# Size of variable arrays: sizeAlgebraic = 4 sizeStates = 5 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] = "P in component P (picomolar)" legend_constants[0] = "k1 in component model_parameters (second_order_rate_constant)" legend_constants[1] = "k1_ in component model_parameters (first_order_rate_constant)" legend_constants[2] = "k2 in component model_parameters (second_order_rate_constant)" legend_constants[3] = "k2_ in component model_parameters (first_order_rate_constant)" legend_constants[4] = "kcl in component model_parameters (first_order_rate_constant)" legend_algebraic[3] = "D in component model_parameters (flux)" legend_states[1] = "Ca in component Ca (picomolar)" legend_states[2] = "Ci in component Ci (picomolar)" legend_states[3] = "Ra in component Ra (picomolar)" legend_states[4] = "Ri in component Ri (picomolar)" legend_constants[5] = "k3 in component model_parameters (first_order_rate_constant)" legend_constants[6] = "k3_ in component model_parameters (first_order_rate_constant)" legend_constants[7] = "k4 in component model_parameters (first_order_rate_constant)" legend_constants[8] = "k4_ in component model_parameters (first_order_rate_constant)" legend_algebraic[1] = "rho in component rho (dimensionless)" legend_constants[9] = "De in component model_parameters (flux)" legend_algebraic[2] = "Dd in component model_parameters (flux)" legend_constants[10] = "dmax in component model_parameters (flux)" legend_constants[11] = "dmin in component model_parameters (flux)" legend_constants[12] = "tau_on in component model_parameters (hour)" legend_constants[13] = "tau_off in component model_parameters (hour)" legend_constants[15] = "cycle_length in component model_parameters (hour)" legend_constants[14] = "j in component model_parameters (dimensionless)" legend_algebraic[0] = "time_hour in component model_parameters (hour)" legend_rates[0] = "d/dt P in component P (picomolar)" legend_rates[3] = "d/dt Ra in component Ra (picomolar)" legend_rates[4] = "d/dt Ri in component Ri (picomolar)" legend_rates[1] = "d/dt Ca in component Ca (picomolar)" legend_rates[2] = "d/dt Ci in component Ci (picomolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 3 constants[0] = 1e-6 constants[1] = 1e-3 constants[2] = 1e-7 constants[3] = 1e-3 constants[4] = 5e-3 states[1] = 4e-4 states[2] = 0.05 states[3] = 16.9 states[4] = 1.7 constants[5] = 1e-3 constants[6] = 1e-4 constants[7] = 2e-3 constants[8] = 0.4 constants[9] = 0 constants[10] = 7.5 constants[11] = 0 constants[12] = 0.5 constants[13] = 0.5 constants[14] = 9 constants[15] = constants[12]+constants[13] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[3] = (constants[1]*states[1]+constants[5]*states[4])-(constants[0]*states[3]*states[0]+constants[6]*states[3]) rates[4] = (constants[3]*states[2]+constants[6]*states[3])-(constants[2]*states[4]*states[0]+constants[5]*states[4]) rates[1] = (constants[0]*states[3]*states[0]+constants[7]*states[2])-(constants[1]*states[1]+constants[8]*states[1]) rates[2] = (constants[2]*states[4]*states[0]+constants[8]*states[1])-(constants[3]*states[2]+constants[7]*states[2]) algebraic[0] = (voi*1.00000)/3600.00 algebraic[2] = custom_piecewise([greater_equal(algebraic[0]/constants[15] , constants[14]), constants[11] , greater_equal(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , 0.00000) & less(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , constants[12]), constants[10] , greater_equal(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , constants[12]) & less(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , constants[15]), constants[11] , True, float('nan')]) algebraic[3] = constants[9]+algebraic[2] rates[0] = (constants[1]*states[1]+constants[3]*states[2]+algebraic[3])-(constants[0]*states[3]*states[0]+constants[2]*states[4]*states[0]+constants[4]*states[0]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (voi*1.00000)/3600.00 algebraic[2] = custom_piecewise([greater_equal(algebraic[0]/constants[15] , constants[14]), constants[11] , greater_equal(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , 0.00000) & less(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , constants[12]), constants[10] , greater_equal(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , constants[12]) & less(algebraic[0]-floor(algebraic[0]/constants[15])*constants[15] , constants[15]), constants[11] , True, float('nan')]) algebraic[3] = constants[9]+algebraic[2] algebraic[1] = (states[3]+states[1])/(states[3]+states[1]+states[4]+states[2]) 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)