qD = sympy.Symbol('qD')
# Parameters as additive pulses
p_add = [qA, qB, qC, qD]
# Symbolic ODE RHS
dA = k3*D**m/(K**m+D**m) - k4*A # frq mRNA
dB = k5*A - k6*B + k7*C - k8*B*D # FRQ Protein
dC = k8*B*D - k7*C - k9*C # WC-1:FRQ complex
dD = k1 - k2*D + k7*C - k8*B*D # WC-1 protein
dY = sympy.Matrix([dA, dB, dC, dD]) # Vector ODE RHS
# Initial values on the limit cycle at frq mRNA max.
Y0 = np.array([0.958658, # A0
0.7892854, # B0
0.3232268, # C0
0.5296776]) # D0
frq_ind = 0
period = 22.
##### Below is example solving and plotting frq mRNA for the simple model #####
ModSimple = ODE('The Simple Model',frq_ind,Y,p,p_add,dY,Y0,period,findQ=False)
tot_time=100
t_test = np.linspace(0,tot_time, 100*tot_time)
sol_test = ModSimple.solve(ModSimple.lim_cyc_vals, t_test)
frq_sol = sol_test[:,frq_ind]
plt.plot(t_test, frq_sol)
0.70541941, # HypoWCCn
0.03008159, # HyperWCCn
0.08212058, # aWCC
0., # laWCC
0., # vvdm
0., # VVDc
0., # VVDn
0.
]) # WVC
frq_ind = 2
period = 21.62451
##### Below is example solving and plotting frq mRNA for Tseng's model #####
ModTseng = ODE('Tseng\'s Model',
frq_ind,
Y,
p,
p_add,
dY,
Y0,
period,
findQ=False)
tot_time = 100
t_test = np.linspace(0, tot_time, 100 * tot_time)
sol_test = ModTseng.solve(ModTseng.lim_cyc_vals, t_test)
frq_sol = sol_test[:, frq_ind]
plt.plot(t_test, frq_sol)
0.0110685024, # Fn0
3.70361114, # Mw0
0.00666226484, # Wc0
0.924361228, # Wn0
0.0820481701, # FWn0
0.05214823, # Mc0
1.93780501
]) # C0
frq_ind = 0
period = 22.3934820284
##### Below is example solving and plotting frq mRNA for Dovzhenok's model #####
ModDovzhenok = ODE('The Dovzhenok Model',
frq_ind,
Y,
p,
p_add,
dY,
Y0,
period,
findQ=False)
tot_time = 100
t_test = np.linspace(0, tot_time, 100 * tot_time)
sol_test = ModDovzhenok.solve(ModDovzhenok.lim_cyc_vals, t_test)
frq_sol = sol_test[:, frq_ind]
plt.plot(t_test, frq_sol)
