# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 11 sizeConstants = 15 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component environment (s)" legend_constants[0] = "kf8 in component PIPtoDAG (per_s)" legend_constants[1] = "kf9 in component PIPtoDAG (per_s)" legend_constants[2] = "km6 in component PIPtoDAG (um)" legend_constants[3] = "Vmax6 in component PIPtoDAG (per_s)" legend_constants[4] = "km7 in component PIPtoDAG (um)" legend_constants[5] = "Vmax7 in component PIPtoDAG (per_s)" legend_states[0] = "PIP2 in component PIPtoDAG (um)" legend_states[1] = "DAG in component PIPtoDAG (um)" legend_states[2] = "IP3 in component PIPtoDAG (um)" legend_states[3] = "CaPLC in component PLC (um)" legend_states[4] = "CaGqPLC in component PLC (um)" legend_states[5] = "Inositol in component PIPtoDAG (um)" legend_states[6] = "PC in component PIPtoDAG (um)" legend_constants[6] = "kf1 in component PLC (per_um_s)" legend_constants[7] = "kb1 in component PLC (per_s)" legend_constants[8] = "kf2 in component PLC (per_um_s)" legend_constants[9] = "kb2 in component PLC (per_s)" legend_constants[10] = "kf3 in component PLC (per_um_s)" legend_constants[11] = "kb3 in component PLC (per_s)" legend_constants[12] = "kf4 in component PLC (per_um_s)" legend_constants[13] = "kb4 in component PLC (per_s)" legend_constants[14] = "kf5 in component PLC (per_s)" legend_states[7] = "PLC in component PLC (um)" legend_states[8] = "Gq in component PLC (um)" legend_states[9] = "Ca in component PLC (um)" legend_states[10] = "GqPLC in component PLC (um)" legend_rates[0] = "d/dt PIP2 in component PIPtoDAG (um)" legend_rates[1] = "d/dt DAG in component PIPtoDAG (um)" legend_rates[2] = "d/dt IP3 in component PIPtoDAG (um)" legend_rates[6] = "d/dt PC in component PIPtoDAG (um)" legend_rates[5] = "d/dt Inositol in component PIPtoDAG (um)" legend_rates[7] = "d/dt PLC in component PLC (um)" legend_rates[8] = "d/dt Gq in component PLC (um)" legend_rates[9] = "d/dt Ca in component PLC (um)" legend_rates[10] = "d/dt GqPLC in component PLC (um)" legend_rates[3] = "d/dt CaPLC in component PLC (um)" legend_rates[4] = "d/dt CaGqPLC in component PLC (um)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.15 constants[1] = 2.5 constants[2] = 5 constants[3] = 48 constants[4] = 19.84166667 constants[5] = 10 states[0] = 10 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 0 states[5] = 0 states[6] = 0 constants[6] = 0.000005 constants[7] = 1 constants[8] = 0.0000042 constants[9] = 1 constants[10] = 0.00005 constants[11] = 1 constants[12] = 0.0000042 constants[13] = 1 constants[14] = 0.0133 states[7] = 0.8 states[8] = 0.15 states[9] = 0.1 states[10] = 0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (-states[3]*constants[5]*states[0])/(constants[4]+states[0])-(states[4]*constants[3]*states[0])/(constants[2]+states[0]) rates[1] = (states[3]*constants[5]*states[0])/(constants[4]+states[0])-constants[0]*states[1] rates[2] = (states[4]*constants[3]*states[0])/(constants[2]+states[0])-constants[1]*states[2] rates[6] = constants[0]*states[1] rates[5] = constants[1]*states[2] rates[7] = ((-states[7]*states[9]*constants[6]+states[3]*constants[7])-states[7]*states[8]*constants[8])+states[10]*constants[9] rates[8] = (-states[7]*states[8]*constants[8]+states[10]*constants[9]+states[4]*constants[13])-states[3]*states[8]*constants[12] rates[9] = ((-states[7]*states[9]*constants[6]+states[3]*constants[7])-states[9]*states[10]*constants[10])+states[4]*constants[11] rates[10] = ((states[7]*states[8]*constants[8]-states[10]*constants[9])-states[9]*states[10]*constants[10])+states[4]*constants[11] rates[3] = ((states[7]*states[9]*constants[6]-states[3]*constants[7])+states[4]*constants[14]+states[4]*constants[13])-states[3]*states[8]*constants[12] rates[4] = (((states[10]*states[9]*constants[10]-states[4]*constants[11])+states[3]*states[8]*constants[12])-states[4]*constants[13])-states[4]*constants[14] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) 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)