- Author:
- aram148 <42922407+aram148@users.noreply.github.com>
- Date:
- 2022-07-22 15:47:05+12:00
- Desc:
- Added documentation for VSM model
- Permanent Source URI:
- https://models.cellml.org/workspace/6b0/rawfile/a8a92308e217ac5626809237dd90a31240b22834/USMC/DM_USM_old.py
import numpy as np
import scipy as sp
import math
import matplotlib.pyplot as plt
# import opencor as oc
# simulation = oc.open_simulation(r"C:\Users\aram148\Desktop\Platform1\EP3\USMC\ca2.cellml")
def DM_funcs_USM(t,R):
# data = simulation.data()
# data.set_starting_point(t)
# data.set_ending_point(trange2)
# data.set_point_interval(1)
# simulation.run()
# results=simulation.results()
# P = results.states()['calcium/P'].values()
f = 0.25
# if t<=32:
# C_cai = 0*np.sin(2*np.pi*f*t)
# elif t>32 and t< 34:
# C_cai = 10*np.sin(2*np.pi*f*t)
# else:
# C_cai= 0*np.sin(2*np.pi*f*t)*(t>=34)
C_cai = 0*np.sin(2*np.pi*f*t)*(t<=32)+3*np.sin(2*np.pi*f*t)*(t>=32 and t<=34)+0*np.sin(2*np.pi*f*t)*(t>34 and t<=60)+\
3*np.sin(2*np.pi*f*t)*(t>=60 and t<=62)+0*np.sin(2*np.pi*f*t)*(t>62)
n = 8.7613
Ca_mlck = 256.98
k1 = (C_cai**n)/((Ca_mlck**n)+(C_cai**n))
k2 = 1.2387
g1 = 0.0756
gp1 = 0.0709
fp1 = 0.2838
r = R
gam = 100
# Mean for cdf
p1 = r[1]/r[0]
p2 = r[4]/r[3]
# Std dev for cdf
q1 = np.sqrt((r[2]/r[0])-(r[1]/r[0])**2)
q2 = np.sqrt((r[5]/r[3])-(r[4]/r[3])**2)
# r, phi and I for M1_lambda
r0 = -p1/q1
r1 = (1-p1)/q1
phi0 = 0.5*(1+math.erf((r0-p1)/(q1*np.sqrt(2))))
phi1 = 0.5*(1+math.erf((r1-p1)/(q1*np.sqrt(2))))
I0 = -(np.exp(-((-p1/q1)**2)/2))/(np.sqrt(2*np.pi))
I1 = -(np.exp(-((((1-p1)/q1))**2)/2))/(np.sqrt(2*np.pi));
# r, phi and I for M2_lambda
r20 = -p2/q2
r21 = (1-p2)/q2
phi20 = 0.5*(1+math.erf((r20-p2)/(q2*np.sqrt(2))))
phi21 = 0.5*(1+math.erf((r21-p2)/(q2*np.sqrt(2))))
I20 = -(np.exp(-((-p2/q2)**2)/2))/(np.sqrt(2*np.pi))
I21 = -(np.exp(-((((1-p2)/q2))**2)/2))/(np.sqrt(2*np.pi))
# Functions for the RHS of M1 PDE
J0 = phi0
J10 = ((p1*phi0) + (q1*I0))
J11 = (p1*phi1) + (q1*I1)
J20=((p1**(2))*phi0)+((2*p1*q1)*I0)+((q1**(2))*(phi0+(r0*I0)))
J21=((p1**(2))*phi1)+((2*p1*q1)*I1)+((q1**(2))*(phi1+(r1*I1)))
J30=(p1**(3)*phi0)+((3*p1**(2)*q1)*I0)+((3*p1*q1**(2))*((phi0)+(r0*I0)))+((q1**(3)*(2+r0**(2))*I0))
J31=(p1**(3)*phi1)+((3*p1**(2)*q1)*I1)+((3*p1*q1**(2))*(phi1+(r1*I1)))+(q1**(3)*(2+(r1**(2)))*I1)
#Functions defined for the RHS of the second PDE M2_lambda
K0 = phi20
K01 = phi21
K10 = (p2*phi20) + (q2*I20)
K11 = (p2*phi21) +( q2*I21)
K20=((p2**(2))*phi20) + ((2*p2*q2)*I20) + ((q2**(2))*(phi20 + (r20*I20)))
K21=((p2**(2))*phi21) + ((2*p2*q2)*I21) + ((q2**(2))*(phi21 + (r21*I21)))
K30=(p2**(3)*phi20) + ((3*p2**(2)*q2)*I20) + ((3*p2*q2**(2))*((phi20) + (r20*I20))) + ((q2**(3)*(2+r20**(2))*I20))
K31=(p2**(3)*phi21) + ((3*p2**(2)*q2)*I21) + ((3*p2*q2**(2))*(phi21 + (r21*I21))) + (q2**(3)*(2+(r21**(2)))*I21)
# Components for the matrix F that will represent each moment,
# M1_lambda and M2_lambda
A0 = ((fp1*(1-r[6]))/1)-(fp1*(J11-J10)*r[0])
A1 = ((fp1*(1-r[6]))/2)-(fp1*(J21-J20)*r[0])
A2 = ((fp1*(1-r[6]))/3)-(fp1*(J31-J30)*r[0])
B0=(3*(fp1+gp1)*J0)+gp1*(J11-J10)+(4*gp1)*(p1-J11)
B1=(3*(fp1+gp1)*J10)+gp1*(J21-J20)+(4*gp1)*((p1**(2)+q1**(2))-J21)
B2=(3*(fp1+gp1)*J20)+gp1*(J31-J30)+(4*gp1)*((p1**(3)+3*p1*q1**(2))-J31)
C0=k1
C1=k1*p2
C2=k1*(p2**(2)+q2**(2))
D0=k2
D1=k2*p1
D2=k2*(p1**(2)+q1**(2))
E0=(20*g1*K0)+g1*(K11-K10)+(g1)*(1-K01)
E1=(20*g1*K10)+g1*(K21-K20)+(g1)*((p2)-K11)
E2=(20*g1*K20)+g1*(K31-K30)+(g1)*(p2**(2)+q2**(2)-K21)
V = gam*(A1-E0-B0)/(1+gam*(D0+C0))
F=np.array([A0-B0*r[0]+C0*r[3]-k2*r[0], A1-B1*r[0]+C1*r[3]-k2*r[1]-V*r[0], A2-B2*r[0]+C2*r[3]-k2*r[2]-2*V*r[1], D0*r[0]-E0*r[3]-k1*r[3], D1*r[0]-E1*r[3]-k1*r[4]-V*r[3], D2*r[0]-E2*r[3]-k1*r[5]-2*V*r[4], -k1*r[6]+(1-r[6])*k2])
return F, C_cai
def USM_DM(trange,N,M,xrange):
T = np.linspace(trange[0], trange[1], N)
X0 = np.linspace(xrange[0], xrange[1], M)
dt=(trange[1]-trange[0])/(N)
M10 = 0.309120293063990
M11 = 0.118325676501984
M12 = 0.066855519431672
M20 = 0.134379171029593
M21 = -0.045132660622671
M22 = 0.101673063419951
C = 0.6
# R = np.zeros(7)
# Calculating the Ca2+ for the same trange
# simulation = oc.open_simulation(r"C:\Users\aram148\Desktop\Platform1\EP3\USMC\ca2.cellml")
# data = simulation.data()
# data.set_starting_point(trange[0])
# data.set_ending_point(trange[1])
# data.set_point_interval(dt)
# simulation.run()
# results=simulation.results()
# C_cai = results.states()['calcium/P'].values()
C_cai = np.zeros([len(T),1])
R = np.array([M10, M11, M12, M20, M21, M22, C])
Rnew = np.zeros([len(T),len(R)])
Rnew[0,:] = R
# i = 0
for i in range(1,len(T)):
t = T[i-1]
F1, C_cai[i] =DM_funcs_USM(t,Rnew[i-1,:])
F2, C_cai[i]=DM_funcs_USM(t+(dt/2),Rnew[i-1,:]+(dt/2)*F1)
F3, C_cai[i]=DM_funcs_USM(t+(dt/2),Rnew[i-1,:]+(dt/2)*F2)
F4, C_cai[i]=DM_funcs_USM(t+(dt),Rnew[i-1,:]+(dt)*F3)
Rnew[i,:] = Rnew[i-1,:]+ (dt/6)*(F1 + (2*F2) + (2*F3) + F4)
# Rnew[i,:] = Rnew[i-1,:] + dt*F1
return Rnew, C_cai
trange = [0, 100]
xrange = [-3, 3]
N = 5000
M = 1000
kappa = 5
T = np.linspace(trange[0], trange[1], N)
Rnew, C_cai = USM_DM(trange, N, M, xrange)
force = (Rnew[:,1]+Rnew[:,4])
stiffness = Rnew[:,0]+Rnew[:,3]
nmp = 1-Rnew[:,6]-Rnew[:,0]
phosphorylation = nmp + Rnew[:,0]
plt.plot(T,force)
# plt.plot(T,C_cai)
plt.show()
