def _add_constraint_for_only_one_captain(
problem: pulp.LpProblem,
players: List[structures.Player],
captain_vars: CaptainVarMap,
) -> None:
problem.addConstraint(
pulp.LpConstraint(
pulp.LpAffineExpression({captain_vars[p]: 1
for p in players}),
pulp.LpConstraintLE,
'There can only be one captain selected',
1,
))
def logistics_network(
tbde,
tbdi,
tbfa,
dep="需要地",
dem="需要",
fac="工場",
prd="製品",
tcs="輸送費",
pcs="生産費",
lwb="下限",
upb="上限",
):
"""
ロジスティクスネットワーク問題を解く
tbde: 需要地 製品 需要
tbdi: 需要地 工場 輸送費
tbfa: 工場 製品 生産費 (下限) (上限)
出力: 解の有無, 輸送表, 生産表
"""
facprd = [fac, prd]
m = LpProblem()
tbpr = tbfa[facprd].sort_values(facprd).drop_duplicates()
tbdi2 = pd.merge(tbdi, tbpr, on=fac)
tbdi2["VarX"] = addvars(tbdi2.shape[0])
tbfa["VarY"] = addvars(tbfa.shape[0])
tbsm = pd.concat(
[tbdi2.groupby(facprd).VarX.sum(),
tbfa.groupby(facprd).VarY.sum()], 1)
tbde2 = pd.merge(tbde, tbdi2.groupby([dep, prd]).VarX.sum().reset_index())
m += lpDot(tbdi2[tcs], tbdi2.VarX) + lpDot(tbfa[pcs], tbfa.VarY)
tbsm.apply(lambda r: m.addConstraint(r.VarX <= r.VarY), 1)
tbde2.apply(lambda r: m.addConstraint(r.VarX >= r[dem]), 1)
if lwb in tbfa:
def flwb(r):
r.VarY.lowBound = r[lwb]
tbfa[tbfa[lwb] > 0].apply(flwb, 1)
if upb in tbfa:
def fupb(r):
r.VarY.upBound = r[upb]
tbfa[tbfa[upb] != np.inf].apply(fupb, 1)
m.solve()
if m.status == 1:
tbdi2["ValX"] = tbdi2.VarX.apply(value)
tbfa["ValY"] = tbfa.VarY.apply(value)
return m.status == 1, tbdi2, tbfa
def logistics_network(tbde,
tbdi,
tbfa,
dep='需要地',
dem='需要',
fac='工場',
prd='製品',
tcs='輸送費',
pcs='生産費',
lwb='下限',
upb='上限'):
"""
ロジスティクスネットワーク問題を解く
tbde: 需要地 製品 需要
tbdi: 需要地 工場 輸送費
tbfa: 工場 製品 生産費 (下限) (上限)
出力: 解の有無, 輸送表, 生産表
"""
import numpy as np, pandas as pd
from pulp import LpProblem, lpDot, lpSum, value
facprd = [fac, prd]
m = LpProblem()
tbpr = tbfa[facprd].sort_values(facprd).drop_duplicates()
tbdi2 = pd.merge(tbdi, tbpr, on=fac)
tbdi2['VarX'] = addvars(tbdi2.shape[0])
tbfa['VarY'] = addvars(tbfa.shape[0])
tbsm = pd.concat(
[tbdi2.groupby(facprd).VarX.sum(),
tbfa.groupby(facprd).VarY.sum()], 1)
tbde2 = pd.merge(tbde, tbdi2.groupby([dep, prd]).VarX.sum().reset_index())
m += lpDot(tbdi2[tcs], tbdi2.VarX) + lpDot(tbfa[pcs], tbfa.VarY)
tbsm.apply(lambda r: m.addConstraint(r.VarX <= r.VarY), 1)
tbde2.apply(lambda r: m.addConstraint(r.VarX >= r[dem]), 1)
if lwb in tbfa:
def flwb(r):
r.VarY.lowBound = r[lwb]
tbfa[tbfa[lwb] > 0].apply(flwb, 1)
if upb in tbfa:
def fupb(r):
r.VarY.upBound = r[upb]
tbfa[tbfa[upb] != np.inf].apply(fupb, 1)
m.solve()
if m.status == 1:
tbdi2['ValX'] = tbdi2.VarX.apply(value)
tbfa['ValY'] = tbfa.VarY.apply(value)
return m.status == 1, tbdi2, tbfa
def _add_constraint_for_salary_cap(
problem: pulp.LpProblem,
players: List[structures.Player],
positions: List[structures.Position],
squads: List[structures.Squad],
player_vars: PlayerVarMap,
salary_cap: float,
) -> None:
problem.addConstraint(
pulp.LpConstraint(
pulp.LpAffineExpression({
player_vars[squad][pos][p]: p.price
for squad in squads for pos in positions for p in players
}), pulp.LpConstraintLE,
'Total cost of all players in team must not exceed the salary cap',
salary_cap))
def _add_constraints_for_each_player_only_selected_once(
problem: pulp.LpProblem,
players: List[structures.Player],
positions: List[structures.Position],
squads: List[structures.Squad],
player_vars: PlayerVarMap,
) -> None:
for p in players:
problem.addConstraint(
pulp.LpConstraint(
pulp.LpAffineExpression({
player_vars[squad][pos][p]: 1
for squad in squads for pos in positions
}), pulp.LpConstraintLE,
'{} can only play for one squad and in one position'.format(
p.name), 1))
def binpacking(c, w):
"""
ビンパッキング問題
列生成法で解く(近似解法)
入力
c: ビンの大きさ
w: 荷物の大きさのリスト
出力
ビンごとの荷物の大きさリスト
"""
from pulp import LpAffineExpression
n = len(w)
rn = range(n)
mkp = LpProblem("knapsack", LpMaximize) # 子問題
mkpva = [addvar(cat=LpBinary) for _ in rn]
mkp.addConstraint(lpDot(w, mkpva) <= c)
mdl = LpProblem("dual", LpMaximize) # 双対問題
mdlva = [addvar() for _ in rn]
for i, v in enumerate(mdlva):
v.w = w[i]
mdl.setObjective(lpSum(mdlva))
for i in rn:
mdl.addConstraint(mdlva[i] <= 1)
while True:
mdl.solve()
mkp.setObjective(lpDot([value(v) for v in mdlva], mkpva))
mkp.solve()
if mkp.status != 1 or value(mkp.objective) < 1 + 1e-6:
break
mdl.addConstraint(lpDot([value(v) for v in mkpva], mdlva) <= 1)
nwm = LpProblem("primal", LpMinimize) # 主問題
nm = len(mdl.constraints)
rm = range(nm)
nwmva = [addvar(cat=LpBinary) for _ in rm]
nwm.setObjective(lpSum(nwmva))
dict = {}
for v, q in mdl.objective.items():
dict[v] = LpAffineExpression() >= q
const = list(mdl.constraints.values())
for i, q in enumerate(const):
for v in q:
dict[v].addterm(nwmva[i], 1)
for q in dict.values():
nwm.addConstraint(q)
nwm.solve()
if nwm.status != 1:
return None
w0, result = list(w), [[] for _ in range(len(const))]
for i, va in enumerate(nwmva):
if value(va) < 0.5:
continue
for v in const[i]:
if v.w in w0:
w0.remove(v.w)
result[i].append(v.w)
return [r for r in result if r]
def _add_constraints_for_squad_position_cap(
problem: pulp.LpProblem,
positions: List[structures.Position],
squads: List[structures.Squad],
player_vars: PlayerVarMap,
) -> None:
for squad in squads:
for pos in positions:
cap = squad.position_caps[pos]
problem.addConstraint(
pulp.LpConstraint(
pulp.LpAffineExpression({
var: 1
for var in player_vars[squad][pos].values()
}), pulp.LpConstraintEQ,
'Choose exactly {} players in position {} in squad {}'.
format(cap, pos.name, squad.name), cap))
def _add_constraints_for_captain_must_be_on_team(
problem: pulp.LpProblem,
players: List[structures.Player],
positions: List[structures.Position],
squads: List[structures.Squad],
player_vars: PlayerVarMap,
captain_vars: CaptainVarMap,
) -> None:
for p in players:
problem.addConstraint(
pulp.LpConstraint(
pulp.lpSum([
pulp.LpAffineExpression({
player_vars[squad][pos][p]: 1
for squad in squads for pos in positions
}),
pulp.LpAffineExpression({captain_vars[p]: -1})
]), pulp.LpConstraintGE,
'{} can only be captain if also in the team'.format(p.name)))
def single_yc_lp_from_t(transition_p, t_atoms, yc_values, alpha, xis=False):
"""
Create LP:
min Sum p_t * I
0 <= xi <= 1/alpha
Sum p_t * xi == 1
I = max{y_cvar}
return y_cvar[alpha]
"""
from pulp import LpVariable, LpProblem, value
if alpha == 0:
return 0.
nb_transitions = len(transition_p)
Xi = [LpVariable('xi_' + str(i)) for i in range(nb_transitions)]
I = [LpVariable('I_' + str(i)) for i in range(nb_transitions)]
prob = LpProblem(name='tamar')
for xi in Xi:
prob.addConstraint(0 <= xi)
prob.addConstraint(xi <= 1. / alpha)
prob.addConstraint(sum([xi * p for xi, p in zip(Xi, transition_p)]) == 1)
for xi, i, yc, atoms in zip(Xi, I, yc_values, t_atoms):
last_yc = 0.
f_params = []
atom_p = atoms[1:] - atoms[:-1]
for ix in range(len(yc)):
# linear interpolation as a solution to 'y = kx + q'
k = (yc[ix] - last_yc) / atom_p[ix]
q = last_yc - k * atoms[ix]
prob.addConstraint(i >= k * xi * alpha + q)
f_params.append((k, q))
last_yc = yc[ix]
# opt criterion
prob.setObjective(sum([i * p for i, p in zip(I, transition_p)]))
prob.solve()
if xis:
return value(prob.objective), [value(xi) * alpha for xi in Xi]
else:
return value(prob.objective)
class OptKnock(object):
def __init__(self, model, solver, verbose=False):
self.model = deepcopy(model)
self.verbose = verbose
self.solver = solver
# locate the biomass reaction
biomass_reactions = [
r for r in self.model.reactions if r.objective_coefficient != 0
]
if len(biomass_reactions) != 1:
raise Exception('There should be only one single biomass reaction')
self.r_biomass = biomass_reactions[0]
self.has_flux_as_variables = False
def create_prob(self, sense=LpMaximize):
# create the LP
self.prob = LpProblem('OptKnock', sense=sense)
self.prob.solver = self.solver(msg=self.verbose)
if not self.prob.solver.available():
raise Exception("solver not available")
def add_primal_variables_and_constraints(self):
# create the continuous flux variables (can be positive or negative)
self.var_v = {}
for r in self.model.reactions:
self.var_v[r] = LpVariable("v_%s" % r.id,
lowBound=r.lower_bound,
upBound=r.upper_bound,
cat=LpContinuous)
# this flag will be used later to know if to expect the flux
# variables to exist
self.has_flux_as_variables = True
# add the mass-balance constraints to each of the metabolites (S*v = 0)
for m in self.model.metabolites:
S_times_v = LpAffineExpression([
(self.var_v[r], r.get_coefficient(m)) for r in m.reactions
])
self.prob.addConstraint(S_times_v == 0, 'mass_balance_%s' % m.id)
def add_dual_variables_and_constraints(self):
# create dual variables associated with stoichiometric constraints
self.var_lambda = dict([(m,
LpVariable("lambda_%s" % m.id,
lowBound=-M,
upBound=M,
cat=LpContinuous))
for m in self.model.metabolites])
# create dual variables associated with the constraints on the primal fluxes
self.var_w_U = dict([(r,
LpVariable("w_U_%s" % r.id,
lowBound=0,
upBound=M,
cat=LpContinuous))
for r in self.model.reactions])
self.var_w_L = dict([(r,
LpVariable("w_L_%s" % r.id,
lowBound=0,
upBound=M,
cat=LpContinuous))
for r in self.model.reactions])
# add the dual constraints:
# S'*lambda + w_U - w_L = c_biomass
for r in self.model.reactions:
S_times_lambda = LpAffineExpression([
(self.var_lambda[m], coeff)
for m, coeff in r._metabolites.iteritems() if coeff != 0
])
row_sum = S_times_lambda + self.var_w_U[r] - self.var_w_L[r]
self.prob.addConstraint(row_sum == r.objective_coefficient,
'dual_%s' % r.id)
def prepare_FBA_primal(self, use_glpk=False):
"""
Run standard FBA (primal)
"""
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
def prepare_FBA_dual(self, use_glpk=False):
"""
Run shadow FBA (dual)
"""
self.create_prob(sense=LpMinimize, use_glpk=use_glpk)
self.add_dual_variables_and_constraints()
w_sum = LpAffineExpression(
[(self.var_w_U[r], r.upper_bound)
for r in self.model.reactions if r.upper_bound != 0] +
[(self.var_w_L[r], -r.lower_bound)
for r in self.model.reactions if r.lower_bound != 0])
self.prob.setObjective(w_sum)
def get_reaction_by_id(self, reaction_id):
if reaction_id not in self.model.reactions:
return None
reaction_ind = self.model.reactions.index(reaction_id)
reaction = self.model.reactions[reaction_ind]
return reaction
def add_optknock_variables_and_constraints(self):
# create the binary variables indicating which reactions knocked out
self.var_y = dict([(r, LpVariable("y_%s" % r.id, cat=LpBinary))
for r in self.model.reactions])
# create dual variables associated with the constraints on the primal fluxes
self.var_mu = dict([(r, LpVariable("mu_%s" % r.id, cat=LpContinuous))
for r in self.model.reactions])
# equate the objectives of the primal and the dual of the inner problem
# to force its optimization:
# sum_j mu_j - v_biomass = 0
constr = (lpSum(self.var_mu.values()) -
self.var_v[self.r_biomass] == 0)
self.prob.addConstraint(constr, 'daul_equals_primal')
# add the knockout constraints (when y_j = 0, v_j has to be 0)
for r in self.model.reactions:
# L_jj * y_j <= v_j
self.prob.addConstraint(
r.lower_bound * self.var_y[r] <= self.var_v[r],
'v_lower_%s' % r.id)
# v_j <= U_jj * y_j
self.prob.addConstraint(
self.var_v[r] <= r.upper_bound * self.var_y[r],
'v_upper_%s' % r.id)
# set the constraints on the auxiliary variables (mu):
# mu_j == y_j * (U_jj * w_u_j - L_jj * w_l_j)
for r in self.model.reactions:
w_sum = LpAffineExpression([(self.var_w_U[r], r.upper_bound),
(self.var_w_L[r], -r.lower_bound)])
# mu_j + M*y_j >= 0
self.prob.addConstraint(self.var_mu[r] + M * self.var_y[r] >= 0,
'aux_1_%s' % r.id)
# -mu_j + M*y_j >= 0
self.prob.addConstraint(-self.var_mu[r] + M * self.var_y[r] >= 0,
'aux_2_%s' % r.id)
# mu_j - (U_jj * w_u_j - L_jj * w_l_j) + M*(1-y_j) >= 0
self.prob.addConstraint(
self.var_mu[r] - w_sum + M * (1 - self.var_y[r]) >= 0,
'aux_3_%s' % r.id)
# -mu_j + (U_jj * w_u_j - L_jj * w_l_j) + M*(1-y_j) >= 0
self.prob.addConstraint(
-self.var_mu[r] + w_sum + M * (1 - self.var_y[r]) >= 0,
'aux_4_%s' % r.id)
def add_knockout_bounds(self, ko_candidates=None, num_deletions=5):
"""
construct the list of KO candidates and add a constraint that
only K (num_deletians) of them can have a y_j = 0
"""
ko_candidate_sum_y = []
if ko_candidates is None:
ko_candidates = [
r for r in self.model.reactions if r != self.r_biomass
]
for r in set(self.model.reactions).difference(ko_candidates):
# if 'r' is not a candidate constrain it to be 'active'
# i.e. y_j == 1
self.prob.addConstraint(self.var_y[r] == 1, 'active_%s' % r.id)
# set the upper bound on the number of knockouts (K)
# sum (1 - y_j) <= K
ko_candidate_sum_y = [(self.var_y[r], 1) for r in ko_candidates]
constr = (LpAffineExpression(ko_candidate_sum_y) >=
len(ko_candidate_sum_y) - num_deletions)
self.prob.addConstraint(constr, 'number_of_deletions')
def prepare_optknock(self,
target_reaction_id,
ko_candidates=None,
num_deletions=5,
use_glpk=False):
# find the target reaction
self.r_target = self.get_reaction_by_id(target_reaction_id)
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.add_dual_variables_and_constraints()
self.add_optknock_variables_and_constraints()
# add the objective of maximizing the flux in the target reaction
self.prob.setObjective(self.var_v[self.r_target])
self.add_knockout_bounds(ko_candidates, num_deletions)
def prepare_optslope(self,
target_reaction_id,
ko_candidates=None,
num_deletions=5,
use_glpk=False):
# add the objective of maximizing the flux in the target reaction
self.r_target = self.get_reaction_by_id(target_reaction_id)
# set biomass maximum to 0
self.r_biomass.lower_bound = 0
self.r_biomass.upper_bound = 0
self.r_target.lower_bound = 0
self.r_target.upper_bound = 0
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.add_dual_variables_and_constraints()
self.add_optknock_variables_and_constraints()
# set the objective as maximizing the shadow price of v_target upper bound
self.prob.setObjective(self.var_w_U[self.r_target] -
self.var_w_L[self.r_target])
self.add_knockout_bounds(ko_candidates, num_deletions)
def write_linear_problem(self, fname):
self.prob.writeLP(fname)
def solve(self):
self.prob.solve()
if self.prob.status != LpStatusOptimal:
if self.verbose:
print("LP was not solved because: " +
LpStatus[self.prob.status])
self.solution = Solution(objective_value=None,
status=self.prob.status,
fluxes=None)
else:
if self.has_flux_as_variables:
x = [self.var_v[r].varValue for r in self.model.reactions]
else:
x = []
self.solution = Solution(
objective_value=self.prob.objective.value(),
status=self.prob.status,
fluxes=x)
return self.solution
def get_objective_value(self):
if self.solution.status != LpStatusOptimal:
return None
else:
return self.prob.objective.value()
def print_primal_results(self, short=True):
obj = self.get_objective_value()
if obj is None:
return
print("Objective : %6.3f" % obj)
if not short:
print("List of reactions : ")
for r in self.model.reactions:
print("%30s (%4g <= v <= %4g) : v = %6.3f" % \
(r.name, r.lower_bound, r.upper_bound, self.var_v[r].varValue))
def print_dual_results(self, short=True):
obj = self.get_objective_value()
if obj is None:
return
print("Objective : %6.3f" % obj)
if not short:
print("List of reactions : ")
for r in self.model.reactions:
print("%30s (%4g <= v <= %4g) : w_L = %5.3f, w_U = %5.3f" % \
(r.id, r.lower_bound, r.upper_bound,
self.var_w_L[r].varValue, self.var_w_U[r].varValue))
print("List of metabolites : ")
for m in self.model.metabolites:
print("%30s : lambda = %5.3f, " % \
(m.id, self.var_lambda[m].varValue))
def print_optknock_results(self, short=True):
if self.solution.status != LpStatusOptimal:
return
print("Objective : %6.3f" % self.prob.objective.value())
print("Biomass rate : %6.3f" % self.var_v[self.r_biomass].varValue)
print("Sum of mu : %6.3f" %
np.sum([mu.varValue for mu in self.var_mu.values()]))
print("Knockouts : ")
print(' ; '.join([
'"%s" (%s)' % (r.name, r.id) for r, val in self.var_y.iteritems()
if val.varValue == 0
]))
if not short:
print("List of reactions : ")
for r in self.model.reactions:
print('%25s (%5s) : %4g <= v=%5g <= %4g ; y = %d ; mu = %g ; w_L = %5g ; w_U = %5g' % \
('"' + r.name + '"', r.id,
r.lower_bound, self.var_v[r].varValue, r.upper_bound,
self.var_y[r].varValue, self.var_mu[r].varValue,
self.var_w_L[r].varValue, self.var_w_U[r].varValue))
print("List of metabolites : ")
for m in self.model.metabolites:
print("%30s : lambda = %6.3f" % \
(m.id, self.var_lambda[m].varValue))
def get_optknock_knockouts(self):
return ','.join(
[r.id for r, val in self.var_y.iteritems() if val.varValue == 0])
def get_optknock_model(self):
if self.solution.status != LpStatusOptimal:
raise Exception('OptKnock failed, cannot generate a KO model')
optknock_model = deepcopy(self.model)
knockout_reactions = [
r for r, val in self.var_y.iteritems() if val.varValue == 0
]
for r in knockout_reactions:
new_r = optknock_model.reactions[optknock_model.reactions.index(
r.id)]
new_r.lower_bound = 0
new_r.upper_bound = 0
return optknock_model
def solve_FBA(self):
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
self.solve()
max_biomass = self.get_objective_value()
return max_biomass
def solve_FVA(self, reaction_id):
"""
Run Flux Variability Analysis on the provided reaction
"""
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
self.solve()
max_biomass = self.get_objective_value()
if max_biomass is None:
raise Exception("Cannot run FVA because the model is infeasible")
self.var_v[self.r_biomass].lowBound = max_biomass - 1e-5
r_target = self.get_reaction_by_id(reaction_id)
self.prob.setObjective(self.var_v[r_target])
self.prob.sense = LpMaximize
self.solve()
max_v_target = self.get_objective_value()
self.prob.sense = LpMinimize
self.solve()
min_v_target = self.get_objective_value()
return min_v_target, max_v_target
def get_PPP_data(self, reaction_id, bm_range=None):
"""
Run FVA on a gradient of biomass lower bounds and generate
the data needed for creating the Phenotype Phase Plane
"""
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
r_target = self.get_reaction_by_id(reaction_id)
if r_target is None:
return None
self.solve()
if bm_range is None:
max_biomass = self.get_objective_value()
if max_biomass is None:
return None
bm_range = np.linspace(1e-5, max_biomass - 1e-5, 50)
self.prob.setObjective(self.var_v[r_target])
data = []
for bm_lb in bm_range:
self.var_v[self.r_biomass].lowBound = bm_lb
self.prob.sense = LpMaximize
self.solve()
max_v_target = self.get_objective_value()
self.prob.sense = LpMinimize
self.solve()
min_v_target = self.get_objective_value()
data.append((bm_lb, min_v_target, max_v_target))
return np.matrix(data)
def get_slope(self, reaction_id, epsilon_bm=0.01):
data = self.get_PPP_data(reaction_id, bm_range=[epsilon_bm])
if data is None:
return None
else:
return data[0, 1] / epsilon_bm
def model_summary(self, html):
import analysis_toolbox
analysis_toolbox.model_summary(self.model, self.solution, html)
@staticmethod
def analyze_kos(carbon_sources,
single_kos,
target_reaction,
knockins="",
n_knockouts=2,
n_threads=2,
carbon_uptake_rate=50,
solver='glpk'):
"""
Args:
target_reaction - the reaction for which the coupling to BM yield is made
knockins - extra reactions to add to the model
max_knockouts - the maximum number of simultaneous knockouts
carbon_uptake_rate - in units of mmol C / (gDW*h)
"""
if solver.lower() == 'gurobi':
solver = solvers.GUROBI
elif solver.lower() == 'glpk':
solver = solvers.GLPK
elif solver.lower() == 'scip':
solver = solvers.SCIP
elif solver.lower() == 'cplex':
solver = solvers.CPLEX
else:
raise ValueError('unknown solver: ' + solver)
wt_model = Model.initialize()
if knockins is not None:
wt_model.knockin_reactions(knockins, 0, 1000)
sys.stdout.write("There are %d single knockouts\n" % len(single_kos))
sys.stdout.write("There are %d carbon sources: %s\n" %
(len(carbon_sources), ', '.join(carbon_sources)))
data = []
kos_and_cs = [(kos, cs)
for kos in combinations(single_kos, n_knockouts)
for cs in carbon_sources]
def calculate_yield_and_slope(params):
kos, carbon_source = params
sys.stderr.write('KOs = ' + ', '.join(kos) + ': ' + carbon_source +
'\n')
temp_model = wt_model.clone()
if carbon_source == 'electrons':
temp_model.knockin_reactions('RED', 0, carbon_uptake_rate * 2)
elif carbon_source != '':
# find out how many carbon atoms are in the carbon source
# and normalize the uptake rate to be in units of mmol
# carbon-source / (gDW*h)
nC = 0
for cs in carbon_source.split(','):
met = wt_model.metabolites[wt_model.metabolites.index(
cs + '_c')]
nC += met.elements['C']
uptake_rate = carbon_uptake_rate / float(nC)
for cs in carbon_source.split(','):
temp_model.set_exchange_bounds(cs,
lower_bound=-uptake_rate)
for ko in kos:
if ko != '':
temp_model.knockout_reactions(ko)
yd = OptKnock(temp_model, solver=solver).solve_FBA() or 0
if (target_reaction is not None) and (yd == 0):
slope = 0
else:
slope = OptKnock(temp_model,
solver=solver).get_slope(target_reaction)
return ('|'.join(kos), carbon_source, yd, slope)
data = map(calculate_yield_and_slope, kos_and_cs)
df = pd.DataFrame(
data=list(data),
columns=['knockouts', 'carbon source', 'yield', 'slope'])
return df
class OptKnock(object):
def __init__(self, model, verbose=False):
self.model = deepcopy(model)
self.verbose = verbose
# locate the biomass reaction
biomass_reactions = [
r for r in self.model.reactions if r.objective_coefficient != 0
]
if len(biomass_reactions) != 1:
raise Exception('There should be only one single biomass reaction')
self.r_biomass = biomass_reactions[0]
self.has_flux_as_variables = False
def create_prob(self, sense=LpMaximize, use_glpk=True):
# create the LP
self.prob = LpProblem('OptKnock', sense=sense)
if use_glpk:
self.prob.solver = solvers.GLPK()
else:
self.prob.solver = solvers.CPLEX(msg=self.verbose)
if not self.prob.solver.available():
raise Exception("CPLEX not available")
def add_primal_variables_and_constraints(self):
# create the continuous flux variables (can be positive or negative)
self.var_v = {}
for r in self.model.reactions:
self.var_v[r] = LpVariable("v_%s" % r.id,
lowBound=r.lower_bound,
upBound=r.upper_bound,
cat=LpContinuous)
# this flag will be used later to know if to expect the flux
# variables to exist
self.has_flux_as_variables = True
# add the mass-balance constraints to each of the metabolites (S*v = 0)
for m in self.model.metabolites:
S_times_v = LpAffineExpression([
(self.var_v[r], r.get_coefficient(m)) for r in m.reactions
])
self.prob.addConstraint(S_times_v == 0, 'mass_balance_%s' % m.id)
def add_dual_variables_and_constraints(self):
# create dual variables associated with stoichiometric constraints
self.var_lambda = dict([(m,
LpVariable("lambda_%s" % m.id,
lowBound=-M,
upBound=M,
cat=LpContinuous))
for m in self.model.metabolites])
# create dual variables associated with the constraints on the primal fluxes
self.var_w_U = dict([(r,
LpVariable("w_U_%s" % r.id,
lowBound=0,
upBound=M,
cat=LpContinuous))
for r in self.model.reactions])
self.var_w_L = dict([(r,
LpVariable("w_L_%s" % r.id,
lowBound=0,
upBound=M,
cat=LpContinuous))
for r in self.model.reactions])
# add the dual constraints:
# S'*lambda + w_U - w_L = c_biomass
for r in self.model.reactions:
S_times_lambda = LpAffineExpression([
(self.var_lambda[m], coeff)
for m, coeff in r._metabolites.iteritems() if coeff != 0
])
row_sum = S_times_lambda + self.var_w_U[r] - self.var_w_L[r]
self.prob.addConstraint(row_sum == r.objective_coefficient,
'dual_%s' % r.id)
def prepare_FBA_primal(self, use_glpk=False):
"""
Run standard FBA (primal)
"""
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
def prepare_FBA_dual(self, use_glpk=False):
"""
Run shadow FBA (dual)
"""
self.create_prob(sense=LpMinimize, use_glpk=use_glpk)
self.add_dual_variables_and_constraints()
w_sum = LpAffineExpression(
[(self.var_w_U[r], r.upper_bound)
for r in self.model.reactions if r.upper_bound != 0] +
[(self.var_w_L[r], -r.lower_bound)
for r in self.model.reactions if r.lower_bound != 0])
self.prob.setObjective(w_sum)
def get_reaction_by_id(self, reaction_id):
if reaction_id not in self.model.reactions:
return None
reaction_ind = self.model.reactions.index(reaction_id)
reaction = self.model.reactions[reaction_ind]
return reaction
def add_optknock_variables_and_constraints(self):
# create the binary variables indicating which reactions knocked out
self.var_y = dict([(r, LpVariable("y_%s" % r.id, cat=LpBinary))
for r in self.model.reactions])
# create dual variables associated with the constraints on the primal fluxes
self.var_mu = dict([(r, LpVariable("mu_%s" % r.id, cat=LpContinuous))
for r in self.model.reactions])
# equate the objectives of the primal and the dual of the inner problem
# to force its optimization:
# sum_j mu_j - v_biomass = 0
constr = (lpSum(self.var_mu.values()) -
self.var_v[self.r_biomass] == 0)
self.prob.addConstraint(constr, 'daul_equals_primal')
# add the knockout constraints (when y_j = 0, v_j has to be 0)
for r in self.model.reactions:
# L_jj * y_j <= v_j
self.prob.addConstraint(
r.lower_bound * self.var_y[r] <= self.var_v[r],
'v_lower_%s' % r.id)
# v_j <= U_jj * y_j
self.prob.addConstraint(
self.var_v[r] <= r.upper_bound * self.var_y[r],
'v_upper_%s' % r.id)
# set the constraints on the auxiliary variables (mu):
# mu_j == y_j * (U_jj * w_u_j - L_jj * w_l_j)
for r in self.model.reactions:
w_sum = LpAffineExpression([(self.var_w_U[r], r.upper_bound),
(self.var_w_L[r], -r.lower_bound)])
# mu_j + M*y_j >= 0
self.prob.addConstraint(self.var_mu[r] + M * self.var_y[r] >= 0,
'aux_1_%s' % r.id)
# -mu_j + M*y_j >= 0
self.prob.addConstraint(-self.var_mu[r] + M * self.var_y[r] >= 0,
'aux_2_%s' % r.id)
# mu_j - (U_jj * w_u_j - L_jj * w_l_j) + M*(1-y_j) >= 0
self.prob.addConstraint(
self.var_mu[r] - w_sum + M * (1 - self.var_y[r]) >= 0,
'aux_3_%s' % r.id)
# -mu_j + (U_jj * w_u_j - L_jj * w_l_j) + M*(1-y_j) >= 0
self.prob.addConstraint(
-self.var_mu[r] + w_sum + M * (1 - self.var_y[r]) >= 0,
'aux_4_%s' % r.id)
def add_knockout_bounds(self, ko_candidates=None, num_deletions=5):
"""
construct the list of KO candidates and add a constraint that
only K (num_deletians) of them can have a y_j = 0
"""
ko_candidate_sum_y = []
if ko_candidates is None:
ko_candidates = [
r for r in self.model.reactions if r != self.r_biomass
]
for r in set(self.model.reactions).difference(ko_candidates):
# if 'r' is not a candidate constrain it to be 'active'
# i.e. y_j == 1
self.prob.addConstraint(self.var_y[r] == 1, 'active_%s' % r.id)
# set the upper bound on the number of knockouts (K)
# sum (1 - y_j) <= K
ko_candidate_sum_y = [(self.var_y[r], 1) for r in ko_candidates]
constr = (LpAffineExpression(ko_candidate_sum_y) >=
len(ko_candidate_sum_y) - num_deletions)
self.prob.addConstraint(constr, 'number_of_deletions')
def prepare_optknock(self,
target_reaction_id,
ko_candidates=None,
num_deletions=5,
use_glpk=False):
# find the target reaction
self.r_target = self.get_reaction_by_id(target_reaction_id)
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.add_dual_variables_and_constraints()
self.add_optknock_variables_and_constraints()
# add the objective of maximizing the flux in the target reaction
self.prob.setObjective(self.var_v[self.r_target])
self.add_knockout_bounds(ko_candidates, num_deletions)
def prepare_optslope(self,
target_reaction_id,
ko_candidates=None,
num_deletions=5,
use_glpk=False):
# add the objective of maximizing the flux in the target reaction
self.r_target = self.get_reaction_by_id(target_reaction_id)
# set biomass maximum to 0
self.r_biomass.lower_bound = 0
self.r_biomass.upper_bound = 0
self.r_target.lower_bound = 0
self.r_target.upper_bound = 0
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.add_dual_variables_and_constraints()
self.add_optknock_variables_and_constraints()
# set the objective as maximizing the shadow price of v_target upper bound
self.prob.setObjective(self.var_w_U[self.r_target] -
self.var_w_L[self.r_target])
self.add_knockout_bounds(ko_candidates, num_deletions)
def write_linear_problem(self, fname):
self.prob.writeLP(fname)
def solve(self):
self.prob.solve()
if self.prob.status != LpStatusOptimal:
if self.verbose:
print "LP was not solved because: ", LpStatus[self.prob.status]
self.solution = Solution(None)
else:
self.solution = Solution(self.prob.objective.value())
if self.has_flux_as_variables:
self.solution.x = [
self.var_v[r].varValue for r in self.model.reactions
]
self.solution.status = self.prob.status
return self.solution
def get_objective_value(self):
if self.solution.status != LpStatusOptimal:
return None
else:
return self.prob.objective.value()
def print_primal_results(self, short=True):
obj = self.get_objective_value()
if obj is None:
return
print "Objective : %6.3f" % obj
if not short:
print "List of reactions : "
for r in self.model.reactions:
print "%30s (%4g <= v <= %4g) : v = %6.3f" % \
(r.name, r.lower_bound, r.upper_bound, self.var_v[r].varValue)
def print_dual_results(self, short=True):
obj = self.get_objective_value()
if obj is None:
return
print "Objective : %6.3f" % obj
if not short:
print "List of reactions : "
for r in self.model.reactions:
print "%30s (%4g <= v <= %4g) : w_L = %5.3f, w_U = %5.3f" % \
(r.id, r.lower_bound, r.upper_bound,
self.var_w_L[r].varValue, self.var_w_U[r].varValue)
print "List of metabolites : "
for m in self.model.metabolites:
print "%30s : lambda = %5.3f, " % \
(m.id, self.var_lambda[m].varValue)
def print_optknock_results(self, short=True):
if self.solution.status != LpStatusOptimal:
return
print "Objective : %6.3f" % self.prob.objective.value()
print "Biomass rate : %6.3f" % self.var_v[self.r_biomass].varValue
print "Sum of mu : %6.3f" % np.sum(
[mu.varValue for mu in self.var_mu.values()])
print "Knockouts : "
print ' ; '.join([
'"%s" (%s)' % (r.name, r.id) for r, val in self.var_y.iteritems()
if val.varValue == 0
])
if not short:
print "List of reactions : "
for r in self.model.reactions:
print '%25s (%5s) : %4g <= v=%5g <= %4g ; y = %d ; mu = %g ; w_L = %5g ; w_U = %5g' % \
('"' + r.name + '"', r.id,
r.lower_bound, self.var_v[r].varValue, r.upper_bound,
self.var_y[r].varValue, self.var_mu[r].varValue,
self.var_w_L[r].varValue, self.var_w_U[r].varValue)
print "List of metabolites : "
for m in self.model.metabolites:
print "%30s : lambda = %6.3f" % \
(m.id, self.var_lambda[m].varValue)
def get_optknock_knockouts(self):
return ','.join(
[r.id for r, val in self.var_y.iteritems() if val.varValue == 0])
def get_optknock_model(self):
if self.solution.status != LpStatusOptimal:
raise Exception('OptKnock failed, cannot generate a KO model')
optknock_model = deepcopy(self.model)
knockout_reactions = [
r for r, val in self.var_y.iteritems() if val.varValue == 0
]
for r in knockout_reactions:
new_r = optknock_model.reactions[optknock_model.reactions.index(
r.id)]
new_r.lower_bound = 0
new_r.upper_bound = 0
return optknock_model
def solve_FBA(self):
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
self.solve()
max_biomass = self.get_objective_value()
return max_biomass
def solve_FVA(self, reaction_id):
"""
Run Flux Variability Analysis on the provided reaction
"""
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
self.solve()
max_biomass = self.get_objective_value()
if max_biomass is None:
raise Exception("Cannot run FVA because the model is infeasible")
self.var_v[self.r_biomass].lowBound = max_biomass - 1e-5
r_target = self.get_reaction_by_id(reaction_id)
self.prob.setObjective(self.var_v[r_target])
self.prob.sense = LpMaximize
self.solve()
max_v_target = self.get_objective_value()
self.prob.sense = LpMinimize
self.solve()
min_v_target = self.get_objective_value()
return min_v_target, max_v_target
def get_PPP_data(self, reaction_id, bm_range=None):
"""
Run FVA on a gradient of biomass lower bounds and generate
the data needed for creating the Phenotype Phase Plane
"""
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
r_target = self.get_reaction_by_id(reaction_id)
if r_target is None:
return None
self.solve()
if bm_range is None:
max_biomass = self.get_objective_value()
if max_biomass is None:
return None
bm_range = np.linspace(1e-5, max_biomass - 1e-5, 50)
self.prob.setObjective(self.var_v[r_target])
data = []
for bm_lb in bm_range:
self.var_v[self.r_biomass].lowBound = bm_lb - 1e-3
self.var_v[self.r_biomass].upBound = bm_lb + 1e-3
self.prob.sense = LpMaximize
self.solve()
max_v_target = self.get_objective_value()
self.prob.sense = LpMinimize
self.solve()
min_v_target = self.get_objective_value()
data.append((bm_lb, min_v_target, max_v_target))
return np.matrix(data)
def get_slope(self, reaction_id, epsilon_bm=0.01):
data = self.get_PPP_data(reaction_id, bm_range=[epsilon_bm])
if data is None:
return None
else:
return data[0, 1] / epsilon_bm
def model_summary(self, html):
import analysis_toolbox
analysis_toolbox.model_summary(self.model, self.solution, html)
def draw_svg(self, html):
# Parse the SVG file of central metabolism
drawer = DrawFlux('data/CentralMetabolism.svg')
#drawer = DrawFlux('data/EcoliMetabolism.svg')
drawer.ToSVG(self.model, self.solution, html)
class OptKnock(object):
def __init__(self, model, verbose=False):
self.model = deepcopy(model)
self.verbose = verbose
# locate the biomass reaction
biomass_reactions = [r for r in self.model.reactions
if r.objective_coefficient != 0]
if len(biomass_reactions) != 1:
raise Exception('There should be only one single biomass reaction')
self.r_biomass = biomass_reactions[0]
self.has_flux_as_variables = False
def create_prob(self, sense=LpMaximize, use_glpk=False):
# create the LP
self.prob = LpProblem('OptKnock', sense=sense)
if use_glpk:
self.prob.solver = solvers.GLPK()
else:
self.prob.solver = solvers.CPLEX(msg=self.verbose)
if not self.prob.solver.available():
raise Exception("CPLEX not available")
def add_primal_variables_and_constraints(self):
# create the continuous flux variables (can be positive or negative)
self.var_v = {}
for r in self.model.reactions:
self.var_v[r] = LpVariable("v_%s" % r.id,
lowBound=r.lower_bound,
upBound=r.upper_bound,
cat=LpContinuous)
# this flag will be used later to know if to expect the flux
# variables to exist
self.has_flux_as_variables = True
# add the mass-balance constraints to each of the metabolites (S*v = 0)
for m in self.model.metabolites:
S_times_v = LpAffineExpression([(self.var_v[r], r.get_coefficient(m))
for r in m.reactions])
self.prob.addConstraint(S_times_v == 0, 'mass_balance_%s' % m.id)
def add_dual_variables_and_constraints(self):
# create dual variables associated with stoichiometric constraints
self.var_lambda = dict([(m, LpVariable("lambda_%s" % m.id,
lowBound=-M,
upBound=M,
cat=LpContinuous))
for m in self.model.metabolites])
# create dual variables associated with the constraints on the primal fluxes
self.var_w_U = dict([(r, LpVariable("w_U_%s" % r.id, lowBound=0, upBound=M, cat=LpContinuous))
for r in self.model.reactions])
self.var_w_L = dict([(r, LpVariable("w_L_%s" % r.id, lowBound=0, upBound=M, cat=LpContinuous))
for r in self.model.reactions])
# add the dual constraints:
# S'*lambda + w_U - w_L = c_biomass
for r in self.model.reactions:
S_times_lambda = LpAffineExpression([(self.var_lambda[m], coeff)
for m, coeff in r._metabolites.iteritems()
if coeff != 0])
row_sum = S_times_lambda + self.var_w_U[r] - self.var_w_L[r]
self.prob.addConstraint(row_sum == r.objective_coefficient, 'dual_%s' % r.id)
def prepare_FBA_primal(self, use_glpk=False):
"""
Run standard FBA (primal)
"""
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
def prepare_FBA_dual(self, use_glpk=False):
"""
Run shadow FBA (dual)
"""
self.create_prob(sense=LpMinimize, use_glpk=use_glpk)
self.add_dual_variables_and_constraints()
w_sum = LpAffineExpression([(self.var_w_U[r], r.upper_bound)
for r in self.model.reactions if r.upper_bound != 0] +
[(self.var_w_L[r], -r.lower_bound)
for r in self.model.reactions if r.lower_bound != 0])
self.prob.setObjective(w_sum)
def get_reaction_by_id(self, reaction_id):
if reaction_id not in self.model.reactions:
return None
reaction_ind = self.model.reactions.index(reaction_id)
reaction = self.model.reactions[reaction_ind]
return reaction
def add_optknock_variables_and_constraints(self):
# create the binary variables indicating which reactions knocked out
self.var_y = dict([(r, LpVariable("y_%s" % r.id, cat=LpBinary))
for r in self.model.reactions])
# create dual variables associated with the constraints on the primal fluxes
self.var_mu = dict([(r, LpVariable("mu_%s" % r.id, cat=LpContinuous))
for r in self.model.reactions])
# equate the objectives of the primal and the dual of the inner problem
# to force its optimization:
# sum_j mu_j - v_biomass = 0
constr = (lpSum(self.var_mu.values()) - self.var_v[self.r_biomass] == 0)
self.prob.addConstraint(constr, 'daul_equals_primal')
# add the knockout constraints (when y_j = 0, v_j has to be 0)
for r in self.model.reactions:
# L_jj * y_j <= v_j
self.prob.addConstraint(r.lower_bound * self.var_y[r] <= self.var_v[r], 'v_lower_%s' % r.id)
# v_j <= U_jj * y_j
self.prob.addConstraint(self.var_v[r] <= r.upper_bound * self.var_y[r], 'v_upper_%s' % r.id)
# set the constraints on the auxiliary variables (mu):
# mu_j == y_j * (U_jj * w_u_j - L_jj * w_l_j)
for r in self.model.reactions:
w_sum = LpAffineExpression([(self.var_w_U[r], r.upper_bound),
(self.var_w_L[r], -r.lower_bound)])
# mu_j + M*y_j >= 0
self.prob.addConstraint(self.var_mu[r] + M*self.var_y[r] >= 0, 'aux_1_%s' % r.id)
# -mu_j + M*y_j >= 0
self.prob.addConstraint(-self.var_mu[r] + M*self.var_y[r] >= 0, 'aux_2_%s' % r.id)
# mu_j - (U_jj * w_u_j - L_jj * w_l_j) + M*(1-y_j) >= 0
self.prob.addConstraint(self.var_mu[r] - w_sum + M*(1-self.var_y[r]) >= 0, 'aux_3_%s' % r.id)
# -mu_j + (U_jj * w_u_j - L_jj * w_l_j) + M*(1-y_j) >= 0
self.prob.addConstraint(-self.var_mu[r] + w_sum + M*(1-self.var_y[r]) >= 0, 'aux_4_%s' % r.id)
def add_knockout_bounds(self, ko_candidates=None, num_deletions=5):
"""
construct the list of KO candidates and add a constraint that
only K (num_deletians) of them can have a y_j = 0
"""
ko_candidate_sum_y = []
if ko_candidates is None:
ko_candidates = [r for r in self.model.reactions if r != self.r_biomass]
for r in set(self.model.reactions).difference(ko_candidates):
# if 'r' is not a candidate constrain it to be 'active'
# i.e. y_j == 1
self.prob.addConstraint(self.var_y[r] == 1, 'active_%s' % r.id)
# set the upper bound on the number of knockouts (K)
# sum (1 - y_j) <= K
ko_candidate_sum_y = [(self.var_y[r], 1) for r in ko_candidates]
constr = (LpAffineExpression(ko_candidate_sum_y) >= len(ko_candidate_sum_y) - num_deletions)
self.prob.addConstraint(constr, 'number_of_deletions')
def prepare_optknock(self, target_reaction_id, ko_candidates=None,
num_deletions=5, use_glpk=False):
# find the target reaction
self.r_target = self.get_reaction_by_id(target_reaction_id)
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.add_dual_variables_and_constraints()
self.add_optknock_variables_and_constraints()
# add the objective of maximizing the flux in the target reaction
self.prob.setObjective(self.var_v[self.r_target])
self.add_knockout_bounds(ko_candidates, num_deletions)
def prepare_optslope(self, target_reaction_id, ko_candidates=None,
num_deletions=5, use_glpk=False):
# add the objective of maximizing the flux in the target reaction
self.r_target = self.get_reaction_by_id(target_reaction_id)
# set biomass maximum to 0
self.r_biomass.lower_bound = 0
self.r_biomass.upper_bound = 0
self.r_target.lower_bound = 0
self.r_target.upper_bound = 0
self.create_prob(sense=LpMaximize, use_glpk=use_glpk)
self.add_primal_variables_and_constraints()
self.add_dual_variables_and_constraints()
self.add_optknock_variables_and_constraints()
# set the objective as maximizing the shadow price of v_target upper bound
self.prob.setObjective(self.var_w_U[self.r_target] - self.var_w_L[self.r_target])
self.add_knockout_bounds(ko_candidates, num_deletions)
def write_linear_problem(self, fname):
self.prob.writeLP(fname)
def solve(self):
self.prob.solve()
if self.prob.status != LpStatusOptimal:
if self.verbose:
print "LP was not solved because: ", LpStatus[self.prob.status]
self.solution = Solution(None)
else:
self.solution = Solution(self.prob.objective.value())
if self.has_flux_as_variables:
self.solution.x = [self.var_v[r].varValue for r in self.model.reactions]
self.solution.status = self.prob.status
return self.solution
def get_objective_value(self):
if self.solution.status != LpStatusOptimal:
return None
else:
return self.prob.objective.value()
def print_primal_results(self, short=True):
obj = self.get_objective_value()
if obj is None:
return
print "Objective : %6.3f" % obj
if not short:
print "List of reactions : "
for r in self.model.reactions:
print "%30s (%4g <= v <= %4g) : v = %6.3f" % \
(r.name, r.lower_bound, r.upper_bound, self.var_v[r].varValue)
def print_dual_results(self, short=True):
obj = self.get_objective_value()
if obj is None:
return
print "Objective : %6.3f" % obj
if not short:
print "List of reactions : "
for r in self.model.reactions:
print "%30s (%4g <= v <= %4g) : w_L = %5.3f, w_U = %5.3f" % \
(r.id, r.lower_bound, r.upper_bound,
self.var_w_L[r].varValue, self.var_w_U[r].varValue)
print "List of metabolites : "
for m in self.model.metabolites:
print "%30s : lambda = %5.3f, " % \
(m.id, self.var_lambda[m].varValue)
def print_optknock_results(self, short=True):
if self.solution.status != LpStatusOptimal:
return
print "Objective : %6.3f" % self.prob.objective.value()
print "Biomass rate : %6.3f" % self.var_v[self.r_biomass].varValue
print "Sum of mu : %6.3f" % np.sum([mu.varValue for mu in self.var_mu.values()])
print "Knockouts : "
print ' ; '.join(['"%s" (%s)' % (r.name, r.id) for r, val in self.var_y.iteritems() if val.varValue == 0])
if not short:
print "List of reactions : "
for r in self.model.reactions:
print '%25s (%5s) : %4g <= v=%5g <= %4g ; y = %d ; mu = %g ; w_L = %5g ; w_U = %5g' % \
('"' + r.name + '"', r.id,
r.lower_bound, self.var_v[r].varValue, r.upper_bound,
self.var_y[r].varValue, self.var_mu[r].varValue,
self.var_w_L[r].varValue, self.var_w_U[r].varValue)
print "List of metabolites : "
for m in self.model.metabolites:
print "%30s : lambda = %6.3f" % \
(m.id, self.var_lambda[m].varValue)
def get_optknock_knockouts(self):
return ','.join([r.id for r, val in self.var_y.iteritems() if val.varValue == 0])
def get_optknock_model(self):
if self.solution.status != LpStatusOptimal:
raise Exception('OptKnock failed, cannot generate a KO model')
optknock_model = deepcopy(self.model)
knockout_reactions = [r for r, val in self.var_y.iteritems() if val.varValue == 0]
for r in knockout_reactions:
new_r = optknock_model.reactions[optknock_model.reactions.index(r.id)]
new_r.lower_bound = 0
new_r.upper_bound = 0
return optknock_model
def solve_FBA(self):
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
self.solve()
max_biomass = self.get_objective_value()
return max_biomass
def solve_FVA(self, reaction_id):
"""
Run Flux Variability Analysis on the provided reaction
"""
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
self.solve()
max_biomass = self.get_objective_value()
if max_biomass is None:
raise Exception("Cannot run FVA because the model is infeasible")
self.var_v[self.r_biomass].lowBound = max_biomass - 1e-5
r_target = self.get_reaction_by_id(reaction_id)
self.prob.setObjective(self.var_v[r_target])
self.prob.sense = LpMaximize
self.solve()
max_v_target = self.get_objective_value()
self.prob.sense = LpMinimize
self.solve()
min_v_target = self.get_objective_value()
return min_v_target, max_v_target
def get_PPP_data(self, reaction_id, bm_range=None):
"""
Run FVA on a gradient of biomass lower bounds and generate
the data needed for creating the Phenotype Phase Plane
"""
self.create_prob(sense=LpMaximize)
self.add_primal_variables_and_constraints()
self.prob.setObjective(self.var_v[self.r_biomass])
r_target = self.get_reaction_by_id(reaction_id)
if r_target is None:
return None
self.solve()
if bm_range is None:
max_biomass = self.get_objective_value()
if max_biomass is None:
return None
bm_range = np.linspace(1e-5, max_biomass - 1e-5, 50)
self.prob.setObjective(self.var_v[r_target])
data = []
for bm_lb in bm_range:
self.var_v[self.r_biomass].lowBound = bm_lb - 1e-3
self.var_v[self.r_biomass].upBound = bm_lb + 1e-3
self.prob.sense = LpMaximize
self.solve()
max_v_target = self.get_objective_value()
self.prob.sense = LpMinimize
self.solve()
min_v_target = self.get_objective_value()
data.append((bm_lb, min_v_target, max_v_target))
return np.matrix(data)
def get_slope(self, reaction_id, epsilon_bm=0.01):
data = self.get_PPP_data(reaction_id, bm_range=[epsilon_bm])
if data is None:
return None
else:
return data[0, 1] / epsilon_bm
def model_summary(self, html):
import analysis_toolbox
analysis_toolbox.model_summary(self.model, self.solution, html)
def draw_svg(self, html):
# Parse the SVG file of central metabolism
drawer = DrawFlux('data/CentralMetabolism.svg')
#drawer = DrawFlux('data/EcoliMetabolism.svg')
drawer.ToSVG(self.model, self.solution, html)
