def _formulate_imat(model, up_regulated, down_regulated, epsilon = 1):
""" Formulates iMAT problem
Arguments:
model: Model -- a metabolic constraint-based model
up_regulated: dict (of str of float): up_regulated reactions with score
down_regulated: dict (of str of float): down_regulated reactions with score
"""
# Constants
active_pos = 'active_+'
active_neg = 'active_-'
inactive = 'inactive_+'
# Initialize model
solver = get_solver()
solver.add_variables(model.get_reactions_bounds())
solver.add_constraints(model.s)
# Initialize binary variables
for name in model.reactions:
solver.add_variable(name + active_pos, var_type=solver.BINARY)
solver.add_variable(name + active_neg, var_type=solver.BINARY)
if name in down_regulated:
solver.add_variable(name + inactive, var_type=solver.BINARY)
# Update model wiht binary variables
solver.update()
# Add binary variables constraints
for name in model.reactions:
lb, ub = model.get_reaction_bounds(name)
# Vi + Yi+ (lb - epsilon) >= lb
solver.add_constraint('imat_up_lower_bound_' + name + active_pos, [(name, 1), (name + active_pos, lb), (name + active_pos, -epsilon)], solver.GREATER_EQUAL, lb)
# Vi + Yi- (ub + epsilon) <= ub
solver.add_constraint('imat_up_upper_bound_' + name + active_neg, [(name, 1), (name + active_neg, ub), (name + active_neg, epsilon)], solver.LESS_EQUAL, ub)
if name in down_regulated:
# lb (1 - Yi+) <= Vi
solver.add_constraint('imat_down_lower_bound_' + name + inactive + '_1', [(name, 1), (name + inactive, lb)], solver.GREATER_EQUAL, lb)
# Vi <= ub (1 - Yi+)
solver.add_constraint('imat_down_upper_bound_' + name + inactive + '_2', [(name, 1), (name + inactive, ub)], solver.LESS_EQUAL, ub)
# Set objective function, max: sum(up_pos + up_neg) + sum(down_pos)
objective = []
for name in up_regulated:
objective.append((name + active_pos, 1))
objective.append((name + active_neg, 1))
for name in down_regulated:
objective.append((name + inactive, 1))
solver.set_objective(objective)
return solver
def pFBA(model, objective=None, maximize=True, relax=0.999999):
""" Performs a parsimonious flux balance analysis (pFBA)
Arguments:
model: Model -- a metabolic constraint-based model
objective: dict(reaction: value) -- objective coefficients (optional)
maximize: bool -- maximize or minimize (maximize by default)
Returns:
solution: Solution -- simulation solution
"""
objective = model.get_objective() if objective is None else objective
# Initialize model
solver = get_solver()
solver.add_variables(model.get_reactions_bounds())
solver.add_constraints(model.s)
# Perform FBA
fba_solution = FBA(model, objective, maximize, solver)
# Split reversible reactions
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
solver.add_variable(k + '_neg', 0, abs(lb))
solver.add_variable(k + '_pos', 0, ub)
solver.update()
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
solver.add_constraint(k + '_neg', {k: 1, k + '_neg': 1}, solver.GREATER_EQUAL, 0)
solver.add_constraint(k + '_pos', {k: -1, k + '_pos': 1}, solver.GREATER_EQUAL, 0)
# Constraint FBA objective to max value
solver.add_constraint('fba_constraint', objective, solver.GREATER_EQUAL, fba_solution.obj_value * relax)
# Set pFBA objective: min (internal reactions)
pfba_objective = {}
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
pfba_objective[k + '_neg'] = 1
pfba_objective[k + '_pos'] = 1
else:
pfba_objective[k] = 1
solver.set_objective(pfba_objective, False)
# Run optimization
pfba_solution = solver.optimize()
# Merge splited reactions values
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
del pfba_solution.values[k + '_neg']
del pfba_solution.values[k + '_pos']
return pfba_solution
def FVA(model, reactions=None, objective=None, percentage=None, return_simulations=False, verbose=1):
""" Performs a Flux Variability Analysis
Arguements:
model: Model -- a metabolic constrain-based model
reaction: list (of str) -- list of reactions to analyse (optional)
objective: dict(reaction: value) -- objective coefficients (optional)
percentage: float -- percentage of the objective to keep (optional)
Returns:
solution: dict (of str of tuple) -- dict with each reaction and the min and max flux value
"""
# Initialise model
solver = get_solver()
solver.add_variables(model.get_reactions_bounds())
solver.add_constraints(model.s)
# Constraint with defined objective
if (objective is not None) and (percentage is not None):
solution = FBA(model, objective, True, solver)
solver.add_constraint('objective_constraint', objective, solver.EQUAL, solution.obj_value * percentage)
# Reactions to analyse
reactions = model.reactions.keys() if reactions is None else reactions
# Maximize and minimize each reaction at a time
fva, solutions = {}, DataFrame(np.NaN, index=reactions, columns={'_'.join([reac, obj]) for reac in reactions for obj in {'min', 'max'}})
for reaction in reactions:
# Minimize
min_solution = FBA(model, {reaction: 1}, False, solver)
min_value = None
if min_solution.solution_status == solver.OPTIMAL:
min_value = min_solution.obj_value
# Maximize
max_solution = FBA(model, {reaction: 1}, True, solver)
max_value = None
if max_solution.solution_status == solver.OPTIMAL:
max_value = max_solution.obj_value
# Store solution
fva[reaction] = [min_value, max_value]
if return_simulations:
solutions['_'.join([reaction, 'min'])] = Series(min_solution.values.values(), index=min_solution.values.keys())[reactions]
solutions['_'.join([reaction, 'max'])] = Series(max_solution.values.values(), index=max_solution.values.keys())[reactions]
return (fva, solutions) if return_simulations else fva
def FBA(model, objective=None, maximize=True, solver=None, opt_abs_values=False):
""" Performs a Flux Balance Analysis simulation
Arguments:
model: Model -- a metabolic constraint-based model
objective: dict(reaction: value) -- objective coefficients (optional)
maximize: bool -- maximize or minimize (maximize by default)
solver: Solver -- Solver instance, reuse formulated problem
Returns:
solution: Solution -- simulation solution
"""
objective = model.get_objective() if objective is None else objective
# Initialize model
if solver is None:
solver = get_solver()
solver.add_variables(model.get_reactions_bounds())
solver.add_constraints(model.s)
# Optimisation with absolute objective values
if opt_abs_values:
# Split reversible reactions
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
solver.add_variable(k + '_neg', 0, abs(lb))
solver.add_variable(k + '_pos', 0, ub)
solver.update()
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
solver.add_constraint(k + '_neg', {k: 1, k + '_neg': 1}, solver.GREATER_EQUAL, 0)
solver.add_constraint(k + '_pos', {k: -1, k + '_pos': 1}, solver.GREATER_EQUAL, 0)
# Set objective: min/max: abs(objective)
abs_objective = {}
for k, (lb, ub) in model.get_reactions_bounds(objective.keys()).items():
if lb < 0 < ub:
abs_objective[k + '_neg'] = 1
abs_objective[k + '_pos'] = 1
else:
abs_objective[k] = 1
objective = abs_objective.copy()
# Set objective function
solver.set_objective(objective, maximize)
# Run optimization
solution = solver.optimize()
# If optimisation with absolute objective values
if opt_abs_values:
# Merge splited reactions values
for k, (lb, ub) in model.get_reactions_bounds().items():
if lb < 0 < ub:
del solution.values[k + '_neg']
del solution.values[k + '_pos']
return solution
def min_differences(model, reference=None, multipliers={}, mode=''):
""" Minimizes the absolute difference between the model simulation and the given flux values.
Arguments:
model: Model -- a metabolic constraint-based model
flux_values: dict (of str and float): reference flux values
multipliers: dict (of str and float): reactions objective multipliers
mode: ['', 'backward', 'forward']: minimise a given direction of the reversible reactions
"""
# Run pFBA if reference is missing
if reference is None:
reference = pFBA(model).values
# Initialize model
solver = get_solver()
solver.add_variables(model.get_reactions_bounds())
solver.add_constraints(model.s)
# Split reversible reactions
for reaction, (lb, ub) in model.get_reactions_bounds().items():
if reaction in reference and lb < 0 < ub:
solver.add_variable(reaction + '_backward', 0, abs(lb))
solver.add_variable(reaction + '_forward', 0, ub)
# Create objective variables
objective = []
for reaction in reference:
# Get reaction boundaries and multiplier
lb, ub = model.get_reaction_bounds(reaction)
r_mul = multipliers[reaction] if reaction in multipliers else 1
# Create positive and negative variables for reversivle and non-reversible reactions
reaction_vars = {reaction + s1 + s2 if lb < 0 < ub else reaction + s1 for s1 in ['_f_neg', '_f_pos'] for s2 in ['_backward', '_forward']}
solver.add_variables_from_list(reaction_vars, lower_bound=0)
# Add variables to objective function according to chosen mode
objective.extend([(r, r_mul) for r in reaction_vars if r.endswith(mode)])
# UPDATE variables then start adding constraints
solver.update()
# Add positive range constrains of splitted reactions
for reaction, (lb, ub) in model.get_reactions_bounds().items():
if reaction in reference and lb < 0 < ub:
solver.add_constraint(reaction + '_backward', {reaction: 1, reaction + '_backward': 1}, solver.GREATER_EQUAL, 0)
solver.add_constraint(reaction + '_forward', {reaction: -1, reaction + '_forward': 1}, solver.GREATER_EQUAL, 0)
# Set difference constraints: F1 - V > -Vref; F2 + V > Vref
for reaction, value in reference.items():
# Get reaction boundaries
lb, ub = model.get_reaction_bounds(reaction)
# Create positive and negative variables for reversivle and non-reversible reactions
if lb < 0 < ub:
for s2 in ['_backward', '_forward']:
solver.add_constraint(reaction + '_f_pos' + s2 + '_c', {reaction + '_f_pos' + s2: 1, reaction: -1}, solver.GREATER_EQUAL, -value)
solver.add_constraint(reaction + '_f_neg' + s2 + '_c', {reaction + '_f_neg' + s2: 1, reaction: 1}, solver.GREATER_EQUAL, value)
else:
solver.add_constraint(reaction + '_f_pos' + '_c', {reaction + '_f_pos': 1, reaction: -1}, solver.GREATER_EQUAL, -value)
solver.add_constraint(reaction + '_f_neg' + '_c', {reaction + '_f_neg': 1, reaction: 1}, solver.GREATER_EQUAL, value)
# Set objective variables: min: F1 + F2
solver.set_objective(objective, False)
# Run optimization
solution = solver.optimize()
return solution
