Analyzing models¶
cameo uses and extends the model data structures defined by cobrapy, our favorite COnstraints-Based Reconstruction and Analysis tool for Python. cameo is thus 100% compatible with cobrapy. For efficiency reasons though cameo implements its own analysis methods that take advantage of a more advanced solver interface.
from cameo import models
model = models.bigg.e_coli_core
Flux Variability Analysis¶
Flux variability analysis (FVA) enables the computation of lower and upper bounds of reaction fluxes.
from cameo import flux_variability_analysis
fva_result = flux_variability_analysis(model)
fva_result.data_frame
| upper_bound | lower_bound | |
|---|---|---|
| ACALD | 9.375217e-16 | -2.000000e+01 |
| ACALDt | 0.000000e+00 | -2.000000e+01 |
| ACKr | -1.862346e-15 | -2.000000e+01 |
| ACONTa | 2.000000e+01 | -4.825168e-16 |
| ACONTb | 2.000000e+01 | -1.999683e-16 |
| ACt2r | 0.000000e+00 | -2.000000e+01 |
| ADK1 | 1.666100e+02 | 0.000000e+00 |
| ... | ... | ... |
| SUCDi | 1.000000e+03 | 0.000000e+00 |
| SUCOAS | -3.552714e-15 | -2.000000e+01 |
| TALA | 2.000000e+01 | -1.545362e-01 |
| THD2 | 3.332200e+02 | 0.000000e+00 |
| TKT1 | 2.000000e+01 | -1.545362e-01 |
| TKT2 | 2.000000e+01 | -4.663728e-01 |
| TPI | 1.000000e+01 | -1.000000e+01 |
95 rows × 2 columns
fva_result.plot(index=fva_result.data_frame.index[:25])
One very useful application of FVA is determining if alternative optimal solution exist.
fva_result2 = flux_variability_analysis(model,fraction_of_optimum=0.5)
fva_result2.data_frame
| upper_bound | lower_bound | |
|---|---|---|
| ACALD | 0.000000e+00 | -12.602453 |
| ACALDt | 3.774758e-15 | -12.602453 |
| ACKr | 0.000000e+00 | -13.358852 |
| ACONTa | 1.383029e+01 | 0.471437 |
| ACONTb | 1.383029e+01 | 0.471437 |
| ACt2r | -6.527569e-14 | -13.358852 |
| ADK1 | 8.433833e+01 | 0.000000 |
| ... | ... | ... |
| SUCDi | 1.000000e+03 | 0.000000 |
| SUCOAS | 0.000000e+00 | -13.358852 |
| TALA | 1.328068e+01 | -0.154536 |
| THD2 | 1.686767e+02 | 0.000000 |
| TKT1 | 1.328068e+01 | -0.154536 |
| TKT2 | 1.312294e+01 | -0.466373 |
| TPI | 9.565355e+00 | -3.793497 |
95 rows × 2 columns
fva_result2.plot()
from cameo.visualization import plotting
Phenotpic Phase Plane¶
The phenotypic phase plane is a modeling technique was developed to do a theoretical accessement of what cell can or cannot do in terms of the stoichiometric constraints [Edawards et al. 2001].
The phenotipic phase plane between growth and a product of interest yields the production envelope: a representation between the trade of between production of the desired product and growth.
from cameo import phenotypic_phase_plane
model.reactions.EX_o2_e.lower_bound = -10
result = phenotypic_phase_plane(model,
variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],
objective=model.reactions.EX_succ_e,
points=10)
result.plot()
The production envelope allows is a quick way to inspect the limitations of the system to design and how the production relates for with growth. In the previous example, succinate prudction is completly decoupled from growth and by decreasing the growth rate it is theoretically possible to produce up to 15 times more succinate.
result.plot(points=[(0.52, 0), (0.23, 12.2)], points_colors=["green", "red"])
The production envelope can show the coupling between growth and production. There is no stoichiometric couple between growth and production for succinate under aerobic conditions, but that is not the case for acetate under anaerobic conditions.
result = phenotypic_phase_plane(model,
variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],
objective=model.reactions.EX_ac_e)
result.plot()
result.data_frame
| BIOMASS_Ecoli_core_w_GAM | objective_lower_bound | objective_upper_bound | |
|---|---|---|---|
| 0 | 0.559051 | 9.90568 | 11.503269 |
| 1 | 0.529627 | 2.62796 | 11.950466 |
| 2 | 0.500203 | 0.00000 | 12.397662 |
| 3 | 0.470779 | 0.00000 | 12.844858 |
| 4 | 0.441356 | 0.00000 | 13.292055 |
| 5 | 0.411932 | 0.00000 | 13.739251 |
| 6 | 0.382508 | 0.00000 | 14.186448 |
| ... | ... | ... | ... |
| 13 | 0.176542 | 0.00000 | 17.316822 |
| 14 | 0.147119 | 0.00000 | 17.764018 |
| 15 | 0.117695 | 0.00000 | 18.211215 |
| 16 | 0.088271 | 0.00000 | 18.658411 |
| 17 | 0.058847 | 0.00000 | 19.105607 |
| 18 | 0.029424 | 0.00000 | 19.552804 |
| 19 | 0.000000 | 0.00000 | 20.000000 |
20 rows × 3 columns
One can imediatly see if a design is feasible within the new defined constraints.
result.plot(points=[(0.2, 8), (0.2, 2)], points_colors=["green", "red"])
The computed data can be inspected in the format of a pandas data frame
by calling result.data_frame
result.data_frame
| BIOMASS_Ecoli_core_w_GAM | objective_lower_bound | objective_upper_bound | |
|---|---|---|---|
| 0 | 0.559051 | 9.90568 | 11.503269 |
| 1 | 0.529627 | 2.62796 | 11.950466 |
| 2 | 0.500203 | 0.00000 | 12.397662 |
| 3 | 0.470779 | 0.00000 | 12.844858 |
| 4 | 0.441356 | 0.00000 | 13.292055 |
| 5 | 0.411932 | 0.00000 | 13.739251 |
| 6 | 0.382508 | 0.00000 | 14.186448 |
| ... | ... | ... | ... |
| 13 | 0.176542 | 0.00000 | 17.316822 |
| 14 | 0.147119 | 0.00000 | 17.764018 |
| 15 | 0.117695 | 0.00000 | 18.211215 |
| 16 | 0.088271 | 0.00000 | 18.658411 |
| 17 | 0.058847 | 0.00000 | 19.105607 |
| 18 | 0.029424 | 0.00000 | 19.552804 |
| 19 | 0.000000 | 0.00000 | 20.000000 |
20 rows × 3 columns
model.reactions.EX_o2_e.lower_bound = 0
result2 = phenotypic_phase_plane(model,
variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],
objective=model.reactions.EX_ac_e,
points=10)
result2.plot()
Flux Balance Impact Degree¶
from cameo.flux_analysis.analysis import flux_balance_impact_degree
model.reactions.EX_o2_e.lower_bound = -10
%time fbid = flux_balance_impact_degree(model, ["EX_o2_e"])
CPU times: user 312 ms, sys: 6.53 ms, total: 318 ms
Wall time: 595 ms
fbid
Flux Balance Impact Degree
- Degree: 9
- Reactions: 62
| perturbed | |
|---|---|
| ACALD | False |
| ACALDt | False |
| ACKr | False |
| ACt2r | False |
| ADK1 | False |
| ALCD2x | False |
| ATPM | False |
| ... | ... |
| PYK | False |
| PYRt2 | False |
| SUCCt2_2 | False |
| SUCCt3 | False |
| SUCDi | False |
| THD2 | False |
| TPI | False |
62 rows × 1 columns
