PEtab import

PEtab is a format for specifying parameter estimation problems in systems biology. This notebook illustrates how the PEtab format can be used together with the ODE simulation toolbox AMICI to define ODE based parameter estimation problems for pyABC. Then, in pyABC we can perform exact sampling based on the algorithms introduced in this preprint.

To use this functionality, you need to have (at least) PEtab and AMICI installed. You can obtain these by installing pyABC with

pip install pyabc[amici-petab]

or installing them manually via

pip install petab amici

See also the tools’ installation guides for amici and petab.

import petab
import pyabc
import amici.petab_import
from pyabc.petab import AmiciPetabImporter
import numpy as np
import os

os.environ["OMP_NUM_THREADS"] = "1"
/home/yannik/anaconda3/lib/python3.7/site-packages/rpy2/robjects/ FutureWarning: pandas.core.index is deprecated and will be removed in a future version.  The public classes are available in the top-level namespace.
  from pandas.core.index import Index as PandasIndex

We illustrate the usage of PEtab models using a model taken from the benchmark collection. Uncomment the following cell to clone the git repository.

!git clone --depth 1 \
    tmp/benchmark-models || (cd tmp/benchmark-models && git pull)
Cloning into 'tmp/benchmark-models'...
remote: Enumerating objects: 3511, done.
remote: Counting objects: 100% (3511/3511), done.
remote: Compressing objects: 100% (922/922), done.
remote: Total 3511 (delta 2695), reused 3170 (delta 2564), pack-reused 0
Receiving objects: 100% (3511/3511), 201.90 MiB | 20.18 MiB/s, done.
Resolving deltas: 100% (2695/2695), done.
Checking out files: 100% (3411/3411), done.

Now we can import a problem, here using the “Boehm_JProteomer2014” example, to AMICI and PEtab:

# read the petab problem from yaml
petab_problem = petab.Problem.from_yaml(

# compile the petab problem to an AMICI ODE model
model = amici.petab_import.import_petab_problem(petab_problem)

# the solver to numerically solve the ODE
solver = model.getSolver()

# import everything to pyABC
importer = AmiciPetabImporter(petab_problem, model, solver)

# extract what we need from the importer
prior = importer.create_prior()
model = importer.create_model()
kernel = importer.create_kernel()

Once everything has been compiled and imported, we can simply call the model:

{'llh': -138.22199570334107}

By default, this only returns the log likelihood value. If also simulated data are to be returned (and stored in the pyABC datastore), pass store_simulations=True to the importer.

That’s all. Now we can run an analysis using pyABC’s exact sequential sampler under the assumption of measurement noise. Note that the following cell takes, depending on the resources, minutes to hours to run through. Also, the resulting database is not provides here.

# this takes some time

sampler = pyabc.MulticoreEvalParallelSampler(n_procs=20)

temperature = pyabc.Temperature()
acceptor = pyabc.StochasticAcceptor(
    pdf_norm_method = pyabc.ScaledPDFNorm())

abc = pyabc.ABCSMC(model, prior, kernel,
                   population_size=1000)"sqlite:///tmp/petab_amici_boehm.db", {})
INFO:Sampler:Parallelizing the sampling on 20 cores.
INFO:History:Start <ABCSMC(id=1, start_time=2020-02-17 22:35:38.746712, end_time=None)>
INFO:ABC:Calibration sample before t=0.
INFO:ABC:t: 0, eps: 49386005.386943504.
INFO:ABC:Acceptance rate: 1000 / 3348 = 2.9869e-01, ESS=1.0000e+03.
INFO:ABC:t: 1, eps: 3707.524037573809.
INFO:ABC:Acceptance rate: 1000 / 3582 = 2.7917e-01, ESS=3.0162e+02.
INFO:ABC:t: 2, eps: 189.0069260595768.
INFO:ABC:Acceptance rate: 1000 / 3753 = 2.6645e-01, ESS=2.9065e+02.
INFO:ABC:t: 3, eps: 94.5034630297884.
INFO:ABC:Acceptance rate: 1000 / 6376 = 1.5684e-01, ESS=3.2931e+02.
INFO:ABC:t: 4, eps: 47.2517315148942.
INFO:ABC:Acceptance rate: 1000 / 16933 = 5.9056e-02, ESS=2.7417e+02.
INFO:ABC:t: 5, eps: 23.6258657574471.
INFO:ABC:Acceptance rate: 1000 / 6990 = 1.4306e-01, ESS=3.6511e+02.
INFO:ABC:t: 6, eps: 11.81293287872355.
INFO:ABC:Acceptance rate: 1000 / 50479 = 1.9810e-02, ESS=2.3205e+02.
INFO:ABC:t: 7, eps: 5.906466439361775.
INFO:ABC:Acceptance rate: 1000 / 141531 = 7.0656e-03, ESS=3.0510e+01.
INFO:ABC:t: 8, eps: 2.9532332196808877.
INFO:ABC:Acceptance rate: 1000 / 54532 = 1.8338e-02, ESS=2.7007e+01.
INFO:ABC:t: 9, eps: 1.4766166098404439.
INFO:ABC:Acceptance rate: 1000 / 21583 = 4.6333e-02, ESS=3.9807e+00.
INFO:ABC:t: 10, eps: 1.0.
INFO:ABC:Acceptance rate: 1000 / 12382 = 8.0762e-02, ESS=1.3817e+01.
INFO:ABC:Stopping: minimum epsilon.
INFO:History:Done <ABCSMC(id=1, start_time=2020-02-17 22:35:38.746712, end_time=2020-02-17 23:03:26.661874)>
< at 0x7fa4da04f3a0>

Now we can use pyABC’s standard analysis and visualization routines to analyze the obtained posterior sample. In particular, we can extract boundaries and literature parameter values from the PEtab problem:

h = pyabc.History("sqlite:///tmp/petab_amici_boehm.db", _id=1)
refval = {k: v for k,v in zip(petab_problem.x_free_ids, petab_problem.x_nominal_free_scaled)}
for i, par in enumerate(petab_problem.x_free_ids):
        h, x=par,
        refval=refval, refval_color='k')

Apparently, in this case seven out of the nine parameters can be estimated with high confidence, while two other parameters can only be bounded.