6. Modal analysis

Modal analysis allows to get insight into the dynamics close the the steady state. The modal matrix provides information on which eigenvalues contribute to the dynamics of each concentration. Similar to MCA, Modal analysis is conducted around a steady-state therefore modal analysis requieres to compute or import a valid set of steady-state concentrations:

from pytfa.io.json import load_json_model
from skimpy.io.yaml import  load_yaml_model
from skimpy.analysis.oracle.load_pytfa_solution import load_concentrations, load_fluxes
from skimpy.analysis.modal import modal_matrix
from skimpy.core.parameters import ParameterValues
from skimpy.utils.namespace import *
from skimpy.utils.tabdict import TabDict

from skimpy.viz.modal import plot_modal_matrix

# Units of the parameters are muM and hr
CONCENTRATION_SCALING = 1e6
TIME_SCALING = 1 # 1hr to 1min
DENSITY = 1200 # g/L
GDW_GWW_RATIO = 0.3 # Assumes 70% Water

kmodel =  load_yaml_model('./../../models/varma_strain_1.yml')
tmodel = load_json_model('./../../models/tfa_varma.json')

# Reference steady-state data
ref_solution = pd.read_csv('./../../data/tfa_reference_strains.csv',
                           index_col=0).loc['strain_1',:]

ref_concentrations = load_concentrations(ref_solution, tmodel, kmodel,
                                         concentration_scaling=CONCENTRATION_SCALING)

parameter_values = {p.symbol:p.value for p in kmodel.parameters.values()}
parameter_values = ParameterValues(parameter_values, kmodel)

To compute the modal-matrix the model needs to have compiled Jacobian expressions, they are build by calling kmodel.prepare() and kmodel.compile_jacobian().

kmodel.prepare()
kmodel.compile_jacobian(sim_type=QSSA,ncpu=8)

M = modal_matrix(kmodel,ref_concentrations,parameter_values)

plot_modal_matrix(M,filename='modal_matrix.html',
                  plot_width=800, plot_height=600,
                  clustered=True,
                  backend='svg',
                  )