Team:NTU-Singapore/Modeling
Modelling
Objective
Our main objective is to propose an optimized model which involves both Flux Balance Analysis (FBA) algorithm and a set of Monod equations that is capable of predicting accurately the metabolism of Shewanella oneidensis MR-1 by minimizing the errors i.e. residuals between our predicted and observed results for 4 key growth measurements: Biomass, Acetate, Lactate and Pyruvate from the model while also optimizing electron activity simultaneously for the design of Shewanella oneidensis MR-1 powered MFCs. Kinetic Monod models have been shown recently to be extremely successful in modelling microbial growth dynamics over cultivation period but lack the ability to determine the flux distributions for more rigorous mathematical computations. Flux Balance Analysis (FBA) has also been widely used to determine flux distributions in order to maximize an objective function (e.g. growth rate) through linear optimization by maintaining their stoichiometric mass balance while allowing varying reaction constraints. However FBA also lacks the machinery to account for transient metabolic states of the studied cells since it only assumes complete steady states. This means that behaviours of cells which are realistically expected to adjust its metabolic fluxes constantly in order to response to constant changes in environmental conditions, cannot be comprehensively and realistically modelled by solely FBA, hence our motivation to propose an integration between two successful methods to overcome these problems. We first consider Proposition 1.1 for a formal introduction of the kinetic Monod model. In our study, the chosen metabolic model for our proposed optimization is iSO783 [1] of Shewanella oneidensis MR-1. Initially used to understand how Shewanella oneidensis MR-1 utilizes its resources for metabolism, iSO783 which was constructed to summarize a network of metabolic reactions comprising of 774 reactions, 783 genes and 634 unique metabolites for all involved cell components is now commonly used in simulation studies in FBA-related studies [1].
Monod Model
Proposition 1.1: Consider an initial 4 reactions that was developed to describe 4 main growth components in Shewanella oneidensis MR-1: cell growth, lactate uptake or production, acetate and pyruvate production or reuse,
Where X is the biomass (in g DCW/L), LACT, ACT, PYR are lactate, acetate and pyruvate concentrations respectively (in mmol/L), μL, μA, μP are the specific growth rates (in h-1) on lactate, acetate and pyruvate respectively, ke is the endogenous metabolism rate constant (in h-1), Yx/L, YX/A, YX/P are biomass yield coefficients (in DCW/mol substrate) of lactate, acetate and pyruvate respectively, rP,L and rA,L are the production rates of pyruvate and acetate from lactate (in mmol/L/h) of acetate and pyruvate from lactate respectively, rA,P is the production rate of acetate from pyruvate, S(t-tL ) is the dimensionless Heaviside unit-step time delay function to describe a lag phase L during cultivation before actual growth which was discovered in [2] s.t.
While the specific cell growth rate can be summarized in the next 3 Monod equations:
Where μL, μA, μP are the maximum growth rates (in h-1) on lactate, acetate and pyruvate respectively, and Ks,l , Ks,a and Ks,p are Monod constants (mmol/L) for lactate, acetate and pyruvate respectively. The acetate and pyruvate production rates are assumed to be proportional to the biomass as expressed below by the last 3 equations:
Where kal and kpl are rate constants of acetate and pyruvate production from lactate respectively (in L⋅(h⋅g DCW)-1) and kap are rate constants of acetate production from pyruvate (in L⋅(h⋅g DCW)-1). In total, there are 14 kinetic parameters in 10 equations in the kinetic Monod model.
To begin, we intend to estimate a set of these 14 kinetic parameters representing influential growth factors that could contribute to the metabolism of Shewanella oneidensis MR-1 so that the simulation can most closely resembles the actual metabolism. This is done based on comparison of our simulation against 3 independent replicates of observed experimental values for the 4 individual measurements: Biomass (g DCW/ L), Pyruvate, Acetate and Lactate (mmol/L) over a time span of 34 hours of metabolic activity [2] with the fore-mentioned SOA as follows:
In order to do so, we would first consider an initial set of values of the parameters for optimization in order to estimate the final set of values of the parameters which can produce a simulation that most closely resembles the observed values as Table R1A-1D by considering multiple sets determined from a number of repeated random sampling over a range of constrained values for each parameter uniformly from the initial set for our model for comparison (referred to here as Monte Carlo).
The value of the residuals (to be minimized) will be the summation of all the differences between predicted and observed results for Biomass, Acetate, Lactate and Pyruvate. Since the 4 different measurements have different scales, we normalize each differences with the maximum value of observed result from that corresponding measurement as shown below for all i observations:
From our simulation the results of the estimated parameters for growth factors summarized in Table R2 suggests that growth rate dependent on lactate, denoted by μmax,L, is much higher than the growth rate which depends on pyruvate, denoted by μmax,P or on acetate, denoted by μmax,A, indicating that lactate is the major carbon substrate for biomass growth. This result was confirmed in many other studies and simulations [2, 3, 4].
Microbial Fuel Cells
MFCs are designed to use micro-organisms as catalysts to transform chemical energy from organic compounds to electrical energy through enzymatic reactions that are associated with their respiration and metabolism [5, 6]. Hence one obvious advantage with MFCs is that they can generate clean and combustion-less electricity directly from mass of organic matter [7]. The second advantage is the natural diversity of micro-organisms available to the design of MFCs as compared to conventional chemical fuel cells. In a typical MFC set-up, the micro-organisms are placed in the compartment with the anodes and uses their biomass for growth while producing electrons and protons with their metabolism. The electrons produced can then be transported out of the cells to the anode with specific redox mediators or by some substrates which are reduced in the process while protons are diffused through the electrolyte to the cathode where is oxidized to water. Since Shewanella oneidensis MR-1 is capable of respiring using various organic compounds and reducing exogenous chemicals such as iron, manganese [9, 10, 12] and chromium [12], it can potentially generate electricity by utilizing extracellular anodes of similar materials as terminal electron acceptors in MFCs.
The respiration of extracellular solid metallic electrodes by MR-1 requires a reliable molecular pathway for transferring electrons from intracellular electron carriers such as NADH and quinones across double-layered membranes of MR-1 in order to reach the electrode. Such a molecular pathway is named as an extracellular electron transfer (EET) pathway where the double-layered membranes are named separately as inner membrane (IM) and outer membrane (OM). A study by Shi et al. [13] had identified the five primary protein components involved in any EET pathway: CymA, MtrA, MtrB, MtrC and OmcA (denoted respectively as SO4591, SO1776, SO1777, SO1778 and SO1779 in iSO783) in MR-1 denoted as a Mtr pathway while a recent study by Sturm et al. [15] has further identified small tetraheme cytochromes known as STC/ CctA and flavo-cytochrome c (FccA) proteins which are also involved in the same EET process. Clearly, these studies shows that in order for MR-1 to effectively conduct electricity, its Mtr pathway must work effectively as an electron conductor in order to link the IM quinone pool to the extracellular electrode by a series of electron-transfer reactions between a set of reliable protein components in OM.
Since there are many proposed theoretical models in literature under both aerobic and anaerobic growth conditions, in our study we only consider our MFCs set-up to harness electricity from the electrons using a derivative of EET, the direct electron transfer (DET) method for partial aerobic with anaerobic growth from applications of similar concepts of DET in EET transfer as summarized by Kouzuma [17]. To understand our motivation, we consider the electron transfer to the anode to be carried out by IM bound c-type cytochromes denoted as CymA protein, which act as the first electron transfer capacity to shuttle the electrons from the IM quinone pool to the next decademe c type cytochrome protein at MtrA bound in OM. These multi-heme proteins, existing in the cell membrane of Shewanella oneidensis MR-1, have also been shown to be chiefly responsible for reducing poisonous heavy metal ions in their living environment through their carefully designed metabolism [18]. MtrA is then involved in the electron transfer to MtrC and OmcA by forming a stable configuration with β-barrel protein MtrB and OM bound c-type cytochromes MtrC on OM at a stoichiometric ratio of 1:1:1 in order to support the electron exchange through OM to the last OM-bound c-type cytochromes OmcA which then finally releases the electrons to the electrode [19, 20, 22].
Fig. R3. Proposed extracellular electron transfer (EET) pathways (Mtr pathway) in Shewanella oneidensis MR-1 involved in direct EET or DET mode [17]: OM refers to outer membrane; IM refers to inner membrane; MQH2 refers to general reduced form of menaquinone or also known as menaquinol 7, i.e. mql7, in iSO783; MQ refers to general oxidized form of menaquinone or also known as menaquinone 7, mqn7, in iSO783.
In DET mode because MFCs are designed to conduct electricity by continuously extracting electrons from all the participating membrane-bound proteins in Mtr pathway to the anode, extra metabolic pressure on specific cellular activities of Shewanella oneidensis MR-1 may exist in order to maintain the electricity. Since it is believed that Shewanella oneidensis MR-1 contains 42 different types of cytochrome c proteins possibly interacting with one another [23], a recent simulation [16] have identified that the surplus flux of the reduced cytochrome c required in order to maintain that electricity in DET mode can be attributed to reaction 175 (ID: CYOO2) in iSO783. Furthermore, since electron transfer from CymA and MtrA involves reactions directed by either CctA or FccA where FccA is involved in only anaerobic conditions, hence one future direction from our research could be that electron transfer in the presence of both CctA and FccA under mixed aerobic-anaerobic growth conditions could be faster than in the presence of only FccA activity in fully aerobic growth.
