# Source code for micom.media

```
"""Manages functions for growth media analysis and manipulation."""
from cobra.core.formula import Formula, elements_and_molecular_weights
from optlang.symbolics import Zero
import numpy as np
import pandas as pd
from micom import Community
from micom.util import (
_format_min_growth,
_apply_min_growth,
check_modification,
)
from micom.logger import logger
from micom.solution import OptimizationError
import warnings
[docs]
def add_linear_obj(community, exchanges, weights):
"""Add a linear version of a minimal medium to the community.
Changes the optimization objective to finding the growth medium requiring
the smallest total import flux::
minimize sum w_i|r_i| for r_i in import_reactions
Arguments
---------
community : micom.Community
The community to modify.
exchanges : list of cobra.Reaction
The reactions to constrain.
weights : dict
Maps each exchange reaction to a weight that is used in the
minimization.
"""
check_modification(community)
scale = 1.0
if isinstance(community, Community):
scale = community.scale
coefs = {}
for rxn in exchanges:
export = len(rxn.reactants) == 1 or (
len(rxn.metabolites) == 2 and rxn.products[0].compartment == "m"
)
met = list(rxn.metabolites)[0]
if export:
coefs[rxn.reverse_variable] = weights[met] * scale
else:
coefs[rxn.forward_variable] = weights[met] * scale
community.objective.set_linear_coefficients(coefs)
community.objective.direction = "min"
community.modification = "minimal medium linear"
[docs]
def add_mip_obj(community, exchanges):
"""Add a mixed-integer version of a minimal medium to the community.
Changes the optimization objective to finding the medium with the least
components::
minimize size(R) where R part of import_reactions
Arguments
---------
community : micom.Community
The community to modify.
exchanges : list of cobra.Reaction
The reactions to constrain.
"""
check_modification(community)
if len(community.variables) > 1e4:
logger.warning(
"the MIP version of minimal media is extremely slow for"
" models that large :("
)
boundary_rxns = exchanges
M = max(np.max(np.abs(r.bounds)) for r in boundary_rxns)
prob = community.problem
coefs = {}
to_add = []
for rxn in boundary_rxns:
export = len(rxn.reactants) == 1 or (
len(rxn.reactants) == 2 and rxn.products[0].compartment == "m"
)
indicator = prob.Variable("ind_" + rxn.id, lb=0, ub=1, type="binary")
if export:
vrv = rxn.reverse_variable
indicator_const = prob.Constraint(
vrv - indicator * M, ub=0, name="ind_constraint_" + rxn.id
)
else:
vfw = rxn.forward_variable
indicator_const = prob.Constraint(
vfw - indicator * M, ub=0, name="ind_constraint_" + rxn.id
)
to_add.extend([indicator, indicator_const])
coefs[indicator] = 1
community.add_cons_vars(to_add)
community.solver.update()
community.objective.set_linear_coefficients(coefs)
community.objective.direction = "min"
community.modification = "minimal medium mixed-integer"
[docs]
def safe_weight(met):
"""Get the weight of a molecule."""
try:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
w = max(Formula(met.formula).weight, 1.0)
except Exception:
w = 1.0
return w
[docs]
def weight(exchanges, what):
"""Obtain elemental weights for metabolites."""
mets = [list(r.metabolites)[0] for r in exchanges]
if what is None:
weights = {m: 1.0 for m in mets}
elif what == "mass":
weights = {m: safe_weight(m) for m in mets}
elif what in elements_and_molecular_weights:
weights = {m: Formula(m.formula).elements.get(what, 1e-2) for m in mets}
else:
raise ValueError(
"%s is not a valid elements. Must be one of: %s."
% (what, ", ".join(elements_and_molecular_weights))
)
return weights
[docs]
def minimal_medium(
community,
community_growth,
min_growth=0.0,
exports=False,
exchanges=None,
minimize_components=False,
open_exchanges=False,
solution=False,
weights=None,
atol=None,
rtol=None,
):
"""Find the minimal growth medium for the community.
Finds the minimal growth medium for the community which allows for
community as well as individual growth. Here, a minimal medium can either
be the medium requiring the smallest total import flux or the medium
requiring the least components (ergo ingredients).
Arguments
---------
community : micom.Community
The community to modify.
community_growth : positive float
The minimum community-wide growth rate.
min_growth : positive float or array-like object.
The minimum growth rate for each individual in the community. Either
a single value applied to all individuals or one value for each.
exports : boolean
Whether to include export fluxes in the returned medium. Defaults to
False which will only return import fluxes.
exchanges : list of cobra.Reactions
The list of exchange reactions that are penalized.
minimize_components : boolean
Whether to minimize the number of components instead of the total
import flux. Might be more intuitive if set to True but may also be
slow to calculate for large communities.
open_exchanges : boolean or number
Whether to ignore currently set bounds and make all exchange reactions
in the model possible. If set to a number all exchange reactions will
be opened with (-number, number) as bounds.
solution : boolean
Whether to also return the entire solution and all fluxes for the
minimal medium.
weights : str
Will scale the fluxes by a weight factor. Can either be "mass" which will
scale by molecular mass, a single element which will scale by
the elemental content (for instance "C" to scale by carbon content).
If None every metabolite will receive the same weight.
Will be ignored if `minimize_components` is True.
atol : float
Absolute tolerance for the growth rates. If None will use the solver tolerance.
rtol : float
Relative tolerqance for the growth rates. If None will use the solver tolerance.
Returns
-------
pandas.Series, dict or None
A series {rid: flux} giving the import flux for each required import
reaction. If `solution` is True retuns a dictionary
{"medium": pandas.Series, "solution": micom.CommunitySolution}.
If the medium optimization failed (usually because the specified growth
rates are not reachable) it will return None.
"""
logger.info("calculating minimal medium for %s" % community.id)
if atol is None:
atol = community.solver.configuration.tolerances.feasibility
if rtol is None:
rtol = community.solver.configuration.tolerances.feasibility
if exchanges is None:
boundary_rxns = community.exchanges
else:
boundary_rxns = community.reactions.get_by_any(exchanges)
if isinstance(open_exchanges, bool):
open_bound = 1000
else:
open_bound = open_exchanges
min_growth = _format_min_growth(min_growth, community.taxa)
with community as com:
if open_exchanges:
logger.info("opening exchanges for %d imports" % len(boundary_rxns))
for rxn in boundary_rxns:
rxn.bounds = (-open_bound, open_bound)
logger.info("applying growth rate constraints")
const = community.problem.Constraint(
community.objective.expression,
lb=community_growth,
name="micom_growth_const",
)
community.add_cons_vars([const])
_apply_min_growth(community, min_growth, atol, rtol)
com.objective = Zero
logger.info("adding new media objective")
if minimize_components:
add_mip_obj(com, boundary_rxns)
else:
scales = weight(boundary_rxns, weights)
add_linear_obj(com, boundary_rxns, scales)
sol = com.optimize(fluxes=True, pfba=False)
if sol is None:
logger.warning("minimization of medium was unsuccessful")
return None
logger.info("formatting medium")
medium = pd.Series(dtype="float64")
set_medium = community.medium
ex = [r for r in com.exchanges if r.id in set_medium]
for rxn in ex:
export = len(rxn.reactants) == 1
flux = sol.fluxes.loc["medium", rxn.id]
if abs(flux) < atol:
continue
if export:
medium[rxn.id] = -flux
elif not export:
medium[rxn.id] = flux
if not exports:
medium = medium[medium > 0.0]
if solution:
return {"medium": medium, "solution": sol}
else:
return medium
[docs]
def complete_medium(
model,
medium,
growth=0.1,
min_growth=0.001,
max_import=1,
minimize_components=False,
weights=None,
strict=[],
):
"""Fill in missing components in a growth medium.
Finds the minimal number of additions to make a model form biomass. In
order to avoid bias all added reactions will have a maximum import
rate of `max_import`.
Note
----
This function fixes the growth medium for a single cobra Model. We also
provide a function `complete_db_medium` in `micom.workflows` that fixes a growth
medium for an entire model database.
Arguments
---------
model : cobra.Model
The model to use.
medium : pandas.Series
A growth medium. Must contain positive floats as elements and
exchange reaction ids as index. Note that reactions not present in the
model will be removed from the growth medium.
growth : positive float
The minimum overall growth rate that has to be achieved. For single COBRA
model this is just the biomass flux and for community models this is the
community biomass flux.
min_growth : positive float or array-like object.
The minimum growth rate for each individual in the community. Either
a single value applied to all individuals or one value for each. Only used
if model is a `micom.Community` model.
minimize_components : boolean
Whether to minimize the number of components instead of the total
import flux. Might be more intuitive if set to True but may also be
slow to calculate for large communities.
max_import: positive float
The import rate applied for the added exchanges.
weights : str
Will scale the fluxes by a weight factor. Can either be "mass" which will
scale by molecular mass, a single element which will scale by
the elemental content (for instance "C" to scale by carbon content).
If None every metabolite will receive the same weight.
Will be ignored if `minimize_components` is True.
strict : list
strict : list
Whether to match the imports in the predefined medium exactly. For reactions IDs
listed here will not allow additional import of the components in the provided
medium. For example, if your input medium has a flux of 10 mmol/(gDW*h) defined
and the requested growth rate can only be fulfilled by ramping this up that
would be allowed in non-strict mode but forbidden in strict mode. To match all
medium components to strict mode use `strict=medium.index`.
Returns
-------
pandas.Series or dict
A series {rid: flux} giving the import flux for each required import
reaction. This will include the initial `medium` as passed to the
function as well as a minimal set of additional changes such that the
model produces biomass with a rate >= `min_growth`.
"""
exids = [r.id for r in model.exchanges]
medium_rxns = [r for r in model.exchanges if r.id in medium.index]
candidates = [r for r in model.exchanges if r.id not in medium.index]
medium = medium[[i for i in medium.index if i in exids]]
tol = model.solver.configuration.tolerances.feasibility
with model:
model.modification = None
const = model.problem.Constraint(
model.objective.expression,
lb=growth,
name="micom_growth_const",
)
if isinstance(model, Community):
min_growth = _format_min_growth(min_growth, model.taxa)
_apply_min_growth(model, min_growth, tol, tol)
model.add_cons_vars([const])
model.objective = Zero
model.medium = medium.to_dict()
extra_imports = []
for ex in medium_rxns:
if ex.id in strict:
continue
ex_copy = ex.copy()
ex_copy.id = ex.id + "_free"
if hasattr(ex, "global_id"):
ex_copy.global_id = ex.global_id + "_free"
ex_copy.community_id = ex.community_id
extra_imports.append(ex_copy)
candidates.append(ex)
model.add_reactions(extra_imports)
for ex in candidates:
export = len(ex.reactants) == 1
if export:
ex.lower_bound = -max_import
else:
ex.upper_bound = max_import
if minimize_components:
add_mip_obj(model, candidates)
else:
scales = weight(candidates, weights)
add_linear_obj(model, candidates, scales)
if isinstance(model, Community):
sol = model.optimize(fluxes=True, pfba=False)
if sol is not None:
fluxes = sol.fluxes.loc["medium", :]
else:
try:
sol = model.optimize(raise_error=True)
fluxes = sol.fluxes
except OptimizationError:
sol = None
if sol is None:
raise OptimizationError(
"Could not find a solution that completes the medium :("
)
completed = pd.Series(dtype="float64")
for rxn in model.exchanges:
export = len(rxn.reactants) == 1
flux = -fluxes[rxn.id] if export else fluxes[rxn.id]
if flux < tol:
flux = 0.0
completed[rxn.id] = flux
if rxn.id in medium.index and rxn.id not in strict:
completed[rxn.id] += medium[rxn.id]
elif rxn.id in medium.index:
completed[rxn.id] = medium[rxn.id]
return completed[completed > 0.0]
```