# Location: BG_GPCR_M2_reduced @ e831afee2206 / parameter_finder / find_BG_parameters.py

Author:
Shelley Fong <s.fong@auckland.ac.nz>
Date:
2022-02-18 13:28:26+13:00
Desc:
Updating way cellml is written
Permanent Source URI:
https://models.cellml.org/workspace/7dd/rawfile/e831afee220663860fb5e91083cf1d4805d59f5f/parameter_finder/find_BG_parameters.py

```# This script calculates the bond graph parameters for all reactions of the
# a given module. Specify the directory.
# based on SERCA model of Pan et al, which is based on Tran et al. (2009).
# Parameters calculated in module's directory, by using the kinetic
# parameters and stoichiometric matrix.

# return W from kinetic_parameters

import os
import csv
import json
import math
import numpy as np
import sympy
from sympy import Matrix, S, nsimplify
from scipy.linalg import null_space
from fractions import Fraction

data = []
with open(path, 'r') as f:
data.append(row[0])
f.close()
return data

matrix = []
with open(stoich_path, 'r') as f:
matrix.append([int(r) for r in row])
f.close()
return matrix

# def rational_nullspace(A, max_denom = 10):
#     v = null_space(A)
#     vFrac = [[Fraction(num).limit_denominator(max_denominator=max_denom) for num in row] for row in v]
#
#     vRat = [] #np.zeros([len(vFrac),len(vFrac[0])])
#     if not v.any():
#         return []
#     all_denom = [[res.denominator for res in row] for row in vFrac]
#     if all_denom.count(all_denom[0]) == len(all_denom):# identical
#         for row in vFrac:
#             largest_denom = max([res.denominator for res in row])
#             vRat.append( [vi.numerator for vi in row] )
#         return vRat
#     else:
#         print('denominators for fractions of rational nullspace are not identical')
#         return []

if __name__ == "__main__":

## booleans
write_parameters_file = True
include_constraints = True
include_type2_reactions = True

## Set directories
current_dir = os.getcwd()
data_dir = current_dir + '\data'
output_dir = current_dir + '\output'
modname = os.path.dirname(current_dir).split('\\')[-1].split('BG_')[-1]
if not os.path.exists(output_dir):
os.mkdir(output_dir)

if ('beta1' in current_dir) and False:
matstr = '_withR_LR_scheme4'
else:
matstr = ''

## Define volumes
V_myo = 34.4  # pL
V = dict()
V['V_myo'] = V_myo

if include_type2_reactions:
stoich_path = data_dir + '\\all_forward_matrix%s.txt' % matstr
else:
stoich_path = data_dir + '\\all_noType2_forward_matrix.txt'

if include_type2_reactions:
stoich_path = data_dir + '\\all_reverse_matrix%s.txt' % matstr
else:
stoich_path = data_dir + '\\all_noType2_reverse_matrix.txt'

N_fT = np.transpose(N_f)
N_rT = np.transpose(N_r)

## Calculate stoichiometric matrix
# I matrix to align with placement of kappa down the column.
# x-axis of stoich matrix (R1a, R1b etc) coincides with the kp km of that kinetic reaction
N = [[N_r[j][i] - N_f[j][i] for i in range(len(N_f[0]))] for j in range(len(N_f))]
N_T = [[N_rT[j][i] - N_fT[j][i] for i in range(len(N_fT[0]))] for j in range(len(N_fT))]

num_rows = len(N)
num_cols = len(N[0])
dims = dict()
dims['num_rows'] = num_rows
dims['num_cols'] = num_cols

I = np.identity(num_cols)

M = np.append(np.append(I, N_fT, 1), np.append(I, N_rT, 1), 0)

func = __import__('kinetic_parameters_%s' % modname)
[k_kinetic, N_cT, K_C, W] = func.kinetic_parameters(M, include_type2_reactions, dims, V)
if not include_constraints:
N_cT = []

try:
M = np.append(M, N_cT, 0)
k = np.append(k_kinetic, K_C, 0)
except:
k = k_kinetic

# Calculate bond graph constants from kinetic parameters
# Note: units of kappa are fmol/s, units of K are fmol^-1
lambda_expo = np.matmul(np.linalg.pinv(M), [math.log(ik) for ik in k])
lambdaW = [math.exp(l) for l in lambda_expo]

# Check that kinetic parameters are reproduced by bond graph parameters
k_est = np.matmul(M, [math.log(k) for k in lambdaW])
k_est = [math.exp(k) for k in k_est]
diff = [(k[i] - k_est[i]) / k[i] for i in range(len(k))]

error = np.sum([abs(d) for d in diff])

# Checks
N_rref = sympy.Matrix(N).rref()
R = nsimplify(Matrix(N), rational=True).nullspace()  # rational_nullspace(N, max_denom=len(N[0]))
if R:
R = np.transpose(np.array(R).astype(np.float64))[0]
# Check that there is a detailed balance constraint
Z = nsimplify(Matrix(M), rational=True).nullspace()  # rational_nullspace(M, 2)
if Z:
Z = np.transpose(np.array(Z).astype(np.float64))[0]

kf = k_kinetic[:num_cols]
kr = k_kinetic[num_cols:]
K_eq = [kf[i] / kr[i] for i in range(len(kr))]
try:
zero_est = np.matmul(np.transpose(R), K_eq)
zero_est_log = np.matmul(np.transpose(R), [math.log(k) for k in K_eq])
except:
print('undefined R nullspace')

# if not R_mat:
#     warning('R_mat is empty: matrix is full rank')

lambdak = [lambdaW[i] / W[i] for i in range(len(W))]
kappa = lambdak[:len(N[0])]
K = lambdak[len(N[0]):]

# ### print outputs ###
for ik in range(len(kappa)):
print('var kappa_%s: fmol_per_sec {init: %g, pub: out};' % (rxnID[ik], kappa[ik]))
for ik in range(len(Kname)):
print('var K_%s: per_fmol {init: %g, pub: out};' % (Kname[ik], K[ik]))

file = open(output_dir + '/all_parameters_out.json', 'w')
data = {"K": K, "kappa": kappa, "k_kinetic": k_kinetic}
json.dump(data, file)

cellmlfilepath = os.getcwd() + '\\output\\TEMP.cellml.txt'
with open(cellmlfilepath, 'w') as cid:
cid.write('def model individual_%s as\n def import using "units_and_constants/units_BG.cellml" for\n\
unit mM using unit mM;\nunit fmol using unit fmol;\nunit per_fmol using unit per_fmol;\n\
unit J_per_mol using unit J_per_mol;\nunit fmol_per_sec using unit fmol_per_sec;\n\
unit C_per_mol using unit C_per_mol;\n  unit J_per_C using unit J_per_C;\n\
unit microm3 using unit microm3;\n  unit fF using unit fF;\n\
unit fC using unit fC;\n  unit fA using unit fA;\n\
unit per_second using unit per_second;\n  unit millivolt using unit millivolt;\n\
unit per_sec using unit per_sec;\n  unit J_per_K_per_mol using unit J_per_K_per_mol;\n\
unit fmol_per_L using unit fmol_per_L;\n  unit fmol_per_L_per_sec using unit fmol_per_L_per_sec;\n\
unit per_sec_per_fmol_per_L using unit per_sec_per_fmol_per_L;\n  unit uM using unit uM;\n\
unit mM_per_sec using unit mM_per_sec;\n  unit uM_per_sec using unit uM_per_sec;\n\
unit pL using unit pL;\n  unit m_to_u using unit m_to_u;\n enddef;\n' % (modname))
cid.write('def import using "units_and_constants/constants_BG.cellml" for\n\
comp constants using comp constants;\nenddef;\n\n')
cid.write("    def comp environment as\n\
var time: second {pub: out};\n\
// initial values\n")
for Kn in Kname:
cid.write('var q_%s: fmol {init: 1e-888, pub: out};\n' % (Kn))
# cid.write('// Global value\n')
# for Kn in Kname:
#     cid.write('var q_%s: fmol {pub: out};\n'%Kn)
cid.write('// From submodule\n')
for rx in rxnID:
cid.write('var v_%s: fmol_per_sec {pub: in};\n' % (rx))
for Kn in Kname:
cid.write('ode(q_%s, time) = vvv;\n' % (Kn))
cid.write('enddef;\n\n')
cid.write('def comp %s_parameters as\n' % (modname))
for ik in range(len(kappa)):
cid.write('var kappa_%s: fmol_per_sec {init: %g, pub: out};\n' % (rxnID[ik], kappa[ik]))
for ik in range(len(Kname)):
cid.write('var K_%s: per_fmol {init: %g, pub: out};\n' % (Kname[ik], K[ik]))
cid.write('enddef;\n')

cid.write('def comp %s as\n' % (modname))
cid.write('        var time: second {pub: in};\n\
var R: J_per_K_per_mol {pub: in};\n\
var T: kelvin {pub: in};\n\
// parameters\n')
for ik in range(len(kappa)):
cid.write('var kappa_%s: fmol_per_sec {pub: in};\n' % (rxnID[ik]))
for ik in range(len(Kname)):
cid.write('var K_%s: per_fmol {pub: in};\n' % (Kname[ik]))

cid.write('// Input from global environment\n')
for Kn in Kname:
cid.write('var q_%s: fmol {pub: in};\n' % Kn)
# cid.write('// Output to global environment\n')
# for Kn in Kname:
#     # cid.write('var q_%s: fmol {init: 1e-16, pub: out};\n'%(Kn))
#     cid.write('var v_%s: fmol_per_sec {pub: out};\n'%(Kn))
cid.write('// Constitutive parameters\n')
for Kn in Kname:
cid.write('var mu_%s: J_per_mol;\n' % (Kn))
for rx in rxnID:
cid.write('var v_%s: fmol_per_sec {pub: out};\n' % (rx))
for Kn in Kname:
cid.write('mu_%s = R*T*ln(K_%s*q_%s);\n' % (Kn, Kn, Kn))
for rx in rxnID:
cid.write('v_%s = ppp;\n' % (rx))
# for Kn in Kname:
#     cid.write('v_%s = rrr;\n' %Kn)
# for Kn in Kname:
#     cid.write('ode(q_%s, time) = qqq;\n'%Kn)
cid.write('enddef;\n')

cid.write('def map between environment and %s for\n' % modname)
cid.write('vars time and time;\n')
for Kn in Kname:
cid.write('vars q_%s and q_%s;\n' % (Kn, Kn))
for rx in rxnID:
cid.write('vars v_%s and v_%s;\n' % (rx, rx))
cid.write('enddef;\n')
cid.write('def map between %s and %s_parameters for\n' % (modname, modname))
for ik in rxnID:
cid.write('vars kappa_%s and kappa_%s;\n' % (ik, ik))
for mod in Kname:
cid.write('vars K_%s and K_%s;\n' % (mod, mod))
cid.write('enddef;\n')
cid.write('def map between constants and %s for\n' % modname)
cid.write('vars R and R;\n vars T and T;\n')
cid.write('enddef;\n')
cid.write('enddef;\n')
cid.close()

print('error =', (error))

```