Weber, J., Petrović, D., Strodel, B., Smits, S.H.J., Kolkenbrock, S., Leggewie, C., and Jaeger, K.E. (2019).
Interaction of carbohydrate-binding modules with poly(ethylene terephthalate).
Appl. Microbiol. Biotechnol. 103, 4801–4812. 3 Kari, J., Olsen, J., Borch, K., Cruys-Bagger, N., Jensen, K., and Westh, P. (2014).
Kinetics of cellobiohydrolase (Cel7A) variants with lowered substrate affinity.
J. Biol. Chem. 289, 32459–32468. 4 Chaplin, M. and Bucke, C. (1992).
Enzyme technology. 1st ed.
Cambridge: Cambridge University Press, pp.139-141.
