"""Implements optimization and model problems."""
from micom.duality import fast_dual
from micom.util import (
_format_min_growth,
_apply_min_growth,
check_modification,
)
from micom.logger import logger
from micom.solution import solve
from optlang.symbolics import Zero
from functools import partial
[docs]
def add_dualized_optcom(community, min_growth):
"""Add dual Optcom variables and constraints to a community.
Uses the original formulation of OptCom and solves the following
multi-objective problem::
maximize community_growth
s.t. maximize growth_rate_i for all i
s.t. Sv_i = 0
lb_i >= v_i >= ub_i
Notes
-----
This method will only find one arbitrary solution from the Pareto front.
There may exist several other optimal solutions.
Arguments
---------
community : micom.Community
The community to modify.
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.
"""
logger.info("adding dual optcom to %s" % community.id)
check_modification(community)
min_growth = _format_min_growth(min_growth, community.taxa)
prob = community.solver.interface
# Temporarily subtitute objective with sum of individual objectives
# for correct dual variables
old_obj = community.objective
community.objective = Zero
for sp in community.taxa:
taxa_obj = community.constraints["objective_" + sp]
community.objective += taxa_obj.expression
_apply_min_growth(community, min_growth)
dual_coefs = fast_dual(community)
logger.info("adding expressions for %d taxa" % len(community.taxa))
for sp in community.taxa:
primal_const = community.constraints["objective_" + sp]
coefs = primal_const.get_linear_coefficients(primal_const.variables)
coefs.update(
{
dual_var: -coef
for dual_var, coef in dual_coefs.items()
if sp in dual_var.name
}
)
obj_constraint = prob.Constraint(
Zero, lb=0, ub=0, name="optcom_suboptimality_" + sp
)
community.add_cons_vars([obj_constraint])
community.solver.update()
obj_constraint.set_linear_coefficients(coefs)
community.objective = old_obj
community.modification = "dual optcom"
logger.info("finished adding dual optcom to %s" % community.id)
[docs]
def add_moma_optcom(community, min_growth, linear=False):
"""Add a dualized MOMA version of OptCom.
Solves a MOMA (minimization of metabolic adjustment) formulation of OptCom
given by::
minimize cooperativity_cost
s.t. maximize community_objective
s.t. Sv = 0
lb >= v >= ub
where community_cost = sum (growth_rate - max_growth)**2
if linear=False or
community_cost = sum |growth_rate - max_growth|
if linear=True
Arguments
---------
community : micom.Community
The community to modify.
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.
linear : boolean
Whether to use a non-linear (sum of squares) or linear version of the
cooperativity cost. If set to False requires a QP-capable solver.
"""
logger.info(
"adding dual %s moma to %s"
% ("linear" if linear else "quadratic", community.id)
)
check_modification(community)
min_growth = _format_min_growth(min_growth, community.taxa)
prob = community.solver.interface
old_obj = community.objective
coefs = old_obj.get_linear_coefficients(old_obj.variables)
# Get maximum individual growth rates
max_gcs = community.optimize_all(progress=False)
_apply_min_growth(community, min_growth)
dual_coefs = fast_dual(community)
coefs.update({v: -coef for v, coef in dual_coefs.items()})
obj_constraint = prob.Constraint(Zero, lb=0, ub=0, name="optcom_suboptimality")
community.add_cons_vars([obj_constraint])
community.solver.update()
obj_constraint.set_linear_coefficients(coefs)
obj_expr = Zero
logger.info("adding expressions for %d taxa" % len(community.taxa))
for sp in community.taxa:
v = prob.Variable("gc_constant_" + sp, lb=max_gcs[sp], ub=max_gcs[sp])
community.add_cons_vars([v])
taxa_obj = community.constraints["objective_" + sp]
ex = v - taxa_obj.expression
if not linear:
ex = ex**2
obj_expr += ex.expand()
community.objective = prob.Objective(obj_expr, direction="min")
community.modification = "moma optcom"
logger.info("finished dual moma to %s" % community.id)
[docs]
_methods = {
"original": [add_dualized_optcom],
"moma": [add_moma_optcom],
"lmoma": [partial(add_moma_optcom, linear=True)],
}
[docs]
def optcom(community, strategy, min_growth, fluxes, pfba):
"""Run OptCom for the community.
OptCom methods are a group of optimization procedures to find community
solutions that provide a tradeoff between the cooperative community
growth and the egoistic growth of each individual [#p1]_. `micom`
provides several strategies that can be used to find optimal solutions:
- "moma": Minimization of metabolic adjustment. Simultaneously
optimizes the community objective (maximize) and the cooperativity
cost (minimize). This method finds an exact maximum but doubles the
number of required variables, thus being slow.
- "lmoma": The same as "moma" only with a linear
representation of the cooperativity cost (absolute value).
- "original": Solves the multi-objective problem described in [#p1]_.
Here, the community growth rate is maximized simultanously with all
individual growth rates. Note that there are usually many
Pareto-optimal solutions to this problem and the method will only
give one solution. This is also the slowest method.
Parameters
----------
community : micom.Community
The community to optimize.
strategy : str
The strategy used to solve the OptCom formulation. Defaults to
"lagrangian" which gives a decent tradeoff between speed and
correctness.
min_growth : float or array-like
The minimal growth rate required for each individual. May be a
single value or an array-like object with the same length as there
are individuals.
fluxes : boolean
Whether to return the fluxes as well.
pfba : boolean
Whether to obtain fluxes by parsimonious FBA rather than
"classical" FBA.
Returns
-------
micom.CommunitySolution
The solution of the optimization. If fluxes==False will only contain
the objective value, community growth rate and individual growth rates.
References
----------
.. [#p1] OptCom: a multi-level optimization framework for the metabolic
modeling and analysis of microbial communities.
Zomorrodi AR, Maranas CD. PLoS Comput Biol. 2012 Feb;8(2):e1002363.
doi: 10.1371/journal.pcbi.1002363, PMID: 22319433
"""
if strategy not in _methods:
raise ValueError("strategy must be one of {}!".format(",".join(_methods)))
funcs = _methods[strategy]
with community as com:
# Add needed variables etc.
funcs[0](com, min_growth)
return solve(community, fluxes=fluxes, pfba=pfba)