# Size of variable arrays: sizeAlgebraic = 16 sizeStates = 6 sizeConstants = 23 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "time in component environment (second)" legend_algebraic[0] = "q_L_B1_init in component environment (fmol)" legend_constants[0] = "q_R_B1_init in component environment (fmol)" legend_constants[1] = "q_Gs_init in component environment (fmol)" legend_constants[2] = "q_LR_B1_init in component environment (fmol)" legend_constants[3] = "q_R_B1Gs_init in component environment (fmol)" legend_constants[4] = "q_LR_B1Gs_init in component environment (fmol)" legend_constants[5] = "stimSt in component environment (second)" legend_constants[6] = "stimDur in component environment (second)" legend_constants[7] = "tR in component environment (second)" legend_constants[8] = "stimMag in component environment (fmol)" legend_constants[9] = "stimHolding in component environment (fmol)" legend_constants[22] = "m in component environment (fmol_per_sec)" legend_algebraic[1] = "q_L_B1 in component environment (fmol)" legend_algebraic[2] = "q_R_B1 in component environment (fmol)" legend_algebraic[3] = "q_Gs in component environment (fmol)" legend_algebraic[4] = "q_LR_B1 in component environment (fmol)" legend_algebraic[5] = "q_R_B1Gs in component environment (fmol)" legend_algebraic[6] = "q_LR_B1Gs in component environment (fmol)" legend_states[0] = "q_L_B1 in component LRGbinding_B1AR (fmol)" legend_states[1] = "q_R_B1 in component LRGbinding_B1AR (fmol)" legend_states[2] = "q_Gs in component LRGbinding_B1AR (fmol)" legend_states[3] = "q_LR_B1 in component LRGbinding_B1AR (fmol)" legend_states[4] = "q_R_B1Gs in component LRGbinding_B1AR (fmol)" legend_states[5] = "q_LR_B1Gs in component LRGbinding_B1AR (fmol)" legend_constants[10] = "kappa_R_C_B1 in component LRGbinding_B1AR_parameters (fmol_per_sec)" legend_constants[11] = "kappa_R_R_B1 in component LRGbinding_B1AR_parameters (fmol_per_sec)" legend_constants[12] = "kappa_R_L_B1 in component LRGbinding_B1AR_parameters (fmol_per_sec)" legend_constants[13] = "K_L_B1 in component LRGbinding_B1AR_parameters (per_fmol)" legend_constants[14] = "K_R_B1 in component LRGbinding_B1AR_parameters (per_fmol)" legend_constants[15] = "K_Gs in component LRGbinding_B1AR_parameters (per_fmol)" legend_constants[16] = "K_LR_B1 in component LRGbinding_B1AR_parameters (per_fmol)" legend_constants[17] = "K_R_B1Gs in component LRGbinding_B1AR_parameters (per_fmol)" legend_constants[18] = "K_LR_B1Gs in component LRGbinding_B1AR_parameters (per_fmol)" legend_constants[19] = "R in component constants (J_per_K_per_mol)" legend_constants[20] = "T in component constants (kelvin)" legend_algebraic[7] = "mu_L_B1 in component LRGbinding_B1AR (J_per_mol)" legend_algebraic[8] = "mu_R_B1 in component LRGbinding_B1AR (J_per_mol)" legend_algebraic[9] = "mu_Gs in component LRGbinding_B1AR (J_per_mol)" legend_algebraic[10] = "mu_LR_B1 in component LRGbinding_B1AR (J_per_mol)" legend_algebraic[11] = "mu_R_B1Gs in component LRGbinding_B1AR (J_per_mol)" legend_algebraic[12] = "mu_LR_B1Gs in component LRGbinding_B1AR (J_per_mol)" legend_algebraic[13] = "v_R_C_B1 in component LRGbinding_B1AR (fmol_per_sec)" legend_algebraic[14] = "v_R_R_B1 in component LRGbinding_B1AR (fmol_per_sec)" legend_algebraic[15] = "v_R_L_B1 in component LRGbinding_B1AR (fmol_per_sec)" legend_constants[21] = "F in component constants (C_per_mol)" legend_rates[0] = "d/dt q_L_B1 in component LRGbinding_B1AR (fmol)" legend_rates[1] = "d/dt q_R_B1 in component LRGbinding_B1AR (fmol)" legend_rates[2] = "d/dt q_Gs in component LRGbinding_B1AR (fmol)" legend_rates[3] = "d/dt q_LR_B1 in component LRGbinding_B1AR (fmol)" legend_rates[4] = "d/dt q_R_B1Gs in component LRGbinding_B1AR (fmol)" legend_rates[5] = "d/dt q_LR_B1Gs in component LRGbinding_B1AR (fmol)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.0004579000 constants[1] = 0.1455400000 constants[2] = 0 constants[3] = 0 constants[4] = 0 constants[5] = 3.1 constants[6] = 0.5e1 constants[7] = 0.3e1 constants[8] = 1e-7 constants[9] = 1e-8 states[0] = 1e-16 states[1] = 1e-16 states[2] = 1e-16 states[3] = 1e-16 states[4] = 1e-16 states[5] = 1e-16 constants[10] = 5573.84 constants[11] = 641.71 constants[12] = 1143.57 constants[13] = 0.885956 constants[14] = 0.834078 constants[15] = 0.18177 constants[16] = 7.24472 constants[17] = 172.108 constants[18] = 2.80863 constants[19] = 8.31 constants[20] = 310 constants[21] = 96485 constants[22] = constants[8]/constants[7] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[2] = states[1]+constants[0] algebraic[8] = constants[19]*constants[20]*log(constants[14]*algebraic[2]) algebraic[3] = states[2]+constants[1] algebraic[9] = constants[19]*constants[20]*log(constants[15]*algebraic[3]) algebraic[5] = states[4]+constants[3] algebraic[11] = constants[19]*constants[20]*log(constants[17]*algebraic[5]) algebraic[13] = constants[10]*exp((algebraic[8]+algebraic[9])/(constants[19]*constants[20]))-exp(algebraic[11]/(constants[19]*constants[20])) rates[4] = algebraic[13] algebraic[4] = states[3]+constants[2] algebraic[10] = constants[19]*constants[20]*log(constants[16]*algebraic[4]) algebraic[6] = states[5]+constants[4] algebraic[12] = constants[19]*constants[20]*log(constants[18]*algebraic[6]) algebraic[14] = constants[11]*exp((algebraic[10]+algebraic[9])/(constants[19]*constants[20]))-exp(algebraic[12]/(constants[19]*constants[20])) rates[2] = -algebraic[13]-algebraic[14] rates[5] = algebraic[14] algebraic[0] = custom_piecewise([less(voi , constants[5]) & greater(voi , constants[5]-constants[7]), constants[9]+constants[22]*((voi-constants[5])+constants[7]) , greater_equal(voi , constants[5]) & less(voi , constants[5]+constants[6]), constants[8]+constants[9] , less(voi , constants[5]+constants[7]+constants[6]) & greater_equal(voi , constants[5]+constants[6]), constants[9]+-constants[22]*(((voi-constants[5])-constants[7])-constants[6]) , True, constants[9]]) algebraic[1] = states[0]+algebraic[0] algebraic[7] = constants[19]*constants[20]*log(constants[13]*algebraic[1]) algebraic[15] = constants[12]*exp((algebraic[8]+algebraic[7])/(constants[19]*constants[20]))-exp(algebraic[10]/(constants[19]*constants[20])) rates[0] = -algebraic[15] rates[1] = -algebraic[13]-algebraic[15] rates[3] = -algebraic[14]+algebraic[15] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[2] = states[1]+constants[0] algebraic[8] = constants[19]*constants[20]*log(constants[14]*algebraic[2]) algebraic[3] = states[2]+constants[1] algebraic[9] = constants[19]*constants[20]*log(constants[15]*algebraic[3]) algebraic[5] = states[4]+constants[3] algebraic[11] = constants[19]*constants[20]*log(constants[17]*algebraic[5]) algebraic[13] = constants[10]*exp((algebraic[8]+algebraic[9])/(constants[19]*constants[20]))-exp(algebraic[11]/(constants[19]*constants[20])) algebraic[4] = states[3]+constants[2] algebraic[10] = constants[19]*constants[20]*log(constants[16]*algebraic[4]) algebraic[6] = states[5]+constants[4] algebraic[12] = constants[19]*constants[20]*log(constants[18]*algebraic[6]) algebraic[14] = constants[11]*exp((algebraic[10]+algebraic[9])/(constants[19]*constants[20]))-exp(algebraic[12]/(constants[19]*constants[20])) algebraic[0] = custom_piecewise([less(voi , constants[5]) & greater(voi , constants[5]-constants[7]), constants[9]+constants[22]*((voi-constants[5])+constants[7]) , greater_equal(voi , constants[5]) & less(voi , constants[5]+constants[6]), constants[8]+constants[9] , less(voi , constants[5]+constants[7]+constants[6]) & greater_equal(voi , constants[5]+constants[6]), constants[9]+-constants[22]*(((voi-constants[5])-constants[7])-constants[6]) , True, constants[9]]) algebraic[1] = states[0]+algebraic[0] algebraic[7] = constants[19]*constants[20]*log(constants[13]*algebraic[1]) algebraic[15] = constants[12]*exp((algebraic[8]+algebraic[7])/(constants[19]*constants[20]))-exp(algebraic[10]/(constants[19]*constants[20])) return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) def solve_model(): """Solve model with ODE solver""" from scipy.integrate import ode # Initialise constants and state variables (init_states, constants) = initConsts() # Set timespan to solve over voi = linspace(0, 10, 500) # Construct ODE object to solve r = ode(computeRates) r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1) r.set_initial_value(init_states, voi[0]) r.set_f_params(constants) # Solve model states = array([[0.0] * len(voi)] * sizeStates) states[:,0] = init_states for (i,t) in enumerate(voi[1:]): if r.successful(): r.integrate(t) states[:,i+1] = r.y else: break # Compute algebraic variables algebraic = computeAlgebraic(constants, states, voi) return (voi, states, algebraic) def plot_model(voi, states, algebraic): """Plot variables against variable of integration""" import pylab (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends() pylab.figure(1) pylab.plot(voi,vstack((states,algebraic)).T) pylab.xlabel(legend_voi) pylab.legend(legend_states + legend_algebraic, loc='best') pylab.show() if __name__ == "__main__": (voi, states, algebraic) = solve_model() plot_model(voi, states, algebraic)