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Zhou-1998-Q10s-mean.py
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#!/usr/bin/env python2
#
# Try to reproduce Q10 values in Zhou et al. 1998
# See Fig. 8-10.
#
from __future__ import print_function
import sys
sys.path.append('../lib')
import os
import numpy as np
import matplotlib
if '--show' not in sys.argv:
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import model_ikr as m
from protocols import Zhou1998_activation_deactivation as prt1
from protocols import Zhou1998_inactivation as prt2
from protocols import Zhou1998_recovery as prt3
# Set parameter transformation
import parametertransform
transform_to_model_param = parametertransform.log_transform_to_model_param
transform_from_model_param = parametertransform.log_transform_from_model_param
debug = False
common_conductance = 1.0
fit_seed = 542811797
temperatures = ['25.0', '37.0'][::-1]
color = {'25.0':'#6baed6',
'37.0':'#fd8d3c'}
FILE_LIST = {
'25.0': ['herg25oc'],
'37.0': ['herg37oc'],
}
#
# Zhou et al. 1998 Q10 values
#
ZhouQ10 = []
T1 = 23.0
T2 = 35.0
dT1 = dT2 = 1.0
def compute_q10(ks, dks, Ts, dTs):
# Parameters:
# ks, Ts each should have two elements for rate constant and temperature
# dks, dTs are the standard deviations of ks, Ts respectively
#
# Return:
# mean Q10 and standard deviation of Q10
a1, a2 = ks
da1, da2 = dks
T1, T2 = Ts
dT1, dT2 = dTs
dT = 10.0 / (T2 - T1)
q10 = (a1 / a2) ** (dT)
mean_q10 = q10
std_q10 = np.sqrt((da1 * dT / a1 * q10) ** 2
+ (da2 * dT / a2 * q10) ** 2
+ (dT1 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2
+ (dT2 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2)
return (mean_q10, std_q10)
ZhouQ10.append(compute_q10((947., 105.),
(87. * np.sqrt(6), 15. * np.sqrt(6)),
(T1, T2), (dT1, dT2)))
ZhouQ10.append(compute_q10((216., 149.),
(19. * np.sqrt(3), 27. * np.sqrt(3)),
(T1, T2), (dT1, dT2)))
ZhouQ10.append(compute_q10((14.2, 3.1),
(1.3 * np.sqrt(3), 0.3 * np.sqrt(3)),
(T1, T2), (dT1, dT2)))
ZhouQ10.append(compute_q10((8.5, 1.8),
(0.6 * np.sqrt(3), 0.1 * np.sqrt(3)),
(T1, T2), (dT1, dT2)))
if debug:
savedir = './figs/Zhou1998/'
for p in ['-act', '-deact', '-inact', '-recovery']:
if not os.path.isdir(savedir + 'Zhou1998-fig%s' % (p)):
os.makedirs(savedir + 'Zhou1998-fig%s' % (p))
#
# Functions to fit time constants
#
def fit_tau_single_exp(current, times,
t_start, t_end,
t_trim, t_fit_until,
func, p0=None,
debug=False, debugout=''):
# use 2-parameters exponential fit to the tail
from scipy.optimize import curve_fit
if func == 0:
def exp_func(t, a, b):
# do a "proper exponential" decay fit
# i.e. shift the t to t' where t' has zero at the start of the
# voltage step
return a * (1.0 - np.exp(-t / b))
elif func == 1:
def exp_func(t, a, b):
# do a "proper exponential" decay fit
# i.e. shift the t to t' where t' has zero at the start of the
# voltage step
return a * np.exp(-(t - x[0]) / b)
time_window = np.where(np.logical_and(times > t_start, times <= t_end))[0]
i_trim = np.argmin(np.abs(times - (t_start + t_trim))) - time_window[0]
i_fit_until = np.argmin(np.abs(times - (t_start + t_fit_until))) \
- time_window[0]
# trim off the first i_trim (100ms) in case it is still shooting up...
x = times[time_window[0] + i_trim:time_window[0] + i_fit_until]
if func == 0:
x = np.copy(x - times[time_window[0]])
y = current[time_window[0] + i_trim:
time_window[0] + i_fit_until]
try:
popt, pcov = curve_fit(exp_func, x, y, p0=p0)
tau = 1e3 * popt[1] # [ms]
except:
raise Exception('Maybe not here!')
if debug:
fig = plt.figure()
plt.plot(times[time_window[0] - 500:time_window[-1] + 500],
current[time_window[0] - 500:time_window[-1] + 500],
c='#d62728')
plot_times = times[time_window[0]:time_window[0] + i_fit_until]
if func == 0:
fitted_times = plot_times - times[time_window[0]]
elif func == 1:
fitted_times = plot_times
fitted = exp_func(fitted_times, *popt)
plt.plot(plot_times, fitted, '--', c='#1f77b4')
plt.plot(times[time_window][0], fitted[0], 'kx')
plt.axvline(x=times[time_window[0] + i_trim])
plt.axvline(x=times[time_window[0] + i_fit_until])
if '--show' in sys.argv:
plt.show()
else:
plt.savefig('figs/Zhou1998/Zhou1998-fig%s/%sC-%s.png'
% (debugout[0], temperature, debugout[1]))
plt.close()
return tau
def fit_tau_double_exp(current, times,
t_start, t_end,
t_trim, t_fit_until,
debug=False, debugout=''):
# use 4-parameters 'double exponential' fit to the current
from scipy.optimize import curve_fit
def exp_func(t, a, b, c, d):
# Shift the t to t' where t' has zero at the start of the
# voltage step
return a * np.exp( -(t - x[0]) / b) + c * np.exp( -(t - x[0]) / d)
time_window = np.where(np.logical_and(times > t_start, times <= t_end))[0]
i_trim = np.argmin(np.abs(times - (t_start + t_trim))) - time_window[0]
i_fit_until = np.argmin(np.abs(times - (t_start + t_fit_until))) \
- time_window[0]
# trim off the first i_trim (100ms) in case it is still shooting up...
x = times[time_window[0] + i_trim:time_window[0] + i_fit_until]
y = current[time_window[0] + i_trim:
time_window[0] + i_fit_until]
try:
popt, pcov = curve_fit(exp_func, x, y, p0=[0.1, 2, 0.1, 3.8],
bounds=([-1, 1e-6, -1, 1e-6], [1, 5, 1, 10]))
fitted = exp_func(times[time_window[0]:
time_window[0] + i_fit_until], *popt)
tau_1 = 1e3 * popt[1] # [ms]
tau_2 = 1e3 * popt[3] # [ms]
except:
raise Exception('Maybe not here!')
if debug:
fig = plt.figure()
plt.plot(times[time_window[0] - 500:time_window[-1] + 500],
current[time_window[0] - 500:time_window[-1] + 500],
c='#d62728')
plt.plot(times[time_window[0]:time_window[0] + i_fit_until], fitted,
'--', c='#1f77b4')
plt.axvline(x=times[time_window[0] + i_trim])
plt.axvline(x=times[time_window[0] + i_fit_until])
if '--show' in sys.argv:
plt.show()
else:
plt.savefig('figs/Zhou1998/Zhou1998-fig%s/%sC-%s.png'
% (debugout[0], temperature, debugout[1]))
plt.close()
return tau_1, tau_2
#
# Simulate
#
times_prt1, ttotal_prt1, tmeasure_prt1 = prt1(None, return_times=True)
tau_act = {}
tau_deact = {}
times_prt2, ttotal_prt2, tmeasure_prt2 = prt2(None, return_times=True)
tau_inact = {}
times_prt3, ttotal_prt3, tmeasure_prt3 = prt3(None, return_times=True)
tau_rec = {}
for i_T, temperature in enumerate(temperatures):
tau_act[temperature] = []
tau_deact[temperature] = []
tau_inact[temperature] = []
tau_rec[temperature] = []
# Model
model_prt1 = m.Model('../mmt-model-files/kylie-2017-IKr.mmt',
protocol_def=prt1,
temperature=273.15 + float(temperature), # K
transform=None,
useFilterCap=False, # ignore capacitive spike
effEK=False) # OK to switch this off here
model_prt2 = m.Model('../mmt-model-files/kylie-2017-IKr.mmt',
protocol_def=prt2,
temperature=273.15 + float(temperature), # K
transform=None,
useFilterCap=False, # ignore capacitive spike
effEK=False) # OK to switch this off here
model_prt3 = m.Model('../mmt-model-files/kylie-2017-IKr.mmt',
protocol_def=prt3,
temperature=273.15 + float(temperature), # K
transform=None,
useFilterCap=False, # ignore capacitive spike
effEK=False) # OK to switch this off here
file_list = FILE_LIST[temperature]
for file_name in file_list:
load_file = './out-mcmc/%s-pseudo2hbm-lognorm-mean.txt' % (file_name)
mean_chain = np.loadtxt(load_file) # transformed
hbm_T_mean = transform_to_model_param(
np.mean(mean_chain, axis=0))
selectedwell = transform_to_model_param(mean_chain[:70, :].T).T
selectedwell = [hbm_T_mean] + list(selectedwell)
for i_cell, p in enumerate(selectedwell):
p[0] = common_conductance
p = np.append(p, 0) # No leak current
i_prt1 = model_prt1.simulate(p, times_prt1)
i_prt2 = model_prt2.simulate(p, times_prt2)
i_prt3 = model_prt3.simulate(p, times_prt3)
tau1 = fit_tau_single_exp(i_prt1, times_prt1,
tmeasure_prt1[0], tmeasure_prt1[0] + 5,
t_trim=0.5, t_fit_until=3,
func=0,
debug=debug, debugout=['-act', i_cell])
tau_act[temperature].append(tau1)
tau2 = fit_tau_single_exp(i_prt1, times_prt1,
tmeasure_prt1[1], tmeasure_prt1[1] + 5,
# t_trim=200e-3, t_fit_until=3.5,
t_trim=200e-3, t_fit_until=1.5,
# t_trim=2, t_fit_until=4,
func=1,
debug=debug, debugout=['-deact', i_cell])
tau_deact[temperature].append(tau2)
tau3 = fit_tau_single_exp(i_prt2, times_prt2,
tmeasure_prt2, tmeasure_prt2 + 20e-3,
t_trim=0.1e-3, t_fit_until=4e-3,
func=1, p0=[0.025, 5e-3],
debug=debug, debugout=['-inact', i_cell])
tau_inact[temperature].append(tau3)
tau4 = fit_tau_single_exp(i_prt3, times_prt3,
tmeasure_prt3, tmeasure_prt3 + 20e-3,
t_trim=0, t_fit_until=12e-3,
func=0,
debug=debug,
debugout=['-recovery', i_cell])
tau_rec[temperature].append(tau4)
#
# Q10s
#
import itertools
T1 = 37.0
T2 = 25.0
dT = 10.0 / (T2 - T1)
dT1 = dT2 = 1.0
# activation
a1 = tau_act[str(T1)][0]
a2 = tau_act[str(T2)][0]
q10_act_hbm = (a1 / a2) ** (10.0 / (T2 - T1))
tau_act[str(T1)] = tau_act[str(T1)][1:]
tau_act[str(T2)] = tau_act[str(T2)][1:]
# method 1
a1 = tau_act[str(T1)][0]
a2 = tau_act[str(T2)][0]
q10_act_hbm = (a1 / a2) ** (10.0 / (T2 - T1))
tau_act[str(T1)] = tau_act[str(T1)][1:]
tau_act[str(T2)] = tau_act[str(T2)][1:]
a1 = np.mean(tau_act[str(T1)])
a2 = np.mean(tau_act[str(T2)])
da1 = np.std(tau_act[str(T1)])
da2 = np.std(tau_act[str(T2)])
q10 = (a1 / a2) ** (dT)
T1_mean_q10_act = (a1 / np.asarray(tau_act[str(T2)])) ** (dT)
T2_mean_q10_act = (np.asarray(tau_act[str(T1)]) / a2) ** (dT)
mean_q10_act = q10
std_q10_act = np.sqrt((da1 * dT / a1 * q10) ** 2 + (da2 * dT / a2 * q10) ** 2
+ (dT1 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2
+ (dT2 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2)
# method 2
q10_act_combinations = []
for a1i, a2i in itertools.product(tau_act[str(T1)], tau_act[str(T2)]):
q10_act_combinations.append((a1i / a2i) ** (dT))
q10_act_mean = np.mean(q10_act_combinations)
q10_act_std = np.std(q10_act_combinations)
# deactivation
a1 = tau_deact[str(T1)][0]
a2 = tau_deact[str(T2)][0]
q10_deact_hbm = (a1 / a2) ** (10.0 / (T2 - T1))
tau_deact[str(T1)] = tau_deact[str(T1)][1:]
tau_deact[str(T2)] = tau_deact[str(T2)][1:]
# method 1
a1 = np.mean(tau_deact[str(T1)])
a2 = np.mean(tau_deact[str(T2)])
da1 = np.std(tau_deact[str(T1)])
da2 = np.std(tau_deact[str(T2)])
q10 = (a1 / a2) ** (dT)
T1_mean_q10_deact = (a1 / np.asarray(tau_deact[str(T2)])) ** (dT)
T2_mean_q10_deact = (np.asarray(tau_deact[str(T1)]) / a2) ** (dT)
mean_q10_deact = q10
std_q10_deact = np.sqrt((da1 * dT / a1 * q10) ** 2 + (da2 * dT / a2 * q10) ** 2
+ (dT1 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2
+ (dT2 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2)
# method 2
q10_deact_combinations = []
for a1i, a2i in itertools.product(tau_deact[str(T1)], tau_deact[str(T2)]):
q10_deact_combinations.append((a1i / a2i) ** (dT))
q10_deact_mean = np.mean(q10_deact_combinations)
q10_deact_std = np.std(q10_deact_combinations)
# inactivation
a1 = tau_inact[str(T1)][0]
a2 = tau_inact[str(T2)][0]
q10_inact_hbm = (a1 / a2) ** (10.0 / (T2 - T1))
tau_inact[str(T1)] = tau_inact[str(T1)][1:]
tau_inact[str(T2)] = tau_inact[str(T2)][1:]
# method 1
a1 = np.mean(tau_inact[str(T1)])
a2 = np.mean(tau_inact[str(T2)])
da1 = np.std(tau_inact[str(T1)])
da2 = np.std(tau_inact[str(T2)])
q10 = (a1 / a2) ** (dT)
T1_mean_q10_inact = (a1 / np.asarray(tau_inact[str(T2)])) ** (dT)
T2_mean_q10_inact = (np.asarray(tau_inact[str(T1)]) / a2) ** (dT)
mean_q10_inact = q10
std_q10_inact = np.sqrt((da1 * dT / a1 * q10) ** 2 + (da2 * dT / a2 * q10) ** 2
+ (dT1 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2
+ (dT2 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2)
# method 2
q10_inact_combinations = []
for a1i, a2i in itertools.product(tau_inact[str(T1)], tau_inact[str(T2)]):
q10_inact_combinations.append((a1i / a2i) ** (dT))
q10_inact_mean = np.mean(q10_inact_combinations)
q10_inact_std = np.std(q10_inact_combinations)
# recovery
a1 = tau_rec[str(T1)][0]
a2 = tau_rec[str(T2)][0]
q10_rec_hbm = (a1 / a2) ** (10.0 / (T2 - T1))
tau_rec[str(T1)] = tau_rec[str(T1)][1:]
tau_rec[str(T2)] = tau_rec[str(T2)][1:]
# method 1
a1 = np.mean(tau_rec[str(T1)])
a2 = np.mean(tau_rec[str(T2)])
da1 = np.std(tau_rec[str(T1)])
da2 = np.std(tau_rec[str(T2)])
q10 = (a1 / a2) ** (dT)
T1_mean_q10_rec = (a1 / np.asarray(tau_rec[str(T2)])) ** (dT)
T2_mean_q10_rec = (np.asarray(tau_rec[str(T1)]) / a2) ** (dT)
mean_q10_rec = q10
std_q10_rec = np.sqrt((da1 * dT / a1 * q10) ** 2 + (da2 * dT / a2 * q10) ** 2
+ (dT1 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2
+ (dT2 * q10 * np.log(a1 / a2) * dT ** 2 / 10.0) ** 2)
# method 2
q10_rec_combinations = []
for a1i, a2i in itertools.product(tau_rec[str(T1)], tau_rec[str(T2)]):
q10_rec_combinations.append((a1i / a2i) ** (dT))
q10_rec_mean = np.mean(q10_rec_combinations)
q10_rec_std = np.std(q10_rec_combinations)
# round up
mean_q10_act = round(mean_q10_act, 3)
std_q10_act = round(std_q10_act, 3)
q10_act_mean = round(q10_act_mean, 3)
q10_act_std = round(q10_act_std, 3)
mean_q10_deact = round(mean_q10_deact, 3)
std_q10_deact = round(std_q10_deact, 3)
q10_deact_mean = round(q10_deact_mean, 3)
q10_deact_std = round(q10_deact_std, 3)
mean_q10_inact = round(mean_q10_inact, 3)
std_q10_inact = round(std_q10_inact, 3)
q10_inact_mean = round(q10_inact_mean, 3)
q10_inact_std = round(q10_inact_std, 3)
mean_q10_rec = round(mean_q10_rec, 3)
std_q10_rec = round(std_q10_rec, 3)
q10_rec_mean = round(q10_rec_mean, 3)
q10_rec_std = round(q10_rec_std, 3)
# N pairs of cells are within Zhou et al. 1998 estimation (1st std)
# method 1
T1_mean_n_act = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T1_mean_q10_act,
ZhouQ10[0][0] + ZhouQ10[0][1] > T1_mean_q10_act))
T2_mean_n_act = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T2_mean_q10_act,
ZhouQ10[0][0] + ZhouQ10[0][1] > T2_mean_q10_act))
T1_mean_n_deact = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T1_mean_q10_deact,
ZhouQ10[0][0] + ZhouQ10[0][1] > T1_mean_q10_deact))
T2_mean_n_deact = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T2_mean_q10_deact,
ZhouQ10[0][0] + ZhouQ10[0][1] > T2_mean_q10_deact))
T1_mean_n_inact = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T1_mean_q10_inact,
ZhouQ10[0][0] + ZhouQ10[0][1] > T1_mean_q10_inact))
T2_mean_n_inact = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T2_mean_q10_inact,
ZhouQ10[0][0] + ZhouQ10[0][1] > T2_mean_q10_inact))
T1_mean_n_rec = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T1_mean_q10_rec,
ZhouQ10[0][0] + ZhouQ10[0][1] > T1_mean_q10_rec))
T2_mean_n_rec = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < T2_mean_q10_rec,
ZhouQ10[0][0] + ZhouQ10[0][1] > T2_mean_q10_rec))
# method 2
n_act = np.sum(np.logical_and(
ZhouQ10[0][0] - ZhouQ10[0][1] < q10_act_combinations,
ZhouQ10[0][0] + ZhouQ10[0][1] > q10_act_combinations))
n_deact = np.sum(np.logical_and(
ZhouQ10[1][0] - ZhouQ10[1][1] < q10_deact_combinations,
ZhouQ10[1][0] + ZhouQ10[1][1] > q10_deact_combinations))
n_inact = np.sum(np.logical_and(
ZhouQ10[2][0] - ZhouQ10[2][1] < q10_inact_combinations,
ZhouQ10[2][0] + ZhouQ10[2][1] > q10_inact_combinations))
n_rec = np.sum(np.logical_and(
ZhouQ10[3][0] - ZhouQ10[3][1] < q10_rec_combinations,
ZhouQ10[3][0] + ZhouQ10[3][1] > q10_rec_combinations))
print('----' * 20)
print('Method 1: Compute mean and std of tau at each temperature.')
print('Q10_activation:', mean_q10_act, '+/-', std_q10_act)
print('Q10_deactivation:', mean_q10_deact, '+/-', std_q10_deact)
print('Q10_inactivation:', mean_q10_inact, '+/-', std_q10_inact)
print('Q10_recovery:', mean_q10_rec, '+/-', std_q10_rec)
print(T1_mean_n_act, T2_mean_n_act)
print(T1_mean_n_deact, T2_mean_n_deact)
print(T1_mean_n_inact, T2_mean_n_inact)
print(T1_mean_n_rec, T2_mean_n_rec)
print('----' * 20)
print('Method 2: Compute all cells combinations between two temperatures.')
print('Q10_activation:', q10_act_mean, '+/-', q10_act_std)
print('Q10_deactivation:', q10_deact_mean, '+/-', q10_deact_std)
print('Q10_inactivation:', q10_inact_mean, '+/-', q10_inact_std)
print('Q10_recovery:', q10_rec_mean, '+/-', q10_rec_std)
print('With %s pairs within Zhou et al. 1998 estimation' \
% min(n_act, n_deact, n_inact, n_rec))
print('----' * 20)
print('Method 3: HBM mean mu model.')
print('Q10_activation:', q10_act_hbm)
print('Q10_deactivation:', q10_deact_hbm)
print('Q10_inactivation:', q10_inact_hbm)
print('Q10_recovery:', q10_rec_hbm)
print('----' * 20)
print('Zhou et al. 1998')
print('Q10_activation:', ZhouQ10[0][0], '+/-', ZhouQ10[0][1])
print('Q10_deactivation:', ZhouQ10[1][0], '+/-', ZhouQ10[1][1])
print('Q10_inactivation:', ZhouQ10[2][0], '+/-', ZhouQ10[2][1])
print('Q10_recovery:', ZhouQ10[3][0], '+/-', ZhouQ10[3][1])
## eof