Team:Heidelberg/Modelling/Gold Recovery
From 2013.igem.org
Line 332: | Line 332: | ||
</body> | </body> | ||
</html> | </html> | ||
+ | |||
{{:Team:Heidelberg/Templates/Footer-Nav}} | {{:Team:Heidelberg/Templates/Footer-Nav}} |
Revision as of 01:45, 29 October 2013
![](https://static.igem.org/mediawiki/2013/a/a6/Heidelberg_go_up2.png)
![](https://static.igem.org/mediawiki/2013/a/ae/Heidelberg_tour2_btn.png)
Introduction
Non-ribosomal peptide synthetases expressed in natural organisms help to develop evolutionary advantages over competitors. This ability has been recognized at the industrial level for example, by pharmaceutical companies like Cubist that produce antibiotics (e.g. Daptomycin [Ref]) based on non-ribosomal peptide synthesis. Of course, we were also fascinated by the idea to elevate our system to a larger scale and to test its industrial feasibility. Accompanying our experimental results confirming the ability of delftibactin to precipitate gold we attempt to use theoretical considerations and metabolic modeling to show the realistic potential of our idea. In particular, the feasibility of utilizing delftibactin for recycling at industrial scale was assessed in the following steps: A genome scale metabolic model of recombinant E.coli cells capable of producing Delftibactin was formulated and then simulated using constraint-based modeling (Flux Balance Analysis). Subsequently, the optimal production envelope was used for simulating the bacterial growth and delftibactin production in a bioreactor, which was used to estimate the cost for the produced delftibactin. Finally, we suggest a workflow for the isolation of gold from printed circuit boards using delftibactin and compare its potential financial impact to two state of the art methods (cite 2 papers from 2009) for gold recovery, which also utilize the same leaching agent (aqua regia).
Suggested Workflow
General overview
Having estimated the cost for delftibactin production, it is now possible to estimate the cost for recovery of gold from printer circuit boards. In particular, our proposed approach is very similar to the one followed in the laboratory experiments: The electronic chip is dissolved in aqua regia, the resulting solution is neutralized with NaOH and then delftibactin is added in a 2:1 molar ratio to the dissolved gold. This ratio was chosen, because...
Our proposed method is compared to a state of the art publication, which builds upon several patents
The two compared processes are summarized in Fig.
chemical equations
$$ HNO_3 \: + \: 3 \: HCl \: \to \: NOCl \: + \: 2 \: Cl_{nasc.} \: + 2 \: H_2O $$
$$ 2 \: Au \: + \: 2 \: NOCl \: + \: 3 \: Cl_2 \: + \: 2 \: HNO_3 \: \to \: 2 \: HAuCl_4 \: + \: 4 \: NO_2 $$
$$ Fe \: + \: 4 \: HNO_3 \: \to \: Fe(NO_3)_3 \: + \: 2 \: H_2O \: + \: NO $$
$$ Fe(NO_3)_3 \cdot 9H_2O \: + \: 3 \: NaOH \: \to \: FeOOH \downarrow \: + \: 3 \: NaNO_3 \: + \: 10 \: H_2O $$
$$ DBC^+/OH^- \: + \: H^+/AuCl_4^- \: \to \: DBC^+/AuCl_4^- \: + \: H_2O $$ $$ DBC^+/AuCl_4^- \: + \: NH_4OH \: \to \: DBC^+ \: + \: NH_4^+AuCl_4^- $$
$$ 2 \: AuCl_4^-NH_4^+ \: + \: 9 \: NH_4OH \: \to \: Au_2O_3 \cdot 3NH_3 \downarrow \: + \: 6 \: H_2O \: + \: 8 \: NH_4^+Cl^- $$
$$ 4 \: Au_2O_3 \cdot 3NH_3 \: + \: 6 \: N_2H_4 \: \to \: 8 \: Au \downarrow \: + \: 12 \: NH_4^+OH^- \: + \: 6 \: N_2 \uparrow $$
Substance |
Molecules/2 Au |
Mol of Substance/Mol of Au |
Amount of substance/Mol of Au |
Price [€]/Mol of Au |
---|---|---|---|---|
HNO3 |
9 |
4.5 |
0.188 |
3.46 |
HCl |
92.86 |
13.5 |
1.41 |
30.879 |
HCl |
92.86 |
13.5 |
1.41 |
30.879 |
NaOH |
6 |
30 |
3 |
0.12 |
DBC+ |
32 |
16 |
4 |
424 |
NH4OH |
9 |
4.5 |
0.085 |
2.79 |
N2H4 |
6 |
3 |
0.104 |
27.66 |
Sum |
489.21 |
Delftibactin Production
To model Delftibactin production, we
Explanation of constraints based modeling
Constraint based modeling is a computational method to mechanistically simulate complex metabolic networks
Interestingly, the constraints define polytopes in a high-dimensional space, which is usually called the flux space. One can easily prove that polytopes are convex sets, which is a property that makes them amenable to several manipulations (REF+EXAMPLES). These polytopes are usually represented as follows:
$$ S\cdot v = 0 $$ $$ v_{min} \leq v \leq v_{max} $$
where $S$ is the stoichiometric matrix, $v_{min},v_{max}$ describe lower and upper bounds of the metabolic fluxes.
As this polytope is high dimensional, methods have to be applied in order to determine probable flux distributions or to compare flux spaces corresponding to different cells or states. The usual procedure describes the maximization of a linear objective function $c^T\ v$ subjected to the constraints defined in ~\ref{eq:steadyState}. This concept is based on the assumption that biological systems have evolved in order to maximize a certain objective for example the growth rate of the organism. To convert this principle into linear programming the following algorithm is formulated: Maximize $c^T\ v$ subject to the above constraints. This method is usually called Flux Balance Analysis (FBA) and the linear objective maximized is in most cases the so-called biomass reaction, though it can also take other forms, such as ethanol production or ATP maximization, depending on the context.
Although linear programs can be solved quickly with an optimal objective function value returned, there can exist many alternate optimal solutions, of which available solvers return only one. In order to capture this alternate solution space, flux variability analysis (FVA) can be employed
Most of the constraint based modeling approaches have also been implemented in diverse software packages. Here, the the very popular COBRA toolbox for Matlab
Metabolic model of Delftibactin producing E.coli
As explained in the previous section, to simulate the metabolism of a cell using flux balance analysis, the stoichiometric representation of the underlying metabolic network has to be available. As the biochemistry of E.coli has been extensively studied, there also exist comprehensive metabolic reconstructions. Here we used the iAF1260 model, which captures 2077 reactions of K-12 MG1655 E.coli corresponding to 1260 genes. Of course, wild type E.coli is not able to produce Delftibactin. Thus the reactions corresponding to the gene products we are trying to introduce into our TOP10 cells (LINK delftibactin project) responsible for the production of this non ribosomal peptide, were appended to the aforementioned model.
In particular, wild type E.coli can produce all the monomers necessary for Delftibactin production, with the exception of methylmalonyl-CoA, which is required for the PKS part of the synthetase. Thus, a reaction converting propanoyl-CoA to methylmalonyl-CoA with the following stoichiometry was added:
$$ 1 \: ppcoa[c] \: + \: 1 atp[c] \: + \: 1 \: hco3[c] \: \to :\ 1 :\ mmcoa-S[c] :\+ :\ 1 :\ pi[c] \: + \; 1 adp[c] \: + \: + 1 h[c] $$
Subsequently, the main delftibactin production reaction was added. The stoichiometry is governed by the amino acids monomers which are combined under usage of 1 ATP each and the Claisen condensation of methyl-malonyl CoA. This core reaction of the synthetase was accompanied with the subsequent modification enzymes [macgarvey2013] which are also necessary for the functional activity of Delftibactin. These comprise the aspartic acid dioxygenase (coded by the gene DelD), the N5-hydroxyornithine formyltransferase (DelP) and finally the lysine/ornithine N-monooxygenase (DelL). The stoichiometry of this lumped reaction is the following:
1 ala-L[c] + 2 ser-L[c] + 1 asp-L[c] + 2 thr-L[c] + 1 gly[c] + 2 orn[c] + 1 arg-L[c] + 10 atp[c] + 1 akg[c] + 2 o2[c] + 1 10fthf[c] + 1 nadph[c] + 1 h[c] + 1 mmcoa-S[c] \to 10 amp[c] + 20 pi[c] + 1 co2[c] + 1 succ[c] + 1 thf[c] + 1 nadp[c] + 1 h2o[c] + 1 coa[c] + 1 co2[c] + 1 delftibactin
In regards to constraints of the metabolic model, it was assumed that E.coli grows on minimal glucose medium under aerobic conditions. The maximal glucose uptake rate was set to 10.5 $ \frac{mmol}{g_{dw}h} $ and the oxygen uptake rate to 15 $\frac{mmol}{g_{dw}h}$ and the ATP maintenance flux (which represents the non-growth associated energy required for maintaining the biological processes of the cells) was set to 7.6 $\frac{mmol}{g_{dw}h}$. Those fluxes have been previously measured for aerobically growing E.coli
As we were interested in the optimum case, that is the maximal possible delftibactin production based on the stoichiometrically imposed constraints, we initially used FBA with delftibactin production as the objective function. The resulting flux was 1.2105 $\frac{mmol}{g_{dw}h}$ but the corresponding specific growth rate was 0. Thus, in the next step, using FBA again, the maximum possible specific growth rate was determined and then the interval was split into 150 parts. For each of these intervals, the growth rate was fixed and FBA was ran again. The resulting plot -also called the production envelope- shows the optimal delftibactin production rate as a function of the specific growth rate (FIGURE). As could have been expected, the delftibactin synthesis drains a lot of resources which are also necessary for growth (ATP, amino acids) and thus these two objectives represent a natural trade-off. The maximal growth rate, when the bacteria are not producing delftibactin at all is 0.8093 $\frac{1}{h}$.
Bioreactor Simulations
The next step in the modeling was the estimation of the cost of delftibactin by use of a fed batch process. A flux balance analysis model only gives estimate for steady-state fluxes and does not capture dynamic behaviours, such as fermentation processes. This is solved by dynamic FBA (dFBA) frameworks
A fed-batch process with an exponential feeding strategy, in which the glucose concentration, remains constant and delftibactin is produced, was modelled by dFBA using the DyMMM (Dynamic Multispecies Metabolic Modeling framework ) MATLAB framework
$$ \frac{dV}{dt}=\left\{\begin{matrix}\frac{v_{glc}XV}{S_{glc}-S_{glc}^{feed}}, if \ V < V_{max} \\ 0, if \ V \geq V_{max} \end{matrix}\right.$$ $$ \frac{dX}{dt}=\mu X $$ $$ \frac{dS_{glc}}{dt} = v_{glc}X + \frac{dV}{dt}\frac{S_{glc}^{feed}-S_{glc}}{V} $$ $$ \frac{dS_{delftibactin}}{dt} = v_{delftibactin}X $$ $$ |v_{glc}| \leq |v_{glc}^{max}| \frac{S_{glc}}{S_{glc} + K_m} $$
(figure : cost/productivity/yield vs different parameters)
where X [g/L] is the E.coli biomass, V, Vmax [L] are the currently and maximally filled volume of the bioreactor, $S_{glc}$, $S_{glc}^{feed}$, $S_{delftibactin}$ [mmol/L] are the concentrations of glucose and delftibactin in the reactor or the feed, $K_m$ [mmol/L] the Michaelis-Menten constant for glucose uptake, $\mu$ [1/h] the growth rate of the bacteria and finally $v_{glc},v_{delftibactin}$ $\frac{mmol{g_{dw}h}$ the flux rates of the corresponding reactions with $v_{glc}^{max}$ being the maximal possible flux.
The starting conditions were set to a volume of 1 L, a biomass of 0.1 g/L and a glucose concentration of 20 mmol/L, as in
Simulations with those conditions was performed for 150 equally spaced growth rate values on the production envelope, as shown previously in Fig.X. Fig. Y shows the resulting time series in regards to biomass concentration and delftibactin concentration for 3 representative points from the envelope. As can be expected, higher growth rates result in the process finishing (reaching steady-state at which point the fermentation would be stopped) a lot quicker with most total times lying around the range of 15 to 100 hours. This is expected, as in the model, the glucose feed is stopped as soon as the 10 L of the bioreactor have been filled. Also, the final concentration of delftibactin ranges from approximately 40 to 80 \frac{mmol}{L}, with higher titers achieved for lower growth rates, while dry biomass (10 to 50 \frac{g}{L}) titer is higher in the case of high growth rates.
The above observations actually give rise to another view of the growth rate - production rate tradeoff, namely the economic aspect. Lower growth rates actually lead to higher final delftibactin concentration in the bioreactor, which is of course wanted, but on the other hand the process takes a lot longer to finish, thus requiring more operational costs. Exactly this trade-off will be explored in the next session.
Delftibactin Production Cost
The ultimate goal of the aforementioned simulations was the optimistic calculation of the cost required for production of delftibactin. Thus, for each of the simulated points, we calculated the costs by starting with the following assumptions:
- The cost of the growth medium of the E.coli is equal to the cost of glucose spent.
- The operation of the 10 L bioreactor requires 1 full time technician with a wage of 2000 euros per month.
- After finishing the operation of the bioreactor, the next cycle can start after a time offset of 3 hours.
- The electricity cost of the bioreactor is calculated based on its power rate and assuming constant operation.
- Delftibactin has been secreted to the supernatant and it does not have to be purified in order to selectively precipitate gold, as shown in our experiments. Instead hydrogen peroxide has to be used to remove reducing agents except delftibactin from the medium.
For these calculations, the following prices were looked up and used:
Glucose |
0.13 Dollar per mol |
|
---|---|---|
Technician |
2000 € per month |
rough estimation based on German wages |
Reactor Power |
2.5 kW/h |
Value for 30 L bioreactor |
Hydrogen peroxide |
6.54 € per Liter |
Carl Roth |
Hydrogen peroxide per Medium |
1/500 |
estimated in our experiments |
Electricity Cost |
0.1879 € per kW |
|
USD-EUR Exchange Rate |
0.7253 € per Dollar |
In particular, let $n_{delftibactin}$ [mol] denote the number of delftibactin mol produced, $n_{glc}$ [mol] the glucose consumed and $t_f$ [h] the time at which the fermentation ends. All of these values can be can be easily calculated based on the results of the previous simulations.
$$ n_{delftibactin} = S_{delftibactin}V_f $$ $$ n_{glc} = S_{glc}^{start}V_0 + S_{glc}^{feed}(V_f-V_0) $$
and $t_f$ is just the time after which $\frac{dS_{delftibactin}}{dt} = 0 $.
Now also let
$t_{offset}$ [h] be the time until the next fermentation cycle can start, $P_{glc}$ [euros/mol glucose] be the price of glucose and p_{reactor}, the cost of operating the reactor per time (equal to the wage for 1 technician per time and the electricity cost). Then the final cost $P_{delftibactin}$ per mol of delftibactin is equal to:
$$ P_{delftibactin} = \frac{n_{glc}P_{glc} + (t_f+t_{offset})p_{reactor}}{n_{delfti}} $$
Based on the above equation equation, for each simulated point of the production envelope, the cost per mmol of delftibactin was calculated (Fig.). In the figure the trade-off between growth rate and delftibactin production immediately becomes obvious. In fact, the relationship of price to growth rate appears to be parabolic and actually has a global minimum. This global minimum of 0.1755 Euro per mmol of Delftibactin achieved to $ \mu = 0.37 h^{-1}$ is the cost we will assume in the next section.
Cost estimation for whole procedure
Having estimated the cost for produced delftibactin, it is now possible to also calculate the cost for the whole gold recovery process. Similarly, to the cost calculation for the gold procedure and using the aforementioned costs for aqua regia and NaOH, we calculated that for recovery of 1 Kg Gold approximately 25 Euros are required in addition to the necessary delftibactin. Under the assumptions that 1 molecule of delftibactin binds and reduces exactly one gold ion, one can then quickly calculate the cost for the whole process. The current gold price, as well as the price for recovery from electronic trash has been summarized in table X.
The above calculation also means that in order for delftibactin production to be profitable, it should cost less than xx per mmol of delftibactin.
Below the Pareto frontier
One important consideration is the fact, that the above modeling assumed that our engineered bacteria actually operate on the pareto optimality frontier in regards to growth rate and delftibactin production rate. As it is very hard to engineer bacteria up to this level, it would be of interest to know at what delftibactin production and growth trade-off point the bacteria would still be profitable in contrast to the chemical method.
In order to describe this, we initally observed that the Pareto Frontier (Fig.X) can be decently represented by a linear equation:
$$ v_{delftibactin}^{pareto} = A\cdot \mu^{pareto} + B $$
A,B were estimated using linear regression ($R^2 =, B=-1.5132, A=1.2319$).
We then defined sub-pareto frontiers to be points lying on parallel lines below the actual product envelope and identified them by their y-Axis intercept. In other words:
$$(\mu, v_{delftibactin}) \in \mathrm{frontier(b)} :\Leftrightarrow v_{delftibactin} = A\cdot \mu + b $$
Discussion
Constraint-based modeling
One of the main assumptions that went into the FBA based modeling was that the E.coli bacteria have been engineered in such a way, so as to maximize the delftibactin production rate. In fact, the simulated points lie on the pareto frontier (product envelope) and they place an upper bound to what is theoretically possible, simply due to stoichiometric considerations.
In order to get an insight to the resulting numbers, it could be useful to compare with two other recent approaches that modelled NRPS/PKS systems in a similar way. Huang et al.
The same group subsequently also did COBRA modeling and experimentally measured production of FK506 (a 23-membered polyketide produced by PKS/NRPS) by Streptomyces tsukubaensis. The experimental production rate was 1.61 $\frac{\mu mol}{g_{dw}h}$ for a C6 uptake rate of 3.47 $\frac{mmol}{g_{dw}h} and a growth rate of 0.0495 1/h.
Bioreactor simulation
In general, there exist three main methods for the cultivation of bacteria in bioreactors: The most classical one is the batch method, in which all of the initial medium is inoculated at the beginning point. In contrast, in the continuous fermentation, new medium keeps flowing into the reactor while also being withdrawn at the same rate. Continuous fermentation of course requires a lot less labour costs, provides higher yields and is more controllable than the batch process. On the other hand, in real processes, the microorganisms often mutate to non producing variants, thus making continuous processes problematic
This method, was simulated using dynamic FBA (dFBA), which quickly proved to be a very valuable method for combining dynamic processes with stoichiometric metabolic models. One disadvantage are the rather long simulation times, but recently methods have been developed in order to efficiently numerically simulate differential equations of which the right hand side actually requires the optimization of a linear program
In particular, one of the problems that appear in aerobic E.coli fermentations is the fact that at high growth rates (almost surely for growth rates above 0.35 1/h) a lot of acetate is produced which actually suppresses growth
Proposed workflow
In order to recover metals from electronic waste, several different methods have been developed and are industrially utilized. In some of the common processes, the trash is incinerates, thus releasing toxic dioxins
Another commonly used method is hydrometallurgical processing, in which diverse chemicals are used for the leaching of the trash in order to dissolve the metals in aqueous solutions. Traditionally, cyanide has been used for this, but due to environmental accidents, it is increasingly avoid [REFERENCE]. Still, hydrometallurgical is often considered to be highly selective and have a good recovery.
Aqua regia used in our proposed pipeline also falls into the category of hydrometallurgical processing. Note that aqua regia is not necessarily the best choice of leaching agent to be used at industrial scale, for example the high cost of the necessary equipment (special stainless steel)
It is important to note again that the method proposed here only requires the existence of Gold ions in a fairly neutral solution. Thus, new developments in ecologically friendly leaching agents or even bioleaching agents could be immediately coupled to the delftibactin process. In fact, it could easily replace the gold extraction step in most used in most industrially used processes in a plug-and-play fashion, whereas the chemical isolation steps would have to be extensively readjusted to the new conditions.
Finally, it has to be mentioned that efficient industrial processes consist of closed-loop systems
Feasibility and benefits of our proposed method
Outlook
- engineering e.g. using NRPSDesigner of molecules similar to delftibactin with specificity for other metals
- pipeline possible to completely recover electronic waste using NRPS as well as previous igem projects (e.g. plastic recycling projects)...