# Size of variable arrays: sizeAlgebraic = 10 sizeStates = 4 sizeConstants = 21 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 (millisecond)" legend_constants[0] = "Cm in component membrane (femtoF)" legend_states[0] = "V in component membrane (millivolt)" legend_algebraic[4] = "ICa in component Ca_current (femtoA)" legend_algebraic[6] = "IK in component rapid_K_current (femtoA)" legend_algebraic[9] = "Il in component leak_current (femtoA)" legend_algebraic[7] = "Is1 in component slow_K_current (femtoA)" legend_algebraic[8] = "Is2 in component very_slow_K_current (femtoA)" legend_constants[1] = "Vm in component Ca_current (millivolt)" legend_constants[2] = "VCa in component Ca_current (millivolt)" legend_constants[3] = "gCa in component Ca_current (picoS)" legend_algebraic[0] = "minf in component Ca_current (dimensionless)" legend_constants[4] = "sm in component Ca_current (millivolt)" legend_constants[5] = "VK in component rapid_K_current (millivolt)" legend_constants[6] = "gK in component rapid_K_current (picoS)" legend_states[1] = "n in component rapid_K_current (dimensionless)" legend_constants[7] = "lambda in component rapid_K_current (dimensionless)" legend_constants[8] = "tnbar in component rapid_K_current (dimensionless)" legend_constants[9] = "Vn in component rapid_K_current (millivolt)" legend_constants[10] = "sn in component rapid_K_current (millivolt)" legend_algebraic[5] = "taun in component rapid_K_current (dimensionless)" legend_algebraic[1] = "ninf in component rapid_K_current (dimensionless)" legend_constants[11] = "gs1 in component slow_K_current (picoS)" legend_states[2] = "s1 in component slow_K_current (dimensionless)" legend_algebraic[2] = "s1inf in component slow_K_current (dimensionless)" legend_constants[12] = "Vs1 in component slow_K_current (millivolt)" legend_constants[13] = "ss1 in component slow_K_current (millivolt)" legend_constants[14] = "taus1 in component slow_K_current (dimensionless)" legend_constants[15] = "Vs2 in component very_slow_K_current (millivolt)" legend_states[3] = "s2 in component very_slow_K_current (dimensionless)" legend_algebraic[3] = "s2inf in component very_slow_K_current (dimensionless)" legend_constants[16] = "ss2 in component very_slow_K_current (millivolt)" legend_constants[17] = "gs2 in component very_slow_K_current (picoS)" legend_constants[18] = "taus2 in component very_slow_K_current (dimensionless)" legend_constants[19] = "gl in component leak_current (picoS)" legend_constants[20] = "Vl in component leak_current (millivolt)" legend_rates[0] = "d/dt V in component membrane (millivolt)" legend_rates[1] = "d/dt n in component rapid_K_current (dimensionless)" legend_rates[2] = "d/dt s1 in component slow_K_current (dimensionless)" legend_rates[3] = "d/dt s2 in component very_slow_K_current (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 4524 states[0] = -43 constants[1] = -22 constants[2] = 100 constants[3] = 280 constants[4] = 7.5 constants[5] = -80 constants[6] = 1300 states[1] = 0.03 constants[7] = 1.1 constants[8] = 9.09 constants[9] = -9 constants[10] = 10 constants[11] = 3 states[2] = 0.1 constants[12] = -40 constants[13] = 0.5 constants[14] = 1000 constants[15] = -42 states[3] = 0.434 constants[16] = 0.4 constants[17] = 32 constants[18] = 120000 constants[19] = 25 constants[20] = -40 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[2] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[13])) rates[2] = (algebraic[2]-states[2])/(constants[14]*1.00000) algebraic[3] = 1.00000/(1.00000+exp((constants[15]-states[0])/constants[16])) rates[3] = (algebraic[3]-states[3])/(constants[18]*1.00000) algebraic[5] = constants[8]/(1.00000+exp((states[0]-constants[9])/constants[10])) algebraic[1] = 1.00000/(1.00000+exp((constants[9]-states[0])/constants[10])) rates[1] = (constants[7]*(algebraic[1]-states[1]))/(algebraic[5]*1.00000) algebraic[0] = 1.00000/(1.00000+exp((constants[1]-states[0])/constants[4])) algebraic[4] = constants[3]*algebraic[0]*(states[0]-constants[2]) algebraic[6] = constants[6]*states[1]*(states[0]-constants[5]) algebraic[9] = constants[19]*(states[0]-constants[20]) algebraic[7] = constants[11]*states[2]*(states[0]-constants[5]) algebraic[8] = constants[17]*states[3]*(states[0]-constants[5]) rates[0] = -(algebraic[4]+algebraic[6]+algebraic[9]+algebraic[7]+algebraic[8])/constants[0] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[2] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[13])) algebraic[3] = 1.00000/(1.00000+exp((constants[15]-states[0])/constants[16])) algebraic[5] = constants[8]/(1.00000+exp((states[0]-constants[9])/constants[10])) algebraic[1] = 1.00000/(1.00000+exp((constants[9]-states[0])/constants[10])) algebraic[0] = 1.00000/(1.00000+exp((constants[1]-states[0])/constants[4])) algebraic[4] = constants[3]*algebraic[0]*(states[0]-constants[2]) algebraic[6] = constants[6]*states[1]*(states[0]-constants[5]) algebraic[9] = constants[19]*(states[0]-constants[20]) algebraic[7] = constants[11]*states[2]*(states[0]-constants[5]) algebraic[8] = constants[17]*states[3]*(states[0]-constants[5]) 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)