Analyzing models
================
**cameo** uses the model data structures defined by
`cobrapy `__, our favorite
**CO**\ nstraints-**B**\ ased **R**\ econstruction and **A**\ nalysis
tool for **Py**\ thon. **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.
.. code:: ipython3
from cameo import models
from cameo.visualization.plotting.with_plotly import PlotlyPlotter
model = models.bigg.e_coli_core
plotter = PlotlyPlotter()
.. container:: alert alert-warning
Note that plotter is passed as the first argument of every plotting
function.
Flux Variability Analysis
-------------------------
Flux variability analysis (FVA) enables the computation of lower and
upper bounds of reaction fluxes.
.. code:: ipython3
from cameo import flux_variability_analysis
.. code:: ipython3
fva_result = flux_variability_analysis(model)
fva_result.data_frame
.. raw:: html
|
lower_bound |
upper_bound |
| PFK |
0.000000e+00 |
176.61 |
| PFL |
0.000000e+00 |
40.00 |
| PGI |
-5.000000e+01 |
10.00 |
| PGK |
-2.000000e+01 |
0.00 |
| PGL |
0.000000e+00 |
60.00 |
| ... |
... |
... |
| NADH16 |
0.000000e+00 |
120.00 |
| NADTRHD |
0.000000e+00 |
378.22 |
| NH4t |
-5.712836e-30 |
10.00 |
| O2t |
0.000000e+00 |
60.00 |
| PDH |
0.000000e+00 |
40.00 |
95 rows × 2 columns
.. code:: ipython3
fva_result.plot(plotter, index=fva_result.data_frame.index[:25])
.. raw:: html
.. raw:: html
One very useful application of FVA is determining if alternative optimal
solution exist.
.. code:: ipython3
fva_result2 = flux_variability_analysis(model,fraction_of_optimum=0.5)
fva_result2.data_frame
.. raw:: html
|
lower_bound |
upper_bound |
| PFK |
0.000000 |
93.903685 |
| PFL |
0.000000 |
28.826782 |
| PGI |
-30.166133 |
9.910423 |
| PGK |
-18.838427 |
-5.479575 |
| PGL |
0.000000 |
40.076556 |
| ... |
... |
... |
| NADH16 |
12.517553 |
81.799493 |
| NADTRHD |
0.000000 |
193.989678 |
| NH4t |
2.382660 |
8.664181 |
| O2t |
6.258776 |
40.899746 |
| PDH |
0.000000 |
28.826782 |
95 rows × 2 columns
.. code:: ipython3
fva_result2.plot(plotter)
.. raw:: html
.. code:: ipython3
from cameo.visualization import plotting
Phenotypic 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.
.. code:: ipython3
from cameo import phenotypic_phase_plane
.. code:: ipython3
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)
.. code:: ipython3
result.plot(plotter)
.. raw:: html
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.
.. code:: ipython3
result.plot(plotter, points=[(0.52, 0), (0.23, 12.2)], points_colors=["green", "red"])
.. raw:: html
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.
.. code:: ipython3
result = phenotypic_phase_plane(model,
variables=[model.reactions.BIOMASS_Ecoli_core_w_GAM],
objective=model.reactions.EX_ac_e)
result.plot(plotter)
.. raw:: html
.. code:: ipython3
result.data_frame
.. raw:: html
|
BIOMASS_Ecoli_core_w_GAM |
objective_lower_bound |
objective_upper_bound |
c_yield_lower_bound |
c_yield_upper_bound |
mass_yield_lower_bound |
mass_yield_upper_bound |
| 0 |
0.000000 |
0.00000 |
20.000000 |
0.000000 |
0.666667 |
0.000000 |
0.655477 |
| 1 |
0.029424 |
0.00000 |
19.552804 |
0.000000 |
0.651760 |
0.000000 |
0.640821 |
| 2 |
0.058847 |
0.00000 |
19.105607 |
0.000000 |
0.636854 |
0.000000 |
0.626164 |
| 3 |
0.088271 |
0.00000 |
18.658411 |
0.000000 |
0.621947 |
0.000000 |
0.611508 |
| 4 |
0.117695 |
0.00000 |
18.211215 |
0.000000 |
0.607040 |
0.000000 |
0.596852 |
| 5 |
0.147119 |
0.00000 |
17.764018 |
0.000000 |
0.592134 |
0.000000 |
0.582195 |
| 6 |
0.176542 |
0.00000 |
17.316822 |
0.000000 |
0.577227 |
0.000000 |
0.567539 |
| 7 |
0.205966 |
0.00000 |
16.869626 |
0.000000 |
0.562321 |
0.000000 |
0.552883 |
| 8 |
0.235390 |
0.00000 |
16.422429 |
0.000000 |
0.547414 |
0.000000 |
0.538226 |
| 9 |
0.264813 |
0.00000 |
15.975233 |
0.000000 |
0.532508 |
0.000000 |
0.523570 |
| 10 |
0.294237 |
0.00000 |
15.528037 |
0.000000 |
0.517601 |
0.000000 |
0.508914 |
| 11 |
0.323661 |
0.00000 |
15.080840 |
0.000000 |
0.502695 |
0.000000 |
0.494257 |
| 12 |
0.353085 |
0.00000 |
14.633644 |
0.000000 |
0.487788 |
0.000000 |
0.479601 |
| 13 |
0.382508 |
0.00000 |
14.186448 |
0.000000 |
0.472882 |
0.000000 |
0.464945 |
| 14 |
0.411932 |
0.00000 |
13.739251 |
0.000000 |
0.457975 |
0.000000 |
0.450288 |
| 15 |
0.441356 |
0.00000 |
13.292055 |
0.000000 |
0.443068 |
0.000000 |
0.435632 |
| 16 |
0.470779 |
0.00000 |
12.844858 |
0.000000 |
0.428162 |
0.000000 |
0.420975 |
| 17 |
0.500203 |
0.00000 |
12.397662 |
0.000000 |
0.413255 |
0.000000 |
0.406319 |
| 18 |
0.529627 |
2.62796 |
11.950466 |
0.087599 |
0.398349 |
0.086128 |
0.391663 |
| 19 |
0.559051 |
9.90568 |
11.503269 |
0.330189 |
0.383442 |
0.324647 |
0.377006 |
One can immediately see if a design is feasible within the new defined
constraints.
.. code:: ipython3
result.plot(plotter, points=[(0.2, 8), (0.2, 2)], points_colors=["green", "red"])
.. raw:: html
The computed data can be inspected in the format of a pandas data frame
by calling `result.data_frame`
.. code:: ipython3
result.data_frame
.. raw:: html
|
BIOMASS_Ecoli_core_w_GAM |
objective_lower_bound |
objective_upper_bound |
c_yield_lower_bound |
c_yield_upper_bound |
mass_yield_lower_bound |
mass_yield_upper_bound |
| 0 |
0.000000 |
0.00000 |
20.000000 |
0.000000 |
0.666667 |
0.000000 |
0.655477 |
| 1 |
0.029424 |
0.00000 |
19.552804 |
0.000000 |
0.651760 |
0.000000 |
0.640821 |
| 2 |
0.058847 |
0.00000 |
19.105607 |
0.000000 |
0.636854 |
0.000000 |
0.626164 |
| 3 |
0.088271 |
0.00000 |
18.658411 |
0.000000 |
0.621947 |
0.000000 |
0.611508 |
| 4 |
0.117695 |
0.00000 |
18.211215 |
0.000000 |
0.607040 |
0.000000 |
0.596852 |
| 5 |
0.147119 |
0.00000 |
17.764018 |
0.000000 |
0.592134 |
0.000000 |
0.582195 |
| 6 |
0.176542 |
0.00000 |
17.316822 |
0.000000 |
0.577227 |
0.000000 |
0.567539 |
| 7 |
0.205966 |
0.00000 |
16.869626 |
0.000000 |
0.562321 |
0.000000 |
0.552883 |
| 8 |
0.235390 |
0.00000 |
16.422429 |
0.000000 |
0.547414 |
0.000000 |
0.538226 |
| 9 |
0.264813 |
0.00000 |
15.975233 |
0.000000 |
0.532508 |
0.000000 |
0.523570 |
| 10 |
0.294237 |
0.00000 |
15.528037 |
0.000000 |
0.517601 |
0.000000 |
0.508914 |
| 11 |
0.323661 |
0.00000 |
15.080840 |
0.000000 |
0.502695 |
0.000000 |
0.494257 |
| 12 |
0.353085 |
0.00000 |
14.633644 |
0.000000 |
0.487788 |
0.000000 |
0.479601 |
| 13 |
0.382508 |
0.00000 |
14.186448 |
0.000000 |
0.472882 |
0.000000 |
0.464945 |
| 14 |
0.411932 |
0.00000 |
13.739251 |
0.000000 |
0.457975 |
0.000000 |
0.450288 |
| 15 |
0.441356 |
0.00000 |
13.292055 |
0.000000 |
0.443068 |
0.000000 |
0.435632 |
| 16 |
0.470779 |
0.00000 |
12.844858 |
0.000000 |
0.428162 |
0.000000 |
0.420975 |
| 17 |
0.500203 |
0.00000 |
12.397662 |
0.000000 |
0.413255 |
0.000000 |
0.406319 |
| 18 |
0.529627 |
2.62796 |
11.950466 |
0.087599 |
0.398349 |
0.086128 |
0.391663 |
| 19 |
0.559051 |
9.90568 |
11.503269 |
0.330189 |
0.383442 |
0.324647 |
0.377006 |
.. code:: ipython3
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(plotter)
.. raw:: html
Flux Balance Impact Degree
--------------------------
.. code:: ipython3
from cameo.flux_analysis.analysis import flux_balance_impact_degree
.. code:: ipython3
model.reactions.EX_o2_e.lower_bound = -10
.. code:: ipython3
%time fbid = flux_balance_impact_degree(model, ["EX_o2_e"])
.. parsed-literal::
CPU times: user 137 ms, sys: 0 ns, total: 137 ms
Wall time: 136 ms
.. code:: ipython3
fbid
.. raw:: html
Flux Balance Impact Degree
|
perturbed |
| PFK |
False |
| PGI |
False |
| PGK |
False |
| ACALD |
False |
| PGM |
False |
| ALCD2x |
False |
| ACALDt |
False |
| ACKr |
False |
| PPC |
False |
| ATPM |
False |
| PPCK |
False |
| PPS |
False |
| ADK1 |
False |
| ATPS4r |
True |
| PTAr |
True |
| PYK |
False |
| PYRt2 |
False |
| CO2t |
False |
| SUCCt2_2 |
False |
| CYTBD |
True |
| D_LACt2 |
False |
| ENO |
False |
| SUCCt3 |
False |
| ETOHt2r |
False |
| SUCDi |
False |
| THD2 |
False |
| TPI |
False |
| EX_acald_e |
True |
| EX_co2_e |
False |
| EX_etoh_e |
False |
| EX_glc__D_e |
False |
| EX_h_e |
False |
| EX_h2o_e |
False |
| EX_lac__D_e |
False |
| EX_pyr_e |
True |
| FBA |
False |
| FBP |
False |
| FRD7 |
False |
| FUM |
False |
| G6PDH2r |
True |
| GAPD |
False |
| GLCpts |
False |
| GLNS |
False |
| GLUDy |
False |
| GLUN |
False |
| GLUSy |
False |
| GND |
True |
| H2Ot |
False |
| LDH_D |
False |
| MDH |
False |
| ME1 |
False |
| ME2 |
False |
| NADH16 |
True |
| NADTRHD |
False |
| PDH |
False |