from IPython.display import display
from cobramod import __version__
from cobra import __version__ as cobra_version
print(f'CobraMod version: {__version__}')
print(f'COBRApy version: {cobra_version}')
# From Escher:
# This option turns off the warning message if you leave or refresh this page
import escher
escher.rc['never_ask_before_quit'] = True

Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
CobraMod version: 0.5.5-alpha.1
COBRApy version: 0.22.1

4.1. Analyising shikimate production using an E. coli core model

4.1.1. Introduction

In this tutorial we use a core model of E. coli [1] and extend it with the shikimate synthesis pathway. Shikimate is an important precursor for aromatic compounds such as phenylalanine, tyrosine, and tryptophan. In this article the authors in vivo engineered five E. coli strains for shikimate overproduction by deactivating genes for the enzymatic regulation of the shikimate metabolism [2]. In our test case, we in silico compare the control strain (W3110) with a strain (SA3) from the article. To this end, we use CobraMod to add the shikimate pathway from the BioCyc sub-database EcoCyc to the E. coli model. We then simulate and visualize shikimate production for the two strains. The shikimate pathway is shown below and is represented by two sub-pathways with the EcoCyc identifiers PWY-6164 and PWY-6163.

Pathway identifier	Pathway name
PWY-6164	3-dehydroquinate biosynthesis I
PWY-6163	chorismate biosynthesis from 3-dehydroquinate

4.1.2. Loading CobraMod, the E.coli model and setting the growth medium for the simulations

We use the E. coli core model from COBRApy as our model. This core model can be found under cobramod.test.textbook. It contains 72 metabolites, 95 reactions and 137 genes. We load the function cobramod.add_pathway() and the Python module pathlib to represent the system path where CobraMod stores the metabolic pathway information. We define the directory for pathway information as dir_data. The pathways with the respective reaction, gene and metabolite information are saved here.

from pathlib import Path

from cobramod import add_pathway
from cobramod.test import textbook

# Defining system path for data
dir_data = Path.cwd().joinpath("data")
# Defining model
model = textbook.copy()

In the selected study, the authors used a culture medium including glucose and several other metabolites. Since only glucose is included in our core model and for the sake of simplicity we only constrain glucose and oxygen uptake.

# limiting glucose
model.exchanges.EX_glc__D_e.bounds = ( -10, 0)
# limiting oxygen
model.exchanges.EX_o2_e.bounds = (0, 0)

4.1.3. Adding the shikimate pathways

To add a pathway to the model we use the function add_pathway(). To do so, the first argument model is the respective model to extend. The argument pathway is the respective database-specific identifier for the pathway (PWY-6164 and PWY-6163) followed by the database identifier ECOLI. We set cytosol (c) as the compartment for the reactions and metabolites of the pathways. Because the two added sub-pathways are part of a larger pathway, we use the argument group to create a single cobramod.Pathway object.

CobraMod tries to avoid duplicate reactions and metabolites. In our case, the textbook model uses BiGG identifiers and the downloaded data contain EcoCyc identifiers. When downloading pathway information, CobraMod checks the cross-references within these data and searches for corresponding objects in the model. In this example CobraMod warns the user that several metabolites, such as Pi (phosphate), WATER and ATP, are already in the model. Calling the pathway object shows a table summarising the pathway attributes.

# first pathway
add_pathway(
    model=model,
    pathway="PWY-6164",
    database="ECOLI",
    compartment="c",
    group="PWY-SHIKIMATE",
    directory=dir_data,
)

# second pathway
add_pathway(
    model=model,
    pathway="PWY-6163",
    database="ECOLI",
    compartment="c",
    group="PWY-SHIKIMATE",
    directory=dir_data,
)

# Show attributes
model.groups.get_by_id("PWY-SHIKIMATE")

/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'PHOSPHO-ENOL-PYRUVATE' was found as 'pep_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'ERYTHROSE-4P' was found as 'e4p_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'WATER' was found as 'h2o_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'Pi' was found as 'pi_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/extension.py:573: UserWarning: Auxiliary sink reaction for "SK_DEHYDROQUINATE_c" created. Consider removing it and adding the synthesis reactions for the metabolite.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'NADP' was found as 'nadp_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)

Number of       new   | removed entities in
*=====================|===================*
Reactions        2    |    0
Metabolites      2    |    0
Exchange         0    |    0
Demand           0    |    0
Sinks            1    |    0
Genes            4    |    0
Groups           1    |    0

/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'PROTON' was found as 'h_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'NADPH' was found as 'nadph_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'ATP' was found as 'atp_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)
/home/stefano/Documents/cobramod/src/cobramod/core/creation.py:161: UserWarning: Metabolite 'ADP' was found as 'adp_c'. Please curate if necessary.
  warn(message=msg, category=UserWarning)

Number of       new   | removed entities in
*=====================|===================*
Reactions        5    |    0
Metabolites      5    |    0
Exchange         0    |    0
Demand           0    |    0
Sinks            1    |    1
Genes            6    |    0
Groups           0    |    0

/home/stefano/Documents/cobramod/src/cobramod/core/extension.py:573: UserWarning: Auxiliary sink reaction for "SK_CHORISMATE_c" created. Consider removing it and adding the synthesis reactions for the metabolite.
  warn(message=msg, category=UserWarning)

Pathway identifier	PWY-SHIKIMATE
Name
Memory address	0x0140192525876816
Reactions involved	DAHPSYN_RXN_c, 3_DEHYDROQUINATE_SYNTHASE_RXN_c, 3_DEHYDROQUINATE_DEHYDRATASE_RXN_c, SHIKIMATE_5_DEHYDROGENASE_RXN_c, SHIKIMATE_KINASE_RXN_c, 2.5.1.19_RXN_c, CHORISMATE_SYNTHASE_RXN_c
Genes involved	EG10078, EG10080, EG10079, EG10074, EG10076, EG10077, EG10081, EG10082, EG10073, EG10075
Visualization attributes	vertical = False color_negative = None color_positive = None color_quantile = False

 

CobraMod does not automatically merge sub-pathways in the visualization. When we call the function Pathway.visualize(), CobraMod shows both sub-pathways one above the other, instead of a single linear pathway. To change this, we use the method Pathway.modify_graph(). This function merges the two sub-pathways by connecting two reactions in the visualization. Here, the argument reaction specifies the last reaction of the first sub-pathway and the argument next_reaction specifies the subsequent reaction of the second sub-pathway.

In the first visualization, 3_DEHYDROQUINATE_SYNTHASE_RXN_c and 3_DEHYDROQUINATE_DEHYDRATASE_RXN_c are not connected. We use the modify_graph method to join both reactions. When we now visualize the pathway, we obtain one linear pathway.

# Show pathway map
display(model.groups.get_by_id("PWY-SHIKIMATE").visualize())
# Merge reactions of the sub-pathways
model.groups.get_by_id("PWY-SHIKIMATE").modify_graph(
    reaction="3_DEHYDROQUINATE_SYNTHASE_RXN_c",
    next_reaction="3_DEHYDROQUINATE_DEHYDRATASE_RXN_c"
)
# Show pathway map
model.groups.get_by_id("PWY-SHIKIMATE").visualize()

4.1.4. Creating biomass reactions for the two E. coli strains

Our reference article lists the following values for biomass an shikimate for the two strains of interest:

Strains	Biomass (g/L)	Shikimate (mg/L)
W3110	3.42 ± 0.26	1.31 ± 0.12
SA3	5.24 ± 0.34	417.20 ± 50.01

We use this data to update the biomass equation of our core model by including the contribution of shikimate to the overall biomass composition. For the sake of our tutorial we make some simplifying assumptions (e.g. the ratios of the other biomass components do not change, shikimate productions is coupled to growth) and use the following relationship:

# Calculate ratios for the strains
shikimate_ratio = {
    "W3110": (1.31 / 1000) / 3.42,
    "SA3": (417.20 / 1000) / 5.24
}
shikimate_ratio

{'W3110': 0.00038304093567251464, 'SA3': 0.07961832061068702}

We calculate the new coefficients for the biomass reactions which include shikimate. The detailed calculations are listed in the supplementary information at the bottom of this page. We obtain the following new biomass equations:

W3110_df = pd.concat(
    [
        W3110_df_negative.loc[:, ["identifier", "new_coefficient"]],
        W3110_df_positive.loc[:, ["identifier", "new_coefficient"]],
    ]
)
W3110_df = W3110_df.reset_index(drop=True)
print("New coefficients for W3110 strain:")
display(W3110_df)

SA3_df = pd.concat(
    [
        SA3_df_negative.loc[:, ["identifier", "new_coefficient"]],
        SA3_df_positive.loc[:, ["identifier", "new_coefficient"]],
    ]
)
SA3_df = SA3_df.reset_index(drop=True)
print("New coefficients for SA3 strain:")
display(SA3_df)

New coefficients for W3110 strain:

	identifier	new_coefficient
0	3pg_c	-1.495427
1	accoa_c	-3.746364
2	atp_c	-59.78709
3	e4p_c	-0.360862
4	f6p_c	-0.070873
5	g3p_c	-0.128951
6	g6p_c	-0.204921
7	gln__L_c	-0.255602
8	glu__L_c	-4.939507
9	h2o_c	-59.78709
10	nad_c	-3.545641
11	nadph_c	-13.02291
12	oaa_c	-1.786016
13	pep_c	-0.518901
14	pyr_c	-2.831715
15	r5p_c	-0.897356
16	SHIKIMATE_c	-0.106557
17	adp_c	59.78709
18	akg_c	4.1182
19	coa_c	3.746364
20	h_c	59.78709
21	nadh_c	3.545641
22	nadp_c	13.02291
23	pi_c	59.78709

New coefficients for SA3 strain:

	identifier	new_coefficient
0	3pg_c	-1.376891
1	accoa_c	-3.449406
2	atp_c	-55.048028
3	e4p_c	-0.332258
4	f6p_c	-0.065255
5	g3p_c	-0.118729
6	g6p_c	-0.188678
7	gln__L_c	-0.235342
8	glu__L_c	-4.547974
9	h2o_c	-55.048028
10	nad_c	-3.264594
11	nadph_c	-11.99064
12	oaa_c	-1.644446
13	pep_c	-0.47777
14	pyr_c	-2.607257
15	r5p_c	-0.826227
16	SHIKIMATE_c	-22.148743
17	adp_c	55.048028
18	akg_c	4.1182
19	coa_c	3.449406
20	h_c	55.048028
21	nadh_c	3.264594
22	nadp_c	11.99064
23	pi_c	55.048028

Finally, we create a function that uses these value to generate the updated strain-specific biomass equations and add it to the model.

from cobra import Reaction


def create_biomass(df: pd.DataFrame, identifier: str):
    """
    Creates a Reaction from the reactant and product DataFrame with new
    coefficients.
    """
    reaction = Reaction(id=identifier)
    # Iterate over dataframe
    for index, row in df.iterrows():
        reaction.add_metabolites(
            {
                model.metabolites.get_by_id(row["identifier"]): row[
                    "new_coefficient"
                ]
            }
        )
    return reaction


biomass_W3110 = create_biomass(W3110_df, "W3110_biomass")

biomass_SA3 = create_biomass(SA3_df, "SA3_biomass")
# Show new reactions
display(biomass_W3110)
display(biomass_SA3)

# Add to model
model.add_reactions([biomass_W3110, biomass_SA3])

Reaction identifier	W3110_biomass
Name
Memory address	0x07f811dac74d0
Stoichiometry	1.495426970760234 3pg_c + 0.10655682044443099 SHIKIMATE_c + 3.746364439181286 accoa_c + 59.78709032163742 atp_c + 0.3608617222222222 e4p_c + 0.07087284239766083 f6p_c + 0.12895058771929824 g3p_c +... 1.495426970760234 3-Phospho-D-glycerate + 0.10655682044443099 shikimate + 3.746364439181286 Acetyl-CoA + 59.78709032163742 ATP + 0.3608617222222222 D-Erythrose 4-phosphate + 0.07087284239766083...
GPR
Lower bound	0.0
Upper bound	1000.0

Reaction identifier	SA3_biomass
Name
Memory address	0x07f811dac7750
Stoichiometry	1.376890992366412 3pg_c + 22.148742610250682 SHIKIMATE_c + 3.4494064580152664 accoa_c + 55.0480282442748 atp_c + 0.33225778625954194 e4p_c + 0.06525506106870228 f6p_c + 0.11872923664122137 g3p_c +... 1.376890992366412 3-Phospho-D-glycerate + 22.148742610250682 shikimate + 3.4494064580152664 Acetyl-CoA + 55.0480282442748 ATP + 0.33225778625954194 D-Erythrose 4-phosphate + 0.06525506106870228...
GPR
Lower bound	0.0
Upper bound	1000.0

4.1.5. Simulating shikimate production in the two E.coli strains

We use COBRApy to run flux balance analysis for the two strains. Using the COBRApy method cobra.model.optimize() we get two solutions objects. We can see that the solution for the W3110 strain has a higher objective value (0.2105) than the SA3 strain objective value (0.0995) which is caused by the different shikimate ratios in the biomass equation.

# W3110 type
model.objective = "W3110_biomass"

solution_W3110 = model.optimize()
display(model.summary(solution=solution_W3110))

# SA3 strain
model.objective = "SA3_biomass"
solution_SA3 = model.optimize()
display(model.summary(solution=solution_SA3))

Objective

1.0 W3110_biomass = 0.21052311090926515

Uptake

Metabolite	Reaction	Flux	C-Number	C-Flux
co2_e	EX_co2_e	0.376	1	0.62%
glc__D_e	EX_glc__D_e	10	6	99.38%
h2o_e	EX_h2o_e	7.062	0	0.00%
nh4_e	EX_nh4_e	1.148	0	0.00%
pi_e	EX_pi_e	0.7742	0	0.00%

Secretion

Metabolite	Reaction	Flux	C-Number	C-Flux
ac_e	EX_ac_e	-8.487	2	33.11%
etoh_e	EX_etoh_e	-8.263	2	32.24%
for_e	EX_for_e	-17.77	1	34.65%
h_e	EX_h_e	-30.5	0	0.00%

Objective

1.0 SA3_biomass = 0.09958679209872245

Uptake

Metabolite	Reaction	Flux	C-Number	C-Flux
co2_e	EX_co2_e	0.1638	1	0.27%
glc__D_e	EX_glc__D_e	10	6	99.73%
h2o_e	EX_h2o_e	1.815	0	0.00%
nh4_e	EX_nh4_e	0.4998	0	0.00%
pi_e	EX_pi_e	0.3372	0	0.00%

Secretion

Metabolite	Reaction	Flux	C-Number	C-Flux
ac_e	EX_ac_e	-6.86	2	33.48%
etoh_e	EX_etoh_e	-6.665	2	32.52%
for_e	EX_for_e	-13.94	1	34.00%
h_e	EX_h_e	-24.77	0	0.00%

4.1.6. Visualization with Escher

The object cobramod.Pathway has a method for visualizing metabolic pathway using the pathway visualization tool Escher. The function Pathway.visualize() generates pathway maps which can be easily customized with user-defined colors, flux ranges and gradient settings.

model.groups.get_by_id("PWY-SHIKIMATE").visualize()

To visually compare our results we set the colors for positive and negative fluxes to blue and red, respectively (By default, all color gradients use grey tones around zero, i.e. more saturated colors indicate larger absolute flux values). We set the map orientation to horizontal. To be able to compare the two flux simulations we set the bounds for the color gradient (color_min_max) to -3 and 3. The coloring of the arrows represents the values of the flux solution. To visualize the solution, we use the argument solution_fluxes. The first visualization displays the flux distributions for the W3110 strain. In this example, the flux values are close to 0 and thus the colors are pale. The second visualization displays the flux distributions for the SA3 strain which has higher fluxes and thus more saturated colors. Note that the reaction SHIKIMATE_5_DEHYDROGENASE_RXN_c has a negative flux because it is operating in the backwards direction (reaction information).

# Customize pathway
model.groups.get_by_id("PWY-SHIKIMATE").vertical = False
model.groups.get_by_id("PWY-SHIKIMATE").color_positive = "blue"
model.groups.get_by_id("PWY-SHIKIMATE").color_negative = "red"
model.groups.get_by_id("PWY-SHIKIMATE").color_min_max = [-3, 3]

# Visualize pathway with solutions
display(model.groups.get_by_id("PWY-SHIKIMATE").visualize(
    solution_fluxes=solution_W3110)
)
display(model.groups.get_by_id("PWY-SHIKIMATE").visualize(
    solution_fluxes=solution_SA3)
)

4.1.7. Supplementary Information: Approximation of biomass compositions

To add shikimate to the biomass reactions, we calculate the shikimate contribution and the contribution of the other metabolite to biomass.

import pandas as pd

# Building dataframe from Biomass
biomass_df = pd.DataFrame(
    [metabolite.id, metabolite.formula, metabolite.formula_weight, value]
    for metabolite, value in model.reactions.get_by_id(
        "Biomass_Ecoli_core"
    ).metabolites.items()
)
biomass_df.columns = ["identifier", "formula", "mol_weight", "coefficient"]
biomass_df["mol_weight*coefficient"] = (
    biomass_df["mol_weight"] * biomass_df["coefficient"]
)
# display(biomass_df)

# Calculate Sum of coefficients multiplied by constants
sum_mol_coefficient_negative = biomass_df["mol_weight*coefficient"][
    biomass_df["mol_weight*coefficient"] < 0
].sum()
sum_mol_coefficient_positive = biomass_df["mol_weight*coefficient"][
    biomass_df["mol_weight*coefficient"] > 0
].sum()
print(
    "Sum of contribution for negative coefficients: "
    + f"{sum_mol_coefficient_negative}"
)
print(
    "Sum of contribution for positive coefficients: "
    + f"{sum_mol_coefficient_positive}"
)

Sum of contribution for negative coefficients: -48165.2120532678
Sum of contribution for positive coefficients: 46624.4458868131

We created a function that returns a table with the updated negative biomass coefficients. In the first part we calculate the contribution of shikimate (shikimate_mol_weight_coefficient) to the biomass followed by the calculations for the remaining metabolites. Finally, we divide the values by the molecular weight of the respective metabolite which gives us the new biomass coefficients.

The two tables below show the new coefficients (new_coefficient) for the two strains.

def new_coefficient(ratio: float):
    """
    Returns the a dataframe with the new coefficient for reactants of the biomass
    equation.
    """
    SHIKIMATE_MOL_WEIGHT = 173.14
    shikimate_mol_weight_coefficient = sum_mol_coefficient_negative * ratio
    # Calculating new multiplication between the coefficients and constants
    new_mol_weight_coefficient = biomass_df["mol_weight*coefficient"][
        biomass_df["mol_weight*coefficient"] < 0
    ] * (1 - ratio)
    new_mol_weight_coefficient[
        len(new_mol_weight_coefficient)
    ] = shikimate_mol_weight_coefficient
    # Verify that the sums are the same
    assert round(new_mol_weight_coefficient.sum(), 4) == round(
        sum_mol_coefficient_negative, 4
    )

    # Creating series with names of metabolites
    identifiers = biomass_df["identifier"][
        biomass_df["mol_weight*coefficient"] < 0
    ]
    identifiers[len(identifiers)] = "SHIKIMATE_c"

    # Creating series with molecular weight of metabolites
    mol_weight = biomass_df["mol_weight"][
        biomass_df["mol_weight*coefficient"] < 0
    ]
    mol_weight[len(mol_weight)] = SHIKIMATE_MOL_WEIGHT

    # Building new dataframe
    new_coefficient_df = pd.DataFrame(
        [identifiers, new_mol_weight_coefficient]
    ).transpose()
    new_coefficient_df["new_coefficient"] = new_coefficient_df[
        "mol_weight*coefficient"
    ].divide(mol_weight)

    # Appending old coefficients
    new_coefficient_df["old_coefficient"] = biomass_df["coefficient"][
        biomass_df["mol_weight*coefficient"] < 0
    ]
    return new_coefficient_df

W3110_df_negative = new_coefficient(ratio=shikimate_ratio["W3110"])
SA3_df_negative = new_coefficient(ratio=shikimate_ratio["SA3"])

# Display and format only relevant information
print("Table with new negative coefficients for W3110 strain")
display(W3110_df_negative.loc[:,["identifier","new_coefficient"]])
print("Table with new negative coefficients for SA3 strain")
SA3_df_negative.loc[:,["identifier","new_coefficient"]]

Table with new negative coefficients for W3110 strain

	identifier	new_coefficient
0	3pg_c	-1.495427
1	accoa_c	-3.746364
2	atp_c	-59.78709
3	e4p_c	-0.360862
4	f6p_c	-0.070873
5	g3p_c	-0.128951
6	g6p_c	-0.204921
7	gln__L_c	-0.255602
8	glu__L_c	-4.939507
9	h2o_c	-59.78709
10	nad_c	-3.545641
11	nadph_c	-13.02291
12	oaa_c	-1.786016
13	pep_c	-0.518901
14	pyr_c	-2.831715
15	r5p_c	-0.897356
16	SHIKIMATE_c	-0.106557

Table with new negative coefficients for SA3 strain

	identifier	new_coefficient
0	3pg_c	-1.376891
1	accoa_c	-3.449406
2	atp_c	-55.048028
3	e4p_c	-0.332258
4	f6p_c	-0.065255
5	g3p_c	-0.118729
6	g6p_c	-0.188678
7	gln__L_c	-0.235342
8	glu__L_c	-4.547974
9	h2o_c	-55.048028
10	nad_c	-3.264594
11	nadph_c	-11.99064
12	oaa_c	-1.644446
13	pep_c	-0.47777
14	pyr_c	-2.607257
15	r5p_c	-0.826227
16	SHIKIMATE_c	-22.148743

Next, we calculate the updated positive coefficients for the biomass equations. In the biomass equation are maintenance related metabolites such as adp_c and atp_c for which we assign the absolute value of their respective counterpart. The only exception is akg_c and for the sake of simplicity for this tutorial, we use the same coefficient for this metabolite.

We create a function that returns a data frame with the new positive coefficient. The tables below shows the updated positive coefficients for both strains.

def new_positive_coefficient(df: pd.DataFrame):
    """
    Returns a DataFrame with the new coefficients for the products of the
    biomass reaction. The input dataframe is the dataframe with the new
    coefficients for the reactants.
    """
    # Copy original biomass df and remove columns
    products = biomass_df[biomass_df["mol_weight*coefficient"] > 0].copy()
    del products["formula"]
    del products["mol_weight*coefficient"]
    products.columns = products.columns.str.replace(
        "coefficient", "old_coefficient"
    )

    # Create new column with the equivalent new coefficients
    products["new_coefficient"] = [
        df["new_coefficient"][2],
        -4.1182,
        df["new_coefficient"][1],
        df["new_coefficient"][2],
        df["new_coefficient"][10],
        df["new_coefficient"][11],
        df["new_coefficient"][2],
    ]
    # Update index and convert to absolute value
    products.index = range(0, len(products["new_coefficient"]))
    products["new_coefficient"] = products["new_coefficient"] * -1
    return products

W3110_df_positive = new_positive_coefficient(W3110_df_negative)
SA3_df_positive = new_positive_coefficient(SA3_df_negative)

# Display and format only relevant information
print("Table with new positive coefficients for W3110 strain")
display(W3110_df_positive.loc[:,["identifier","new_coefficient"]])

print("Table with new positive coefficients for SA3 strain")
display(SA3_df_positive.loc[:,["identifier","new_coefficient"]])

Table with new positive coefficients for W3110 strain

	identifier	new_coefficient
0	adp_c	59.787090
1	akg_c	4.118200
2	coa_c	3.746364
3	h_c	59.787090
4	nadh_c	3.545641
5	nadp_c	13.022910
6	pi_c	59.787090

Table with new positive coefficients for SA3 strain

	identifier	new_coefficient
0	adp_c	55.048028
1	akg_c	4.118200
2	coa_c	3.449406
3	h_c	55.048028
4	nadh_c	3.264594
5	nadp_c	11.990640
6	pi_c	55.048028

4.1.8. References

1. Orth, Jeffrey D., R. M. T. Fleming, and Bernhard Ø. Palsson. “Reconstruction and Use of Microbial Metabolic Networks: The Core Escherichia Coli Metabolic Model as an Educational Guide.” EcoSal Plus 4, no. 1 (February 1, 2010). https://doi.org/10.1128/ecosalplus.10.2.1.

2. Chen, Xianzhong, Mingming Li, Li Zhou, Wei Shen, Govender Algasan, You Fan, and Zhengxiang Wang. “Metabolic Engineering of Escherichia Coli for Improving Shikimate Synthesis from Glucose.” Bioresource Technology 166 (August 1, 2014): 64–71. https://doi.org/10.1016/j.biortech.2014.05.035.