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Commit 01485754 authored by Lars Hubatsch's avatar Lars Hubatsch
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Update plots for revisions at eLife. 

New plot for PLYS ATP spatial recovery.
New plot for boundary condition PGL
New plot for valley in cost function
New plot for relative partition coefficient
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Plots_Droplet_FRAP.ipynb
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%% Cell type:code id: tags:
``` python
from fem_sol import frap_solver
from matplotlib import cm, rc, rcParams
from matplotlib.ticker import MaxNLocator
import fem_utils
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
from scipy.interpolate import interp1d
fol = '/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/'
# sns.set_style("ticks")
rcParams['axes.linewidth'] = 0.75
rcParams['xtick.major.width'] = 0.75
rcParams['ytick.major.width'] = 0.75
# rcParams['text.usetex']=True
```
%% Cell type:code id: tags:
``` python
# Define colors
pa = sns.color_palette("Set2")
sns.set_palette(pa)
grey = (0.6, 0.6, 0.6)
dark_grey = (0.2, 0.2, 0.2)
green = pa[0]
blue = pa[2]
red = pa[1]
pink = (233/255, 72/255, 119/255)
```
%% Cell type:code id: tags:
``` python
import pylab as pl
params = {'legend.fontsize': 9,
'legend.handlelength': 1}
pl.rcParams.update(params)
def nice_fig(xla, yla, xli, yli, size, fs=12):
rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
# rc('font',**{'family':'serif','serif':['Palatino']})
plt.gcf().set_size_inches(size[0], size[1])
plt.xlabel(xla,fontsize=fs)
plt.ylabel(yla,fontsize=fs)
plt.xlim(xli)
plt.ylim(yli)
plt.tick_params(axis='both', which='major', labelsize=fs)
def save_nice_fig(name, form='pdf', dpi=300):
plt.savefig(name, format=form, dpi=dpi, bbox_inches='tight',
transparent=True)
```
%% Cell type:markdown id: tags:
### FRAP geometries
%% Cell type:code id: tags:
``` python
# For radial average: define angles and radial spacing
alphas = np.linspace(0,2*np.pi, 20)
ns = np.c_[np.cos(alphas), np.sin(alphas), np.zeros(len(alphas))]
eps = np.linspace(0, 0.23, 100)
```
%% Cell type:markdown id: tags:
#### Multi Drop
%% Cell type:code id: tags:
``` python
me = ['Meshes/multi_drop_gauss.xml', 'Meshes/multi_drop_gauss_med.xml',
'Meshes/multi_drop_gauss_far.xml', 'Meshes/multi_drop_gauss.xml',
'Meshes/multi_drop_gauss_med.xml', 'Meshes/multi_drop_gauss_far.xml']
point_lists = [[[4, 4.5, 0.25], [4, 3.5, 0.25], [3.5, 4, 0.25], [4.5, 4, 0.25]],
[[4, 5, 0.25], [4, 3, 0.25], [3, 4, 0.25], [5, 4, 0.25]],
[[4, 5.5, 0.25], [4, 2.5, 0.25], [2.5, 4, 0.25], [5.5, 4, 0.25]],
[[4, 4.5, 0.25], [4, 3.5, 0.25], [3.5, 4, 0.25], [4.5, 4, 0.25]],
[[4, 5, 0.25], [4, 3, 0.25], [3, 4, 0.25], [5, 4, 0.25]],
[[4, 5.5, 0.25], [4, 2.5, 0.25], [2.5, 4, 0.25], [5.5, 4, 0.25]]]
phi_tot_int = [.99, .99, .99, .9, .9, .9]
phi_tot_ext = [.01, .01, .01, .1, .1, .1]
G_in = [1, 1, 1, .1, .1, .1]
G_out = [1, 1, 1, 0.99/0.9, 0.99/0.9, 0.99/0.9]
f_i = []
for p, m, p_i, p_e, G_i, G_o in zip(point_lists, me, phi_tot_int,
phi_tot_ext, G_in, G_out):
f = frap_solver([4, 4, 0.25], m, name='FRAP_multi/FRAP_multi_'+m[:-4]+str(G_i), point_list=p,
T=240, dt=0.02, phi_tot_int=p_i, phi_tot_ext=p_e, G_in=G_i, G_out=G_o)
# f.solve_frap()
f_i.append(f)
```
%% Cell type:code id: tags:
``` python
profs = []
for i in range(len(f_i)):
# if i>2:
profs.append([])
for j in range(240):
values=[]
fs = fem_utils.load_time_point(f_i[i].name+'t_p_'+str(j)+'.h5',
f_i[i].mesh)
print('Reading time point ' + str(j) + ' of simulation ' + str(i))
for n in ns:
values.append([fs([4, 4, 0.25]+e*n) for e in eps])
profs[i].append(np.mean(np.transpose(values), 1))
```
%% Cell type:code id: tags:
``` python
# Write out profiles to .csv
for i in [0, 1, 2, 3, 4, 5]:
dist = str(point_lists[i][0][1]-4)
P = str(f_i[i].phi_tot_int/f_i[i].phi_tot_ext)
np.savetxt('eps_multi_'+str(i)+'.csv', eps, delimiter=',')
np.savetxt('t_p_multi_' + P + '_' + dist +'.csv',
profs[i][1:], delimiter=',')
meta_data = np.r_[f_i[i].dt, f_i[i].T-1, eps, 0.25] # last param: droplet radius
np.savetxt('meta_data_multi_' + P + '_' + dist + '.csv', meta_data, delimiter=',')
```
%% Cell type:code id: tags:
``` python
ft = f_i[1]
meta_data = np.r_[ft.dt, ft.T, eps]
np.savetxt('meta_data.csv', meta_data, delimiter=',')
```
%% Cell type:code id: tags:
``` python
plt.plot(eps,np.transpose(profs)[:,:])
```
%% Cell type:code id: tags:
``` python
nice_fig('time $t$ [s]', 'intensity [a.u.]', [0,4], [0,1.05], [1.5,2])
plt.plot(np.linspace(0, (f_i[0].T-1)*f_i[0].dt, f_i[0].T),
[np.mean(x)/f_i[0].phi_tot_int for x in profs[0]],
lw=2, label='d=0.5', ls='-')
plt.plot(np.linspace(0, (f_i[1].T-1)*f_i[1].dt, f_i[1].T),
[np.mean(x)/f_i[1].phi_tot_int for x in profs[1]],
lw=2, label='d=1', ls='--')
plt.plot(np.linspace(0, (f_i[2].T-1)*f_i[2].dt, f_i[2].T),
[np.mean(x)/f_i[2].phi_tot_int for x in profs[2]],
lw=2, label='d=1.5', ls=':')
plt.plot(range(0, 100), np.ones(100), linestyle='--', color='k')
plt.title('$P=99}$', size=12)
plt.gca().get_yaxis().set_visible(False)
save_nice_fig(fol+'Fig3/tot_recov_neighbours_bad.pdf')
```
%% Cell type:code id: tags:
``` python
nice_fig('time $t$ [s]', r'av. volume fraction $\bar{\phi}_\mathrm{u}$', [0,4.], [0,1.05], [1.5,2])
plt.plot(np.linspace(0, (f_i[3].T-1)*f_i[3].dt, f_i[3].T),
[np.mean(x)/f_i[3].phi_tot_int for x in profs[3]],
lw=2, label='$d=0.5 \,\mathrm{\mu m}$', ls='-')
plt.plot(np.linspace(0, (f_i[4].T-1)*f_i[4].dt, f_i[4].T),
[np.mean(x)/f_i[4].phi_tot_int for x in profs[4]],
lw=2, label='$d=1 \,\mathrm{\mu m}$', ls='--')
plt.plot(np.linspace(0, (f_i[5].T-1)*f_i[5].dt, f_i[5].T),
[np.mean(x)/f_i[5].phi_tot_int for x in profs[5]],
lw=2, label='$d=1.5 \,\mathrm{\mu m}$', ls=':')
plt.plot(range(0, 100), np.ones(100), linestyle='--', color='k')
plt.title('$P=9$', size=12)
plt.legend(prop={'size': 9}, frameon=False, loc=(0.2, 0.025),
handletextpad=0.4, labelspacing=0.2)
save_nice_fig(fol+'Fig3/tot_recov_neighbours_good.pdf')
```
%% Cell type:code id: tags:
``` python
ml = np.loadtxt('/Users/hubatsch/Desktop/DropletFRAP/matlab_fit_multi.csv',
delimiter=',')
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'volume fraction $\phi_\mathrm{u}$', [0,0.23], [0,1.05], [3.8,2])
l_sim = plt.plot(eps, np.transpose(profs[0])[:,1:181:22]/f_i[0].phi_tot_int, c=green,
lw=4.5, alpha=0.7)
plt.plot(range(0, 100), np.ones(100), linestyle='--', color='k')
l_fit = plt.plot(np.linspace(0, 0.23, 100), np.transpose(ml)[:,:180:22], c='k', lw=1.5)
plt.legend([l_sim[0], l_fit[0]], ['Model, eq. (6)', 'Fit, eq. (1)'], loc=(0.1, 0.77),
prop={'size': 9}, frameon=False, labelspacing=0.1, handlelength=0.1, ncol=2)
save_nice_fig(fol+'Fig3/spat_recov_neighbours.pdf')
```
%% Cell type:markdown id: tags:
#### Coverslip
%% Cell type:code id: tags:
``` python
# Define parameters for all simulations
point_list = [[4, 4, 0.25], [4, 4, 1.5], [4, 4, 4],
[4, 4, 0.25], [4, 4, 1.5], [4, 4, 4]]
me = ['coverslip.xml', '1_5.xml', 'symmetric.xml',
'coverslip.xml', '1_5.xml', 'symmetric.xml']
phi_tot_int = [.99, .99, .99, .9, .9, .9]
phi_tot_ext = [.01, .01, .01, .1, .1, .1]
G_in = [1, 1, 1, .1, .1, .1]
G_out = [1, 1, 1, 0.99/0.9, 0.99/0.9, 0.99/0.9]
f_cs = []
# Zip all parameters, iterate
for p, m, p_i, p_e, G_i, G_o, i in zip(point_list, me, phi_tot_int,
phi_tot_ext, G_in, G_out, range(len(me))):
if i in [0, 1, 2, 3, 4, 5]:
f_cs.append(frap_solver(p, 'Meshes/single_drop_'+m,
name='FRAP_coverslip/FRAP_'+m[:-4]+str(G_i), T=240,
phi_tot_int=p_i, dt=0.02, phi_tot_ext=p_e, G_in=G_i,
G_out=G_o))
# f_cs[-1].solve_frap()
```
%% Cell type:code id: tags:
``` python
z = [0.25, 1.5, 4, 0.25, 1.5, 4]
# eps = np.linspace(0, 3.5, 100) # for full profile
# eps = np.r_[np.linspace(0, 0.4, 100), np.linspace(0.41, 2, 20)]
eps = np.linspace(0, 0.23, 100)
profs_cs = []
for i, z_i in enumerate(z):
profs_cs.append([])
for j in range(240):
values=[]
fs = fem_utils.load_time_point(f_cs[i].name+
't_p_'+str(j)+'.h5', f_cs[i].mesh)
for n in ns:
values.append([fs([4, 4, z_i]+e*n) for e in eps])
profs_cs[i].append(np.mean(np.transpose(values), 1))
```
%% Cell type:code id: tags:
``` python
# Write out profiles to .csv
for i in [0, 1, 2, 3, 4, 5]:
z_str = str(f_cs[i].cent_poin[-1])
P = str(f_cs[i].phi_tot_int/f_cs[i].phi_tot_ext)
np.savetxt('eps_'+str(i)+'.csv', eps, delimiter=',')
np.savetxt('t_p_long_coverslip_' + P + '_' + z_str +'.csv',
profs_cs[i][1:], delimiter=',')
meta_data = np.r_[f_cs[i].dt, f_cs[i].T-1, eps, 0.25] # last param: droplet radius
np.savetxt('meta_data_long_coverslip_' + P + '_' + z_str + '.csv', meta_data, delimiter=',')
```
%% Cell type:code id: tags:
``` python
nice_fig('time $t$ [s]', '', [0,4], [0,1.05], [1.5,2])
ls = ['-', '--', '-.']
for i, f in enumerate(f_cs[0:3]):
plt.plot(np.linspace(0, (f.T-1)*f.dt, f.T),
[np.mean(x)/f.phi_tot_int for x in profs_cs[i]],
label='d='+str(z[i]), ls=ls[i], lw=2)
plt.plot(range(0, 100), np.ones(100), linestyle='--', color='k')
plt.title('$P=99$', size=12)
plt.gca().get_yaxis().set_visible(False)
save_nice_fig(fol+'Fig3/tot_recov_cs_bad.pdf')
```
%% Cell type:code id: tags:
``` python
nice_fig('time $t$ [s]', r'av. volume fraction $\bar{\phi}_\mathrm{u}$', [0,4], [0,1.05], [1.5,2])
ls = ['-', '--', '-.']
for i, f in enumerate(f_cs[3:]):
plt.plot(np.linspace(0, (f.T-1)*f.dt, f.T),
[np.mean(x)/f.phi_tot_int for x in profs_cs[i+3]],
label='$h=$'+str(z[i])+'$\,\mathrm{\mu m}$', lw=2, ls=ls[i])
plt.plot(range(0, 100), np.ones(100), linestyle='--', color='k')
plt.title('$P=9$', size=12)
plt.legend(prop={'size': 9}, frameon=False, loc=(0.18, 0.025),
handletextpad=0.4, labelspacing=0.2)
save_nice_fig(fol+'Fig3/tot_recov_cs_good.pdf')
```
%% Cell type:code id: tags:
``` python
ml_neigh = np.loadtxt('/Users/hubatsch/Desktop/DropletFRAP/matlab_fit_coverslip.csv',
delimiter=',')
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'volume fraction $\phi_\mathrm{u}$', [0,0.23], [0,1.05], [3.8,2])
l_sim = plt.plot(eps, np.transpose(profs_cs[0])[:,1::22]/f_cs[0].phi_tot_int, c=green,
lw=4.5, alpha=0.7)
plt.plot(range(0, 100), np.ones(100), linestyle='--', color='k')
l_fit = plt.plot(np.linspace(0, 0.23, 100), np.transpose(ml_neigh)[:,::22],
ls='-', c='k', lw=1)
plt.legend([l_sim[0], l_fit[0]], ['Model, eq. (6)', 'Fit, eq. (1)'], frameon=False, loc=(0.1, 0.77), ncol=2)
save_nice_fig(fol+'Fig3/spat_recov_coverslip.pdf')
```
%% Cell type:markdown id: tags:
### Figure 1: Fitting $D_{in}$ and data analysis.
%% Cell type:markdown id: tags:
**Panel: comparison PGL-3 diffusivity with Louise's viscosity**
%% Cell type:code id: tags:
``` python
louise = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig1/Louise.csv')
lars = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig1/Lars.csv')
```
%% Cell type:code id: tags:
``` python
# Calculate rough molecular radius, based on Stokes-Einstein and Louise's
# viscosity data from the Science paper supplement (Fig. S5G), email from Louise:
# earliest point is 10.4 Pa*s .
# Einstein kinetic theory: D=kB*T/(6*pi*eta*r)
D = lars.D[lars.conc==75].mean()
eta = 10.4
kBT = 4.11*10**-21
r = kBT/(D*6*np.pi*eta)
print(r)
```
%% Cell type:code id: tags:
``` python
fig, ax1 = plt.subplots()
ax2 = ax1.twinx()
plt.sca(ax1)
nice_fig('c_\mathrm{salt} [\mathrm{mM}]', '$\eta^{-1} \;[Pa\cdot s]^{-1}$', [40,190], [0,7.24], [2.3,2])
sns.lineplot(x="conc", y="D", data=lars, color=sns.color_palette()[1])
sns.scatterplot(x="conc", y="D", data=lars, color=sns.color_palette()[1], alpha=0.8)
plt.xlabel('$c_\mathrm{salt}\; [\mathrm{mM}]$')
plt.ylabel('$D_{\mathrm{in}} \;[\mathrm{\mu m^2\cdot s^{-1}}]$', color=red)
plt.yticks([0, 0.05, 0.1], rotation=90, color = pa[1])
plt.ylim(0, 0.1)
ax1.set_zorder(1)
ax1.patch.set_visible(False)
plt.sca(ax2)
sns.lineplot(x="conc", y="vis", data=louise, color=grey, label='data from Jawerth \net al. 2018')
plt.yticks(color = grey, fontsize=12)
plt.ylabel('$\eta^{-1} \;[\mathrm{Pa\cdot s}]^{-1}$ ', color = grey, fontsize=12)
plt.legend(frameon=False, fontsize=9)
# save_nice_fig(fol+'Fig1/Lars_vs_Louise.pdf')
```
%% Cell type:markdown id: tags:
**Ratio between $D_{out}$ for maximum and minimum salt concentrations for PGL-3**
%% Cell type:code id: tags:
``` python
lars[lars.conc==180].mean()/lars[lars.conc==50].mean()
```
%% Cell type:markdown id: tags:
**Panel:coacervates PLYS/ATP, CMD/PLYS**m
%% Cell type:code id: tags:
``` python
coacervates = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig1/Coacervates.csv')
sns.stripplot(data=coacervates, palette=[green, blue], jitter=0.35,**{'marker': '.', 'size': 10})
ax = sns.barplot(data=coacervates, palette=pa, facecolor=(1, 1, 1, 0), edgecolor=[pa[0], pa[2]], capsize=.15, ci='sd', errwidth=1.5)
plt.setp(ax.lines, zorder=100)
nice_fig(None, '$D_\mathrm{in} \;[\mathrm{\mu m^2\cdot s^{-1}}]$', [None, None], [0,7], [2.3,2])
plt.xticks([0,1], ('CMD/PLYS', 'PLYS/ATP'), rotation=20)
ax.get_xticklabels()[0].set_color(green)
ax.get_xticklabels()[1].set_color(blue)
plt.xlim(-0.7, 1.7)
# save_nice_fig(fol+'Fig1/Coacervates.pdf')
```
%% Cell type:markdown id: tags:
**Panel: time course CMD**
%% Cell type:code id: tags:
``` python
CMD = np.loadtxt(fol+'/Fig1/CMD_timecourse_D.csv', delimiter=',')
CMD_fit = np.loadtxt(fol+'/Fig1/CMD_fit_timecourse_D.csv', delimiter=',')
l_sim = plt.plot(CMD[:, 0], CMD[:, 1::40], '.', c=green)
l_fit = plt.plot(CMD_fit[:, 0], CMD_fit[:, 1::40], '-', lw=1, c='k')
plt.plot(range(0, 10), np.ones(10)*np.min(CMD_fit[:, 1]), linestyle='--', color=grey, lw=1.5)
plt.legend([l_sim[0], l_fit[0]], ['data', 'fit'], ncol=2, loc=(0, 0.85), frameon=False)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]', [0,np.max(CMD_fit[:, 0])], [0,0.65], [2.3,2])
save_nice_fig(fol+'Fig1/CMD_spat_recov.pdf')
# save_nice_fig(fol+'Fig1/CMD_spat_recov.pdf')
```
%% Cell type:markdown id: tags:
**Panel: time course PLYS**
%% Cell type:code id: tags:
``` python
PLYS = np.loadtxt(fol+'/Fig1/PLYS_timecourse_D.csv', delimiter=',')
PLYS_fit = np.loadtxt(fol+'/Fig1/PLYS_fit_timecourse_D.csv', delimiter=',')
l_sim = plt.plot(PLYS[:, 0], PLYS[:, 1::40], '.', c=blue)
l_fit = plt.plot(PLYS_fit[:, 0], PLYS_fit[:, 1::40], '-', lw=1, c='k')
plt.plot(range(0, 10), np.ones(10)*np.min(PLYS_fit[:, 1]), linestyle='--', color=grey, lw=1.5)
plt.legend([l_sim[0], l_fit[0]], ['data', 'fit'], ncol=2, loc=(0, 0.85), frameon=False)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]', [0,np.max(PLYS_fit[:, 0])], [0,0.79], [2.3,2])
save_nice_fig(fol+'Fig1/PLYS_spat_recov.pdf')
```
%% Cell type:markdown id: tags:
**Panel: time course PGL-3**
%% Cell type:code id: tags:
``` python
PGL = np.loadtxt(fol+'/Fig1/PGL_timecourse_D.csv', delimiter=',')
PGL_fit = np.loadtxt(fol+'/Fig1/PGL_fit_timecourse_D.csv', delimiter=',')
l_sim = plt.plot(PGL[:, 0], PGL[:, 1::130], '.', c=red)
l_fit = plt.plot(PGL_fit[:, 0], PGL_fit[:, 1::130], '-', lw=1, c='k')
plt.plot(range(0, 10), np.ones(10)*np.min(PGL_fit[:, 1]), linestyle='--', color=grey, lw=1.5)
plt.legend([l_sim[0], l_fit[0]], ['data', 'fit'], ncol=2, loc=(0.015, 0.865), frameon=False)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]', [0,np.max(PGL_fit[:, 0])], [0, 0.65], [2.3,2])
save_nice_fig(fol+'Fig1/PGL_spat_recov.pdf')
```
%% Cell type:code id: tags:
``` python
l_sim = plt.plot(PGL[:, 0], PGL[:, 1], '-', c=red)
nice_fig('', '', [0,np.max(PGL_fit[:, 0])], [0, 0.55], [0.7,0.7], fs=5)
plt.yticks([0, 0.5], ['', ''])
plt.xticks([0, 3], ['', ''])
plt.gca().tick_params(direction='in', length=3, width=1)
save_nice_fig(fol+'Fig1/PGL_spat_90.pdf')
```
%% Cell type:code id: tags:
``` python
l_sim = plt.plot(PGL[:, 0], PGL[:, 4*80], '-', c=red)
nice_fig('', '', [0,np.max(PGL_fit[:, 0])], [0, 0.55], [0.7,0.7], fs=5)
plt.yticks([0, 0.5], ['', ''])
plt.xticks([0, 3], ['', ''])
plt.gca().tick_params(direction='in', length=3, width=1)
save_nice_fig(fol+'Fig1/PGL_spat_300.pdf')
```
%% Cell type:code id: tags:
``` python
l_sim = plt.plot(PGL[:, 0], PGL[:, 7*80], '-', c=red)
nice_fig('', '', [0,np.max(PGL_fit[:, 0])], [0, 0.55], [0.7,0.7], fs=5)
plt.yticks([0, 0.5], ['', ''])
plt.xticks([0, 3], ['', ''])
plt.gca().tick_params(direction='in', length=3, width=1)
save_nice_fig(fol+'Fig1/PGL_spat_510.pdf')
```
%% Cell type:markdown id: tags:
**Supplement: movie PLYS**
%% Cell type:code id: tags:
``` python
PLYS = np.loadtxt(fol+'/Fig1/PLYS_timecourse_D.csv', delimiter=',')
PLYS_fit = np.loadtxt(fol+'/Fig1/PLYS_fit_timecourse_D.csv', delimiter=',')
CMD = np.loadtxt(fol+'/Fig1/CMD_timecourse_D.csv', delimiter=',')
CMD_fit = np.loadtxt(fol+'/Fig1/CMD_fit_timecourse_D.csv', delimiter=',')
PGL = np.loadtxt(fol+'/Fig1/PGL_timecourse_D.csv', delimiter=',')
PGL_fit = np.loadtxt(fol+'/Fig1/PGL_fit_timecourse_D.csv', delimiter=',')
```
%% Cell type:code id: tags:
``` python
zipped = zip([PLYS, CMD, PGL], [PLYS_fit, CMD_fit, PGL_fit],
[blue, green, red], ['PLYS/ATP', 'CMD/PLYS', 'PGL-3'],
[0.9, 0.7, 0.8])
for mov, mov_fit, c, l, yl in zipped:
for i in range(np.shape(mov)[1]-1):
l_sim = plt.plot(mov[:, 0], mov[:, 1+i], '-', c=c)
l_fit = plt.plot(mov_fit[:, 0], mov_fit[:, 1+i], '-', lw=1, c='k')
plt.plot(range(0, 10), np.ones(10)*np.min(mov_fit[:, 1]), linestyle='--', color=grey, lw=1.5)
plt.legend([l_sim[0], l_fit[0]], [l, 'Fit to Eq. (1)'], ncol=2, loc=(0, 0.85), frameon=False,
columnspacing=0.8, handletextpad=0.5, handlelength=0.65)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]', [0,np.max(mov_fit[:, 0])], [0, yl], [2.3,2])
plt.yticks([0.2, 0.4, 0.6])
if l=='PLYS/ATP':
plt.yticks([0.2, 0.4, 0.6, 0.8])
save_nice_fig(fol+'Fig4/Movies/'+l[:3]+'_spat_recov_mov_'+str(i)+'.png', form='png', dpi=149.5)
plt.show();
```
%% Cell type:markdown id: tags:
**Panel: time course total intensity**
%% Cell type:code id: tags:
``` python
PGL = np.loadtxt(fol+'/Fig1/PGL_bc.csv', delimiter=',')
ATP = np.loadtxt(fol+'/Fig1/ATP_bc.csv', delimiter=',')
CMD = np.loadtxt(fol+'/Fig1/CMD_bc.csv', delimiter=',')
# fig, ax1 = plt.subplots()
# ax2 = ax1.twiny()
# plt.sca(ax1)
nice_fig('$t/T_\mathrm{max}$', 'intensity [a.u.]', [0,200], [0,0.62], [2.3,2])
# plt.sca(ax2)
# ax2.tick_params(axis="x",direction="in")
plt.plot(PGL[::10, 0]/np.max(PGL[1:-1:2, 0]), PGL[::10,1], '.', label='PGL-3', c='#CC406E', markersize=3, alpha=0.7, lw=2)
plt.plot(ATP[::1, 0]/np.max(ATP[:, 0]), ATP[::1,1], '.', label='PLYS/ATP', c='#FF508A', markersize=3, alpha=0.7, lw=2)
plt.plot(CMD[::5, 0]/np.max(CMD[:, 0]), CMD[::5,1], '.', label='CMD/PLYS', c='#7F2845', markersize=3, alpha=0.7, lw=2)
plt.legend(frameon=False, fontsize=9)
plt.xlim(0, 1)
# save_nice_fig(fol+'Fig1/tot_recov.pdf')
```
%% Cell type:code id: tags:
``` python
PGL = []
for i in range(8):
PGL.append(np.loadtxt(fol+'/Fig1/PGL_bc'+str(i+1)+'.csv', delimiter=','))
conc = np.loadtxt(fol+'/Fig1/PGL_conc.csv', delimiter=',')
rads = [25, 24, 29, 26, 25, 53, 33, 26]
# PGL = [PGL[i] for i in [0, 1, 2, 3, 4, 5, 7]]
# rads =
```
%% Cell type:code id: tags:
``` python
nice_fig('time $t$ [s]', 'boundary intensity', [0,140], [0,0.82], [1,2])
temp = sns.color_palette()
sns.set_palette(sns.color_palette("rocket", 9))
# plt.sca(ax2)
# ax2.tick_params(axis="x",direction="in")
# plt.plot(PGL[::10, 0], PGL[::10,1], '.', label='PGL-3', c='#CC406E', markersize=3, alpha=0.7, lw=2)
for jj, i in enumerate(PGL):
if jj != 10:
plt.plot(i[::, 0]/(0.136*rads[jj])**2, i[::,1], '-', color=sns.color_palette()[jj], lw=1.5)
plt.legend([str(x)[:-2] for x in conc], columnspacing=0.2, frameon=False,
fontsize=7, handletextpad=0.4, handlelength=0.5, labelspacing=0.1,
loc=(0.3, 0), ncol=2)
# plt.xticks([0, 500])
save_nice_fig(fol+'Fig1/tot_recov_PGL.pdf')
# save_nice_fig(fol+'Fig1/tot_recov_PGL.pdf')
sns.set_palette(temp)
```
%% Cell type:code id: tags:
``` python
PGL_bc_ill = np.loadtxt(fol+'/Fig1/PGL_bc_illustr.csv', delimiter=',')
plt.plot(PGL_bc_ill[:, 0], PGL_bc_ill[:, 1], c=pink)
nice_fig('', 'intensity', [0,150], [0,0.55], [2.3,0.75], fs=9)
plt.xticks([0, 150])
plt.tick_params(axis='x', which='major', pad=1)
save_nice_fig(fol+'Fig1/PGL_bc_ill.pdf')
```
%% Cell type:code id: tags:
``` python
nice_fig('time $t$ [s]', 'intensity [a.u.]', [0,10], [0,0.72], [1,2])
plt.plot(ATP[::1, 0], ATP[::1,1], '-', label='PLYS/ATP', c=blue, markersize=3, alpha=0.7, lw=1.5)
plt.plot(CMD[::5, 0], CMD[::5,1], '-', label='CMD/PLYS', c=green, markersize=3, alpha=0.7, lw=1.5)
plt.legend(frameon=False, fontsize=7, loc=(0.1, 0), handletextpad=0.5)
plt.yticks([]); plt.ylabel('')
save_nice_fig(fol+'Fig1/tot_recov_coac.pdf')
```
%% Cell type:markdown id: tags:
**Valley in cost function**
%% Cell type:code id: tags:
``` python
PGL_cost = np.loadtxt(fol+'/Fig1/PGL_cost.csv', delimiter=',')
plt.plot(PGL_cost[:, 0], 100000*PGL_cost[:, 1], c=red)
nice_fig('$D_\mathrm{in} \;[\mathrm{\mu m^2\cdot s^{-1}}]$', '$cost$ [a.u.]', [0.8,1.5], [0,5.5], [2.3,2], fs=12)
plt.xticks([1, 1.2, 1.4])
plt.tick_params(axis='x', which='major', pad=1)
plt.legend(['Sample PGL-3 droplet'], loc=(0, 0.85), frameon=False)
# save_nice_fig(fol+'Fig1/PGL_cost.pdf')
```
%% Cell type:markdown id: tags:
### Figure 2: model sketches
%% Cell type:code id: tags:
``` python
model = np.loadtxt(fol+'Fig2/model_timecourse.csv', delimiter=',')
l_fit = plt.plot(model[:, 0], model[:, 1:], '-', lw=1,
c=green, label='Simulation')
nice_fig('radial distance $r/R$', 'volume fraction $\phi_\mathrm{u}$', [0, 2],
[0,1], [2.3,2])
plt.plot(model[:, 0], model[:, -1], c=green, lw=2)
plt.plot(model[:, 0], model[:, -1], 'k', lw=2)
# plt.annotate('$t \longrightarrow \infty$', (0.97, 0.89), (1.3,0.85), fontsize=12)
# plt.annotate('$t \longrightarrow \infty$', (0.97, 0.89), (1.3,0.85), fontsize=12)
plt.annotate('$\phi_\mathrm{tot}$', (1, 0.5), (1.5,0.5), fontsize=10)
save_nice_fig(fol+'Fig2/full_time_course.pdf')
```
%% Cell type:code id: tags:
``` python
l_fit = plt.plot(model[:, 0], model[:, 2], '-', lw=1,
c=dark_grey, label='Simulation')
plt.plot(model[:, 0], model[:, -1], 'k', lw=2)
nice_fig('radial distance $r/R$', 'volume fraction $\phi_\mathrm{u}$', [0, 2],
[0,1], [2.3,2])
plt.title('$t=0.22 \;R^2/D_\mathrm{in}$')
plt.text(0.75, 0.18, '$\phi_\mathrm{u}$', fontsize=10)
plt.gca().fill_between(model[:, 0], 0, model[:, 2], color=green)
plt.gca().fill_between(model[:, 0], model[:, -1], model[:, 2], color=grey)
plt.annotate('$\phi_\mathrm{tot}$', (1, 0.5), (1.5,0.5), fontsize=10)
save_nice_fig(fol+'Fig2/snap_shot.pdf')
```
%% Cell type:code id: tags:
``` python
l_fit = plt.plot(model[:, 0], model[:, 1], '-', lw=1,
c=dark_grey, label='Simulation')
plt.plot(model[:, 0], model[:, -1], 'k', lw=2)
nice_fig('radial distance $r/R$', 'volume fraction $\phi_\mathrm{u}$', [0, 2],
[0,1], [2.3,2])
plt.title('$t=0.22 \;R^2/D_\mathrm{in}$')
plt.text(1.45, 0.02, '$\phi_\mathrm{u}$', fontsize=10)
plt.gca().fill_between(model[:, 0], 0, model[:, -1], color=green)
plt.gca().fill_between(model[:, 0], model[:, -1], model[:, 1], color=grey)
plt.annotate('$\phi_\mathrm{tot}$', (1, 0.5), (1.5,0.5), fontsize=10)
save_nice_fig(fol+'Fig2/snap_shot_bleach.pdf')
```
%% Cell type:code id: tags:
``` python
l_fit = plt.plot(model[:, 0], model[:, -2], '-', lw=1,
c=dark_grey, label='Simulation')
plt.plot(model[:, 0], model[:, -1], 'k', lw=2)
nice_fig('radial distance $r/R$', 'volume fraction $\phi_\mathrm{u}$', [0, 2],
[0,1], [2.3,2])
plt.title('$t=0.22 \;R^2/D_\mathrm{in}$')
plt.text(0.47, 0.4, '$\phi_\mathrm{u}$', fontsize=10)
plt.gca().fill_between(model[:, 0], 0, model[:, -2], color=green)
plt.gca().fill_between(model[:, 0], model[:, -2], model[:, -1], color=grey)
plt.annotate('$\phi_\mathrm{tot}$', (1, 0.5), (1.5,0.5), fontsize=10)
save_nice_fig(fol+'Fig2/snap_shot_late.pdf')
```
%% Cell type:code id: tags:
``` python
# l_fit = plt.plot(model[:, 0], model[:, -2], '-', lw=1,
# c=dark_grey, label='Simulation')
plt.plot(model[:, 0], model[:, -1], 'k', lw=2)
nice_fig('radial distance $r/R$', 'volume fraction $\phi_\mathrm{u}$', [0, 2],
[0,1], [2.3,2])
plt.title('$t=0.22 \;R^2/D_\mathrm{in}$')
plt.text(0.47, 0.4, '$\phi_\mathrm{u}$', fontsize=10)
plt.gca().fill_between(model[:, 0], 0, model[:, -1], color=green)
plt.annotate('$\phi_\mathrm{tot}$', (1, 0.5), (1.5,0.5), fontsize=10)
save_nice_fig(fol+'Fig2/snap_shot_before.pdf')
```
%% Cell type:markdown id: tags:
### Figure 4: Obtaining info about outside: experiments.
%% Cell type:markdown id: tags:
**Panel: data time course with full model.**
%% Cell type:code id: tags:
``` python
CMD = np.loadtxt(fol+'Fig4/CMD_timecourse.csv', delimiter=',')
CMD_fit = np.loadtxt(fol+'Fig4/CMD_fit_timecourse.csv', delimiter=',')
CMD_t = np.loadtxt(fol+'Fig4/CMD_fit_time.csv', delimiter=',')
l_data = plt.plot(CMD[:, 0], CMD[:, 1::30], c=green, lw=2,
label='Experiment')
l_fit = plt.plot(CMD_fit[:, 0], CMD_fit[:, 2::30], '-', lw=1,
c=dark_grey, label='Simulation')
l_fit = plt.plot(CMD_fit[:, 0], CMD_fit[:, 1], '-', lw=1,
c=dark_grey) # Initial condition
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]',
[0, 2.4*np.max(CMD[:, 0])], [0,0.7], [2.3,2])
plt.legend([l_data[0], l_fit[0]], ['CMD/PLYS', 'Full model'], frameon=False,
fontsize=9, handletextpad=0.4, handlelength=0.8, loc=(0.52, 0.7))
save_nice_fig(fol+'Fig4/CMD_spat_recov_new.pdf')
```
%% Cell type:code id: tags:
``` python
PLYS = np.loadtxt(fol+'Fig4/PLYS_timecourse.csv', delimiter=',')
PLYS_fit = np.loadtxt(fol+'Fig4/PLYS_fit_timecourse.csv', delimiter=',')
PLYS_t = np.loadtxt(fol+'Fig4/PLYS_fit_time.csv', delimiter=',')
l_data = plt.plot(PLYS[:, 0], PLYS[:, 1::30], c=blue, lw=2)
l_fit = plt.plot(PLYS_fit[:, 0], PLYS_fit[:, 2::30], '-', lw=1,
c=dark_grey, label='Simulation') # time course
l_fit = plt.plot(PLYS_fit[:, 0], PLYS_fit[:, 1], '-', lw=1,
c=dark_grey) # Initial condition
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]',
[0, 2.4*np.max(PLYS[:, 0])], [0,0.75], [2.3,2])
plt.legend([l_data[0], l_fit[0]], ['PLYS/ATP', 'Full model'], frameon=False,
fontsize=9, handletextpad=0.4, handlelength=0.8, loc=(0.52, 0.7))
save_nice_fig(fol+'Fig4/PLYS_spat_recov_new.pdf')
```
%% Cell type:code id: tags:
``` python
PGL = np.loadtxt(fol+'Fig4/PGL_timecourse.csv', delimiter=',')
PGL_fit = np.loadtxt(fol+'Fig4/PGL_fit_timecourse.csv', delimiter=',')
PGL_t = np.loadtxt(fol+'Fig4/PGL_fit_time.csv', delimiter=',')
l_data = plt.plot(PGL[:, 0], PGL[:, 1::140], c=red, lw=2,
label='Experiment')
l_fit = plt.plot(PGL_fit[:, 0], PGL_fit[:, 2::140], '-', lw=1,
c=dark_grey, label='Simulation')
plt.plot(PGL_fit[:, 0], PGL_fit[:, 1], '-', lw=1, c=dark_grey)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u.]',
[0, 2.7*np.max(PGL[:, 0])], [0,0.7], [2.3,2])
plt.legend([l_data[0], l_fit[0]], ['PGL-3', 'Full model'],
frameon=False, fontsize=9, handletextpad=0.4,
handlelength=0.8, loc=(0.54, 0.7))
save_nice_fig(fol+'Fig4/PGL_spat_recov.pdf')
```
%% Cell type:code id: tags:
``` python
zipped = zip([PLYS, CMD, PGL], [PLYS_fit, CMD_fit, PGL_fit],
[PLYS_t, CMD_t, PGL_t], [blue, green, red],
['PLYS/ATP', 'CMD/PLYS', 'PGL-3'], [0.9, 0.7, 0.8])
for (mov, mov_fit, mov_t, c, l, yl) in zipped:
for i in range(np.shape(mov)[1]-1):
l_data = plt.plot(mov[:, 0], mov[:, 1+i], c=c, lw=2)
l_fit = plt.plot(mov_fit[:, 0], mov_fit[:, 2+i], '-', lw=1,
c=dark_grey) # time course
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u]',
[0, 2.7*np.max(mov[:, 0])], [0, yl], [2.35,2.005])
plt.legend([l_data[0], l_fit[0]], [l, 'Fit to Eq. (6)'], frameon=False,
fontsize=9, handletextpad=0.4, handlelength=0.8, loc=(0.48, 0.7))
t = str(np.round(mov_t[i+1], 2))
plt.text(0.5, yl-0.11/0.8*yl, t.ljust(4, '0') + ' s')
plt.yticks([0.2, 0.4, 0.6])
if l=='PLYS/ATP':
plt.yticks([0.2, 0.4, 0.6, 0.8])
save_nice_fig(fol+'Fig4/Movies/'+l[:3]+'_spat_recov_model_'+str(i)+'.png',
form='png', dpi=149)
plt.show();
```
%% Cell type:markdown id: tags:
**Panel: Experimental Partition coefficient vs $D_{out}$ for CMD**
%% Cell type:code id: tags:
``` python
PLYS = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PLYS.csv')
CMD = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/CMD.csv')
```
%% Cell type:code id: tags:
``` python
fig, ax1 = plt.subplots()
plt.sca(ax1)
sns.lineplot(x="P", y="D_out", data=CMD, color=green, ci='sd')
sns.lineplot(x="P", y="D_out", data=PLYS, color=blue, ci='sd')
plt.plot(np.logspace(1, 3, 10), 1.5*np.logspace(1, 3, 10), '--', c='grey', alpha=0.5)
# plt.plot(np.logspace(0, 2, 10), 0.2*np.logspace(0, 2, 10)**2, '--', c='grey')
ax1.set_yscale('log')
ax1.set_xscale('log')
nice_fig('Partition coefficient $P$', '$D_\mathrm{out} \;[\mathrm{\mu m^2s^{-1}}]$',
[1,340], [0.08,450], [2.3,2])
plt.legend(['CMD/PLYS', 'PLYS/ATP'], frameon=False, fontsize=9, loc=(0.44,0.05))
plt.text(1.1, 2, '$D_\mathrm{in, P/A}$', color=blue)
plt.text(1.1, 7, '$D_\mathrm{in, C/P}$', color=green)
# plt.plot([1, 9], [1.7, 1.7], '--', color=blue)
# plt.plot([1, 12], [6, 6], '--', color=green)
plt.xticks([1, 10, 100]);
plt.yticks([0.1, 1, 10, 100]);
save_nice_fig(fol+'Fig4/PLYS_CMD.pdf')
```
%% Cell type:markdown id: tags:
**Panel: Experimental Partition coefficient vs $D_out$ for PGL-3**
%% Cell type:code id: tags:
``` python
PGL_50 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_50.csv')
PGL_60 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_60.csv')
PGL_75 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_75.csv')
PGL_90 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_90.csv')
PGL_100 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_100.csv')
PGL_120 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_120.csv')
PGL_150 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_150.csv')
PGL_180 = pd.read_csv('/Users/hubatsch/Desktop/DropletFRAP/Latex/Figures/Fig4/PGL_180.csv')
```
%% Cell type:code id: tags:
``` python
fig, ax1 = plt.subplots()
plt.sca(ax1)
temp = sns.color_palette()
sns.set_palette(sns.color_palette("rocket", 9))
l50 = sns.lineplot(x="P", y="D_out", data=PGL_50,
color=sns.color_palette()[1], ci=None)
l60 = sns.lineplot(x="P", y="D_out", data=PGL_60,
color=sns.color_palette()[2], ci=None)
l75 = sns.lineplot(x="P", y="D_out", data=PGL_75,
color=sns.color_palette()[3], ci=None)
l90 = sns.lineplot(x="P", y="D_out", data=PGL_90,
color=sns.color_palette()[4], ci=None)
l100 = sns.lineplot(x="P", y="D_out", data=PGL_100,
color=sns.color_palette()[5], ci=None)
ls = plt.gca().get_lines()
leg1 = plt.legend([ls[4], ls[3], ls[2], ls[1], ls[0]], ['100 mM', '90 mM', '75 mM', '60 mM', '50 mM'],
labelspacing=0.3, loc=(0.63, 0.0),
handletextpad=0.4, handlelength=0.5, frameon=0)
l120 = sns.lineplot(x="P", y="D_out", data=PGL_120,
color=sns.color_palette()[6], ci=None)
l150 = sns.lineplot(x="P", y="D_out", data=PGL_150,
color=sns.color_palette()[7], ci=None)
l180 = sns.lineplot(x="P", y="D_out", data=PGL_180,
color=sns.color_palette()[8], ci=None)
plt.plot(np.logspace(0, 4, 10), 0.07*np.logspace(0, 4, 10),
'--', c='grey', alpha=0.5)
# plt.plot(np.logspace(2, 3, 10), 30*np.ones(10), '--', c='m', lw=2)
ax1.set_yscale('log')
ax1.set_xscale('log')
nice_fig('Partition coefficient $P$',
'$D_\mathrm{out} \;[\mathrm{\mu m^2 s^{-1}}]$',
[1,20000], [0.0003,600], [2.3,2])
plt.xticks([1, 10, 100, 1000, 10000]);
plt.legend(loc=1)
ls = plt.gca().get_lines()
plt.legend([ls[7], ls[6],ls[5]], ['180 mM', '150 mM', '120 mM'], labelspacing=0.3,
loc=(0, 0.66), handletextpad=0.4, handlelength=0.5, frameon=0)
plt.gca().add_artist(leg1)
save_nice_fig(fol+'Fig4/PGL-3.pdf')
# save_nice_fig(fol+'Fig4/PGL-3.pdf')
sns.set_palette(temp)
```
%% Cell type:code id: tags:
``` python
le_egfp = 239
le_pgl3 = 693
ratio = le_egfp/(le_egfp+le_pgl3)
D_factor = np.sqrt(ratio)
D_GFPw = 87 # micron^2/s, Arrio-Dupont et al. 2000 BJ, GFP in water
D = D_GFPw*np.sqrt(ratio)
```
%% Cell type:code id: tags:
``` python
P_anatol = np.array([686, 533, 590, 474])/np.array([1.6, 5.5, 7.5, 19.3])
salt_anatol = np.array([100, 150, 175, 200])
P = PGL_50['P']
def i_P(df, Pa):
return interp1d(np.array(df.groupby('P').mean()).flatten(),
P.unique())(Pa)
Ps_2 = [i_P(PGL, 2) for PGL in [PGL_50, PGL_60, PGL_75, PGL_90,
PGL_100, PGL_120, PGL_150, PGL_180]]
Ps_10 = [i_P(PGL, 10) for PGL in [PGL_50, PGL_60, PGL_75, PGL_90,
PGL_100, PGL_120, PGL_150, PGL_180]]
Ps_50 = [i_P(PGL, 50) for PGL in [PGL_50, PGL_60, PGL_75, PGL_90,
PGL_100, PGL_120, PGL_150, PGL_180]]
salts = [50, 60, 75, 90, 100, 120, 150, 180]
nice_fig('$c_\mathrm{salt} \; [\mathrm{mM}]$', 'Partition coefficient $P$',
[50, 180], [12,20000], [2.3,2])
plt.plot(salts, Ps_2, color=red, label='$D_{\mathrm{out}}=2$')
plt.plot(salts, Ps_10, color=green, label='$D_{\mathrm{out}}=10$')
plt.plot(salts, Ps_50, color=blue, label='$D_{\mathrm{out}}=50$')
# plt.plot(salt_anatol, P_anatol)
# plt.gca().fill_between(salts, Ps_15, Ps_30, color=red, alpha=0.2)
plt.yticks(rotation=45)
plt.yscale('log')
plt.legend(frameon=False, ncol=2, columnspacing=0.2, handletextpad=0.1,
labelspacing=0.2, loc=(0.005, -0.02), handlelength=0.5)
# plt.text(110, 6200, '$D_\mathrm{out}=30\;\mathrm{\mu m^2/s}$',
# color=red, size=8)
# plt.text(54, 700, '$D_\mathrm{out}=15\;\mathrm{\mu m^2/s}$',
# color=red, size=8)
save_nice_fig(fol+'Fig4/PGL-3_part.pdf')
# save_nice_fig(fol+'Fig4/PGL-3_part.pdf')
```
%% Cell type:code id: tags:
``` python
P = PGL_50['P']
def i_P(df, Pa):
return interp1d(np.array(df.groupby('P').mean()).flatten(),
P.unique())(Pa)
# def i_P_std(df, Pa):
# return interp1d(np.array(df.groupby('P').std()).flatten(),
# P.unique())(Pa)
Ps_10 = [i_P(PGL, 10) for PGL in [PGL_50, PGL_60, PGL_75, PGL_90,
PGL_100, PGL_120, PGL_150, PGL_180]]
# Ps_10_std = [i_P_std(PGL, 10) for PGL in [PGL_50, PGL_60, PGL_75, PGL_90,
# PGL_100, PGL_120, PGL_150, PGL_180]]
salts = [50, 60, 75, 90, 100, 120, 150, 180]
salts = [50, 60, 75, 90, 100, 120, 150, 180]
nice_fig('$c_\mathrm{salt} \; [\mathrm{mM}]$', '$P$ / $P(c_\mathrm{salt}=50mM)$',
[50, 180], [0,1], [2.3,2])
# plt.plot(salts, Ps_2/Ps_2[0], color=red, label='$D_{\mathrm{out}}=2$')
plt.plot(salts, Ps_10/Ps_10[0], color=green, label='$D_{\mathrm{out}}=10$')
# plt.plot(salts, Ps_50/Ps_50[0], color=blue, label='$D_{\mathrm{out}}=50$')
plt.yticks(rotation=45)
# plt.yscale('log')
# plt.legend(frameon=False, ncol=2, columnspacing=0.2, handletextpad=0.1,
# labelspacing=0.2, loc=(0.005, -0.02), handlelength=0.5)
save_nice_fig(fol+'Fig4/PGL-3_relative_part.pdf')
```
%% Cell type:markdown id: tags:
### Figure 5: Obtaining info about outside: theory.
%% Cell type:markdown id: tags:
**Panel: Partition coefficient vs. $D_{out}$, showcasing four different simulation start cases.**
%% Cell type:code id: tags:
``` python
sns.set_palette(sns.color_palette("Set2"))
P_Do = np.loadtxt(fol+'/Fig4/Part_vs_Do_220121.csv', delimiter=',')
sns.set_style("white")
sns.set_palette([sns.color_palette()[i] for i in [3, 0, 1, 2]])
P = [5, 150, 5, 150]
D_o = [0.1, 0.1, 1, 1]
plt.gca().set_prop_cycle(None)
nice_fig('Partition coefficient $P$', '$D_\mathrm{out}$ [$\mathrm{\mu m^2/s}$]', [0.9,320], [0.000001,340], [2.3,2])
lines = plt.loglog(P_Do[0, :], P_Do[1:, :].transpose())
plt.plot(P_Do[0, :], P_Do[0, :], '--', c='grey')
# plt.legend([lines[2], lines[0], lines[3], lines[1]],
# ['0.2', '0.02', '0.0067', '0.00067'], ncol=2, frameon=False,
# title=r'$D_\mathrm{out}$/P [$\mathrm{\mu m^2/s}$]:', columnspacing=0.5, labelspacing=0.3,
# loc=(0.4, 0), handletextpad=0.4, handlelength=0.5)
plt.gca().set_prop_cycle(None)
lines[0] = plt.plot(P[0], D_o[0], 'o', mfc='none', markersize=8)
lines[1] = plt.plot(P[1], D_o[1], 'o', mfc='none', markersize=8)
lines[2] = plt.plot(P[2], D_o[2], 'o', mfc='none', markersize=8)
lines[3] = plt.plot(P[3], D_o[3], 'o', mfc='none', markersize=8)
def circle(i):
return plt.Line2D(range(1), range(1), color=sns.color_palette()[i],
marker='o', markersize=5, markerfacecolor="white")
plt.legend([circle(2), circle(0), circle(3), circle(1)],
['0.2', '0.02', '0.0067', '0.00067'], ncol=2, frameon=False,
title=r'$D_\mathrm{out}$/P [$\mathrm{\mu m^2/s}$]:', columnspacing=0.5, labelspacing=0.3,
loc=(0.4, 0), handletextpad=0.4, handlelength=0.5)
plt.annotate('$D_{out}$/P = 1 $\mathrm{\mu m^2/s}$', [1,40], c='grey')
plt.xticks([1, 10, 100]);
save_nice_fig(fol+'Fig4/D_vs_P.pdf')
```
%% Cell type:markdown id: tags:
**Panel: Cost function**
%% Cell type:code id: tags:
``` python
P_Cost = np.loadtxt(fol+'/Fig4/Part_vs_Cost_220121.csv', delimiter=',')
nice_fig('Partition coefficient $P$', '$Cost_\mathrm{min} (P)$ [a.u.]', [0.9,320], [0.000000001,0.01], [2.3,2])
lines = plt.loglog(P_Cost[0, :], P_Cost[1:, :].transpose())
# plt.legend([lines[2], lines[0], lines[3], lines[1]],
# ['0.2', '0.02', '0.0067', '0.00067'], ncol=2, frameon=False,
# title=r'$D_\mathrm{out}$/P set to:', columnspacing=0.5, labelspacing=0.3,
# loc=(0.081, 0), handletextpad=0.4, handlelength=0.5)
plt.xticks([1, 10, 100]);
# save_nice_fig(fol+'Fig4/D_vs_Cost.pdf')
```
%% Cell type:code id: tags:
``` python
P_Cost = np.loadtxt(fol+'/Fig4/Part_vs_Cost_220121.csv', delimiter=',')
nice_fig('Partition coefficient $P$', '$Cost_\mathrm{min} (P)$ [a.u.]', [0.9,100], [0,2], [2.3,2])
lines = plt.plot(P_Cost[0], P_Cost[1:].transpose()/[x[0] for x in P_Cost[1:]])
plt.gca().set_xscale('log')
plt.plot([150, 150], [0, 1], '--', lw=2, c=grey)
# save_nice_fig(fol+'Fig4/D_vs_Cost_single.pdf')
```
%% Cell type:markdown id: tags:
**Panel: Valley in parameter space**
%% Cell type:code id: tags:
``` python
con = np.loadtxt(fol+'Fig4/Valley_220121.csv', delimiter=',')
levels = MaxNLocator(nbins=100).tick_values(np.log10(con[:, 2:].min()), np.log10(con[:, 2:].max()))
nice_fig('Partition coefficient $P$', '$D_\mathrm{out} \;[\mathrm{\mu m^2 s^{-1}}]$', [1, 3], [-2,1], [2.3,2])
CS = plt.contourf(np.log10(con[:, 0]), np.log10(con[:, 1]), np.log10(con[:, 2:]), levels=levels, cmap=cm.coolwarm)
plt.plot(np.log10(150), np.log10(10**-1), 'o', c=sns.color_palette()[1], label='Reference Simulation', mfc='none', markersize=8)
le = plt.legend(loc=(0, 0.83), frameon=False, handletextpad=0.2)
# plt.plot(np.log10(P_Do[0, :]), np.log10(P_Do[2, :].transpose()), '--', c=green, lw = 1)
le.get_texts()[0].set_color('white')
plt.xticks([1, 2, 3], ['$10^1$', '$10^2$', '$10^3$'])
plt.yticks([-2, -1, 0, 1], ['$10^{-2}$', '$10^{-1}$', '$10^0$', '$10^1$'])
plt.tick_params('x', pad=5)
fig1 = plt.gcf()
clb = fig1.colorbar(CS, ticks=[0, -2, -4, -6])
clb.ax.set_title('Cost')
save_nice_fig(fol+'Fig4/Sim_D_out_P.pdf')
```
%% Cell type:markdown id: tags:
**Panel: Zoom in for valley in parameter space**
%% Cell type:code id: tags:
``` python
# levels = MaxNLocator(nbins=15).tick_values(np.log10(con[:, 2:].min()), np.log10(con[:, 2:].max()))
nice_fig('Partition coefficient $P$', '', [1.9, 2.4], [-1.5,-0.5], [2.3,2])
CS = plt.contourf(np.log10(con[16:-27, 0]), np.log10(con[16:-27, 1]),
np.log10(con[16:-27, 2+16:-27]), levels=levels,
cmap=cm.coolwarm, vmax=-1.5)
plt.plot(np.log10(150), np.log10(10**-1), 'd', c=sns.color_palette()[1], label='Initial Simul.', markersize=6)
le = plt.legend(loc=(0, 0.83), frameon=False, handletextpad=0.4)
le.get_texts()[0].set_color('white')
plt.xticks([2, 2.25], ['$10^2$', '$10^{2.25}$'])
plt.yticks([-1.5, -1, -0.5], ['$10^{-1.5}$', '$10^{-1}$', '$10^{-0.5}$'])
plt.tick_params('x', pad=5)
fig1 = plt.gcf()
clb = fig1.colorbar(CS, ticks=[-2, -4, -6])
clb.ax.set_title('Cost')
# save_nice_fig(fol+'Fig4/Sim_D_out_P_inset.pdf')
```
%% Cell type:code id: tags:
``` python
con_fine = np.loadtxt(fol+'Fig4/Valley_fine_210121.csv', delimiter=',')
# nice_fig('Partition coefficient $P$', '', [2.172, 2.1795], [-1.005,-0.9955], [2.3,2])
P = np.log10(con_fine[:,0])
D_o = np.log10(con_fine[:,1])
fval = np.log10(con_fine[:,2])
# levels = np.linspace(-fval.max(), -fval.min(), 100)
levels = MaxNLocator(nbins=50).tick_values(fval.min(), fval.max())
plt.plot(np.log10(150), np.log10(10**-1), 'd', c=sns.color_palette()[1], label='Initial Simul.', markersize=6)
cs = plt.tricontourf(P, D_o, -fval, levels=np.flip(-levels))
plt.yticks([-1.005, -1, -0.996], ['$10^{-1.005}$', '$10^{-1}$', '$10^{-0.996}$'], rotation=30)
plt.xticks([2.173, 2.178], ['$10^{2.173}$', '$10^{2.178}$'])
plt.tick_params(axis='x',direction='out', which='minor', length=10)
fig1 = plt.gcf()
clb = fig1.colorbar(cs, ticks=[5, 7, 9, 11])
clb.ax.set_title('Cost')
```
%% Cell type:markdown id: tags:
### Figure: supplement. Scaling at early and late times
%% Cell type:code id: tags:
``` python
scal1 = np.loadtxt('scaling_test_1.csv', delimiter=',')
scal2 = np.loadtxt('scaling_test_2.csv', delimiter=',')
scal3 = np.loadtxt('scaling_test_3.csv', delimiter=',')
s1 = plt.plot(scal1[:, 0], scal1[:, 14::2], '-', lw=1, c=dark_grey)
s2 = plt.plot(scal2[:, 0], scal2[:, 14::2], '-', lw=1, c=red, alpha=0.3)
s3 = plt.plot(scal3[:, 0], scal3[:, 14::2], '-', lw=1, c=green)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u]',
[0, 2], [0,1], [3,2])
plt.legend([s1[0], s2[0], s3[0]], ['Reference', '$D_\mathrm{out}\propto P^2$',
'$D_\mathrm{out}\propto P$'], frameon=False,
fontsize=9, handletextpad=0.4, handlelength=0.8, loc=(0.57, 0.5))
save_nice_fig(fol+'Supp/scal_late.pdf')
```
%% Cell type:code id: tags:
``` python
s1 = plt.plot(scal1[:, 0], scal1[:, 14::2], '-', lw=1, c=dark_grey)
s2 = plt.plot(scal2[:, 0], scal2[:, 14::2], '-', lw=1, c=red, alpha=0.3)
s3 = plt.plot(scal3[:, 0], scal3[:, 14::2], '-', lw=1, c=green)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u]',
[0, 1.2], [0.35,1], [3,2])
save_nice_fig(fol+'Supp/scal_late_zoom.pdf')
```
%% Cell type:code id: tags:
``` python
s1 = plt.plot(scal1[:, 0], scal1[:, 2:10:2], '-', lw=1, c=dark_grey)
s2 = plt.plot(scal2[:, 0], scal2[:, 2:10:2], '-', lw=1, c=red)
s3 = plt.plot(scal3[:, 0], scal3[:, 2:10:2], '-', lw=1, c=green, alpha=0.4)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u]',
[0, 2], [0,1], [3,2])
plt.legend([s1[0], s2[0], s3[0]], ['Reference', '$D_\mathrm{out}\propto P^2$',
'$D_\mathrm{out}\propto P$'], frameon=False,
fontsize=9, handletextpad=0.4, handlelength=0.8, loc=(0.57, 0.54))
save_nice_fig(fol+'Supp/scal_early.pdf')
```
%% Cell type:code id: tags:
``` python
s1 = plt.plot(scal1[:, 0], scal1[:, 4:11:2], '-', lw=1, c=dark_grey, label='Original')
s2 = plt.plot(scal2[:, 0], scal2[:, 4:11:2], '-', lw=1, c=red, label='Original')
s3 = plt.plot(scal3[:, 0], scal3[:, 4:11:2], '-', lw=1, c=green, label='Original', alpha=0.4)
nice_fig('radial distance $r$ [$\mathrm{\mu m}$]', 'intensity [a.u]',
[0.97,1.03], [0, 0.35], [3,2])
save_nice_fig(fol+'Supp/scal_early_zoom.pdf')
```
%% Cell type:code id: tags:
``` python
```
......
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