Introduction

MIOM (Mixed Integer Optimization for Metabolism) is a python library for creating and solving complex optimization problems using genome-scale metabolic networks, in just a few lines.

MIOM offers a high-level API that leverages the power of modern Mixed Integer Optimization (MIO) solvers to easily define steady-state metabolic optimization problems, from simple Flux Balance Analysis (FBA) simulations, to more complex problems, such as sparse FBA or context-specific reconstruction algorithms, and solve them the required level of optimality. It supports many free and commercial solvers thanks to the integration with the PICOS and the Python-MIP. It is also compatible and complementary to cobrapy.

Here is a simple example of the differences of implementing from scratch a simple Flux Balance Analysis (FBA), which is typically implemented as a Linear Program (LP) problem, and the Sparse FBA problem which is an Integer Programmming (IP) problem that solves the same FBA problem but minimizing the number of active reactions:

import miom
model = (miom
         .load('@BiGG/Recon3D.miom')
         .steady_state()
         .set_rxn_objective('biomass_reaction')
         .solve(verbosity=1))
print("Optimal flux:", model.get_fluxes('biomass_reaction'))
print("Number of active reactions:", sum(abs(model.get_fluxes()) > 1e-8))

import miom
model = (miom
         .load('@BiGG/Recon3D.miom')
         .setup(opt_tol=0.05, verbosity=1)
         .steady_state()
         .set_rxn_objective('biomass_reaction')
         .solve()
         .set_fluxes_for('biomass_reaction')
         .subset_selection(-1)
         .solve())
print("Optimal flux:", model.get_fluxes('biomass_reaction'))
print("Number of active reactions:", sum(abs(model.get_fluxes()) > 1e-8))

Installation

Recommended installation

The recommended installation with pip using the option all includes PICOS and Python-MIP backends, and the interfaces for GLPK, Gurobi and Mosek:

pip install miom[all]

Minimal installation

By default, MIOM comes only with the Python-MIP backend and the COIN-OR CBC solver. The minimal installation is perfect to use in online notebooks and for sharing minimal reproducible examples. To install MIOM with minimal dependencies, run:

pip install miom

Full installation

The full install option of miom comes with all the packages included with the all option, and the additional COBRA package. This adds also support for importing any kind of genome-scale metabolic network supported by cobra with the miom.load_gem() method:

pip install miom[full]

Installing CPLEX

CPLEX is also supported but requires a prior installation of CPLEX in the system with a valid license that cannot be configured through pip. To install MIOM with CPLEX support, follow the instructions on the CPLEX page to install your current version of cplex in your python environment.

Quick start

Importing a Genome-Scale Metabolic Network (GEMs)

First step is to import a Genome-Scale Metabolic Network. The method load_gem() can be used to import a network from a local file or a URL. This method requires the cobrapy and scipy packages to import networks in the SBML, YAML, JSON, and Matlab formats (see Full install). Here is an example of importing the BiGG Recon3D network:

import miom
network = miom.load_gem('https://github.com/SBRG/bigg_models_data/raw/master/models/Recon3D.mat')
print("Number of reactions in the network:", network.num_reactions)

By default, MIOM uses its own format (.miom) which is a lightweight, compressed and portable format based on numpy structured arrays to store only the essential information required to perform common tasks. To improve reproducibility of experiments, a repository of already converted models is available at pablormier/miom-gems. Any model from this repository can be imported using shorthand links in the following forma: @relative/path/to/model. For example, in order to import the Human-GEM v1.9.0, you only need to run:

network = miom.load_gem('@SysBioChalmers/Human-Gem/v1.9.0')

This is a very convenient way of importing models and sharing reproducible experiments, making sure that other users are going to test the same models.

Managing Metabolic Networks

MIOM is not intended to provide functions for creating and managing metabolic networks, since there are already other libraries for this purpose (e.g. cobrapy). If you rely on cobrapy for model manipulation, you can still use MIOM for the optimization after you prepare your metabolic network, as MIOM is nicely integrated with COBRA:

from cobra.test import create_test_model
network = create_test_model("textbook")
medium = network.medium
medium["EX_o2_e"] = 0.0
network.medium = medium

# Use MIOM for optimization
flux = (miom
        .load(miom.mio.cobra_to_miom(network))
        .steady_state()
        .set_rxn_objective('Biomass_Ecoli_core')
        .solve()
        .get_fluxes('Biomass_Ecoli_core'))

Metabolic Networks in MIOM are represented by a miom.mio.MiomNetwork class. This class encodes the network into three matrices: R (reactions), S (stoichiometry), and M (metabolites). The R matrix is a numpy structured array that contains the list of the reactions defined in the network, including the reaction ID, the reaction name, the reaction bounds, the subsystem and the Gene-Protein-Rules:

>>> miom.load_gem('@BiGG/Recon3D.miom').R[:5]

array([('10FTHF5GLUtl', '5-Glutamyl-10Fthf Transport, Lysosomal', 0., 1000., 'Transport, lysosomal', ''),
       ('10FTHF5GLUtm', '5-Glutamyl-10Fthf Transport, Mitochondrial', 0., 1000., 'Transport, mitochondrial', ''),
       ('10FTHF6GLUtl', '6-Glutamyl-10Fthf Transport, Lysosomal', 0., 1000., 'Transport, lysosomal', ''),
       ('10FTHF6GLUtm', '6-Glutamyl-10Fthf Transport, Mitochondrial', 0., 1000., 'Transport, mitochondrial', ''),
       ('10FTHF7GLUtl', '7-Glutamyl-10Fthf Transport, Lysosomal', 0., 1000., 'Transport, lysosomal', '')],
      dtype=[('id', 'O'), ('name', 'O'), ('lb', '<f8'), ('ub', '<f8'), ('subsystem', 'O'), ('gpr', 'O')])

Basic manipulation, for example, changing the bounds of a reaction, can be done just by modifying the corresponding attribute of the reaction:

rxn = network.R[0]
rxn['lb'] = 0
rxn['ub'] = 10

Numpy structured arrays make it easy to modify properties of the network. For example, in order to change the lower bound of all reactions in the network at the same time, you only need to do:

network.R['lb'] = -1000

Structured arrays also support indexing:

import numpy as np
# List all reactions with a negative lower bound
network.R[network.R['lb'] < 0]
# Get the indexes of the reactions with a negative lower bound
idxs = np.flatnonzero(network.R['lb'] < 0)

Constraint-based optimization problems

MIOM can be seen as a high-level API for creating constraint-based optimization problems by applying successive composable operations that add new constraints to the problem. The basic operation is the steady_state() method, which adds the system of equations S * V = 0 to the optimization model, where S is the stoichiometric matrix and V is the vector of fluxes:

model = (miom
        .load('@BiGG/Recon3D.miom')
        .steady_state())

Now the optimization model contains the system of equations for the steady state condition of the fluxes. Now, it can be extended by adding new constraints or changing properties of the model. For example, in order to find the maximum flux of the biomass_reaction (limiting the max production to 10) can be done as follows:

flux = (model
        .set_rxn_objective('biomass_reaction')
        .set_flux_bounds('biomass_reaction', max_flux=10.0)
        .solve()
        .get_fluxes('biomass_reaction'))

More complex constraints can be added by using the add_constraint() method. This method accepts an affine expression involving the variables in the model. Here is an example of how to perform FBA again but with a constraint that ensures that the sum through all non-reversible reactions is less than or equal to 10:

import numpy as np

# Load the Recon3D model from the MIOM repository
network = miom.load_gem('@BiGG/Recon3D.miom')

# The objective is to maximize the flux through the biomass reaction
model = miom.load(network).steady_state().set_rxn_objective('biomass_reaction')

# Find reactions that are not reversible (i.e. can have only positive fluxes)
non_reversible = np.flatnonzero(network.R['lb'] >= 0)

# Add the constraint that the sum through all non-reversible reactions is less than or equal to 10
# (note that both PICOS and Python-MIP are symbolic, and expressions involving the variables are allowed)
constraint = sum(model.variables.fluxvars[i] for i in non_reversible) <= 10

# Add to the model and solve 
model.add_constraint(constraint).solve(verbosity=1)

Starting solution of the Linear programming problem using Dual Simplex

Coin0506I Presolve 2242 (-3594) rows, 6144 (-4456) columns and 33659 (-12128) elements
Clp0014I Perturbing problem by 0.001% of 1.9797539 - largest nonzero change 1.4130091e-06 ( 7.1372964e-05%) - largest zero change 1.412981e-06
Clp0006I 0  Obj 0.0015868455 Primal inf 3303572.7 (1175) Dual inf 1.9797525 (1)
Clp0000I Optimal - objective value 9.062223
Coin0511I After Postsolve, objective 9.062223, infeasibilities - dual 0 (0), primal 0 (0)
Clp0032I Optimal objective 9.062223036 - 1675 iterations time 0.142, Presolve 0.07

By default, an optimization model is mutable. This means that every time a method that modifies the model is invoked, the original model is modified. For example, the set_flux_bounds() method modifies the bounds of the reactions in the model. If you want to create a copy of the model, you can use the copy() method to create a full copy of the model.

Mixed Integer Optimization

Many constraint-based metabolic problems consist of selecting a subset of reactions from a generic metabolic network, subject to some biological-based constraints. For example, Sparse FBA consists of selecting the minimum number of active reactions that lead to a desired optimal flux. Context-specific network reconstruction methods such as iMAT, Fastcore, mCADRE, MBA, etc., have also the same purpose: select a subset of reactions from a network based on some experimental data and some objective function. All these problems are instances of a more general problem, known as best subset selection problem, which can be modelled using Mixed Integer Optimization (MIO). However, instances of this problem are usually hard to solve, and some implementations like Fastcore or MBA use different heuristics or relaxations to find sub-optimal solutions in short time.

Unfortunately, there are a few problems with these type of approximations. First, we don't know how good is the solution obtained, and in practice many studies that use those methods assume that the solution they obtained is the best one. Second, even though most of these techniques solve the same type of problem, they look very different or hard to understand for practitioners. Third, many of these implementations do not exploit the potential of the modern MIO solvers which are nowadays able to solve very large problems in a short time, and to adjust the desired level of optimality, which gives the user an idea of how good is the solution obtained.

MIOM incorporates specific methods to easily model and solve such problems. Just by calling the method subset_selection(), which takes as input a weight for all reactions or a list of weights for each reaction, it transforms the current problem into a best subset selection problem, in which the objective function is the sum of the weights of the reactions in the solution (where positive weighted reactions contribute to the objective function if they are selected, and negative weighted reactions contribute to the objective function if they are not selected).

This simple method makes it possible to model a wide variety of complex constraint-based optimization problems. See for example how easy it is to implement the exact version of the weighted Fastcore with MIOM:

import miom
import numpy as np

# Use the flux-consistent subnetwork (fcm) of the Human1 GEM model
# NOTE: Fastcore requires that reactions in the core are flux consistent,
# otherwise the problem would be infeasible. 
m = miom.load_gem('@homo_sapiens_human1_fcm.miom')
# Select reactions from the cholesterol metabolism as the core reactions to keep
core_rxn = m.find_reactions_from_pathway("Cholesterol metabolism")
# Assign a negative weight for reactions not in the core
weights = -1 * np.ones(m.num_reactions)
weights[core_rxn == 1] = 1

fmc = (miom
        .load(m)
        .setup(opt_tol=0.05, verbosity=1)
        .steady_state()
        .subset_selection(weights)
        .keep(core_rxn == 1)
        .solve()
        .select_subnetwork(
            mode=miom.ExtractionMode.ABSOLUTE_FLUX_VALUE,
            comparator=miom.Comparator.GREATER_OR_EQUAL,
            value=1e-8
        )
        .network
)
print(fmc.num_reactions)

Advantages

• It's flexible: MIOM uses the PICOS and the Python-MIP libraries, which means you can use any solver supported by those libraries.
• It's easy to extend: MIOM is written in pure python, so you can easily extend it to solve more complex optimization problems.
• It makes the problem explicit: MIOM uses a declarative way to express the problem, so you can easily read and understand what you are solving and differences between algorithms.
• It's fast: MIOM leverages the power of MIO solvers to solve complex optimization problems. You can control the quality and speed of the solutions for your problem and get better solutions that the approximations (LP) of the original problem available in other constraint-based modeling libraries.
• It's lightweight: The library has a small number of dependencies, so it's easy to install and distribute also in HPC environments.
• It includes a compressed GEM format: MIOM can load and save the minimal information of the metabolic networks required for performing simulations into a compressed file compatible with numpy. The small size of the files allows you to quickly run online experiments so other people can reproduce your results. It also supports SBML and matlab formats if cobratoolbox is installed.
• It's open-source: MIOM is open-source and free to use. You can contribute to the development of MIOM by forking the repository and sending pull requests.

Documentation

The documentation of the library can be found at https://metexplore.github.io/miom/

How to cite

Manuscript in progress

License

GNU General Public License v3.0