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plot_multiple_phase_planes_Umin_Cfmax_AND.py
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plot_multiple_phase_planes_Umin_Cfmax_AND.py
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"""
This script generates plots comparing multiple phase planes and timecourses
for specified parameterization of the U-switch, Cf-switch and AND-switch models. The data files
(in .npy format) should be supplied as list of stings containing the path to the data files.
Data files of the correct format are generated from either the plat_* scripts or the gridsearch_*
scripts that calculate Pareto fronts. Additionally, the user should supply the indices of the
points on the Pareto front for which the phase planes and trajectories will be calculated.
Written by Wylie Stroberg in 2018
"""
import numpy as np
import matplotlib as mpl
mpl.use('TkAgg')
mpl.rc('axes', linewidth=2)
import matplotlib.pyplot as plt
import matplotlib.colors as mplcolors
from pydelay import dde23
import delayed_nf_upr_piecewise_u_switch as upw
import delayed_nf_upr_piecewise_cf_switch as cpw
import delayed_nf_upr_piecewise_and_switch as apw
import plat_Uswitch as platU
import plat_Cfswitch as platC
import plat_ANDswitch as platA
from gridsearch_compare_switches import calc_costsU
#----------------------------------------------------------------------
def g_u(x,m):
''' Input: x - u-umin
m - slope
Returns: normalized response between 0 and 1.
'''
if x <= 0.0:
return 0.0
elif x >= 1.0/m:
return 1.0
else:
return x*m
#----------------------------------------------------------------------
def g_c(x,m):
''' Input: x - cf-cmax
m - slope
Returns: normalized response between 0 and 1.
'''
if x>=0.0:
return 0.0
elif x <= -1.0/m:
return 1.0
else:
return -x*m
#----------------------------------------------------------------------
def truncate_colormap(cmap, minval=0.0, maxval=1.0, n=100):
new_cmap = mplcolors.LinearSegmentedColormap.from_list(
'trunc({n},{a:.2f},{b:.2f})'.format(n=cmap.name, a=minval, b=maxval),
cmap(np.linspace(minval, maxval, n)))
return new_cmap
#----------------------------------------------------------------------
#----------------------------------------------------------------------
if __name__=="__main__":
# Specifiy paths for input data files
param_tag = "_1.0_0.5_100000"
pareto_front_data_file = ['./Data/U_switch/plat/pareto_front'+param_tag+'_NSGAII_dtmax0.003.npy',
'./Data/Cf_switch/plat/fixedGain/pareto_front'+param_tag+'_NSGAII_dtmax0.003.npy',
'./Data/AND_switch/plat/fixedGain/pareto_front'+param_tag+'_NSGAII_dtmax0.003_relaxedBounds.npy']
prob_dims = [(2,2),(2,2),(4,2)] # list of (Nvars,Nobjs) for each model
Pareto_points = []
Pareto_costs = []
for i,pf in enumerate(pareto_front_data_file):
pareto_data = np.load(pf)
nv = prob_dims[i][0]
Pareto_points.append(pareto_data[:,0:nv])
Pareto_costs.append(pareto_data[:,nv:])
print("Parameters at minimum mu_U:")
print(pareto_data[np.argmin(pareto_data[:,nv+1]),:])
plot_indices = [73,77,26] # Points for plot 1 (fig 4b)
#plot_indices = [76,23,36] # Points for plot 2 (fig 4c)
free_params = [pp[plot_indices[i],:] for i,pp in enumerate(Pareto_points)]
cost_vals = [pp[plot_indices[i],:] for i,pp in enumerate(Pareto_costs)]
umin = free_params[0][0]
mu = free_params[0][1]
cmax = free_params[1][0]
mc = free_params[1][1]
uminAnd = free_params[2][0]
muAnd = free_params[2][1]
cmaxAnd = free_params[2][2]
mcAnd = free_params[2][3]
#----- Set up model for trajectory simulations -----#
# Physical Parameters
KCAT = 8.15e-4
KM = 1.1e4
VU = 200.
VC = 60.
B = 1.85e-4
G = 5.0
TAU_UPR = 15.*60.
kcat = KCAT+B
# Non-dimensional parameters
nu = VU/VC
alpha = kcat/B
beta = KM*B/VC
tau_upr = TAU_UPR*B
# Pulse Parameters
split_tag = param_tag.split('_')
if split_tag[1]=='totaluin':
d = float(split_tag[4])
tau_p = float(split_tag[6])
else:
d = float(param_tag.split('_')[1]) #1.
tau_p = float(param_tag.split('_')[2]) #1000.0*60.
teq = 30.*tau_upr
# Initialize dde solvers
params_u = {
'alpha' : alpha,
'beta' : beta,
'nu' : nu,
'G' : G,
'umin' : umin,
'm' : mu,
'tau_upr' : tau_upr,
'd' : d,
'tau_p' : tau_p,
'teq' : teq
}
params_c = {
'alpha' : alpha,
'beta' : beta,
'nu' : nu,
'G' : G,
'cmax' : cmax,
'm' : mc,
'tau_upr' : tau_upr,
'd' : d,
'tau_p' : tau_p,
'teq' : teq
}
params_a = {
'alpha' : alpha,
'beta' : beta,
'nu' : nu,
'G' : G,
'umin' : uminAnd,
'mu' : muAnd,
'cmax' : cmaxAnd,
'mc' : mcAnd,
'tau_upr' : tau_upr,
'd' : d,
'tau_p' : tau_p,
'teq' : teq
}
params = [params_u,params_c,params_a]
#tfinal = 2000.*60 + teq
tfinal = teq + tau_p + 30.*tau_upr
dde_u = upw.initialize_dde_nf_upr(params=params_u,tfinal=tfinal,dtmax=0.001)
dde_c = cpw.initialize_dde_nf_upr(params=params_c,tfinal=tfinal,dtmax=0.001)
dde_a = apw.initialize_dde_nf_upr(params=params_a,tfinal=tfinal,dtmax=0.001)
sols = [upw.run_dde(dde_u,params_u),cpw.run_dde(dde_c,params_c),apw.run_dde(dde_a,params_a)]
c_minmax = (min([np.min(soli['c']) for soli in sols]),max([np.max(soli['c']) for soli in sols]))
u_minmax = (min([np.min(soli['u']) for soli in sols]),max([np.max(soli['u']) for soli in sols]))
costs = [platU.objective_function(dde_u,params_u),platC.objective_function(dde_c,params_c),platA.objective_function(dde_a,params_a)]
print(costs)
USS,CSS = platU.calc_steady_state(params_u)
CFSS = CSS*(1.-USS/(beta+USS))
print("********************************************************")
print("Maximal unfolded protein levels:")
print("U-switch: {}".format(np.max(sols[0]['u'])))
print("Cf-switch: {}".format(np.max(sols[1]['u'])))
print("Steady-state concentrations:")
print("Uss = {}, Css = {}, CFss = {}".format(USS,CSS,CFSS))
print("********************************************************")
#------ Calculate threshold values for activation --------#
c_range = np.linspace(c_minmax[0],c_minmax[1],10)
act_thresh_u = params_u['umin']*np.ones(c_range.shape)
act_thresh_c = params_c['beta']*(c_range/params_c['cmax'] - 1.)
act_thresh_uAND = params_a['umin']*np.ones(c_range.shape)
act_thresh_cAND = params_a['beta']*(c_range/params_a['cmax'] - 1.)
act_thresh = [act_thresh_u,act_thresh_c,[act_thresh_uAND,act_thresh_cAND]]
#----- Plot switch function and dynamic response -----#
fig,ax = plt.subplots(1,1,figsize=(4,4))
fig_traj,ax_traj = plt.subplots(2,1,figsize=(5,4))
colors = ['blue','red','green']
labels = ['$U$-Switch','$C_{F}$-Switch','AND-Switch']
plot_thresholds = [True,True,True]
for i,soli in enumerate(sols):
ax.plot(soli['c'],soli['u'],'-',color=colors[i],linewidth=2,label=labels[i])
if plot_thresholds[i]:
if isinstance(act_thresh[i],(list,)):
[ax.plot(c_range,threshj,'--',color=colors[i]) for threshj in act_thresh[i]]
else:
ax.plot(c_range,act_thresh[i],'--',color=colors[i])
start_ind = int(len(soli['t'])*0.1)
end_ind = int(len(soli['t'])*0.9)
shifted_time = soli['t'] - soli['t'][start_ind]
ax_traj[0].plot(shifted_time[start_ind:end_ind],soli['u'][start_ind:end_ind],color=colors[i])
ax_traj[1].plot(shifted_time[start_ind:end_ind],soli['c'][start_ind:end_ind],color=colors[i])
# Set axis properties for phase plane
ax.set_xlabel(r'$c_{T}$',fontsize=18)
ax.set_ylabel(r'$u$',fontsize=18)
ax.legend()
ax.locator_params(axis='both', nbins=5)
pad = 0.05
ax.set_xlim((c_minmax[0]*(1.-pad),c_minmax[1]*(1.+pad)))
ax.set_ylim((u_minmax[0]*(1.-pad),u_minmax[1]*(1.+pad)))
fig.tight_layout()
# Plot activation levels as heat map on phase-plane trajectories axis
plot_activation_levels = True
if plot_activation_levels:
ct = np.linspace(ax.get_xlim()[0],ax.get_xlim()[1],40)
u = np.linspace(ax.get_ylim()[0],ax.get_ylim()[1],40)
C,U = np.meshgrid(ct,u)
positions = np.vstack([C.ravel(),U.ravel()])
GU = []
GC = []
GA = []
for i in range(positions.shape[1]):
c = positions[0,i]
u = positions[1,i]
GU.append(g_u(u-params_u['umin'],params_u['m']))
cf = c*(1.0 - u/(params_c['beta']+u))
GC.append(g_c(cf-params_c['cmax'],params_c['m']))
GA.append(g_u(u-params_a['umin'],params_a['mu'])*g_c(cf-params_a['cmax'],params_a['mc']))
GU = np.reshape(np.array(GU),U.shape)
GC = np.reshape(np.array(GC),U.shape)
GA = np.reshape(np.array(GA),U.shape)
fig1,ax1 = plt.subplots(1,3,figsize=(10,4))
zmin = 0.
zmax = np.max([np.max(GU),np.max(GC),np.max(GA)])
cmap = plt.get_cmap('viridis')
cmap = truncate_colormap(cmap,0.3,1.0)
c0 = ax1[0].pcolormesh(C,U,GU,vmin=zmin,vmax=zmax,shading='gouraud',cmap=cmap)
ax1[1].pcolormesh(C,U,GC,vmin=zmin,vmax=zmax,shading='gouraud',cmap=cmap)
ax1[2].pcolormesh(C,U,GA,vmin=zmin,vmax=zmax,shading='gouraud',cmap=cmap)
ax1[0].set_ylabel(r'$u$',fontsize=18)
ax1[0].set_xlabel(r'$c_{T}$',fontsize=18)
ax1[1].set_xlabel(r'$c_{T}$',fontsize=18)
ax1[2].set_xlabel(r'$c_{T}$',fontsize=18)
ax1[1].set_yticks([])
ax1[2].set_yticks([])
for axi,soli in zip(ax1,sols):
axi.plot(soli['c'],soli['u'],'-',color='black',linewidth=2)
fig1.subplots_adjust(bottom=0.15, top=0.9, left=0.1, right=0.8,
wspace=0.1, hspace=0.02)
cb_ax = fig1.add_axes([0.83, 0.15, 0.02, 0.75])
cbar = fig1.colorbar(c0, cax=cb_ax)
cbar.ax.set_title(r'$G/G_{0}$')
fig1.savefig('./Figures/PhasePlane_wActLevel_U_Cf_AND_1'+param_tag+'.pdf',edgecolor='black')
#fig1.savefig('./Figures/PhasePlane_wActLevel_U_Cf_AND_2'+param_tag+'.pdf',edgecolor='black')
# Set axis properties for trajectories
ax_traj[1].set_xlabel(r'Time',fontsize=18)
ax_traj[0].set_ylabel(r'$u$',fontsize=18)
ax_traj[1].set_ylabel(r'$c_{T}$',fontsize=18)
ax_traj[0].tick_params(
axis='x', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom=False, # ticks along the bottom edge are off
top=False, # ticks along the top edge are off
labelbottom=False) # labels along the bottom edge are off
ax_traj[0].locator_params(axis='both',nbins=5)
ax_traj[1].locator_params(axis='both',nbins=5)
fig_traj.subplots_adjust(hspace=0.1)
fig_traj.tight_layout()
#fig.savefig('./Figures/PhasePlaneCompare_U_Cf_AND_2'+param_tag+'.eps',edgecolor='black')
#fig_traj.savefig('./Figures/TrajectoryCompare_U_Cf_AND_2'+param_tag+'.eps',edgecolor='black')
plt.show()