# Size of variable arrays: sizeAlgebraic = 1 sizeStates = 9 sizeConstants = 10 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] = "x1 in component x1 (nanomolar)" legend_states[1] = "x2 in component x2 (nanomolar)" legend_states[2] = "x3 in component x3 (nanomolar)" legend_states[3] = "x4 in component x4 (nanomolar)" legend_states[4] = "x5 in component x5 (nanomolar)" legend_states[5] = "x6 in component x6 (nanomolar)" legend_states[6] = "x7 in component x7 (nanomolar)" legend_states[7] = "x8 in component x8 (nanomolar)" legend_states[8] = "x9 in component x9 (nanomolar)" legend_constants[0] = "k1 in component rate_variables (second_order_rate_constant)" legend_constants[1] = "k1_ in component rate_variables (first_order_rate_constant)" legend_constants[2] = "k2 in component rate_variables (second_order_rate_constant)" legend_constants[3] = "k2_ in component rate_variables (first_order_rate_constant)" legend_constants[4] = "k4 in component rate_variables (second_order_rate_constant)" legend_constants[5] = "k4_ in component rate_variables (first_order_rate_constant)" legend_constants[6] = "k5 in component rate_variables (second_order_rate_constant)" legend_constants[7] = "k5_ in component rate_variables (first_order_rate_constant)" legend_algebraic[0] = "scatchard in component x1 (dimensionless)" legend_constants[8] = "k3 in component rate_variables (second_order_rate_constant)" legend_constants[9] = "k3_ in component rate_variables (first_order_rate_constant)" legend_rates[0] = "d/dt x1 in component x1 (nanomolar)" legend_rates[1] = "d/dt x2 in component x2 (nanomolar)" legend_rates[2] = "d/dt x3 in component x3 (nanomolar)" legend_rates[3] = "d/dt x4 in component x4 (nanomolar)" legend_rates[4] = "d/dt x5 in component x5 (nanomolar)" legend_rates[5] = "d/dt x6 in component x6 (nanomolar)" legend_rates[6] = "d/dt x7 in component x7 (nanomolar)" legend_rates[7] = "d/dt x8 in component x8 (nanomolar)" legend_rates[8] = "d/dt x9 in component x9 (nanomolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 10 states[1] = 0.1 states[2] = 1.0 states[3] = 1.0 states[4] = 1.0 states[5] = 1.0 states[6] = 1.0 states[7] = 1.0 states[8] = 1.0 constants[0] = 1000000 constants[1] = 0.0004 constants[2] = 1000000 constants[3] = 0.04 constants[4] = 1000000 constants[5] = 0.0004 constants[6] = 10000000 constants[7] = 0.004 constants[8] = 1000000 constants[9] = 0.0004 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = ((((((constants[1]*states[2]-constants[0]*states[0]*states[1])+constants[3]*states[3])-constants[2]*states[0]*states[2])+constants[5]*(states[5]+states[6]))-constants[4]*states[0]*(states[4]+states[8]))+constants[7]*(states[6]+states[7]+states[8]))-constants[6]*states[0]*(states[4]+states[5]+states[6]) rates[1] = ((constants[1]*states[2]-constants[0]*states[0]*states[1])+constants[9]*(states[4]+states[8]))-constants[8]*states[1]*(states[2]+states[3]) rates[2] = (((((constants[0]*states[0]*states[1]-constants[1]*states[2])+constants[3]*states[3])-constants[2]*states[0]*states[2])+constants[9]*states[4])-constants[8]*states[1]*states[2]) rates[3] = ((constants[2]*states[0]*states[2]-constants[3]*states[3])+constants[9]*states[8])-constants[2]*states[1]*states[3] rates[4] = ((((constants[8]*states[1]*states[2]-constants[9]*states[4])+constants[5]*states[5])-constants[4]*states[0]*states[4])+constants[7]*states[8])-constants[6]*states[0]*states[4] rates[5] = ((constants[4]*states[0]*states[4]-constants[5]*states[5])+constants[7]*states[6])-constants[6]*states[0]*states[5] rates[6] = (constants[4]*states[0]*states[8]-constants[5]*states[6])+constants[7]*(states[7]-states[6])+constants[6]*states[0]*(states[5]-states[6]) rates[7] = constants[6]*states[0]*states[6]-constants[7]*states[7] rates[8] = ((((constants[8]*states[1]*states[3]-constants[9]*states[8])+constants[5]*states[6])-constants[4]*states[0]*states[8])+constants[6]*states[0]*states[4])-constants[7]*states[8] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (states[2]+states[3]+states[6]+states[7]+states[8])/states[0] 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)