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auxilary_functions.py
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auxilary_functions.py
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#-------------------------------------------------------------------------------------------------------------------#
# Auxilary functions.
# Writen by Marcelo Boareto: marceloboareto@gmail.com
# Last update: 01/2017
#-------------------------------------------------------------------------------------------------------------------#
from PyDSTool import *
from PyDSTool.Toolbox import phaseplane as pp
from matplotlib import cm
import numpy as np
import random as rand
import matplotlib.pyplot as plt
import random as rand
import copy as cp
from scipy.ndimage import measurements
import matplotlib.colors as cl
import math
#----------------------------------------------------------------------------------------#
# parameters used in the simulations
def parameters(onecell=False):
dic = {'km' : 5.0e-1
,'kP' : 1.0e+2
#----------EMT circuit----------
#-- see table SI4a (L>Y) --
,'gu200' : 2.1e+3, 'gZ': 1.1e+1, 'Z0u200': 2.2e+5, 'Z0Z': 2.5e+4
# -- see table SI4b --
,'nZu200': 3.0e+0, 'nZZ': 2.0e+0, 'nu200' : 6.0e+0, 'nSu200': 2.0e+0, 'nSZ': 2.0e+0
,'lZu200': 1.0e-1, 'lZZ': 7.5e+0, 'lSu200': 1.0e-1, 'lSZ' : 1.0e+1
,'ku200' : 5.0e-2, 'kZ' : 1.0e-1
,'S0u200': 1.8e+5, 'S0Z': 1.8e+5
,'u0200' : 1.0e+4
# -- see table SI4c --
,'nSu34' : 1.0e+0, 'nSS': 1.0e+0, 'nu34' : 2.0e+0, 'nI' : 2.0e+0
,'lSu34' : 1.0e-1, 'lSS': 1.0e-1, 'lZu34': 2.0e-1, 'lIS': 6.5e+0
,'ku34' : 5.0e-2, 'kS' : 1.25e-1
,'gu34' : 1.35e+3,'gS' : 9.0e+1
,'S0u34' : 3.0e+5, 'S0S': 2.0e+5
,'Z0u34' : 6.0e+5
,'u034' : 1.0e+4
,'I0S' : 3.0e+2
#-------------------------------------------
#----------Notch Signaling circuit----------
,'k' : 1.0e-1, 'kI' : 5.0e-1
,'kc' : 1.0e-4, 'kt' : 1.0e-5
,'p' : 2.0e+0, 'pf' : 1.0
,'gN' : 0.8e+1, 'gD' : 7.0e+1, 'gJ' : 2.0e+1
,'I0' : 1.0e+2
,'Nt' : 0.0e+0, 'Dt' : 0.0e+0, 'Jt' : 0.0e+0
,'Nn' : 0.0e+0, 'Dn' : 0.0e+0, 'Jn' : 0.0e+0
,'ln' : 7.0e+0, 'ld' : 0.0e+0, 'lj' : 2.0e+0
,'ldf': 3.0, 'ljf': 0.3
,'It' : 0.0
}
# ---------see table SI1---------
if onecell:
dic.update({'l0': 1.0e+0,'l1': 6.0e-1,'l2': 3.0e-1
,'l3': 1.0e-1,'l4': 5.0e-2,'l5': 5.0e-2,'l6': 5.0e-2
,'gm0': 0.0e+0,'gm1': 4.0e-2,'gm2': 2.0e-1
,'gm3': 1.0e+0,'gm4': 1.0e+0,'gm5': 1.0e+0,'gm6': 1.0e+0
,'gu0': 0.0e+0,'gu1': 1*5.0e-3,'gu2': 2*5.0e-2,'gu3': 3*5.0e-1
,'gu4': 4*5.0e-1,'gu5': 5*5.0e-1,'gu6': 6*5.0e-1
})
else:
dic.update({'l' : [1.0e+0, 6.0e-1, 3.0e-1, 1.0e-1, 5.0e-2, 5.0e-2, 5.0e-2]
,'gm': [0.0e+0, 4.0e-2, 2.0e-1, 1.0e+0, 1.0e+0, 1.0e+0, 1.0e+0]
,'gu': [0.0e+0, 1*5.0e-3, 2*5.0e-2, 3*5.0e-1, 4*5.0e-1, 5*5.0e-1, 6*5.0e-1]
,'HS' : HS, 'Pl' : Pl, 'Py' : Py
})
return dic
#----------------------------------------------------------------------------------------#
# equations used in the simulations
def equations(onecell=False):
if onecell:
return {'W' : 'gu200*HS(Z,Z0u200,nZu200,lZu200)*HS(S,S0u200,nSu200,lSu200) - gZ*HS(Z,Z0Z,nZZ,lZZ)*HS(S,S0Z,nSZ,lSZ)*Py(W,km,6) - gJ*HS(I,I0,p,lj)*Py(W,km,5) - ku200*W'
,'Y' : 'gu34*HS(S,S0u34,nSu34,lSu34)*HS(Z,Z0u34,nu34,lZu34) - gS*HS(S,S0S,nSS,lSS)*HS(I,I0S,nI,lIS)*HS(It,I0S,nI,lIS)*Py(Y,km,2) - gN*HS(I,I0,p,ln)*Py(Y,km,2) - gD*HS(I,I0,p,ld)*Py(Y,km,3) - ku34*Y'
,'Z' : 'kP*gZ*HS(Z,Z0Z,nZZ,lZZ)*HS(S,S0Z,nSZ,lSZ)*Pl(W,km,6) - kZ*Z'
,'S' : 'kP*gS*HS(S,S0S,nSS,lSS)*HS(I,I0S,nI ,lIS)*HS(It,I0S,nI,lIS)*Pl(Y,km,2) - kS*S'
,'N' : 'kP*gN*HS(I,I0,p,ln)*Pl(Y,km,2) - N*( (kc*D + kt*Dt)*HS(I,I0,pf,ldf) + (kc*J + kt*Jt)*HS(I,I0,pf,ljf) ) - k*N'
,'D' : 'kP*gD*HS(I,I0,p,ld)*Pl(Y,km,3) - D*( kc*N*HS(I,I0,pf,ldf) + kt*Nt ) - k*D'
,'J' : 'kP*gJ*HS(I,I0,p,lj)*Pl(W,km,5) - J*( kc*N*HS(I,I0,pf,ljf) + kt*Nt ) - k*J'
,'I' : 'kt*N*( Dt*HS(I,I0,pf,ldf) + Jt*HS(I,I0,pf,ljf) ) - kI*I'
}
else:
return {'W' : 'gu200*HS(Z,Z0u200,nZu200,lZu200)*HS(S,S0u200,nSu200,lSu200) - gZ*HS(Z,Z0Z,nZZ,lZZ)*HS(S,S0Z,nSZ,lSZ)*Py(W,6,km,u0200) - gJ*HS(I,I0,p,lj)*Py(W,5,km,u0200) - ku200*W'
,'Y' : 'gu34*HS(S,S0u34,nSu34,lSu34)*HS(Z,Z0u34,nu34,lZu34) - gS*HS(S,S0S,nSS,lSS)*HS(I,I0S,nI,lIS)*HS(It,I0S,nI,lIS)*Py(Y,2,km,u034) - gN*HS(I,I0,p,ln)*Py(Y,2,km,u034) - gD*HS(I,I0,p,ld)*Py(Y,3,km,u034) - ku34*Y'
,'Z' : 'kP*gZ*HS(Z,Z0Z,nZZ,lZZ)*HS(S,S0Z,nSZ,lSZ)*Pl(W,6,km,u0200) - kZ*Z'
,'S' : 'kP*gS*HS(S,S0S,nSS,lSS)*HS(I,I0S,nI ,lIS)*HS(It,I0S,nI,lIS)*Pl(Y,2,km,u034) - kS*S'
,'N' : 'kP*gN*HS(I,I0,p,ln)*Pl(Y,2,km,u034) - N*( (kc*D + kt*(Dn + Dt))*HS(I,I0,pf,ldf) + (kc*J + kt*(Jn + Jt))*HS(I,I0,pf,ljf) ) - k*N'
,'D' : 'kP*gD*HS(I,I0,p,ld)*Pl(Y,3,km,u034) - D*( kc*N*HS(I,I0,pf,ldf) + kt*(Nn + Nt) ) - k*D'
,'J' : 'kP*gJ*HS(I,I0,p,lj)*Pl(W,5,km,u0200) - J*( kc*N*HS(I,I0,pf,ljf) + kt*(Nn + Nt) ) - k*J'
,'I' : 'kt*N*( (Dn + Dt)*HS(I,I0,pf,ldf) + (Jn + Jt)*HS(I,I0,pf,ljf) ) - kI*I'
}
#----------------------------------------------------------------------------------------#
# Auxilary functions used in the tisse level simulations
def HS(X,X0,nX,lamb):
return lamb + (1.0-lamb)/(1.0 + (X/X0)**nX)
def M(X,X0,i,n):
return ((X/X0)**i)/((1. + (X/X0))**n)
def C(i,n):
return gamma(n+1)/(gamma(n-i+1)*gamma(i+1))
def Py(X, n, k, u0, gu=[0.0e+0, 1*5.0e-3, 2*5.0e-2, 3*5.0e-1, 4*5.0e-1, 5*5.0e-1, 6*5.0e-1],
gm=[0.0e+0, 4.0e-2, 2.0e-1, 1.0e+0, 1.0e+0, 1.0e+0, 1.0e+0]):
v1 = 0
v2 = 0
# for i in range(n):
# corrected at 01/2017
for i in range(n+1):
v1 += gu[i]*C(i,n)*M(X,u0,i,n)
v2 += gm[i]*C(i,n)*M(X,u0,i,n)
return v1/(v2+k)
def Pl(X, n, k, u0, l=[1.0e+0, 6.0e-1, 3.0e-1, 1.0e-1, 5.0e-2, 5.0e-2, 5.0e-2],
gm=[0.0e+0, 4.0e-2, 2.0e-1, 1.0e+0, 1.0e+0, 1.0e+0, 1.0e+0]):
v1 = 0
v2 = 0
# for i in range(n):
# corrected at 01/2017
for i in range(n+1):
v1 += l[i]*C(i,n)*M(X,u0,i,n)
v2 += gm[i]*C(i,n)*M(X,u0,i,n)
return v1/(v2+k)
#----------------------------------------------------------------------------------------#
# auxilary functions used in the 1 cell simulations
def functions():
return {'HS': (['X','X0','nX','lamb'], 'lamb + (1.0-lamb)/(1.0 + (X/X0)**nX)')
,'M' : (['X','X0','i','n'], '((X/X0)**i)/((1. + (X/X0))**n)' )
,'C' : (['i','n'],'special_gamma(n+1)/(special_gamma(n-i+1)*special_gamma(i+1))' )
,'Py': (['X','kd','n'],'sum(i, 0, 6, if([i]>n, 0, gu[i]*C([i],n)*M(X,u0200,[i],n)))/(sum(i, 0, 6, if([i]>n, 0, gm[i]*C([i],n)*M(X,u0200,[i],n))) + kd)')
,'Pl': (['X','kd','n'],'sum(i, 0, 6, if([i]>n, 0, l[i]*C([i],n)*M(X,u0200,[i],n)))/(sum(i, 0, 6, if([i]>n, 0, gm[i]*C([i],n)*M(X,u0200,[i],n))) + kd)')
}
# variable limits
def vlim(c=None):
if c=='E':
return {'N': [0.0e+4, 3.0e+4], 'D': [0.0e+4, 0.2e+4], 'J': [0.0e+4, 1.0e+4], 'I': [0.0e+4, 0.002e+4]
,'W': [1.5e+4, 3.5e+4], 'Z': [0.0e+5, 0.1e+4], 'Y': [1.6e+4, 2.2e+4], 'S': [0.5e+5, 2.0e+5]
}
elif c=='E/M':
return {'N': [3.0e+4, 4.0e+4], 'D': [0.0e+4, 0.1e+4], 'J': [0.1e+3, 1.0e+3], 'I': [0.5e+3, 1.5e+3]
,'W': [0.5e+4, 1.5e+4], 'Z': [1.0e+4, 1.5e+5], 'Y': [1.5e+4, 1.7e+4], 'S': [1.7e+5, 2.1e+5]
}
elif c=='M':
return {'N': [2.0e+4, 3.0e+4], 'D': [0.0e+4, 0.1e+4], 'J': [2.0e+3, 5.0e+3], 'I': [0.4e+3, 1.6e+3]
,'W': [0.0e+4, 0.5e+4], 'Z': [4.0e+5, 8.5e+5], 'Y': [0.6e+4, 1.5e+4], 'S': [2.0e+5, 3.0e+5]
}
else:
return {'N': [0.0e+4, 3.0e+4], 'D': [0.0e+4, 0.2e+4], 'J': [0.0e+4, 1.0e+4], 'I': [0.0e+4, 0.2e+4]
,'W': [0.0e+4, 4.0e+4], 'Z': [0.0e+5, 9.0e+5], 'Y': [0.6e+4, 2.4e+4], 'S': [5.0e+4, 3.0e+5]
}
#----------------------------------------------------------------------------------------#
# Euler method for solving EDO equations
def euler_traj(eqs, p, pts=None, vlim=None, hexagonal=True,
nsignal_dict={'N': ['D', 'J'], 'I': ['D', 'J'], 'D': ['N'], 'J': ['N']}):
if pts==None:
if vlim==None:
print 'ERROR: Give me a starting point (pts) or the limits for a random start point (vlim)'
return 0
pts = {}
for j in eqs.keys():
pts[j] = np.random.uniform(vlim[j][0],vlim[j][1],(p['n'],p['n']))
pts_new = {}
for t in range(int(p['t']/p['dt'])):
for key in eqs.keys():
if key in nsignal_dict.keys():
for k in nsignal_dict[key]:
p[k+'n'] = nsignal_sum(p, pts, k, key, hexagonal=hexagonal)
pts_new[key] = pts[key] + p['dt']*eval(eqs[key], p, pts)
pts = pts_new
return pts
#----------------------------------------------------------------------------------------#
# Sum the amount of proteins of the neighboring cells
def nsignal_sum(p, pts, k, key, hexagonal=True):
n = p['n']
fng_dic={'D': 'HS(I,I0,pf,ldf)'
,'J': 'HS(I,I0,pf,ljf)'
}
fng = 1.0
if k=='N':
fng = eval(fng_dic[key],p,pts)
X = periodic_bcondition(pts[k]*fng, n)
if hexagonal:
return (1.0/6.0)*( X[0:n,1:(n+1)] + X[1:(n+1),0:n] + X[2:(n+2),1:(n+1)] + X[1:(n+1),2:(n+2)]
+ X[0:n,2:(n+2)] + X[2:(n+2),2:(n+2)] )
return (1.0/4.0)*( X[0:n,1:(n+1)] + X[1:(n+1),0:n] + X[2:(n+2),1:(n+1)] + X[1:(n+1),2:(n+2)] )
#----------------------------------------------------------------------------------------#
# Expand the matrix from nxn to (n+2)x(n+2) where the extra rows and columns are chosen by
# a periodic boundary condition
def periodic_bcondition(f, n):
out = np.zeros((n+2,n+2))
out[1:(n+1),1:(n+1)] = f
out[0 ,1:(n+1)] = out[n ,1:(n+1)]
out[n+1 ,1:(n+1)] = out[1 ,1:(n+1)]
out[1:(n+1),0 ] = out[1:(n+1),n ]
out[1:(n+1),n+1 ] = out[1:(n+1),1 ]
out[0 ,0 ] = out[n ,n ]
out[0 ,n+1 ] = out[n ,1 ]
out[n+1 ,n+1 ] = out[1 ,1 ]
out[n+1 ,0 ] = out[1 ,n ]
return out
#----------------------------------------------------------------------------------------#
# Plot a hexagonal lattice from a matrix M
def plot_hex(M, clim=None, cmap=None, clabel=None, fig_name=None, title=None, tr=None, c=None,
cbar=True, dpi=200):
m = cp.copy(M)
plt.rcParams.update({'font.size': 18})
n = np.shape(m)[0]
x = np.zeros((n,n))
y = np.zeros((n,n))
for i in range(n):
y[i,:] = np.arange(1,n+1,1)
for i in range(n):
if i % 2 != 0:
x[:,i] = np.arange(1,n+1,1)
else:
x[:,i] = np.arange(1,n+1,1) + 0.5
fig, ax = plt.subplots(figsize=(11.6,10.0))
if cmap==None:
cmap = plt.cm.Spectral_r
if tr==None:
im = ax.scatter(x, y, c=m, s=700000/(n*n), cmap=cmap, linewidths=1, marker=(6, 0, 0))
else:
t = {}
for i in np.arange(0,len(tr),1):
t[i] = m<tr[i]
m[m>np.max(tr)] = c[len(tr)]
for i in np.arange(len(tr),0,-1):
m[t[i-1]] = c[i-1]
im = ax.scatter(x, y, c=m, s=700000/(n*n), cmap=cmap,linewidths=1, marker=(6, 0, 0))
plt.xlim([1.0,n])
plt.ylim([1.0,n])
if title!=None:
plt.title(title)
if clim!=None:
im.set_clim(clim)
if cbar:
cax = fig.add_axes([0.91, 0.2, 0.04, 0.65])
cbar = fig.colorbar(im, cax, orientation='vertical')
if clabel!=None:
cbar.set_label(clabel)
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=dpi)
plt.show()
def plot_relativeLevel(eqs, p, v, r_v, key, pts_i=None, vlim=None, nsignal_dict=None, fig_name=None, clim=None,
show_snapshot=False, c=['b','r','g','m','k']):
fs = {}
for k in key:
fs[k] = np.zeros(len(r_v))
for i in range(len(r_v)):
if v=='fng':
p['ldf'] = 1.0 + 4.0*r_v[i]
p['ljf'] = 1.0 - 0.9*r_v[i]
elif v=='t':
if i==0:
p[v] = r_v[i]
else:
p[v] = r_v[i] - r_v[i-1]
else:
p[v] = r_v[i]
pts = euler_traj(eqs, p, pts=pts_i, vlim=vlim, nsignal_dict=nsignal_dict)
if v=='t':
pts_i = pts
if show_snapshot:
plot_hex(pts[key[0]], clim=clim,clabel=key)
for k in key:
fs[k][i] = np.mean(pts[k])
plt.figure(figsize=(9,6))
for k in range(len(key)):
plt.plot(r_v, np.log2(fs[key[k]]/fs[key[k]][0]), 'go-', lw=2, ms=16, label=key[k], color=c[k])
plt.xlabel(v)
plt.ylabel('Relative level of proteins')
plt.legend()
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
plt.show()
def fractionStates(X, tr):
N = np.float(np.size(X))
if len(tr)==1:
return np.sum(X<tr[0])/N, np.sum(X>tr[0])/N
elif len(tr)==2:
return [np.sum(X<tr[0])/N, np.sum((X>tr[0]) & (X<tr[1]))/N, np.sum(X>tr[1])/N]
def plot_fractionStates(eqs, p, v, r_v, key, tr, pts_i=None, vlim=None, l=['M','E/M','E'], c=['#e8656c','#e4fc36','#00ff9c'],
show_snapshot=False, nsignal_dict={'N': ['D', 'J'], 'I': ['D', 'J'], 'D': ['N'], 'J': ['N']}, fig_name=None):
fs = []
for i in range(len(r_v)):
if v=='fng':
p['ldf'] = 1.0 + 4.0*r_v[i]
p['ljf'] = 1.0 - 0.9*r_v[i]
elif v=='t':
if i==0:
p[v] = r_v[i]
else:
p[v] = r_v[i] - r_v[i-1]
else:
p[v] = r_v[i]
pts = euler_traj(eqs, p, pts=pts_i, vlim=vlim, nsignal_dict=nsignal_dict)
if v=='t':
pts_i = pts
if show_snapshot:
plot_hex(pts[key], clim=clim, clabel=key)
fs += [fractionStates(pts[key],tr[key])]
fs = np.array(fs)
fig = plt.figure(figsize=(9,6))
colors=['#e8656c','#e4fc36','#00ff9c']
for i in range(len(tr[key])+1):
plt.plot(r_v, fs[:,i], ['o-','>-','s-'][i], c=c[i], lw=2, ms=16, label=l[i])
plt.xlabel(v)
plt.ylabel('Fraction states')
plt.legend()
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
plt.show()
#----------------------------------------------------------------------------------------#
#----------------------------------------------------------------------------------------#
# PyDSTool auxilary functions
#----------------------------------------------------------------------------------------#
def eliminate_redundants(fp, eps=10):
for i in range(len(fp)):
for k, v in fp[i].items():
v = round(v,eps)
fp[i][k] = v
seen = set()
new_l = []
for d in fp:
t = tuple(d.items())
if t not in seen:
seen.add(t)
new_l.append(d)
return new_l
#-------------------------------------------------------------------------------------------------------------------#
def stability(FPs, ODE, eps=0.1):
out = []
for i in range(len(FPs)):
X = {}
stable = True
for k in FPs[0].keys():
X[k] = FPs[i][k]*(1 + eps*rand.sample(list([-1,1]),1)[0])
ODE.set(ics = X)
traj = ODE.compute('traj')
X = traj.sample()[-1]
for k in FPs[0].keys():
if np.abs(X[k]-FPs[i][k]) > eps*FPs[i][k]:
stable = False
out += ['S'] if stable else ['I']
return out
#-------------------------------------------------------------------------------------------------------------------#
def PyCont_args(nmodel, freepar, maxnumpoints, maxstep=1e+1, minstep=1e-1, stopAt=['B'],
step=1e-0, LocBifPoints=['BP','LP','B'], saveeigen=False, Type='EP-C'):
PCargs = PyDSTool.args(name=nmodel, type=Type) # 'EP-C' stands for Equilibrium Point Curve.
PCargs.freepars = [freepar] # control parameter
PCargs.MaxNumPoints = maxnumpoints # The following 3 parameters are set after trial-and-error
PCargs.MaxStepSize = maxstep
PCargs.MinStepSize = minstep
PCargs.StepSize = step
PCargs.StopAtPoints = stopAt
PCargs.LocBifPoints = LocBifPoints # detect limit points / saddle-node bifurcations
PCargs.SaveEigen = saveeigen # to tell unstable from stable branches
return PCargs
#-------------------------------------------------------------------------------------------------------------------#
# Plot functions
#-------------------------------------------------------------------------------------------------------------------#
def hist_clustersize(dic, keys, tr, clim, norm=True, bars=False, fig_name=None, higher=True):
plt.figure(figsize=(7,5), dpi=200)
for k in keys:
h = np.zeros((len(dic),clim[1]-clim[0]+1))
for j in range(len(dic)):
x = np.array(dic[j][k])
if higher:
x[x<tr[k][0]] = 0.0
x[x>tr[k][0]] = 1.0
else:
x[x<tr[k][0]] = 1.0
x[x>tr[k][0]] = 0.0
xs, n_clusters = measurements.label(x)
print n_clusters, 'clusters found'
a = measurements.sum(x, xs, index=arange(xs.max() + 1))
ma = np.max(a)
h[j,:] = np.asarray([np.sum(a==i) for i in np.arange(clim[0],clim[1]+1,1)])
hm = np.mean(h,axis=0)
if norm:
hm = hm/np.sum(hm)
plt.ylim([0.0,1.0])
if bars:
plt.bar(np.arange(clim[0]-0.4, clim[1], 1.0 ),hm)
else:
plt.plot(np.arange(clim[0], clim[1]+1, 1.0 ),hm, 'ob-', ms=10)
plt.xlim([clim[0]-0.5,clim[1]+0.5])
plt.xticks(range(clim[0], clim[1]+1,1))
plt.xlabel('Cluster size')
plt.ylabel('Number of clusters')
#plt.title(k)
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
#-------------------------------------------------------------------------------------------------------------------#
def plot_fates(dic, keys, tr, colors=['#e8656c','#e4fc36','#00ff9c'], vlim=[0.0, 1.0], ncomb=1, fontsize=16, fig_name=None):
plt.figure(figsize=(8,7), dpi=200)
cmap = cl.ListedColormap(colors)
for k in keys:
for j in range(len(dic)):
x = np.array(dic[j][k])
if len(tr[k])==1:
x[x < tr[k][0]] = 0.0
x[x > tr[k][0]] = 1.0
elif len(tr[k])==2:
x[x < tr[k][0]] = 0.0
x[x > tr[k][1]] = 1.0
x[(x<tr[k][1]) & (x>tr[k][0])] = 0.5
plt.pcolor(x, edgecolors='k', linewidths=1, cmap=cmap, vmin=vlim[0], vmax=vlim[1])
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
#-------------------------------------------------------------------------------------------------------------------#
def plot_pcolors(dic, keys, fs=[10,7], ncol=None, nrow=None, fontsize=12, fig_name=None):
if ncol == None:
ncol = len(keys)
if nrow == None:
nrow = 1
plt.figure(figsize=(fs[0]*ncol,fs[1]*nrow), dpi=200)
for k in range(len(keys)):
plt.subplot(nrow,ncol,k+1)
plt.title(keys[k])
plt.pcolor(np.asarray(dic[0][keys[k]]))
plt.colorbar()
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
#-------------------------------------------------------------------------------------------------------------------#
def hist_dist(dic, key, hr, tr=None, a=None, fig_name=None, nbins=20, bar_width=1, bar=False, c='b', m='-o', leg=False):
tr_key = tr.keys()[0]
h = np.zeros((len(dic),nbins))
bar_width = (hr[key][1] - hr[key][0])/float(nbins)
for j in range(len(dic)):
x = np.array(dic[j][key])
if a==None or tr==None:
h[j,:] = np.histogram(x, range=hr[key], bins=nbins)[0]
elif a==-1:
h[j,:] = np.histogram(x[x<tr[tr_key][0]], range=hr[key], bins=nbins)[0]
elif a==0:
h[j,:] = np.histogram(x[(x>tr[tr_key][0]) & (x<tr[tr_key][1])], range=hr[key], bins=nbins)[0]
elif a==+1:
h[j,:] = np.histogram(x[x>tr[tr_key][1]], range=hr[key], bins=nbins)[0]
hm = np.mean(h,axis=0)
if bar:
plt.bar(np.arange(hr[key][0],hr[key][1], bar_width), hm/np.sum(hm), bar_width)
else:
plt.plot(np.arange(hr[key][0],hr[key][1], bar_width), hm/np.sum(hm), m, color=c, ms=8, mew=2)
plt.xlim(hr[key])
plt.xlabel('amount of protein')
plt.ylabel('fraction of cells')
plt.legend(key)
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
#-------------------------------------------------------------------------------------------------------------------#
def plot_continuation(ODE, freepar, keys, bif_startpoint, LocBifPoints=['LP','B'], PCargs=None, returnLP=None, ics=None,
xlim=None, ylim=None, xticks=False, yticks=False, maxstep=1e+2, minstep=1e-2, step=5e+1, maxpoints=500,
off_points=True, nrow=None, ncol=None, showcurve=True, n_form_coef=False, silence=False,
fs=[6,5], fontsize=18, fig_name=False):
plt.rcParams.update({'font.size': fontsize})
ODE.set(pars = {freepar: bif_startpoint})
if silence:
class NullDevice():
def write(self, s):
pass
original_stdout = sys.stdout
sys.stdout = NullDevice()
if showcurve:
if ncol == None:
ncol = len(keys)
if nrow == None:
nrow = 1
plt.figure(figsize=(fs[0]*ncol,fs[1]*nrow), dpi=200)
if ics==None:
ics = [eliminate_redundants(pp.find_fixedpoints(ODE, n=2, maxsearch=1e+4, eps=1e-12), 4)[0]]
if PCargs==None:
PCargs = PyCont_args(ODE.name, freepar, maxpoints, saveeigen=True, LocBifPoints=LocBifPoints,
maxstep=maxstep, minstep=minstep, step=step)
for j in range(len(ics)):
ODE.set(ics = ics[j])
PyCont = PyDSTool.ContClass(ODE)
PyCont.newCurve(PCargs)
PyCont[ODE.name].forward()
PyCont[ODE.name].backward()
if showcurve:
for i in range(len(keys)):
PyCont.display((freepar,keys[i]), stability=True, axes=(nrow,ncol,i+1), color='k', linewidth=3)
if off_points:
PyCont.plot.toggleLabels('off')
plt.xlabel(freepar, fontsize=18)
plt.ylabel(keys[i], fontsize=18)
plt.title('')
if xlim != None:
plt.xlim([xlim[0],xlim[1]])
if ylim != None:
plt.ylim([ylim[0],ylim[1]])
if xticks:
plt.xticks(xticks)
if yticks:
plt.yticks(yticks)
if n_form_coef:
i = 1
while PyCont[ODE.name].getSpecialPoint('LP'+str(i)):
print("LP"+str(i), PyCont[ODE.name].getSpecialPoint('LP'+str(i)).labels['LP']['data'])
i += 1
if fig_name:
plt.savefig(fig_name, format='pdf', dpi=200)
if silence:
sys.stdout = original_stdout
if returnLP!=None:
P = []
for k in returnLP:
i=1
while PyCont[ODE.name].getSpecialPoint(k+str(i)):
P += [PyCont[ODE.name].getSpecialPoint(k+str(i))[freepar]]
i +=1
return P
plt.show()
#-------------------------------------------------------------------------------------------------------------------#
def plot_continuation_twocells(ODE, freepar, keys, bif_startpoint, LocBifPoints=['LP','BP','B'], xlim=False, ylim=False,
maxpoints=500, fig_name=False, saveeigen=True, maxstep=1e-0, minstep=1e-2, step=5e-2, silence=False):
if silence:
class NullDevice():
def write(self, s):
pass
original_stdout = sys.stdout
sys.stdout = NullDevice()
fp = eliminate_redundants(pp.find_fixedpoints(ODE, n=2, maxsearch=1e+4, eps=1e-10),6)
p = plot_continuation(ODE, freepar, keys, bif_startpoint, ics=[fp[0]], maxstep=maxstep, minstep=minstep,
step=step, off_points=True, LocBifPoints=LocBifPoints, returnLP='BP')
figure(figsize=(6*len(keys),5))
l = sorted(p + ODE.pdomain[freepar])
for i in range(len(p)):
plt.axvline(x=p[i],color='k')
for i in range(len(l)-1):
ODE.set(pars = {freepar: (l[i] + l[i+1])/2} )
fp = eliminate_redundants(pp.find_fixedpoints(ODE, n=2, maxsearch=1e+4, eps=1e-10),6)
print(len(fp), fp)
PCargs = PyCont_args(ODE.name, freepar, maxpoints, stopAt=['B','BP'], maxstep=maxstep, minstep=minstep, step=minstep)
for j in range(len(fp)):
ODE.set(ics = fp[j])
PyCont = PyDSTool.ContClass(ODE)
PyCont.newCurve(PCargs)
PyCont[ODE.name].forward()
PyCont[ODE.name].backward()
for k in range(len(keys)):
PyCont.display((freepar,keys[k]), axes=(1,len(keys),k+1), stability=True, linewidth=2)
PyCont.plot.toggleLabels('off')
plt.title('')
plt.xlim(xlim)
if ylim:
plt.ylim(ylim)
if fig_name:
plt.savefig(fig_name, format='pdf', dpi=200)
if silence:
sys.stdout = original_stdout
#-------------------------------------------------------------------------------------------------------------------#
def plot_phasediagram(ODE, freepar, v, r_v, bif_startpoint, keys=False, xlim=False, ylim=False, xticks=False, yticks=False,
show_continuation=False, maxstep=1e+2, minstep=1e-2, step=5e+1, maxpoints=500, nrow=None, ncol=None,
LocBifPoints=['LP','B'], BifPoints=['LP'], silence=False, fig_name=False, fast_fp=False, returnLPs=False):
if silence:
class NullDevice():
def write(self, s):
pass
original_stdout = sys.stdout
sys.stdout = NullDevice()
if keys==False:
keys = ODE.variables.keys()
x = []
for i in r_v:
ODE.set(pars = {v: i, freepar: bif_startpoint})
if fast_fp:
fp = fast_fixedpoint(ODE)
else:
fp = eliminate_redundants(pp.find_fixedpoints(ODE, n=2, maxsearch=1e+4, eps=1e-12),4)[0]
ODE.set(ics = fp)
PCargs = PyCont_args(ODE.name, freepar, maxpoints, saveeigen=True, maxstep=maxstep, minstep=minstep, step=step, LocBifPoints=LocBifPoints)
lp = plot_continuation(ODE, freepar, keys, bif_startpoint, PCargs=PCargs, returnLP=BifPoints, showcurve=show_continuation, ics=[fp],
fs=[4,3], fontsize=12,nrow=nrow, ncol=ncol)
x += [lp]
plt.show()
if silence:
sys.stdout = original_stdout
figure(figsize=(6,5), dpi=200)
x = np.asarray(x)
for i in range(shape(x)[1]):
plot(x[:,i], r_v, color='k')
plt.xlabel(freepar, fontsize= 18)
plt.ylabel(v, fontsize= 18)
if xlim:
plt.xlim(xlim)
if xticks:
plt.xticks(xticks)
if ylim:
plt.ylim(ylim)
if yticks:
plt.yticks(yticks)
if fig_name:
plt.savefig(fig_name, format='pdf', dpi=200)
plt.show()
if returnLPs:
return x
#-------------------------------------------------------------------------------------------------------------------#
def nullclines(axis, DSargs, stab, fp, nfp=0, vlim=None, c = ['b','g'], maxpoints=[1000,1000], step=5e+1, minstep=1e-1,
maxstep=1e+3, fs=[6,5], fig_name=False, plotaxis=[0,1], loc=0, fontsize=18, pcontour=None, silence=False,
xticks=False, yticks=False):
plt.rcParams.update({'font.size': fontsize})
if silence:
class NullDevice():
def write(self, s):
pass
original_stdout = sys.stdout
sys.stdout = NullDevice()
figure(figsize=(fs[0],fs[1]), dpi=200)
DSnc = cp.deepcopy(DSargs)
for i in plotaxis:
keys = list(DSargs.varspecs.keys())
keys.remove(axis[i])
DSnc.pars[axis[i]] = fp[nfp][axis[i]]
DSnc.varspecs = {}
DSnc.ics = {}
DSnc.xdomain = {}
DSnc.pdomain = {}
if vlim != None:
DSnc.pdomain[axis[i]] = vlim[axis[i]]
for k in keys:
DSnc.varspecs[k] = DSargs.varspecs[k]
DSnc.ics[k] = fp[nfp][k]
DSnc.xdomain[k] = DSargs.xdomain[k]
ODEnc = Vode_ODEsystem(DSnc)
PCargs = PyCont_args('nullclines', axis[i], maxpoints[i], maxstep=maxstep, minstep=minstep, step=step, LocBifPoints=['B'])
PCargs.StopAtPoints = ['B']
PyCont = PyDSTool.ContClass(ODEnc)
PyCont.newCurve(PCargs)
PyCont['nullclines'].forward()
PyCont['nullclines'].backward()
PyCont.display((axis[0],axis[1]), stability=True, linewidth=3, color=c[i], label='d'+axis[i]+'/dt'+' != 0' )
PyCont.plot.toggleLabels('off')
PyCont.plot.togglePoints('off')
del DSnc.pars[axis[i]]
for i in range(len(fp)):
plt.plot(fp[i][axis[0]],fp[i][axis[1]], 'ok', markersize=12, markerfacecolor='r' if stab[i]=='S' else 'w')
if pcontour!=None:
H, xedges, yedges = np.histogram2d(asarray(pcontour[axis[0]])[:,0], asarray(pcontour[axis[1]])[:,0], bins=100)
H = np.rot90(H)
H = np.flipud(H)
xbin = 0.5*(xedges[1] - xedges[0])
ybin = 0.5*(yedges[1] - yedges[0])
plt.contour(xedges[1:]-xbin, yedges[1:]-ybin, H)
plt.xlabel(axis[0])
plt.ylabel(axis[1])
plt.title('')
plt.legend(loc=loc)
if vlim != None:
plt.xlim((vlim[axis[0]][0],vlim[axis[0]][1]))
plt.ylim((vlim[axis[1]][0],vlim[axis[1]][1]))
if xticks:
plt.xticks(xticks)
if yticks:
plt.yticks(yticks)
if fig_name:
plt.savefig(fig_name, format='pdf', dpi=200)
if silence:
sys.stdout = original_stdout
#-------------------------------------------------------------------------------------------------------------------#
def param_sensitivity_bars(list_pars, ODE, DSargs, var, fig_name=False, fs=[10,5], delta=[0.0, 0.1, -0.1]):
change = {}
for pars in list_pars:
if DSargs.pars[pars] != 0:
a = []
for d in delta:
ODE.set(pars = {pars: (1.0 + d)*DSargs.pars[pars]} )
a += [eliminate_redundants(pp.find_fixedpoints(ODE, n=2, maxsearch=1e+4, eps=1e-12),6)[0][var]]
change[pars] = [100*(a[2] - a[0])/a[0],100*(a[1] - a[0])/a[0]]
else:
change[pars] = [0,0]
l = change.keys()
isort = np.argsort([np.abs(change[i][0])+np.abs(change[i][1]) for i in l])[::-1]
figure(figsize=(fs[0],fs[1]), dpi=200)
plt.bar(range(len(change.keys())), [change[l[i]][0] for i in isort], color='r', align='center', alpha=0.8)
plt.bar(range(len(change.keys())), [change[l[i]][1] for i in isort], color='b', align='center', alpha=0.8)
plt.xticks(np.arange(len(list_pars)+1), [l[i] for i in isort])
plt.xlim([-1,len(list_pars)])
plt.ylabel('Change in the signal (%)', fontsize= 18)
plt.legend( ('- 10%', '+10%'), loc='upper right')
if fig_name:
plt.savefig(fig_name, format='pdf', dpi=200)
plt.show()
#-------------------------------------------------------------------------------------------------------------------#
def param_sensitivity_bifurcations(DSargs, freepar, key, list_pars, bif_startpoint, d=[0.0, 0.1, -0.1], c=['k', 'b', 'r'],
ylim=False, xlim=False, xticks=False, yticks=False, fig_name=False, ncol=False,
nrow=False, maxstep=1e+2, minstep=1e-2, step=5e+1, silence=False):
if silence:
class NullDevice():
def write(self, s):
pass
original_stdout = sys.stdout
sys.stdout = NullDevice()
if ncol==False:
nrow=1
ncol=len(list_pars)
else:
plt.figure(figsize=(6*ncol,5*nrow), dpi=200)
for i in range(len(list_pars)):
ODE = Vode_ODEsystem(DSargs)
for j in range(len(d)):
ODE.set(pars = {list_pars[i]: (1.0 + d[j])*DSargs.pars[list_pars[i]]} )
fp_coord = eliminate_redundants(pp.find_fixedpoints(ODE, n=2, maxsearch=1e+4, eps=1e-10),6)
ODE.set(ics = fp_coord[0])
PCargs = PyCont_args('psensit', freepar, 200, saveeigen=True, maxstep=maxstep, minstep=minstep, step=step,
LocBifPoints=['B','LP'])
PyCont = PyDSTool.ContClass(ODE)
PyCont.newCurve(PCargs)
PyCont['psensit'].forward()
PyCont['psensit'].backward()
PyCont.display((freepar,key), stability=True, axes=(nrow,ncol,i+1), color=c[j], linewidth=3)
plot(0, 0, linewidth=3, color=c[j])
PyCont.plot.toggleLabels('off')
plt.title(list_pars[i])
if i == 0:
plt.legend(('0%','+10%','- 10%'))
if ylim:
plt.ylim(ylim)
if ylim:
plt.ylim(ylim)
if xticks:
plt.xticks(xticks)
if yticks:
plt.yticks(yticks)
if fig_name:
plt.savefig(fig_name, format='pdf', dpi=200)
if silence:
sys.stdout = original_stdout
#-------------------------------------------------------------------------------------------------------------------#
def plot_3Dpotential(x1, x2, npoints, xlim=False, ylim=False, zlim=False, offset=5, cut=9.5, fig_name=False,
nbins=100, scale=1000.0):
plt.rcParams.update({'font.size': 22})
j = np.isfinite(x1) & np.isfinite(x2)
x = x1[j]
y = x2[j]
H, xedges, yedges = np.histogram2d(x, y, bins=nbins)
H = np.rot90(H)
H = np.flipud(H)
V = -np.log(H/npoints)
V[V==np.inf]=float('NaN')
V[V>cut]=float('NaN')
Z = V
X,Y = np.meshgrid(xedges[1:]/scale, yedges[1:]/scale)
fig = plt.figure(figsize=(10,8))
ax = fig.add_subplot(1, 1, 1, projection='3d')
cset = ax.contour(X, Y, Z, zdir='z', offset=offset, cmap=cm.coolwarm)
pc = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha=0.4, cmap=cm.coolwarm, linewidth=0.1)
pc.set_clim(np.min(V[V>0]),np.max(V[V>0]))
ax.view_init(45,-135)
if xlim:
ax.set_xlim3d(xlim)
if ylim:
ax.set_ylim3d(ylim)
if zlim:
ax.set_zlim3d(zlim)
ax.zaxis.set_rotate_label(False) # disable automatic rotation
ax.set_zlabel('Effective Potential', rotation=95)
if fig_name:
plt.savefig(fig_name+'.png', format='png', dpi=200)
plt.savefig(fig_name+'.pdf', format='pdf', dpi=200)
plt.show()
#----------------------------------------------------------------------------------------#
def plot_trajectory(ODE, keys, dt=None, t=None, linewidth=2, fontsize=18):
traj = ODE.compute('test_traj')
pts = traj.sample()
plt.rcParams.update({'font.size': fontsize})
plt.plot(pts[keys[0]], pts[keys[1]], color='k', linewidth=linewidth)
plt.xlabel(keys[0])
plt.ylabel(keys[1])
plt.show()
#----------------------------------------------------------------------------------------#
def dist2D(dic, keys, tr={}, fig_name=None, leg=False):
plt.figure(figsize=(6,5), dpi=200)
for j in range(len(dic)):
w = np.array(dic[j]['W'])
if len(keys[0]) > 1:
x = np.array(dic[j][keys[0][0]]) + np.array(dic[j][keys[0][1]])
else:
x = np.array(dic[j][keys[0]])
y = np.array(dic[j][keys[1]])
plt.plot(x[w<tr['W'][0]] , y[w<tr['W'][0]] , 'o', c='#e8656c')
plt.plot(x[(w>tr['W'][0]) & (w<tr['W'][1])], y[(w>tr['W'][0]) & (w<tr['W'][1])], 'o', c='#e4fc36')
plt.plot(x[w>tr['W'][1]] , y[w>tr['W'][1]] , 'o', c='#00ff9c')
plt.xlabel(keys[0])
plt.ylabel(keys[1])
#if lim != None:
#if lim[]
if leg:
plt.legend(leg)
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
#----------------------------------------------------------------------------------------#
def hist_dist(dic, key, hr, tr={}, a=None, fig_name=None, nbins=10, bar_width=1, bar=False,
c='b', m='-o', leg=False):
tr_key = tr.keys()[0]
h = np.zeros((len(dic),nbins))
bar_width = (hr[key][1] - hr[key][0])/float(nbins)
for j in range(len(dic)):
x = np.array(dic[j][key])
y = np.array(dic[j][tr_key])
if a==None:
h[j,:] = np.histogram(x, range=hr[key], bins=nbins)[0]
elif a==-1:
h[j,:] = np.histogram(x[y<tr[tr_key][0]], range=hr[key], bins=nbins)[0]
elif a==0:
h[j,:] = np.histogram(x[(y>tr[tr_key][0]) & (y<tr[tr_key][1])], range=hr[key], bins=nbins)[0]
elif a==+1:
h[j,:] = np.histogram(x[y>tr[tr_key][1]], range=hr[key], bins=nbins)[0]
hm = np.mean(h,axis=0)
print hm, a
if np.sum(hm)>0.0:
if bar:
plt.bar(np.arange(hr[key][0],hr[key][1], bar_width), hm/np.sum(hm), bar_width, color=c)
else:
plt.plot(np.arange(hr[key][0],hr[key][1], bar_width), hm/np.sum(hm), m, color=c, ms=12, mew=2)
plt.xlim(hr[key])
plt.xlabel('amount of protein')
plt.ylabel('fraction of cells')
plt.title(key)
if fig_name!=None:
plt.savefig(fig_name, format='pdf', dpi=200)
#-------------------------------------------------------------------------------------------------------------------#
def fast_fixedpoint(ODE, tdomain=[0, 100000]):
ODE.set(tdomain=tdomain)
traj = ODE.compute('traj')
pts = traj.sample()
return dict(pts[-1])