# Size of variable arrays: sizeAlgebraic = 7 sizeStates = 3 sizeConstants = 16 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_states[0] = "V in component membrane (millivolt)" legend_constants[0] = "tau in component membrane (millisecond)" legend_algebraic[4] = "i_K in component potassium_current (picoA)" legend_algebraic[6] = "i_K_ATP in component ATP_sensitive_potassium_current (picoA)" legend_algebraic[3] = "i_Ca in component calcium_current (picoA)" legend_algebraic[5] = "i_s in component slow_current (picoA)" legend_constants[1] = "g_Ca in component calcium_current (nanoS)" legend_constants[2] = "V_Ca in component calcium_current (millivolt)" legend_algebraic[0] = "m_infinity in component calcium_current_m_gate (dimensionless)" legend_constants[3] = "V_m in component calcium_current_m_gate (millivolt)" legend_constants[4] = "theta_m in component calcium_current_m_gate (millivolt)" legend_constants[5] = "V_K in component potassium_current (millivolt)" legend_constants[6] = "g_K in component potassium_current (nanoS)" legend_states[1] = "n in component potassium_current_n_gate (dimensionless)" legend_algebraic[1] = "n_infinity in component potassium_current_n_gate (dimensionless)" legend_constants[7] = "V_n in component potassium_current_n_gate (millivolt)" legend_constants[8] = "theta_n in component potassium_current_n_gate (millivolt)" legend_constants[9] = "lambda in component potassium_current_n_gate (dimensionless)" legend_constants[10] = "g_s in component slow_current (nanoS)" legend_states[2] = "s in component slow_current_s_gate (dimensionless)" legend_algebraic[2] = "s_infinity in component slow_current_s_gate (dimensionless)" legend_constants[11] = "V_s in component slow_current_s_gate (millivolt)" legend_constants[12] = "theta_s in component slow_current_s_gate (millivolt)" legend_constants[13] = "tau_s in component slow_current_s_gate (millisecond)" legend_constants[14] = "g_K_ATP in component ATP_sensitive_potassium_current (nanoS)" legend_constants[15] = "p in component ATP_sensitive_potassium_current (dimensionless)" legend_rates[0] = "d/dt V in component membrane (millivolt)" legend_rates[1] = "d/dt n in component potassium_current_n_gate (dimensionless)" legend_rates[2] = "d/dt s in component slow_current_s_gate (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = -64.0 constants[0] = 20.0 constants[1] = 3.6 constants[2] = 25.0 constants[3] = -20.0 constants[4] = 12.0 constants[5] = -75.0 constants[6] = 10.0 states[1] = 0.01 constants[7] = -17.0 constants[8] = 5.6 constants[9] = 0.9 constants[10] = 4.0 states[2] = 0.01 constants[11] = -22.0 constants[12] = 8.0 constants[13] = 20000.0 constants[14] = 1.2 constants[15] = 0.5 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[1] = 1.00000/(1.00000+exp((constants[7]-states[0])/constants[8])) rates[1] = (constants[9]*(algebraic[1]-states[1]))/constants[0] algebraic[2] = 1.00000/(1.00000+exp((constants[11]-states[0])/constants[12])) rates[2] = (algebraic[2]-states[2])/constants[13] algebraic[4] = constants[6]*states[1]*(states[0]-constants[5]) algebraic[6] = constants[14]*constants[15]*(states[0]-constants[5]) algebraic[0] = 1.00000/(1.00000+exp((constants[3]-states[0])/constants[4])) algebraic[3] = constants[1]*algebraic[0]*(states[0]-constants[2]) algebraic[5] = constants[10]*states[2]*(states[0]-constants[5]) rates[0] = -(algebraic[3]+algebraic[4]+algebraic[6]+algebraic[5])/constants[0] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = 1.00000/(1.00000+exp((constants[7]-states[0])/constants[8])) algebraic[2] = 1.00000/(1.00000+exp((constants[11]-states[0])/constants[12])) algebraic[4] = constants[6]*states[1]*(states[0]-constants[5]) algebraic[6] = constants[14]*constants[15]*(states[0]-constants[5]) algebraic[0] = 1.00000/(1.00000+exp((constants[3]-states[0])/constants[4])) algebraic[3] = constants[1]*algebraic[0]*(states[0]-constants[2]) algebraic[5] = constants[10]*states[2]*(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)