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stelmo committed Nov 26, 2021
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272 changes: 119 additions & 153 deletions docs/src/notebooks/9_max_min_driving_force_analysis.jl
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Expand Up @@ -11,165 +11,152 @@
# strategy as a tradeoff between energy yield and protein cost.", Proceedings
# of the National Academy of Sciences 110.24 (2013): 10039-10044.

using COBREXA, Tulip

# Let's first make a model of glycolysis fermentation.

mets = [
"13dpg",
"2pg",
"3pg",
"adp",
"atp",
"dhap",
"f6p",
"fdp",
"g3p",
"g6p",
"glc__D",
"h",
"h2o",
"lac__D",
"nad",
"nadh",
"pep",
"pi",
"pyr",
]

rxns = Dict(
"ENO" => Dict("2pg" => -1.0, "h2o" => 1.0, "pep" => 1.0),
"FBA" => Dict("fdp" => -1.0, "dhap" => 1.0, "g3p" => 1.0),
"GAPD" => Dict(
"g3p" => 1.0,
"nad" => 1.0,
"pi" => 1.0,
"h" => -1.0,
"nadh" => -1.0,
"13dpg" => -1.0,
),
"HEX" =>
Dict("atp" => -1.0, "glc__D" => -1.0, "g6p" => 1.0, "adp" => 1.0, "h" => 1.0),
"LDH" =>
Dict("pyr" => -1.0, "nadh" => -1.0, "h" => -1.0, "nad" => 1.0, "lac__D" => 1.0),
"PFK" => Dict("f6p" => -1.0, "atp" => -1.0, "adp" => 1.0, "h" => 1.0, "fdp" => 1.0),
"PGI" => Dict("g6p" => -1.0, "f6p" => 1.0),
"PGK" => Dict("13dpg" => -1.0, "adp" => -1.0, "atp" => 1.0, "3pg" => 1.0),
"PGM" => Dict("3pg" => -1.0, "2pg" => 1.0),
"PYK" =>
Dict("pep" => -1.0, "adp" => -1.0, "h" => -1.0, "atp" => 1.0, "pyr" => 1.0),
"TPI" => Dict("dhap" => -1.0, "g3p" => 1.0),
)

model = StandardModel("Glycolysis")
using COBREXA, GLPK, Tulip

add_metabolites!(model, Metabolite.(mets))
add_reactions!(model, collect(Reaction(rid; metabolites = mets) for (rid, mets) in rxns))
# Let's load the core E. coli model

model
model = load_model("e_coli_core.json")

# We need some thermodynamic data. You can get Gibbs free energies (ΔG⁰) e.g.
# from [eQuilibrator](https://equilibrator.weizmann.ac.il/), possibly using the
# We need some thermodynamic data. You can get reaction Gibbs free energies (ΔG⁰) from
# e.g. [eQuilibrator](https://equilibrator.weizmann.ac.il/), possibly using the
# [Julia wrapper](https://github.com/stelmo/eQuilibrator.jl) that allows you to
# automate this step. Here, we make a dictionary that maps the metabolite IDs to
# calculated Gibbs free energy of formation and the associated error.

metabolite_gibbs_free_energy_errors = Dict(
"2pg" => 0.803992,
"h2o" => 0.759034,
"pep" => 0.821512,
"3pg" => 0.769,
"h" => 0.0,
"nadh" => 6.69724,
"pyr" => 0.758545,
"atp" => 1.48999,
"adp" => 1.22579,
"g3p" => 0.666567,
"glc__D" => 0.638157,
"13dpg" => 1.06993,
"dhap" => 0.561421,
"nad" => 6.69391,
"pi" => 0.748723,
"fdp" => 1.08147,
"g6p" => 0.645544,
"f6p" => 0.667625,
"lac__D" => 2.23563,
# automate this step. Here, we make a dictionary that maps the reaction IDs to
# calculated Gibbs free energy of reaction for each reaction (including the transporters).

reaction_standard_gibbs_free_energies = Dict( # kJ/mol
"ACALD" => -21.26,
"PTAr" => 8.65,
"ALCD2x" => 17.47,
"PDH" => -34.24,
"PYK" => -24.48,
"CO2t" => 0.00,
"MALt2_2" => -6.83,
"CS" => -39.33,
"PGM" => -4.47,
"TKT1" => -1.49,
"ACONTa" => 8.46,
"GLNS" => -15.77,
"ICL" => 9.53,
"FBA" => 23.37,
"SUCCt3" => -43.97,
"FORt2" => -3.42,
"G6PDH2r" => -7.39,
"AKGDH" => -28.23,
"TKT2" => -10.31,
"FRD7" => 73.61,
"SUCOAS" => -1.15,
"FBP" => -11.60,
"ICDHyr" => 5.39,
"AKGt2r" => 10.08,
"GLUSy" => -47.21,
"TPI" => 5.62,
"FORt" => 13.50,
"ACONTb" => -1.62,
"GLNabc" => -30.19,
"RPE" => -3.38,
"ACKr" => 14.02,
"THD2" => -33.84,
"PFL" => -19.81,
"RPI" => 4.47,
"D_LACt2" => -3.42,
"TALA" => -0.94,
"PPCK" => 10.65,
"ACt2r" => -3.41,
"NH4t" => -13.60,
"PGL" => -25.94,
"NADTRHD" => -0.01,
"PGK" => 19.57,
"LDH_D" => 20.04,
"ME1" => 12.08,
"PIt2r" => 10.41,
"ATPS4r" => -37.57,
"PYRt2" => -3.42,
"GLCpts" => -45.42,
"GLUDy" => 32.83,
"CYTBD" => -59.70,
"FUMt2_2" => -6.84,
"FRUpts2" => -42.67,
"GAPD" => 0.53,
"H2Ot" => 0.00,
"PPC" => -40.81,
"NADH16" => -80.37,
"PFK" => -18.54,
"MDH" => 25.91,
"PGI" => 2.63,
"O2t" => 0.00,
"ME2" => 12.09,
"GND" => 10.31,
"SUCCt2_2" => -6.82,
"GLUN" => -14.38,
"ETOHt2r" => -16.93,
"ADK1" => 0.38,
"ACALDt" => 0.00,
"SUCDi" => -73.61,
"ENO" => -3.81,
"MALS" => -39.22,
"GLUt2r" => -3.49,
"PPS" => -6.05,
"FUM" => -3.42,
)

metabolite_gibbs_free_energies = Dict(
"2pg" => -1333.96,
"h2o" => -151.422,
"pep" => -1186.86,
"3pg" => -1336.81,
"h" => 0.0,
"nadh" => -1065.92,
"pyr" => -338.467,
"atp" => -2267.13,
"adp" => -1391.96,
"g3p" => -1072.56,
"glc__D" => -436.249,
"13dpg" => -2194.16,
"dhap" => -1078.59,
"nad" => -1134.53,
"pi" => -1055.34,
"fdp" => -2176.61,
"g6p" => -1287.63,
"f6p" => -1286.74,
"lac__D" => -293.006,
)
# In general you cannot be certain that all fluxes will be positive. This poses problems
# for systematically enforcing that ΔᵣG ≤ 0 as done in the original formulation. In COBREXA
# ΔᵣG ⋅ vᵢ ≤ 0 is instead enforced, where vᵢ is the flux of reaction i. By default all fluxes
# are assumed to be positive, but by supplying thermodynamically consistent flux solution
# it is possible to drop this implicit assumption and makes it easier to directly incorporate
# the max min driving force into non-customized models.

# In this model GAPD was purposely written such that negative flux for this reaction
# corresponds to glycolysis going forward. In general you cannot be certain that positive
# fluxes correspond to reactions in the expected direction. To fix this, we supply a dictionary
# of a thermodynamically feasible flux solution.

flux_solution = Dict(
"HEX" => 1.0,
"PGI" => 1.0,
"PFK" => 1.0,
"FBA" => 1.0,
"TPI" => 1.0,
"GAPD" => -2.0,
"PGK" => 2.0,
"PGM" => 2.0,
"ENO" => 2.0,
"PYK" => 2.0,
"LDH" => 2.0,
flux_solution = flux_balance_analysis_dict(
model,
GLPK.Optimizer;
modifications = [add_loopless_constraints()],
)

# Run max min driving force analysis with some reasonable constraints. Protons and water are
# removed from the concentration calculation of the optimization problem, thus we specify
# their IDs explicitly. The reason for this is that the Gibbs free energies of biochemical
# reactions is measured at constant pH, so proton concentrations is fixed; likewise we
# assume that reactions occur in aqueous environments, hence water excluded too.
# assume that reactions occur in aqueous environments, hence water is excluded too.

res = max_min_driving_force(
sol = max_min_driving_force(
model,
metabolite_gibbs_free_energies,
reaction_standard_gibbs_free_energies,
Tulip.Optimizer;
flux_solution = flux_solution,
reaction_gibbs_free_energy_adjustments = reaction_gibbs_free_energy_adjustments,
metabolite_gibbs_free_energy_errors = metabolite_gibbs_free_energy_errors,
proton_ids = ["h"],
water_ids = ["h2o"],
concentration_lb = 1e-6, # 1 uM
concentration_ub = 10e-3, # 10 mM
proton_ids = ["h_c", "h_e"],
water_ids = ["h2o_c", "h2o_e"],
concentration_ratios = Dict(
("atp_c", "adp_c") => 10.0,
("nadh_c", "nad_c") => 0.13,
("nadph_c", "nadp_c") => 1.3,
),
concentration_lb = 1e-6,
concentration_ub = 100e-3,
ignore_reaction_ids = [
"H2Ot", # ignore water transport because water's concentration CANNOT change in the implementation of this function (also protons)
],
)

sol.mmdf

# Plot the results to show how the concentrations can be used to ensure that
# each reach proceeds "down hill" (ΔᵣG < 0) and that the driving force is as
# large as possible across all the reactions in the model. Compare this to the
# driving forces at standard conditions.
# driving forces at standard conditions. Note, we only plot glycolysis for simplicity.

# We additionally scale the fluxes according to their stoichiometry in the
# pathway. From the output, it is clear that that metabolite concentrations
# play a large role in ensuring the thermodynamic consistency of in vivo enzyme
# reactions.

rids = ["HEX", "PGI", "PFK", "FBA", "TPI", "GAPD", "PGK", "PGM", "ENO", "PYK", "LDH"] # in order of pathway
rids = ["GLCpts", "PGI", "PFK", "FBA", "TPI", "GAPD", "PGK", "PGM", "ENO", "PYK"] # glycolysis
rid_rf = [flux_solution[rid] for rid in rids]
dg_standard = [gibbs_free_energies[rid] for rid in rids]
dg_opt = [res.dg_reactions[rid] for rid in rids]
dg_standard = cumsum([
reaction_standard_gibbs_free_energies[rid] * flux_solution[rid] for rid in rids
])
dg_standard .-= first(dg_standard)
dg_opt = cumsum([sol.dg_reactions[rid] * flux_solution[rid] for rid in rids])
dg_opt .-= first(dg_opt)

using CairoMakie

Expand All @@ -181,29 +168,8 @@ ax = Axis(
ylabel = "Cumulative ΔG [kJ/mol]",
);

lines!(
ax,
1:length(rids),
(cumsum(dg_standard) .- first(dg_standard)) .* rid_rf;
color = :red,
label = "Standard",
)
lines!(
ax,
1:length(rids),
(cumsum(dg_opt) .- first(dg_opt)) .* rid_rf;
color = :blue,
label = "Optimized",
)
lines!(ax, 1:length(rids), dg_standard; color = :red, label = "Standard")
lines!(ax, 1:length(rids), dg_opt, color = :blue, label = "Optimized")
ax.xticks = (1:length(rids), rids)
fig[1, 2] = Legend(fig, ax, "ΔG'", framevisible = false)
fig

#md # !!! tip "Directions of reactions"
#md # Be careful when constructing models for MMDFA, the reaction directions in the model
#md # and thermodynamic data need to be consistent with the overall flux
#md # direction implied by the model. For example, in BiGG, `LDH_D` is written
#md # `lac__D + nad ⟷ h + nadh + pyr` and the associated ΔrG'⁰ is 23.6803 kJ/mol.
#md # For MMDFA no flux is calculated, so you need to write the reaction
#md # in the direction of flux, i.e. `h + nadh + pyr ⟶ lac__D + nad` with ΔrG'⁰ as
#md # -23.6803 kJ/mol.
2 changes: 1 addition & 1 deletion test/analysis/max_min_driving_force.jl
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Expand Up @@ -24,7 +24,7 @@
),
concentration_lb = 1e-6,
concentration_ub = 100e-3,
ignore_rids = ["H2Ot"],
ignore_reaction_ids = ["H2Ot"],
)

@test isapprox(sol.mmdf, 1.7661155558545698, atol = TEST_TOLERANCE)
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