AMICI Python example “Experimental Conditions”

In this example we will explore some more options for the initialization of experimental conditions, including how to reset initial conditions based on changing values for fixedParameters as well as an additional presimulation phase on top of preequilibration. This notebook is expected to run from the python/example_presimulation directory.

# SBML model we want to import
sbml_file = "model_presimulation.xml"
# Name of the model that will also be the name of the python module
model_name = "model_presimulation"
# Directory to which the generated model code is written
model_output_dir = model_name

from pprint import pprint

import libsbml
import numpy as np

import amici.plotting

Model Loading

Here we load a simple model of protein phosphorylation that can be inhibited by a drug. This model was created using PySB (see createModel.py)

sbml_reader = libsbml.SBMLReader()
sbml_doc = sbml_reader.readSBML(sbml_file)
sbml_model = sbml_doc.getModel()

print("Species:")
pprint([(s.getId(), s.getName()) for s in sbml_model.getListOfSpecies()])

print("\nReactions:")
for reaction in sbml_model.getListOfReactions():
    reactants = " + ".join(
        [
            "{} {}".format(
                int(r.getStoichiometry()) if r.getStoichiometry() > 1 else "",
                r.getSpecies(),
            )
            for r in reaction.getListOfReactants()
        ]
    )
    products = " + ".join(
        [
            "{} {}".format(
                int(r.getStoichiometry()) if r.getStoichiometry() > 1 else "",
                r.getSpecies(),
            )
            for r in reaction.getListOfProducts()
        ]
    )
    reversible = "<" if reaction.getReversible() else ""
    print(
        "%3s: %10s %1s->%10s\t\t[%s]"  # noqa: UP031
        % (
            reaction.getName(),
            reactants,
            reversible,
            products,
            libsbml.formulaToL3String(reaction.getKineticLaw().getMath()),
        )
    )

print("Parameters:")
pprint([(p.getId(), p.getName()) for p in sbml_model.getListOfParameters()])

Species:
[('__s0', "PROT(kin=None, drug=None, phospho='u')"),
 ('__s1', 'DRUG(bound=None)'),
 ('__s2', 'KIN(bound=None)'),
 ('__s3', "DRUG(bound=1) ._br_PROT(kin=None, drug=1, phospho='u')"),
 ('__s4', "KIN(bound=1) ._br_PROT(kin=1, drug=None, phospho='u')"),
 ('__s5', "PROT(kin=None, drug=None, phospho='p')")]

Reactions:
PROT_DRUG_bind:  __s0 +  __s1 <->      __s3               [-(koff_prot_drug * __s3) + kon_prot_drug * __s0 * __s1]
PROT_KIN_bind:  __s0 +  __s2  ->      __s4           [kon_prot_kin * __s0 * __s2]
PROT_KIN_phospho:       __s4  -> __s2 +  __s5                [kphospho_prot_kin * __s4]
PROT_dephospho:       __s5  ->      __s0             [kdephospho_prot * __s5]
Parameters:
[('initProt', 'initProt'),
 ('initDrug', 'initDrug'),
 ('initKin', 'initKin'),
 ('pPROT_obs', 'pPROT_obs'),
 ('PROT_0', 'PROT_0'),
 ('DRUG_0', 'DRUG_0'),
 ('KIN_0', 'KIN_0'),
 ('kon_prot_drug', 'kon_prot_drug'),
 ('koff_prot_drug', 'koff_prot_drug'),
 ('kon_prot_kin', 'kon_prot_kin'),
 ('kphospho_prot_kin', 'kphospho_prot_kin'),
 ('kdephospho_prot', 'kdephospho_prot'),
 ('__obs0', 'pPROT'),
 ('__obs1', 'tPROT')]

# Create an SbmlImporter instance for our SBML model
sbml_importer = amici.SbmlImporter(sbml_file)

For this example we want to specify the initial drug and kinase concentrations as experimental conditions. Accordingly, we specify them as fixedParameters. The meaning of fixedParameters is defined in the Glossary, which we display here for convenience.

from IPython.display import IFrame

IFrame(
    "https://amici.readthedocs.io/en/latest/glossary.html#term-fixed-parameters",
    width=600,
    height=175,
)

fixedParameters = ["DRUG_0", "KIN_0"]

The SBML model specifies a single observable named pPROT which describes the fraction of phosphorylated Protein. We load this observable using amici.assignmentRules2observables.

# Retrieve model output names and formulae from AssignmentRules and remove the respective rules
observables = amici.assignmentRules2observables(
    sbml_importer.sbml,  # the libsbml model object
    filter_function=lambda variable: variable.getName() == "pPROT",
)
print("Observables:")
pprint(observables)

Observables:
{'__obs0': {'formula': '__s5', 'name': 'pPROT'}}

Now the model is ready for compilation using sbml2amici. Note that we here pass fixedParameters as arguments to constant_parameters, which ensures that amici is aware that we want to have them as fixedParameters:

sbml_importer.sbml2amici(
    model_name,
    model_output_dir,
    verbose=False,
    observables=observables,
    constant_parameters=fixedParameters,
)
# load the generated module
model_module = amici.import_model_module(model_name, model_output_dir)

To simulate the model we need to create an instance via the getModel() method in the generated model module.

# Create Model instance
model = model_module.getModel()

# Create solver instance
solver = model.getSolver()

The only thing we need to simulate the model is a timepoint vector, which can be specified using the setTimepoints method. If we do not specify any additional options, the default values for fixedParameters and parameters that were specified in the SBML file will be used.

# Run simulation using default model parameters and solver options
model.setTimepoints(np.linspace(0, 60, 60))
rdata = amici.runAmiciSimulation(model, solver)
amici.plotting.plotObservableTrajectories(rdata)

Simulation options can be specified either in the Model or in an ExpData instance. The ExpData instance can also carry experimental data. To initialize an ExpData instance from simulation results, amici offers some convenient constructors. In the following we will initialize an ExpData object from simulation results, but add noise with standard deviation 0.1 and specify the standard deviation accordingly. Moreover, we will specify custom values for DRUG_0=0 and KIN_0=2. If fixedParameter is specified in an ExpData instance, runAmiciSimulation will use those parameters instead of the ones specified in the Model instance.

edata = amici.ExpData(rdata, 0.1, 0.0)
edata.fixedParameters = [0, 2]
rdata = amici.runAmiciSimulation(model, solver, edata)
amici.plotting.plotObservableTrajectories(rdata)

For many biological systems, it is reasonable to assume that they start in a steady state. In this example we want to specify an experiment where a pretreatment with a drug is performed before the kinase is added. We assume that the pretreatment is sufficiently long such that the system reaches steadystate before the kinase is added. To implement this in amici, we can specify fixedParametersPreequilibration in the ExpData object. This automatically adds a preequilibration phase where the model is run to steadystate, before regular simulation starts. Here we set DRUG_0=3 and KIN_0=0 for the preequilibration. This means that there is no kinase available in the preequilibration phase.

edata.fixedParametersPreequilibration = [3, 0]
rdata = amici.runAmiciSimulation(model, solver, edata)
amici.plotting.plotObservableTrajectories(rdata)

The resulting trajectory is definitely not what one may expect. The problem is that the DRUG_0 and KIN_0 set initial conditions for species in the model. By default, these initial conditions are only applied at the very beginning of the simulation, i.e., before the preequilibration. Accordingly, the fixedParameters that we specified do not have any effect. To fix this, we need to set the reinitializeFixedParameterInitialStates attribute to True, to specify that AMICI reinitializes all states that have fixedParameter-dependent initial states.

edata.reinitializeFixedParameterInitialStates = True

With this option activated, the kinase concentration will be reinitialized after the preequilibration and we will see the expected change in fractional phosphorylation:

rdata = amici.runAmiciSimulation(model, solver, edata)
amici.plotting.plotObservableTrajectories(rdata)

On top of preequilibration, we can also specify presimulation. This option can be used to specify pretreatments where the system is not assumed to reach steadystate. Presimulation can be activated by specifying t_presim and edata.fixedParametersPresimulation. If both fixedParametersPresimulation and fixedParametersPreequilibration are specified, preequilibration will be performed first, followed by presimulation, followed by regular simulation. For this example we specify DRUG_0=10 and KIN_0=0 for the presimulation and DRUG_0=10 and KIN_0=2 for the regular simulation. We do not overwrite the DRUG_0=3 and KIN_0=0 that was previously specified for preequilibration.

edata.t_presim = 10
edata.fixedParametersPresimulation = [10.0, 0.0]
edata.fixedParameters = [10.0, 2.0]
print(edata.fixedParametersPreequilibration)
print(edata.fixedParametersPresimulation)
print(edata.fixedParameters)
rdata = amici.runAmiciSimulation(model, solver, edata)
amici.plotting.plotObservableTrajectories(rdata)

(3.0, 0.0)
(10.0, 0.0)
(10.0, 2.0)