Team:Hong Kong HKUST/Model
MODELLING
Overview
According to our project modules, we try to categorize our modelling into three parts. The first one is from the Laccase Module, where we attempt to characterize our laccase construct using our lab and previous iGEM data. The second one is from the Alkane Metabolism Module, as we aspire to use the stoichiometric ratio of the ASS catalySed reaction to observe the activity of ASS and observe the rate of conversion from alkane to succinate. While for the MFC module, we focus our modelling to establish data to find the optimum concentration for Shewanella sp. growth, as well as estimating the voltage and power density that can be produced.According to our project modules, we try to categorize our modelling into three parts. The first one is from the Laccase Module, where we attempt to characterize our laccase construct using our lab and previous iGEM data. The second one is from the Alkane Metabolism Module, as we aspire to use the stoichiometric ratio of the ASS catalySed reaction to observe the activity of ASS and observe the rate of conversion from alkane to succinate. While for the MFC module, we focus our modelling to establish data to find the optimum concentration for Shewanella sp. growth, as well as estimating the voltage and power density that can be produced.
Laccase Module
As there is little documentation about the usage of laccase from E. coli, we rely on the literature [1] of laccase secreted by fungi to correlate with the number of alkane and alkene chains can be formed. Using simple calculation, it can easily be translated that 2900 alkane chains (30%) and 900 alkene chains (10%) should be formed after polyethylene is treated with laccase for every centimeters squared. Using UCL iGEM 2012 [2] finding about polyethylene degradation, we assume that the rate of degradation will eventually be linear with 0.9 PE molecule degraded per second, of which 28 molecules of alkane and 9 molecules of alkene will be formed in 100 seconds. Using the weight and the density of polyethylene, there would be 3.86*10^-12 mm^3 or 82,000 polyethylene molecules degraded within one day.. To improve BBa_K863006 obtained from the Bielefeld iGEM 2012, we try to characterize it by adding OmpA and his-tag. However, due to time constraint, our wet lab experiment could not acquire any valuable data and the modelling team will only rely on literature findings. OmpA itself is a major protein that can be found in the outer membranes of most gram-negative bacteria, including E. coli. It will signal and facilitate E. coli to secrete enzyme more efficiently, in this case laccase.
It it known that the average secretion efficiency of E. coli using OmpA can be increased by 3% during the first hour of incubation, and the fold changes by 2.11 within the first 20 hours [3]. Here, fold change indicates the relative values of the yields or secretion efficiencies of constructs from OmpA Sp divided by native Sp. We collaborate this data with the available characterization result on iGEM Registry for BBa_K863006 [4].
The graph above denotes the estimated activity with ABTS as substrate. Here, the measurement of 308 ng ECOL (BBa_K863005) was done in pH 5 at 25° C (Bielefeld, 2012). The 8mM concencentration of ABTS was assigned to be substrate saturated. The bars on the right indicates the assessed amount of oxidized ABTS when ECOL is ligated with OmpA.
CO2 to methane
Carbon dioxides can be converted into methane after undergoing reduction process, in which the molecule uses the energy from the sun / catalyst to break up the CO2 molecule into carbon and oxygen atoms, then combine with hydrogen to form methane and water, as explained on the chemical equation below.
Using irreversible Henri-Michaelis-Menten Kinetics, we try to consolidate an enzyme-catalyzed reaction with a single reaction and and reaction rate equation with Vmax of 0.8 ± 0.07 nmol/min and a Km for CO2 of 23.3 ± 3.7 mM [1].
From this graph, it can be seen that it takes over 3 hours to fully convert 10 nmol of CO2 into methane. It appears to verify that common features of homogeneous catalysts for CO2 reduction to CH4 are low reaction rates (e.g., turnover frequencies) and limited number of turnovers (e.g., turnover number) before inactivation of the catalyst [2].
Alkane and MFC Modules
FBA
In the alkane degradation and MFC modules, we adopted Flux Balance Analysis (FBA) model to capture the relationship between different variables and characterize the theoretical maximum values of target outputs. The FBA model is widely used to simulate a genome-wide metabolic network, and the flux distribution between metabolites. With this algorithm, it is possible to maximize an objective function under a set of constraints provided by the user or the genome database, without specific enzyme kinetics inputs. By using FBA, we can analyse the alkane degradation pathway and electron generating reaction while taking into consideration of the complex metabolism network. This algorithm also helped us bypass the enzyme kinetics part, since little has been documented about the ASS enzyme complex in current literature. However, this method was limited to simulate equilibrium state only, and the theoretical limits are highly dependent on the database and constraints provided.[1] In our project, we used iSO783 as Shewanella Oneidensis MR-1 metabolic model, and made adjustment upon it. iSO783 is a widely-used S. Oneidensis MR-1 model containing 774 reactions, and 783 genes. [2]
Hopefully, this mathematical modelling can provide an insight into the interdependence of conditional factors and serve as a guide of our experimental design.
Extracellular Electron Transport
In the MFC, S. oneidensis MR-1 has been reported to transport electrons to electrode in three ways, (1) direct electron transport (DET) mode based on the c-type cytochromes and conductive pili called nanowires, (2) self-secreted flavins to convey electrons and 3) the mediated electron transfer (MET) mode, which relies on exogenous mediators [1]. The DET route, which is a more dominant transport mode without the help of exogenous mediators, is modelled and studied. As reviewed in the MFC part of our wiki, the DET route depends on the c-type cytochrome (MtrC and OmcA) in the cytoplasmic membrane interacting with the electrode. It can also use nanowires to transfer electrons to the electrode that is located distantly from the cells.
In the iSO783, we considered the reaction flux of CYOO2 as our optimization objective as it involved in the reduction of a type of cytochrome c protein, denoted as Cco (SO2361 and SO2362 and SO2363 and SO2364) or Cyco (SO4606 and SO4607 and SO4609) in iSO783). In such case, the reaction flux of CYOO2 is taken to estimate the DET flux.
DET- Lactate
As noticed the ability of S. oneidensis MR-1 utilizing lactate to generate electricity [2], we first examined the FBA model using lactate as the carbon source for electricity generation. We examined the effect of varying lactate uptake flux on two separate objectives, i.e. maximizing biomass growth and maximizing DET flux. We assume 5% of maximum growth as the boundary of biomass growth flux, which would be the minimum viable growth rates in practice as described by Mao [1].
The graph showed that the DET flux reached a plateau at 81.68 mmol/gDW/h as lactate uptake flux increased. An upper bound existed such that increasing lactate uptake would no longer increase the electricity generation.
Noted that the biomass growth is driven to its lower bound when the optimization objective is set as DET flux, we studied the relationship between DET flux with biomass flux at constant lactate input. The DET flux first sustained at 81.68 mmol/gDW/h but then decreased when biomass flux increased beyond 0.164h-1. This implies the electricity generation could possibly be maximized when below a certain growth rate, however, higher growth rate could possibly decrease the electricity generation.
Shewanella Growth in Hexane
In this part, we used FBA to generate the maximized growth flux of Shewanella oneidensis MR-1 when providing hexane as energy source. Reaction constraints were set based on literature [1] values and genome database was adjusted to suit our engineered construct by adding the alkane degradation reactions. Results show that the maximized growth under aerobic condition is around 0.513 h-1 , while the anaerobic growth flux is around 0.298h-1 , both enough to sustain growth. This means theoretically, Shewanella oneidensis MR-1 is able to grow in a hexane-containing media without provision of lactate or glucose under both aerobic and anaerobic conditions. [1]
Maximum current generation and power output
Current is given by the derivative of the electric charge over time. The electron flux can be converted to current using Faraday’s constant 96485 C/mol
Given the maximum DET flux is 81.68mmol/gDW/h, therefore, the Shewanella oneidensis MR-1 is possible to generate current up to 2.189A/gDW.
The upper limit of MFC cell voltage is calculated based on the difference of standard cell potential in the anode and cathode. The standard potential are summarized in the table.
| Redox Couple | Eo(V) | |
|---|---|---|
| Anode | Cytochrome c (Fe3+) + e− → Cytochrome c (Fe2+) | +0.254[3] |
| Cathode | Ferricyanide [Fe(CN)6]3− + e− → Ferrocyanide [Fe(CN)6]4− | +0.436[4] |
| O2 + 4H++4e− → 2H2O | +0.51 [5] |
In the MFC design that uses ferricyanide as cathode, the maximum voltage would be 0.182V. If oxygen is used as cathode, the maximum cell voltage would be 0.256V. The maximum power output could be 0.398W/gDW in ferricyanide while 0.56W/gDW could be reached using oxygen as cathode.
Effect of fumarate
In pursuit of an overall higher electron output, we tried to identify how the nutritional factors in culturing media affect DET flux and growth flux. Hexane concentration was found to play a minor role since the actual uptake flux was restricted to be low(around -6.04*10-7 mmol/gDW/h) by internal factors of the bacteria.
However, fumarate was found to be an essential factor since it affects for growth, DET, and hexane uptake. The blue curve shows a positive correlation between fumarate uptake and DET flux (with growth flux set to 5%), and DET achieves its maximum value 81.68mmol/gDW/h at a fumarate uptake flux of 8 mmol/gDW/h. The green curve is the corresponding growth flux when DET was optimized. Since DET and growth cannot be optimized simultaneously, we separately constructed the red curve to describe the relationship between growth flux and fumarate uptake when optimizing growth. The curve shows a positive correlation and growth flux achieves its maximum value 0.9408h-1 when fumarate uptake flux reaches 94 mmol/gDW/h.
Aeration effect on DET flux
We also explored the difference of DET flux under aerobic and anaerobic condition. In anaerobic condition, we assumed fumarate as the electron acceptor. It is surprising that the DET flux is driven to extremely small negative value under anaerobic condition, while DET flux can reach 81.68mmol/gDW/h when oxygen flux is set as 20.42mmol/gDW/h according to literature[EET 1].
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