# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 1 sizeConstants = 29 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_constants[0] = "k_p1 in component SERCA (second_order_rate_constant)" legend_constants[1] = "k_p2 in component SERCA (first_order_rate_constant)" legend_constants[2] = "k_p3 in component SERCA (first_order_rate_constant)" legend_constants[3] = "k_m1 in component SERCA (first_order_rate_constant)" legend_constants[4] = "k_m2 in component SERCA (second_order_rate_constant)" legend_constants[5] = "k_m3 in component SERCA (second_order_rate_constant)" legend_constants[6] = "kdcai in component SERCA (millimolar)" legend_constants[7] = "kdcasr in component SERCA (millimolar)" legend_constants[8] = "kdh1 in component SERCA (millimolar)" legend_constants[9] = "kdhi in component SERCA (millimolar_squared)" legend_constants[10] = "kdhsr in component SERCA (millimolar_squared)" legend_constants[11] = "kdh in component SERCA (millimolar)" legend_constants[12] = "n in component SERCA (dimensionless)" legend_constants[13] = "Ca_i in component SERCA (millimolar)" legend_states[0] = "Ca_sr in component SERCA (millimolar)" legend_constants[14] = "H_i in component SERCA (millimolar)" legend_constants[15] = "ATP in component SERCA (millimolar)" legend_constants[16] = "ADP in component SERCA (millimolar)" legend_constants[17] = "P_i in component SERCA (millimolar)" legend_constants[18] = "T_Cai in component SERCA (dimensionless)" legend_algebraic[0] = "T_Casr in component SERCA (dimensionless)" legend_constants[19] = "T_H1 in component SERCA (dimensionless)" legend_constants[20] = "T_Hi in component SERCA (dimensionless)" legend_constants[21] = "T_Hsr in component SERCA (dimensionless)" legend_constants[22] = "T_H in component SERCA (dimensionless)" legend_constants[23] = "a_p1 in component SERCA (first_order_rate_constant)" legend_constants[24] = "a_p2 in component SERCA (first_order_rate_constant)" legend_algebraic[1] = "a_p3 in component SERCA (first_order_rate_constant)" legend_constants[25] = "a_m1 in component SERCA (first_order_rate_constant)" legend_algebraic[2] = "a_m2 in component SERCA (first_order_rate_constant)" legend_constants[26] = "a_m3 in component SERCA (first_order_rate_constant)" legend_algebraic[3] = "s1 in component SERCA (per_second_squared)" legend_algebraic[4] = "s2 in component SERCA (per_second_squared)" legend_constants[27] = "s3 in component SERCA (per_second_squared)" legend_algebraic[5] = "v_cycle in component SERCA (first_order_rate_constant)" legend_rates[0] = "d/dt Ca_sr in component SERCA (millimolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 25900 constants[1] = 2540 constants[2] = 20.5 constants[3] = 16 constants[4] = 67200 constants[5] = 149 constants[6] = 0.9 constants[7] = 2.24 constants[8] = 1.09e-5 constants[9] = 3.54e-3 constants[10] = 1.05e-8 constants[11] = 7.24e-5 constants[12] = 2 constants[13] = 150e-6 states[0] = 0 constants[14] = 1e-4 constants[15] = 5 constants[16] = 36.3e-3 constants[17] = 1 constants[18] = constants[13]/constants[6] constants[28] = 1.00000 constants[19] = constants[14]/constants[8] constants[20] = (power(constants[14], constants[12]))/constants[9] constants[21] = (power(constants[14], constants[12]))/constants[10] constants[22] = constants[14]/constants[11] constants[23] = constants[0]*constants[15] constants[24] = (constants[1]*(power(constants[18], 2.00000)))/(power(constants[18], 2.00000)+(power(constants[18], 2.00000))*constants[20]+constants[20]*(1.00000+constants[19])) constants[25] = (constants[3]*constants[20])/(power(constants[18], 2.00000)+(power(constants[18], 2.00000))*constants[20]+constants[20]*(1.00000+constants[19])) constants[26] = constants[5]*constants[17] constants[27] = constants[23]*constants[24]+constants[26]*constants[25]+constants[26]*constants[24] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[28] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[0]/constants[7] algebraic[1] = (constants[2]*constants[21])/((power(algebraic[0], 2.00000))*constants[22]+constants[22]+constants[21]*(1.00000+constants[22])) algebraic[2] = (constants[4]*constants[16]*(power(algebraic[0], 2.00000))*constants[22])/((power(algebraic[0], 2.00000))*constants[22]+constants[22]+constants[21]*(1.00000+constants[22])) algebraic[3] = constants[24]*algebraic[1]+constants[25]*algebraic[1]+constants[25]*algebraic[2] algebraic[4] = constants[23]*algebraic[1]+algebraic[2]*constants[23]+algebraic[2]*constants[26] algebraic[5] = (constants[23]*constants[24]*algebraic[1]-constants[25]*algebraic[2]*constants[26])/(algebraic[3]+algebraic[4]+constants[27]) return algebraic 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)