# Size of variable arrays: sizeAlgebraic = 1 sizeStates = 17 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 (second)" legend_states[0] = "Py in component Py (nanomolar)" legend_constants[0] = "Zn in component model_parameters (nanomolar)" legend_states[1] = "Py1 in component Py1 (nanomolar)" legend_constants[1] = "r3 in component model_parameters (third_order_rate_constant)" legend_constants[2] = "r4 in component model_parameters (first_order_rate_constant)" legend_states[2] = "Dw in component Dw (nanomolar)" legend_states[3] = "Qw2 in component Qw2 (nanomolar)" legend_constants[3] = "k_1 in component model_parameters (first_order_rate_constant)" legend_constants[4] = "k1a in component model_parameters (second_order_rate_constant)" legend_states[4] = "Qw1 in component Qw1 (nanomolar)" legend_states[5] = "Rw in component Rw (nanomolar)" legend_constants[5] = "k2 in component model_parameters (second_order_rate_constant)" legend_constants[6] = "k_2 in component model_parameters (first_order_rate_constant)" legend_algebraic[0] = "k3 in component model_parameters (first_order_rate_constant)" legend_states[6] = "Mw in component Mw (nanomolar)" legend_states[7] = "Px in component Px (nanomolar)" legend_states[8] = "Px1 in component Px1 (nanomolar)" legend_states[9] = "Dz in component Dz (nanomolar)" legend_states[10] = "Qz4 in component Qz4 (nanomolar)" legend_constants[7] = "r1 in component model_parameters (second_order_rate_constant)" legend_constants[8] = "r2 in component model_parameters (first_order_rate_constant)" legend_constants[9] = "k1b in component model_parameters (second_order_rate_constant)" legend_states[11] = "Qz2 in component Qz2 (nanomolar)" legend_constants[10] = "k1 in component model_parameters (second_order_rate_constant)" legend_states[12] = "Qz1 in component Qz1 (nanomolar)" legend_states[13] = "Rz in component Rz (nanomolar)" legend_constants[11] = "k2a in component model_parameters (second_order_rate_constant)" legend_states[14] = "Qz3 in component Qz3 (nanomolar)" legend_states[15] = "Qz5 in component Qz5 (nanomolar)" legend_constants[12] = "k2b in component model_parameters (second_order_rate_constant)" legend_constants[13] = "k2c in component model_parameters (second_order_rate_constant)" legend_states[16] = "Mz in component Mz (nanomolar)" legend_constants[14] = "td0 in component model_parameters (second)" legend_constants[15] = "td in component model_parameters (second)" legend_rates[0] = "d/dt Py in component Py (nanomolar)" legend_rates[1] = "d/dt Py1 in component Py1 (nanomolar)" legend_rates[2] = "d/dt Dw in component Dw (nanomolar)" legend_rates[5] = "d/dt Rw in component Rw (nanomolar)" legend_rates[4] = "d/dt Qw1 in component Qw1 (nanomolar)" legend_rates[3] = "d/dt Qw2 in component Qw2 (nanomolar)" legend_rates[6] = "d/dt Mw in component Mw (nanomolar)" legend_rates[7] = "d/dt Px in component Px (nanomolar)" legend_rates[8] = "d/dt Px1 in component Px1 (nanomolar)" legend_rates[9] = "d/dt Dz in component Dz (nanomolar)" legend_rates[13] = "d/dt Rz in component Rz (nanomolar)" legend_rates[12] = "d/dt Qz1 in component Qz1 (nanomolar)" legend_rates[11] = "d/dt Qz2 in component Qz2 (nanomolar)" legend_rates[14] = "d/dt Qz3 in component Qz3 (nanomolar)" legend_rates[10] = "d/dt Qz4 in component Qz4 (nanomolar)" legend_rates[15] = "d/dt Qz5 in component Qz5 (nanomolar)" legend_rates[16] = "d/dt Mz in component Mz (nanomolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 25.0 constants[0] = 1E-5 states[1] = 0.0 constants[1] = 4.41E10 constants[2] = 9E-3 states[2] = 4.0 states[3] = 0.0 constants[3] = 0.9 constants[4] = 1.0 states[4] = 0.0 states[5] = 50.0 constants[5] = 0.02 constants[6] = 0.3 states[6] = 0.0 states[7] = 25.0 states[8] = 0.0 states[9] = 4.0 states[10] = 0.0 constants[7] = 2.73E2 constants[8] = 3.437E-4 constants[9] = 1.253E-2 states[11] = 0.0 constants[10] = 0.025 states[12] = 0.0 states[13] = 50.0 constants[11] = 0.00005 states[14] = 0.0 states[15] = 0.0 constants[12] = 0.0002 constants[13] = 0.0037 states[16] = 0.0 constants[14] = 1800.0 constants[15] = 2700 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[2]*states[1]-constants[1]*(power(constants[0], 2.00000))*states[0] rates[1] = (constants[1]*(power(constants[0], 2.00000))*states[0]+constants[3]*states[3])-(constants[2]*states[1]+constants[4]*states[2]*states[1]) rates[3] = constants[4]*states[2]*states[1]-constants[3]*states[3] rates[7] = (constants[8]*states[8]+constants[3]*states[10])-(constants[7]*constants[0]*states[7]+constants[9]*states[9]*states[7]) rates[8] = (constants[7]*constants[0]*states[7]+constants[3]*states[11])-(constants[8]*states[8]+constants[10]*states[9]*states[8]) algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , constants[14]), 0.00000 , greater_equal(voi , constants[14]) & less(voi , constants[15]), 0.0110000 , True, float('nan')]) rates[2] = (constants[3]*states[3]+algebraic[0]*states[4]+constants[6]*states[4])-(constants[4]*states[2]*states[1]+constants[5]*states[2]*states[5]) rates[5] = (algebraic[0]*states[4]+constants[6]*states[4])-constants[5]*states[2]*states[5] rates[4] = constants[5]*states[2]*states[5]-(algebraic[0]*states[4]+constants[6]*states[4]) rates[6] = algebraic[0]*states[4] rates[9] = (constants[3]*states[11]+algebraic[0]*states[12]+constants[6]*states[12]+constants[3]*states[10])-(constants[9]*states[9]*states[7]+constants[10]*states[9]*states[8]+constants[11]*states[9]*states[13]) rates[13] = (algebraic[0]*states[12]+constants[6]*states[12]+algebraic[0]*states[14]+constants[6]*states[14]+algebraic[0]*states[15]+constants[6]*states[15])-(constants[11]*states[9]*states[13]+constants[12]*states[10]*states[13]+constants[13]*states[11]*states[13]) rates[12] = constants[11]*states[9]*states[13]-(algebraic[0]*states[12]+constants[6]*states[12]) rates[11] = (constants[10]*states[9]*states[8]+algebraic[0]*states[14]+constants[6]*states[14])-(constants[3]*states[11]+constants[13]*states[11]*states[13]) rates[14] = constants[13]*states[11]*states[13]-(algebraic[0]*states[14]+constants[6]*states[14]) rates[10] = (constants[9]*states[9]*states[7]+algebraic[0]*states[15]+constants[6]*states[15])-(constants[3]*states[10]+constants[12]*states[10]*states[13]) rates[15] = constants[12]*states[10]*states[13]-(algebraic[0]*states[15]+constants[6]*states[15]) rates[16] = algebraic[0]*states[12]+algebraic[0]*states[14]+algebraic[0]*states[15] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , constants[14]), 0.00000 , greater_equal(voi , constants[14]) & less(voi , constants[15]), 0.0110000 , True, float('nan')]) return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) 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)