- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-10-22 15:27:06+13:00
- Desc:
- Adding parameter finder in python and tidied cellml code
- Permanent Source URI:
- https://models.cellml.org/workspace/6d7/rawfile/f5b524a95e7b8d1946196533d3ed7c2f9277f324/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.
# 19 Jul INITIAL CONDITIONS
# given dq/dt = A.q + c where A is a square matrix, use null(A) to find ICs
# of q.
# A is constructed from linearising equations through lm, and
# contains BG parameters
# K kappa are contained in c, but disregarding this
# as this is not dependent on q.
# return W from kinetic_parameters
import os
import csv
import json
import math
import numpy as np
import sympy
from scipy.linalg import null_space
from kinetic_parameters import kinetic_parameters
def read_IDs(path):
data = []
with open(path,'r') as f:
reader = csv.reader(f)
for row in reader:
data.append(row[0])
f.close()
return data
def load_matrix(stoich_path):
matrix = []
with open(stoich_path,'r') as f:
reader = csv.reader(f,delimiter=',')
for row in reader:
matrix.append([int(r) for r in row])
f.close()
return matrix
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('_')[-1]
if ('beta1' in current_dir) and False:
matstr = '_withR_LR_scheme4'
else:
matstr = ''
## Define constants
R = 8.314 # unit J/mol/K
T = 310
F = 96485
#
N_A = 6.022e23
A_cap = 1.534e-4 # Unit cm^2
V = dict()
x_LCC = 50000/N_A*1e15 # unit fmol
V['x_LCC'] = x_LCC
## Define volumes
V_myo = 34.4 # pL
V_e = 5.182
V['V_myo'] = V_myo
V['V_e'] = V_e
## Load forward matrix
if include_type2_reactions:
stoich_path = data_dir + '\\all_forward_matrix%s.txt'%matstr
else:
stoich_path = data_dir + '\\all_noType2_forward_matrix.txt'
N_f = load_matrix(stoich_path)
## Load reverse matrix
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_r = load_matrix(stoich_path)
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)
# addpath(current_dir)
# addpath(data_dir)
[k_kinetic, N_cT, K_C, W] = 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])
# Check that there is a detailed balance constraint
Z = null_space(np.transpose(M))
N_rref = sympy.Matrix(N).rref()
R_mat = null_space(N)
kf = k_kinetic[:num_cols]
kr = k_kinetic[num_cols:]
K_eq = [kf[i]/kr[i] for i in range(len(kr))]
zero_est = np.matmul(np.transpose(R_mat),K_eq)
zero_est_log = np.matmul(np.transpose(R_mat),[math.log(k) for k in K_eq])
# 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]):]
rxnID = read_IDs('data\\rxnID.txt')
Kname = read_IDs('data\\Kname.txt')
# separate Kname of channel and the gating variables
Kname_channel = Kname[:4]
Kname_gate = Kname[4:]
rxnID_channel = rxnID[:4]
rxnID_gate = rxnID[4:]
# ### 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)
if False:
if False:
for j in range(len(K)):
print('var q_%s: fmol {init: 1e-13}'%Kname[j])
for j in range(len(kappa)):
print('var v%s: fmol_per_sec'%rxnID[j])
for j in range(len(K)):
print('var mu_%s: J_per_mol'%Kname[j])
for j in range(len(kappa)):
print('v%s = kappa_%s*exp(mu_a/(R*T))'%rxnID[j], rxnID[j])
for j in range(len(K)):
print('ode(q_%s, time) = p'%Kname[j])
print('\n')
print('// Global value')
for j in range(len(Kname_channel)):
print('var q_%s: fmol {pub: out}'%Kname_channel[j])
print('// From submodule')
for j in range(len(Kname_channel)):
print('var q_%s_m%s: fmol {pub: in}'%(Kname_channel[j], modname))
for j in range(len(K_channel)):
print('q_%s = q_%s_m%s + q_%s_init'%(Kname_channel[j], Kname_channel[j],
modname,Kname_channel[j]))
print('\n')
print('// Input from global environment')
for j in range(len(Kname_channel)):
print('var q_%s_global: fmol {pub: in}'%Kname_channel[j])
print('// Output to global environment')
for j in range(len(Kname_channel)):
print('var q_%s: fmol {init: 1e-16, pub: out}'%(Kname_channel[j]))
for j in range(len(K)):
print('mu_%s = R*T*ln(K_%s*q_%s_global)'%(Kname_channel[j],Kname_channel[j],Kname_channel[j]))
print('\n')
print('def map between environment and %s for'%modname)
print('vars time and time')
for j in range(len(K)):
print('vars q_%s_m%s and q_%s'%(Kname_channel[j], modname,Kname_channel[j]))
print('vars q_%s and q_%s_global'%(Kname_channel[j], Kname_channel[j]))
print('enddef')
