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Wageningen UR iGEM 2014

Modeling Overview

Three aspects of the BananaGuard system have been modeled. (I) Accurate balancing of the different promoters elements in the the kill switch is required in order to maintain a bi-stable system. Using statistical mechanics an estimation for the optimal promoter configuration was made, balancing the amount of different repressors with number of repressor binding sites and their respective position on the promoter. The obtained results have inspired the design of promoters for the kill-switch. Having designed an optimal system its performance in the soil can be estimated in order to gain insight in its functionality. From a modeling perspective the most interesting questions that can be answered are: the metabolic price that has to be paid for the introduced genetic circuit and the stability and performance of the genetic circuit. (II) A genome scale metabolic model was extended outlining and answering the cost query and subsequently the biological control agents ability to not be outcompeted in the soil by other rizhosphere populating micro-organisms. (III) A stochastic model was made in order to quantify and characterize the stability and performance of the introduced genetic circuit. The model takes into account rates predicted by the metabolic model, cell division, the anti-gene transfer toxin antitoxin systems effect on cell growth and the kill-switch.

Schematic overview of the integration between the modelers themselves and the wetlab experimentalists

Kill-switch promoter design

Introduction

Promoter design for a stable kill-switch involves balancing of different regulatory components. Two elements, the number of repressor binding sites and the position of those binding sites with respect to the gene, control two key variables; the chance a repressor binds to the regulatory region and the affinity with which it binds. These variables, in turn, determine the effectiveness of the repressor protein [1].

It has been shown that repressor proteins are more effective when there are more repressor binding sites in front of a gene, confirming that the increased chance of repressor protein binding leads to a significant increase in its effectiveness [2]. With respect to binding affinity, it has been shown for TetR proteins that a repressor binding site positioned in front of the open reading frame is more effective than those positioned at the back [3].

Because of slight variations in the position of a repressor binding site or variations in experimental conditions, a range of different repressor binding strength values are reported for the same repressor (sometimes varying several orders of magnitude)[4].

This means that case specific designs cannot be modeled accurately but the likelihood of designing a functioning system can be estimated. By taking all the possible repressor binding site combinations and varying the different binding affinities (thereby simulating their position) and production rates, the robustness of the repressor binding site combinations can be determined (Figure 1). Statistical mechanics is an ideal tool because it can incorporate both repressor binding strength and binding sites. Learn more about the statistical mechanics approach or view the results.

**Figure 1.** The figure shows the kill-switch with arbitrarily chosen repressor binding sites. (I) Altering the position of the TetR repressor binding sites change the effectiveness; a large space of basepairs between the binding site and the LacI will result in weaker repression [8]. (II) Adding a LacI repressor binding site will increase the chance that LacI binds to the promoter region.

Theory and experimental design

Statistical Mechanics

Statistical mechanics provides a way to understand how the macroscopic properties of a system arise from the individual components within this system. In effect there are two states to consider in statistical mechanic descriptions. A macrostate specifies a system in terms of quantities that average over the microscopic constituents of the system. For example if you consider a closed container of gas, quantities for the macrostate would be pressure or volume. This means that these macrostate quantities only work if you consider a system with a very large number of particles. Talking about a macrostate of a single molecule makes no sense since the terms are inherently descriptive of large systems. A microstate, however, does describe the properties of a single molecule e.g. kinetic energy and position. The macro- and micro-states come together in the key concept of statistical mechanics. A lot of different microstates can result in the same macrostate, but characterizing the macrostate imposes restraints on the possible microstates.

Modeling Biological Systems using Statistical Mechanics

The logic of macrostates and microstates can also be applied to cells, replacing the container of the previous example with the cell and the different particle constituents with RNA polymerases and repressor proteins. The condition and production states of the various proteins can be considered a macrostate. Modeling with statistical mechanics provides an insight in transcription regulation of a genetic circuit by generating ‘parameter-free’ predictions for the levels of gene expression. Assuming transcription of a gene to be proportional to chance that a RNA polymerase binds to the promoter of interest a statistical mechanics model has two microstate outcomes:

(I) A state where none of the polymerases are bound to the gene of interest and distributed among non-specific binding sites (non-specific binding).

(II) A state where the promoter of the gene of interest is occupied and the remaining polymerases are distributed among the non-specific binding sites (specific binding)6. In order to determine the probability that either state will be realized we need to know the total number of possible micro-sates and the chance that a particular microstate will be achieved. For the non-specific binding by RNA polymerases combinatorics can be used 5,6.

$\frac{N_{n s}!}{P! (N_{n s} - P)!} = N u m b e r o f n o n - s p e c i f i c b i n d i n g p o s s i b i l i t i e s$

Where P is the number of RNA polymerases and N_ns the number of non-specific binding sites. Because there is a difference in the binding strength between specific and non-specific binding sites a Boltzmann weight needs to be included:

$Z (P) = \frac{N_{n s}!}{P! (N_{n s} - P)!} e^{- \frac{P ε_{p d}^{N S}}{K_{b} T}}$

The Boltzmann weight describes difference between strength of specific and non-specific binding. For the non-specific binding of RNA polymerases the Boltzmann weight ε_pd^NS is going to be very low compared to specific binding compensating for the high number of binding site arrangements. In order to get the total statistical weight the microstate for RNA polymerase bound to the promoter needs to be added.

$Z_{t o t} (p) = Z (P) + Z (P - 1) e^{- \frac{ε_{p d}^{S}}{K_{b} T}}$

ε_pd^S is the specific binding energy of the RNA polymerase binding to the promoter. To obtain the chance an RNA polymerase is bound we divide the specific binding chance by the total chance.

$P b o u n d = \frac{Z (P - 1) e^{- \frac{ε_{p d}^{S}}{K_{b} T}}}{Z_{t o t} (p)}$

By dividing top and bottom by Z(P^-1)e^{(-(ε_pd^S)/(K_bT))} the equation takes the form of a Hill function where the assumption was made that the amount of polymerases is a lot smaller than the amount of non-specific binding sites

$P b o u n d = \frac{1}{1 + \frac{N_{n s}}{P} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}}}$

In this form a fold change of mRNA expression can be correlated to the chance that a polymerase binds. If the situation is thus N_ns/P e^{(-(∆ε_pd^S)/(K_bT))} = 0, that the chance of an RNA polymerase binding is equal one, there is no change in expression (i.e. the fold change in expression remains one). This will most likely be the case in a system without interference. Most biological systems however are dependent on regulators, repression is the main method of gene regulation in our designed circuit (fig.1). The effect of repressors can be taken up in equation (1.4) by adding the microstate ‘repressor protein bound’ as a regulatory region to the total statistical weight. The term ‘repressor binding’ states that if a repressor is bound a polymerase cannot bind. The equation assumes a high basal level of expression in the absence of repressors. Note that as equation (1.5) takes the form of a Hill function, the expression fold change is dependent on the number of repressors.

$F o l d C h a n g e = \frac{P b o u n d (R \neq 0)}{P b o u n d (R = 0)} = \frac{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}}}{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}} + (\frac{R}{N_{n s}} e^{- \frac{∆ ε_{d}^{r}}{K_{b} T}})^{n}}$

In equation (1.5) R is the number of repressor proteins and ∆ε_d^r the specific binding energy of the repressor proteins, the same combinatorics rules apply. n is the number of repression regulators should those regulators have the same binding energy. Because they act independently on whether or not an RNA polymerase can bind, the regulatory values are multiplied7. Equation (1.5) can now be incorporated into the model describing the kill-switch by tying production rates to the fold change of expression (K_prod x Fold change), i.e. the production rate will decrease proportionally to changes in expression.

Model Equations

Ordinary differential equations describe the genetic circuit (fig.4), three of which use a statistical mechanics based Hill function. The deg_protein and Dil_div terms represent the half-life dilution rate of the proteins. Because equation (2.3) (the CIλ production) relies on an external input and is not dependent on any of the other equations, the ODE uses Michaelis-Menten kinetics to simulate a Rhamnose input. In every simulation rhamnose is inputted at t = 10 hours

$\frac{d L a c I}{d t} = K_{p r o d_{L a c I}} \frac{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}}}{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}} + (\frac{A V T e t R}{N_{n s}} e^{- \frac{∆ ε_{d}^{T e t R_L a c}}{K_{b} T}})^{n T e t_L a c}} {- d e g}_{L a c I} L a c I - {D i l}_{d i v}$

$\frac{d T e t R}{d t} = K_{p r o d_{T e t R}} \frac{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}}}{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}} + (\frac{A V L a c I}{N_{n s}} e^{- \frac{∆ ε_{d}^{L a c I}}{K_{b} T}})^{n L a c} (\frac{A V C I λ}{N_{n s}} e^{- \frac{∆ ε_{d}^{C I λ_T e t}}{K_{b} T}})^{n C I λ_T e t r}} {- d e g}_{T e t R} T e t R - {D i l}_{d i v}$

$\frac{d C I λ}{d t} = K_{p r o d_{λ C I}} \frac{[R H A]}{[R H A] + K_{d}} - {d e g}_{λ C I} C I λ - {D i l}_{d i v}$

$\frac{d G F P}{d t} = K_{p r o d_{L a c I}} \frac{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}}}{1 + \frac{P}{N_{n s}} e^{- \frac{∆ ε_{p d}^{S}}{K_{b} T}} + (\frac{A V T e t R}{N_{n s}} e^{- \frac{∆ ε_{d}^{T e t R_{G F P}}}{K_{b} T}})^{n T e t_{G F P}} (\frac{A V C I λ}{N_{n s}} e^{- \frac{∆ ε_{d}^{C I λ_{G F P}}}{K_{b} T}})^{n C I λ_G F P}} {- d e g}_{G F P} G F P - {D i l}_{d i v}$

Results

System Behaviour and Optimal Repressor Binding Site Configuration

Before the optimal configuration of repressor binding sites could be determined, the behavior of the system had to be assigned scores representing a functioning or non-functioning toggle switch (see Parameters). The scores range from zero to two, three different behaviors could be identified:

2: The system performs to design, after a rhamnose input the toggle switch changes state

1: The system performs less efficiently, though the toggle switch changes state, the GFP promoter is leaky

0: The system does not work, the toggle switch is out of balance and does not function

In total eight different configurations of repressor binding sites that were tested. Two, F and H, were found to be moderately robust towards variations in binding strengths and production rates.

**Figure 1.** Color maps indicating functioning and non-functioning systems. Each letter represents different repressor binding site configurations. Each small square within the colour maps represents a score for a simulation of the system with a unique set of parameters. The colours correspond to the previously given description

Binding Sites	A	B	C	D	E	F	G	H
*TetR Promoter_LacI*	1	1	1	1	2	2	2	2
*TetR Promoter_GFP*	1	1	2	2	1	1	2	2
*CI Promoter_GFP*	2	2	1	1	2	2	1	1
*CI Promoter_TetR*	2	1	2	1	2	1	2	1
*LacI Promoter_TetR*	1	2	1	2	1	2	1	2

The result of the best scoring configuration H has been magnified (figure 2). The repressor binding site configuration corresponding to this map has the highest chance of working in an experimental set-up. The x-axis shows the production rates in micro-molar per minute, the y-axis has increased binding strengths for individual repressors by an order of magnitude each row. The color map indicates that increases in repressor binding strengths can be compensated for by increased production rates of either the target gene or decreased production of the repressor itself.

Statistical Mechanics in Practice

Statistical mechanics allows you to describe the system in terms of the number of repressors and repressor binding sites, their binding affinity and the position of the repressor binding on the promoter. In contrast to Michaelis-Menten kinetics, statistical mechanics offers more freedom studying the behavior of differently designed promoters. Should Michaelis-Menten kinetics have been used the dissociation constant of a protein to DNA would need to be experimentally determined for different promoter configurations in order to obtain an indication of system behavior, a ‘parameter dependent’ method of modeling. Statistical mechanics is not bound by experimentation in making a rough predictions. Though the model still needs parameters e.g. number of RNA polymerases in a cell, number of non-specific binding sites, these are accessible without a need for experimentation1. The model predicts the only functioning repressor binding site configurations to be those where LacI and TetR are placed pairwise on the promoter, a result that is confirmed in the literature2. This means the statistical mechanics approaches can estimate which repressor binding site configuration is most likely to work. The information provided by this model has inspired the design of the promoters for the kill-switch. The next modeling step would be to assess the Cost and Performance of our entire system. This will give insight in the overall capacity and behavior of our biological control agent in the soil.

System Cost

Introduction

The BananaGuard system is designed with the assumption that our engineered Pseudomonas putida is not outcompeted by other bacteria and fungi found in the rhizosphere of banana roots[1,2]. However, our system consists of multiple constitutively expressed genes controlling the kill switch and toxin-antitoxin system. Moreover, when the system is switched to the active state by sensing fusaric acid, Pseudomonas putida produces multiple antifungal enzymes and compounds. The integrated synthetic pathways use metabolic resources that would otherwise be dedicated to cellular maintenance or growth. Thereby, the synthetic pathways reduce the bacteria’s potential to sustain themselves in the rhizosphere. Therefore, we wondered to what degree P. putida metabolism was affected by our system and, if need be, how the system could be changed to lessen the impact. To approach this problem a genome-scale metabolic model (GSMM) is used[3]. Our new GSMM predicts the interaction of our integrated plasmids with genes originating from endogenous pathways. With this indication of the metabolic stress we get an insight in the metabolic burden caused by the integration of our plasmids and whether the engineered Pseudomonas putida strain is losing the capability to compete with other rhizosphere-populating microorganisms in the resting state.

Theory and experimental design

In order to solve our problem with a GSMM we need a model that:

contains a comprehensive representation of P. putida metabolism
is capable of predicting growth rates in various environments
contains the most reactions that are necessary for our system

For this reason a comparison was made between various GSMM for P. putida. There are multiple genome-scale metabolic models available for Pseudomonas Putida but only two of them are up-to-date, published and verified: iJP962 and iJN746[4,5]. For the necessary work to model the metabolic stress in Pseudomonas Putida, the best starting model needs to be chosen which has the most potential for accurately modeling the metabolic stress of our system.

Genomic Model	iJP962	iJN746
Reactions	1070	957
Metabolites	959	685
Compartments	1	2
Focus of the model (based on metabolites and reactions)	This model has a broad spectrum of reactions in every class, but is lacking the in-depth reactions.	This model has a focus on the production of interesting compounds for use in biotechnology (aromatic compounds, alkenes, alkanoates).

Taking the above arguments in consideration, model iJP962 is most suitable for modeling our system. Even though the reactions and metabolites in iJN747 are divided in 2 compartments this is not an advantage. Many of the reactions are over the internal membrane and not functional for the core intermediate metabolites. On top of that iJN747 has a focus on compounds that are in a different class of metabolites then the toxins we chose for our system[5]. Therefore iJP962 is more representative of the real system due to more reactions and more metabolites in a broader spectrum. The primary category of concern for toxin production is the amino acid metabolism and iJP962 has the most reactions in this category[3,4,6]. Both models did not include all the specific reactions, metabolites and genes that are necessary for modeling the toxin metabolites. These reactions were added manually.

Metabolic modeling

Traditionally, metabolic models only predict metabolic fluxes. Although this is directly applicable to the metabolites that we want to produces, such as DMDS, this does not suffice to answer our questions regarding the impact of the whole system. Therefore, we added the production of all the proteins of interest as if they are metabolites. For this the protein sequences are used to determine the correct stoichiometric ratio of amino acids[7]. The necessary energy and other side-substrate/products are in the same ratio as described for production of proteins for the biomass reaction in the GSMM. In the model Promoter Design the protein production rate is estimated.

As our metabolites of interest (DAPG, DMDS, DMTS) were not yet included in the GSMM, we had to deduce their production pathways based on databases and literature information[8,9,10,11](link notebook with all reactions). Furthermore, we took special care that all added pathways are stoichiometrically balanced, which is essential for proper and reliable integration in a GSMM. To calculate the metabolic stress as accurately as possible, the correct constraints have to be set in the model to be certain that all the calculated production rates are biological relevant. To find which constraints are biological relevant in vivo data validation is important. Using this information an estimation can be made about the production range of the toxins which are relevant for P. putida.

Programs and toolboxes

Matlab[12] was used in combination with the Cobra toolbox[13] for handling the model. The Cobra toolbox is designed for working with genome-scale metabolic models. To solve the flux balance analysis a linear equation solver is needed. Gurobi[14] was chosen because of its compatibility with Matlab and the Cobra toolbox.

Flux Balance Analysis

Flux Balance Analysis (FBA) is a framework for investigating the theoretical capabilities of a stoichiometric metabolic model S and can be solved by using a linear solver program. This is possible because of linear objective function and linear constraints[4,6]. FBA is based on the following assumptions to ensure its linearity:

steady state: The fluxes are considered to have attained a static equilibrium value and do not change through time.
Thermodynamic constraints: (ir)reversibility of reactions
No enzyme saturation: The maximum flux for every reaction is not dependent on the concentration of the enzymes used for that reaction.
There is no accumulation of intermediate metabolites in the model.

The FBA method uses a representation of the metabolic reaction network in the form of a stoichiometry matrix (S) where :

Each column corresponds to a reaction R_i
Each row corresponds to a metabolite C_j

The definition of S is :

S_{i, j} = k s . t . \{\begin{matrix} k < 0 \to C_{j} i s a s u b s t r a t e o f r e a c t i o n R_{i} w i t h s t o i c h i o m e t r y k \\ k > 0 \to C_{j} i s a p r o d u c t o f r e a c t i o n R_{i} w i t h s t o i c h i o m e t r y k \\ k = 0 \to C_{j} d o e s n o t p a r t i c i p a t e i n r e a c t i o n R_{i} \end{matrix}

The FBA problem is then formulated as a maximization or minimization problem under the determined constraints:

\{\begin{matrix} M a x i m i z e c^{T} v \\ S u b j e c t t o S v = 0 \\ L o w e r b o u n d \leq v \leq U p p e r b o u n d \end{matrix}

Where :

v is the vector of unknown reaction fluxes
c is a vector of constants defining the objective function
S is the stoichiometry matrix
lowerbound and upperbound are vectors of constraints (minimal and maximal flux values for each reaction)

Media composition

For metabolic modeling the constraints of your exchange reactions are important for the results. With these exchange reactions you can dictate what’s available in the model, you need arbitrary bounds as actual uptake rates are unknown. This also enforces the later decision to not include all root components but only the most prevalent. You don’t want that rare compounds have a huge impact on the model predictions. This does imply that the model predictions could be slightly negative: with including the other available compounds the system may work even better.

In order to set the medium constraints of the models all lower and upper bounds are first set to the value of 0 and 1000 arbitrary units, respectively. Then one by one the lower and upper limit of the reaction bounds are set to -1000 for one reaction at a time to your composition of interest. If the lower bound is set to a value higher than zero a minimum flux of that value is forced in a FBA. To get the most realistic approximation for our engineered P. putida in the soil the M9 media composition was used with carbon as limiting nutrient. The carbon source is based on the exudates of banana roots and consists of 34% sucrose and 66% divided over multiple amino acids[15]. We have neglected other secondary metabolites in banana roots exudates because they are exudated in relatively small amounts[16].

Results

To check if BananaGuard is still viable in its resting and active state, a comparison is necessary between the wild type P. putida and BananaGuard. If the growth rate of BananaGuard approximates the growth rate of wild type P. putida in the resting state it is safe to assume that the disadvantage of the introduced synthetic pathway does not have a huge impact on competitiveness with other rhizosphere-populating microorganisms. This means that BananaGuard should be able to populate the rhizosphere of the banana roots. When looking at the active state we are not interested in the capability to compete with other microorganisms but the capability to produce all the anti-fungals with a constant rate around the roots, without overloading a metabolic pathway and causing shortage of intermediates.

P. putida is able to grow in the rhizosphere with a doubling time of 3 hours resulting in a growth rate of 0.23 h^-1[1]. Because of the linearity of the growth rate and carbon uptake rate in this model we expect that the carbon uptake rate is ≈4.5 mmol gDW^-1hr^-1 in the rhizosphere of the banana roots. Figure 1 depicts how the growth rate of BananaGuard compares to the growth rate of the wild type P. putida depending on the carbon uptake rate of the organism in the resting state and active state of the kill switch. To get the best case scenario glucose was chosen as carbon source reference, because of the efficient degradation of glucose. BananaGuard is still able to grow at almost max growth rate (>99%) compared to the wild type in the resting state. We can conclude out of this that BananaGuard is not getting outcompeted by other rhizosphere-populating microorganisms because of the synthetic pathway. When the kill switch is activated by fusaric acid BananaGuard is still able to growth with 50-70% of the maximum growth of the wild type (Figure 1). This indicates that metabolic stress is not a bottleneck for the production of anti-fungals in our fusaric acid activated system.

To get a more realistic result for the soil in banana farms the carbon source is changed to have the same ratio of carbohydrates and amino acids as found in the exudate's of banana roots[15]. This new carbon composition causes a reduced growth rate because of less efficient degradation of these compounds. In figure 1 the relative growth rate is shown for the resting and active state of the kill switch with the new carbon source. These changes in the carbon composition do not change our conclusion previously made. The range of the relative growth rate has changed from 50-70% to 45-60% indicating it still has the capacity to grow and maintain the constant toxin production with one condition that BananaGuard needs to stay close to the roots to maintain its carbon uptake rate.

Figure 2: The relative growth rate compared to the wild type *P. putida* for different carbon uptake rates. The realistic solution is with the banana exudates as carbon source and the other sulution is with glucose as reference. The expected carbon uptake rate of *P. putida* in the rhizosphere is indicated with transparent red.

Oxygen necessity in the soil

P. putida is a strict aerobic bacteria[2]. This means that without oxygen available the bacteria cannot grow. To inhibit the growth of the Fusarium oxysporum our engineered Pseudomonad must grow in the rhizosphere of the banana roots. If there is not enough oxygen present in the rhizosphere it might not be possible anymore to sustain anti-fungals production or other anaerobic bacteria can outcompete our P. putida. In figure 2 the growth rate in the active state is plotted as a function of the oxygen and carbon availability. If there is little oxygen available the growth rate drops and so will the production of the toxins. However the depletion of oxygen should not be a problem because there is a layer of oxygen present closely to the roots[17]. This supports the task of our P. putida to protect the banana roots from F. oxysporum invasion and will contain our engineered P. putida close to the banana roots.

Parameter analysis results

Every parameter in this metabolic model is an estimation based on literature growth experiments except for the pyoverdin production rate. This parameter has been determined from growth experiments with P. putida (Link notebook walter pyoverdin) . So every parameter is biological relevant, but because different studies report different values a mean has to be taken between the different data points. This means that the parameter can fluctuate in a small range. To compensate this a parameter analysis has been performed. Every parameter that could have a significant impact on the results has been checked over a range, dependent on the accuracy of the calculated parameter. The same analysis has been performed for all the fluctuations in the parameter set combined. This analysis shows the possible fluctuations of the modeled system and which parameters has greatest impact on the system.

System performance over cell division

Introduction

Theory and experimental design

Results

Appendix

Table of parameters

Metabolic modeling

Designation	Value	Description	Reference
model iJP962	-	Genomic-scale metabolic model	[6,18]
carbonsource	-	Fructose, Glucose, Alanine, Asparagine, Aspartate, L-Leucine, Serine, L-Threonine, L-Proline, D-Glutamate	[15]
glucuptake	4.43 mmol gDW^-1hr^-1	Carbon uptake rate	[1]
NGAM	3.96 mmol gDW^-1hr^-1	Non-growth maintenance factor	[6]
KS_rate	0.2 μM min^-1	Protein production rate	Promoter Design
TAT_rate	1 nM min^-1	Toxin/anti-toxin production rate	Promoter Design
Cell density	0.040 gDW l^-1	gDW/OD600=0.1	[20]
ncells	1e⁸ cells ml^-1	cells/OD600=0.1	[21]
Chitinase	0.2 μM min^-1	Chitinase production rate	[7] and Promoter Design
Pyoverdine	150 μmol gDW^-1hr^-1	Pyoverdine production rate	[10,11,22]
DAPG	25 μmol gDW^-1hr^-1	DAPG production rate	[8]
DMDS	0.845 μmol gDW^-1hr^-1	DMDS production rate	[9]
Nplasmids	10 plasmids cell^-1	Number of plasmids per cell (low copy number)	[23]
plasmidTD	0.3 h^-1	Time needed for at least a doubling of the number of plasmids per cell	[1]
TDrhizo	3 hr	Doubling time P. putida in the rhizosphere	[1]

Dynamic modeling

References

Bennett, R. A., & Lynch, J. M. (1981). Bacterial growth and development in the rhizosphere of gnotobiotic cereal plants. Journal of General Microbiology, 125(1), 95-102.
Molina, L., Ramos, C., Duque, E., Ronchel, M. C., Garcı́a, J. M., Wyke, L., & Ramos, J. L. (2000). Survival of< i> Pseudomonas putida KT2440 in soil and in the rhizosphere of plants under greenhouse and environmental conditions. Soil Biology and Biochemistry, 32(3), 315-321.
Puchałka J, Oberhardt MA, Godinho M, Bielecka A, Regenhardt D, et al. (2008) Genome-Scale Reconstruction and Analysis of the a KT2440 Metabolic Network Facilitates Applications in Biotechnology. PLoS Comput Biol 4(10): e1000210. doi: 10.1371/journal.pcbi.1000210.
Oberhardt, M. A., Puchałka, J., Dos Santos, V. A. M., & Papin, J. A. (2011). Reconciliation of genome-scale metabolic reconstructions for comparative systems analysis. PLoS computational biology, 7(3), e1001116.
Nogales, J., Palsson, B. Ø., & Thiele, I. (2008). A genome-scale metabolic reconstruction of Pseudomonas putida KT2440: iJN746 as a cell factory. BMC systems biology, 2(1), 79.
van Duuren, J. B., Pucha, J., Mars, A. E., Bücker, R., Eggink, G., Wittmann, C., & dos Santos, V. A. (2013). Reconciling in vivo and in silico key biological parameters of Pseudomonas putida KT2440 during growth on glucose under carbon-limited condition. BMC biotechnology, 13(1), 93.
The UniProt Consortium,Activities at the Universal Protein Resource (UniProt),[Pyocin,Q88ID3].
Schnider-Keel, U., Seematter, A., Maurhofer, M., Blumer, C., Duffy, B., Gigot-Bonnefoy, C., ... & Keel, C. (2000). Autoinduction of 2, 4-diacetylphloroglucinol biosynthesis in the biocontrol agent Pseudomonas fluorescensCHA0 and repression by the bacterial metabolites salicylate and pyoluteorin. Journal of Bacteriology, 182(5), 1215-1225.
Arfi, K., Landaud, S., & Bonnarme, P. (2006). Evidence for distinct L-methionine catabolic pathways in the yeast Geotrichum candidum and the bacterium Brevibacterium linens. Applied and environmental microbiology, 72(3), 2155-2162.
Salah El Din, A. L. M., Kyslík, P., Stephan, D., & Abdallah, M. A. (1997). Bacterial iron transport: Structure elucidation by FAB-MS and by 2D NMR (H¹,C¹³,N¹⁵) of pyoverdin G4R, a peptidic siderophore produced by a nitrogen-fixing strain of Pseudomonas putida. Tetrahedron, 53(37), 12539-12552.
Boukhalfa, H., Reilly, S. D., Michalczyk, R., Iyer, S., & Neu, M. P. (2006). Iron (III) coordination properties of a pyoverdin siderophore produced by Pseudomonas putida ATCC 33015. Inorganic chemistry, 45(14), 5607-5616.
Matlab
Cobra Toolbox
Gurobi
Buxton, E. W. (1962). Root exudates from banana and their relationship to strains of the Fusarium causing Panama wilt. Annals of Applied Biology, 50(2), 269-282.
Bais, H. P., Weir, T. L., Perry, L. G., Gilroy, S., & Vivanco, J. M. (2006). The role of root exudates in rhizosphere interactions with plants and other organisms. Annu. Rev. Plant Biol., 57, 233-266.
Armstrong, W., & Drew, M. C. (2002). Root growth and metabolism under oxygen deficiency. Plant roots: the hidden half, 3, 729-761.
Oberhardt, M.A., J. Puchalka, V.A.P. Martins dos Santos, and J.A. Papin. 2011. Reconciliation of genome-scale metabolic reconstructions for comparative systems analysis. PLoS Computational Biology, 7(3).
BNID 107924, Milo et al 2010.
BNID 100985, Milo et al 2010.
Gross, H., & Loper, J. E. (2009). Genomics of secondary metabolite production by Pseudomonas spp. Natural product reports, 26(11), 1408-1446.
Stoker, N. G., Fairweathe, N. F., & Spratt, B. G. (1982). Versatile low-copy-number plasmid vectors for cloning in< i> Escherichia coli. Gene, 18(3), 335-341.

Team:Wageningen UR/project/model

From 2014.igem.org

Model

Appendix

Modeling Overview

Kill-switch promoter design

Introduction

Theory and experimental design

Statistical Mechanics

Modeling Biological Systems using Statistical Mechanics

Model Equations

Results

System Behaviour and Optimal Repressor Binding Site Configuration

Statistical Mechanics in Practice

System Cost

Introduction

Theory and experimental design

Metabolic modeling

Programs and toolboxes

Flux Balance Analysis

Media composition

Results

Oxygen necessity in the soil

Parameter analysis results

System performance over cell division

Introduction

Theory and experimental design

Results

Appendix

Table of parameters

Metabolic modeling

Dynamic modeling

References