# Size of variable arrays: sizeAlgebraic = 5 sizeStates = 4 sizeConstants = 26 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_states[0] = "R_des in component R_des (micromolar)" legend_constants[24] = "K_plus in component model_parameters (per_micromolar_per_second)" legend_states[1] = "C_cyto in component C_cyto (micromolar)" legend_constants[0] = "n_i in component model_parameters (dimensionless)" legend_constants[1] = "K_act in component model_parameters (micromolar)" legend_constants[2] = "n_a in component model_parameters (dimensionless)" legend_constants[3] = "K_minus in component model_parameters (per_second)" legend_constants[4] = "K_1 in component model_parameters (per_second)" legend_constants[5] = "b in component model_parameters (per_second)" legend_algebraic[2] = "I_ra in component I_ra (micromolar)" legend_constants[6] = "Ca_tot in component model_parameters (micromolar)" legend_constants[7] = "alpha in component model_parameters (dimensionless)" legend_constants[8] = "V_MP in component model_parameters (micromolar_per_second)" legend_constants[9] = "n_p in component model_parameters (dimensionless)" legend_constants[10] = "K_p in component model_parameters (micromolar)" legend_algebraic[0] = "I_rable in component I_rable (micromolar)" legend_states[2] = "IP3 in component IP3 (micromolar)" legend_constants[11] = "K_IP in component model_parameters (micromolar)" legend_constants[25] = "V_PLC in component V_PLC (micromolar)" legend_algebraic[1] = "V_3K in component V_3K (micromolar)" legend_algebraic[3] = "V_5P in component V_5P (micromolar)" legend_constants[12] = "V_plc in component model_parameters (micromolar_per_second)" legend_constants[13] = "gamma in component model_parameters (dimensionless)" legend_constants[14] = "V_k in component model_parameters (micromolar_per_second)" legend_constants[15] = "K_k in component model_parameters (micromolar)" legend_constants[16] = "n_d in component model_parameters (dimensionless)" legend_constants[17] = "K_d in component model_parameters (micromolar)" legend_states[3] = "IP4 in component IP4 (micromolar)" legend_constants[18] = "V_p1 in component model_parameters (micromolar_per_second)" legend_constants[19] = "K_p1 in component model_parameters (micromolar)" legend_constants[20] = "K_p2 in component model_parameters (micromolar)" legend_algebraic[4] = "V_15P in component V_15P (micromolar)" legend_constants[21] = "k in component model_parameters (per_second)" legend_constants[22] = "V_p2 in component model_parameters (micromolar_per_second)" legend_constants[23] = "K_inh in component model_parameters (micromolar)" legend_rates[0] = "d/dt R_des in component R_des (micromolar)" legend_rates[1] = "d/dt C_cyto in component C_cyto (micromolar)" legend_rates[2] = "d/dt IP3 in component IP3 (micromolar)" legend_rates[3] = "d/dt IP4 in component IP4 (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.1 states[1] = 0.1 constants[0] = 4 constants[1] = 0.56 constants[2] = 3 constants[3] = 0.5 constants[4] = 2.57 constants[5] = 7e-4 constants[6] = 80 constants[7] = 0.1 constants[8] = 4 constants[9] = 2 constants[10] = 0.35 states[2] = 0.1 constants[11] = 1 constants[12] = 1.3 constants[13] = 0.2 constants[14] = 0.5 constants[15] = 1 constants[16] = 2 constants[17] = 0.3 states[3] = 0.1 constants[18] = 5 constants[19] = 10 constants[20] = 2 constants[21] = 0.01 constants[22] = 0.2 constants[23] = 0.15 constants[24] = constants[3]/(power(constants[23], constants[0])) constants[25] = constants[13]*constants[12]*1.00000 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[24]*(power(states[1], constants[0]))*1.00000*(((1.00000-states[0])/(1.00000+power(states[1]/constants[1], constants[2])))*1.00000)-constants[3]*states[0] algebraic[0] = ((1.00000-states[0])*states[2])/(constants[11]+states[2]) algebraic[2] = (algebraic[0]*1.00000)/(1.00000+power(constants[1]/states[1], constants[2])) rates[1] = constants[4]*1.00000*(constants[5]*1.00000+algebraic[2]*1.00000)*((constants[6]-states[1]*(constants[7]+1.00000))*1.00000)-constants[8]*(((power(states[1], constants[9]))/(power(constants[10], constants[9])+power(states[1], constants[9])))*1.00000) algebraic[1] = constants[14]*(states[2]/(constants[15]+states[2]))*((power(states[1], constants[16]))/(power(constants[17], constants[16])+power(states[1], constants[16])))*1.00000 algebraic[3] = constants[18]*1.00000*(states[2]/(constants[19]*(1.00000+states[3]/constants[20])+states[2])) rates[2] = ((constants[25]-algebraic[1])-algebraic[3])/1.00000 algebraic[4] = (constants[22]*1.00000*states[3])/(constants[20]*(1.00000+states[2]/constants[19])+states[3]) rates[3] = (algebraic[1]-algebraic[4])*1.00000-constants[21]*states[3] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = ((1.00000-states[0])*states[2])/(constants[11]+states[2]) algebraic[2] = (algebraic[0]*1.00000)/(1.00000+power(constants[1]/states[1], constants[2])) algebraic[1] = constants[14]*(states[2]/(constants[15]+states[2]))*((power(states[1], constants[16]))/(power(constants[17], constants[16])+power(states[1], constants[16])))*1.00000 algebraic[3] = constants[18]*1.00000*(states[2]/(constants[19]*(1.00000+states[3]/constants[20])+states[2])) algebraic[4] = (constants[22]*1.00000*states[3])/(constants[20]*(1.00000+states[2]/constants[19])+states[3]) 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)