Modeling Gold Recycling with Delftibactin. Is upscaling feasible?

Introduction

Non ribosomal peptide synthetases are used by natural organisms in order to solve many different problems and gain evolutionary advantages. This utility has also been recognized at the industrial scale with pharmaceutical companies such as Cubist producing antibiotics (e.g. Daptomycin [Ref]) which are non-ribosomal peptides. Still, we were also fascinated by applications of our systems to the environment. Therefore, we conducted a lot of experiments with delftibactin, the molecule that can selectively bind and recover gold from solutions, and the corresponding NRPS genes. Concurrently with these experiments, as an additional proof of principle for the applicability of NRPS to the problem of electronic waste, we tried to use theoretical considerations and metabolic modeling to show the feasibility of our idea.

In particular, the feasibility of utilizing delftibactin for recycling at industrial scale was assessed by the next steps: A genome scale metabolic model of recombinant E.coli cells capable of producing Delftibactin was constructed and then simulated using constraint-based modeling (Flux Balance Analysis). The optimal production envelope was then used for further simulations of the bacterial growth and delftibactin production in a bioreactor, which was then used in order to estimate the cost for the produced delftibactin. Finally, a workflow for isolation of gold from printed circuit boards, which are leached using aqua regia, is suggested and then compared in regard to financial impact to state of the art methods (cite 2 papers from 2009) for gold recovery, which also utilize the same leaching agent (aqua regia).

chemical equations

$$ HNO_3 \: + \: 3 \: HCl \: \to \: NOCl \: + \: 2 \: Cl_{nasc.} \: + 2 \: H_2O $$

$$ 2 \: Au \: + \: 2 \: NOCl \: + \: 3 \: Cl_2 \: + \: 2 \: HNO_3 \: \to \: 2 \: HAuCl_4 \: + \: 4 \: NO_2 $$

$$ Fe \: + \: 4 \: HNO_3 \: \to \: Fe(NO_3)_3 \: + \: 2 \: H_2O \: + \: NO $$

$$ Fe(NO_3)_3 \cdot 9H_2O \: + \: 3 \: NaOH \: \to \: FeOOH \downarrow \: + \: 3 \: NaNO_3 \: + \: 10 \: H_2O $$

$$ DBC^+/OH^- \: + \: H^+/AuCl_4^- \: \to \: DBC^+/AuCl_4^- \: + \: H_2O $$ $$ DBC^+/AuCl_4^- \: + \: NH_4OH \: \to \: DBC^+ \: + \: NH_4^+AuCl_4^- $$

$$ 2 \: AuCl_4^-NH_4^+ \: + \: 9 \: NH_4OH \: \to \: Au_2O_3 \cdot 3NH_3 \downarrow \: + \: 6 \: H_2O \: + \: 8 \: NH_4^+Cl^- $$

$$ 4 \: Au_2O_3 \cdot 3NH_3 \: + \: 6 \: N_2H_4 \: \to \: 8 \: Au \downarrow \: + \: 12 \: NH_4^+OH^- \: + \: 6 \: N_2 \uparrow $$

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 [@Orth2010], that operates based one one key assumption: The system is assumed to be in steady-state, which means that the concentration of all of the cell’s inner metabolites remains constant throughout the process. Based on these assumptions, constraint based modeling, allows to make quantitative predictions about the cellular behavior, by utilizing a minimal set of information. The essential prerequisite of any type of constraint based modeling is the existence of a reconstructed metabolic network, where all reactions of the network have been characterized stoichiometrically. Once this is done, one constructs the stoichiometric matrix S of the network, which includes the stoichiometric coefficients of all metabolites in each of the reactions. In particular, each column of the matrix corresponds to a reaction and each row to a metabolite (example scheme). This represents a mass balance of the network. Beyond the stoichiometric coefficients, another essential part of the model are the boundary constraints: These place upper and lower bounds on the flux (turnover rate) of some of these reactions, based on physicochemical considerations and experimental data. For example, lower or upper bounds are set to 0 if a given reaction is considered as irreversible.

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 [@mahadevan2003]. In FVA, for each reaction $i$, the flux $v_i$ is maximized, then minimized, subject to \ref{eq:steadyState} and $c^Tv \geq s \cdot \max(c^Tv)$ with $s \in [0,1]$ and usually equal to 1.

Most of the constraint based modeling approaches have also been implemented in diverse software packages. Here, the the very popular COBRA toolbox for Matlab [@Schellenberger2011a] was used.

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] -> 1 mmcoa-S[c] + 1 pi[c] + 1 adp[c] + 1 h[c]

1 ppcoa[c] + 1 atp[c] + 1 hco3[c] -> 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] -> 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 [@Varma1994].

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 …, 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 .. 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.

In addition, as in bioreactor processes, as we reasoned that Oxygen consumption could be a limiting factor, for each of the previously sampled points, flux variability analysis was conducted in order to find the minimal oxygen flux supporting a particular growth rate and the corresponding optimal delftibactin production (figure …). All resulting fluxes were higher than the experimentally measured maximal oxygen uptake rate (15 $\frac{mmol}{g_{dw}h}$) and consequently the oxygen uptake parameter couldn’t be further optimized.

graph of maximal delftibactin production VS growth rate (vlt auch graph of oxygen consumption vS growth rate bei optimal delftibactin production?)

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 [@Mahadevan2004], which essentially discretize time into small steps. Flux and growth rates are calculated by FBA, then those are used in appropriate differential equations, the results are used to constrain the metabolic network in next time step, etc.

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 [@Zhuang2012] with the following equations adapted from Zhuang et al. [@Zhuang2013].

$$ \frac{dV}{dt}=\left\{\begin{matrix}\frac{v_{glc}XV}{S_{glc}-S_{glc}^{feed}}, if \ V < V_{max} \\ 0, if \ V \geq V_{max} \end{matrix}\right.$$ $$ \frac{dX}{dt}=\mu X $$ $$ \frac{dS_{glc}}{dt} = v_{glc}X + \frac{dV}{dt}\frac{S_{glc}^{feed}-S_{glc}}{V} $$ $$ \frac{dS_{delftibactin}}{dt} = v_{delftibactin}X $$ $$ |v_{glc}| \leq |v_{glc}^{max}| \frac{S_{glc}}{S_{glc} + K_m} $$

(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 [@Zhuang2013]. The other bioreactor parameters were set as follows: The concentration of glucose in the feed was equal to 1 mol/L, $K_m$ equal to 1 mmol/L [@Zhuang2013] and finally, the maximal glucose uptake rate was set to 10.5 \frac{mmol}{g_{dw}h} [@Varma1994]. The time step was set to 0.1 h.

Simulations with those conditions was performed for 150 equally spaced growth rate values on the production envelope (Fig. x)…

• figure with example concentration change or biomass change for 1 point
• figure with titer, volumetric productivity as a function of simulated points etc

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. Glucose costs 0.13$/mol (us department link), which is x euros/mol.
• 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 immediately start.
• The power supply of the bioreactor is equal to 2.5 kW (in Chmiel reference described for a 30 L bioreactor). This corresponds to a cost of …
• 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 (link). but h2o2 has to be used.

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

$P_{glc}$ [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:

$$ P_{delftibactin} = \frac{n_{glc}P_{glc} + t_fp_{reactor}}{n_{delfti}} $$

Figure: Price delftibactin as function of e.coli specific growth rate… Figure:

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… [@macgarvey2013]. The gold ions are reduced and gold is then precipitated in the form of nanoparticles.

Our proposed method is compared to a state of the art publication, which builds upon several patents [@byoung2009]. This method was chosen, because it starts with exactly the same steps as our proposed workflow, namely dissolution in aqua regia and neutralization with NaOH and also aims at gold recovery, thus making the comparison possible. On the other hand, in order to selectively extract gold from the aqua regia solutions many more chemical reactions, extraction using dibutyl carbitol, chromatography and reduction of the gold ions. This is contrasted to our method, in which delftibactin both bind selectively to gold ions and then also reduces them.

The two compared processes are summarized in Fig.

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:

$$(\mu, v_{delftibactin}) \in \mathrm{b-frontier} :\Leftrightarrow v_{delftibactin} = A\cdot \mu + b $$

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. [@Huang2012] used metabolic flux analysis in order to simulate the production of the antibiotic Daptomycin by Streptomyces roseosporus. Here the maximum daptomycin production was approximately equal to 0.06 $\frac{mmol}{g_{dw}h}$ for a glucose uptake rate of 0.7 $\frac{mmol}{g_{dw}h}$. Thus, the yield of daptomycin per glucose is appropriately equal to 0.1. This compares to our simulations …… Also the experimentally measured titer of daptomycin in fed-batch culture was 581.5 mg/L. This compares to our modelled fed-batch process titer of …….

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 [@villaedsen]. In between these methods lies the fed-batch, which was chosen here, in which medium keeps being added to the reactor, but is not withdrawn.

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 [@Hoefner2013]. Applying such methods could have allowed a greater coverage of the parameter space and in a quicker way.

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 [@Lee1999]. This is something that was not considered in the simulations here, but could definitely be easily added to the simulations ran here, by adding an appropriate inhibition term to the differential equations and also tracking the acetate concentration in the dFBA model.

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 [@Cui2007]. Pyrometallurgical processing, which is based on smelting, is a very common process, but also one that is often considered to be non-selective, requiring huge energy inputs and releasing harmful products in an uncontrolled way [@Chehade2013].

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) . There’s also toxic by-products, such as chlorine gas, especially if plastic is not separated from the metals in a initial step. Thus, the environmental impact could be improved for example by using bacteria in a first step in order to recycle the plastic, as has been done in several iGEM projects.

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 [@Owens2013] and pipelines, which try to isolate as many metals as possible, e.g. by iterative steps of electrolysis at different voltages so at to precipitate and reduce the different metals. Such processes of course are best from an economic perspective, but are difficult to compare to our suggestion in a quantitative manner. Of course, further developments could allow the creation of similar pipelines based almost exclusively on bioengineering, which could then be compared.

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)…