# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 10 sizeConstants = 30 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] = "kf2 in component GEF (per_s)" legend_constants[1] = "kb2 in component GEF (per_s)" legend_constants[2] = "kf5 in component GEF (per_um_s)" legend_constants[3] = "kb5 in component GEF (per_s)" legend_constants[4] = "kf7 in component GEF (per_s)" legend_constants[5] = "kb7 in component GEF (per_s)" legend_constants[6] = "kf8 in component GEF (per_um_s)" legend_constants[7] = "kb8 in component GEF (per_s)" legend_constants[8] = "km1 in component GEF (um)" legend_constants[9] = "Vmax1 in component GEF (per_s)" legend_constants[10] = "km6 in component GEF (um)" legend_constants[11] = "Vmax6 in component GEF (per_s)" legend_states[0] = "GEF_inact in component GEF (um)" legend_states[1] = "GEF in component GEF (um)" legend_constants[12] = "PKA in component undefinedVariables (um)" legend_states[2] = "Ca4CAM in component GEF (um)" legend_constants[13] = "PKC in component undefinedVariables (um)" legend_states[3] = "Gby in component GEF (um)" legend_states[4] = "CaM_GEF in component GEF (um)" legend_states[5] = "Gby_GEF in component GEF (um)" legend_constants[14] = "kf12 in component GTPRAS (per_s)" legend_constants[15] = "kb12 in component GTPRAS (per_s)" legend_constants[16] = "km9 in component GTPRAS (um)" legend_constants[17] = "Vmax9 in component GTPRAS (per_s)" legend_constants[18] = "km10 in component GTPRAS (um)" legend_constants[19] = "Vmax10 in component GTPRAS (per_s)" legend_constants[20] = "km11 in component GTPRAS (um)" legend_constants[21] = "Vmax11 in component GTPRAS (per_s)" legend_constants[22] = "km13 in component GTPRAS (um)" legend_constants[23] = "Vmax13 in component GTPRAS (per_s)" legend_states[6] = "GTP_RAS in component GTPRAS (um)" legend_states[7] = "GDP_RAS in component GTPRAS (um)" legend_states[8] = "GAP in component GAP (um)" legend_constants[24] = "kf4 in component GAP (per_s)" legend_constants[25] = "kb4 in component GAP (per_s)" legend_constants[26] = "km3 in component GAP (um)" legend_constants[27] = "Vmax3 in component GAP (per_s)" legend_states[9] = "GAPstar in component GAP (um)" legend_constants[28] = "Ca4CAM in component undefinedVariables (um)" legend_constants[29] = "Gby in component undefinedVariables (um)" legend_rates[0] = "d/dt GEF_inact in component GEF (um)" legend_rates[1] = "d/dt GEF in component GEF (um)" legend_rates[3] = "d/dt Gby in component GEF (um)" legend_rates[4] = "d/dt CaM_GEF in component GEF (um)" legend_rates[2] = "d/dt Ca4CAM in component GEF (um)" legend_rates[5] = "d/dt Gby_GEF in component GEF (um)" legend_rates[6] = "d/dt GTP_RAS in component GTPRAS (um)" legend_rates[7] = "d/dt GDP_RAS in component GTPRAS (um)" legend_rates[8] = "d/dt GAP in component GAP (um)" legend_rates[9] = "d/dt GAPstar in component GAP (um)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1 constants[1] = 0 constants[2] = 0.0001 constants[3] = 1 constants[4] = 1 constants[5] = 0 constants[6] = 0.00001 constants[7] = 1 constants[8] = 7.5 constants[9] = 9 constants[10] = 3.33333333333 constants[11] = 4 states[0] = 0.1 states[1] = 0 constants[12] = 1 states[2] = 1 constants[13] = 1 states[3] = 1 states[4] = 0 states[5] = 0 constants[14] = 0.0001 constants[15] = 0 constants[16] = 0.50505 constants[17] = 0.02 constants[18] = 0.50505 constants[19] = 0.02 constants[20] = 0.50505 constants[21] = 0.02 constants[22] = 1.0104 constants[23] = 10 states[6] = 0 states[7] = 0.2 states[8] = 0.002 constants[24] = 0.1 constants[25] = 0 constants[26] = 3.33333333333 constants[27] = 4 states[9] = 0 constants[28] = 1 constants[29] = 1 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (((constants[12]*constants[9]*states[1])/(constants[8]+states[1])+(constants[13]*constants[11]*states[1])/(constants[10]+states[1]))-constants[0]*states[0])-constants[4]*states[0] rates[1] = (((-((((constants[12]*constants[9]*states[1])/(constants[8]+states[1])+(constants[13]*constants[11]*states[1])/(constants[10]+states[1]))-constants[0]*states[0])-constants[4]*states[0])-constants[2]*states[2]*states[1])+constants[3]*states[4])-constants[6]*states[1]*states[3])+constants[7]*states[5] rates[3] = -constants[6]*states[1]*states[3]+constants[7]*states[5] rates[4] = -constants[3]*states[4]+constants[2]*states[1]*states[2] rates[2] = -(-constants[3]*states[4]+constants[2]*states[1]*states[2]) rates[5] = -(-constants[6]*states[1]*states[3]+constants[7]*states[5]) rates[6] = ((-states[8]*constants[23]*states[6])/(constants[22]+states[6])-constants[14]*states[6])+(states[0]*constants[19]*states[7])/(constants[18]+states[7])+(states[5]*constants[21]*states[7])/(constants[20]+states[7])+(states[4]*constants[17]*states[7])/(constants[16]+states[7]) rates[7] = -(((-states[8]*constants[23]*states[6])/(constants[22]+states[6])-constants[14]*states[6])+(states[0]*constants[19]*states[7])/(constants[18]+states[7])+(states[5]*constants[21]*states[7])/(constants[20]+states[7])+(states[4]*constants[17]*states[7])/(constants[16]+states[7])) rates[8] = (-constants[13]*constants[27]*states[8])/(constants[26]+states[8])+constants[24]*states[9] rates[9] = (constants[13]*constants[27]*states[8])/(constants[26]+states[8])-constants[24]*states[9] 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)