def ideal_dwell_time_pdf_components(QAA, phiA):
"""
Calculate time constants and areas for an ideal (no missed events)
exponential open time probability density function.
For shut time pdf A by F in function call.
Parameters
----------
t : float
Time (sec).
QAA : array_like, shape (kA, kA)
Submatrix of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
taus : ndarray, shape(k, 1)
Time constants.
areas : ndarray, shape(k, 1)
Component relative areas.
"""
kA = QAA.shape[0]
w = np.zeros(kA)
eigs, A = qml.eigs_sorted(-QAA)
uA = np.ones((kA, 1))
#TODO: remove 'for'
for i in range(kA):
w[i] = np.dot(np.dot(np.dot(phiA, A[i]), (-QAA)), uA)
return eigs, w
def weighted_taus(mec, cmax, width, eff='c'):
"""
Calculate weighted on and off time constants for a square concentration
pulse.
Parameters
----------
mec : dcpyps.Mechanism
The mechanism to be analysed.
cmax : float
Pulse concentration.
width : float
Pulse width.
Returns
-------
tau_on_weighted, tau_off_weighted : floats
Weighted time constants.
"""
mec.set_eff(eff, 0)
eigs0, A0 = qml.eigs_sorted(mec.Q)
P0 = qml.pinf(mec.Q)
mec.set_eff(eff, cmax)
eigsInf, Ainf = qml.eigs_sorted(mec.Q)
w_on = coefficient_calc(mec.k, Ainf, P0)
Pt = P_t(width, eigsInf, w_on)
w_off = coefficient_calc(mec.k, A0, Pt)
ampl_on = np.sum(w_on[:, :mec.kA], axis=1)
max_ampl_on = np.max(np.abs(ampl_on))
rel_ampl_on = ampl_on / max_ampl_on
tau_on_weighted = np.sum(-rel_ampl_on[:-1] * (-1 / eigsInf[:-1]))
tau_on = -1 / eigsInf[:-1]
ampl_off = np.sum(w_off[:, :mec.kA], axis=1)
max_ampl_off = np.max(np.abs(ampl_off))
rel_ampl_off = ampl_off / max_ampl_off
tau_off_weighted = np.sum(rel_ampl_off[: -1] * (-1 / eigs0[:-1]))
tau_off = -1 / eigs0[:-1]
return tau_on_weighted, tau_on, tau_off_weighted, tau_off
def calc_jump (mec, reclen, step, cfunc, cargs):
"""
Calculate response to a concentration pulse directly from Q matrix.
Parameters
----------
mec : dcpyps.Mechanism
The mechanism to be analysed.
reclen : float
Trace length.
step : float
Sampling time interval.
cfunc : function
Concentration profile.
cargs : tuple
Arguments for cfunc(t, cargs).
Returns
-------
t : ndarray
Time samples.
c : ndarray
Concentration profile.
P : ndarray
All state occupancies.
Popen : ndarray
Open probability.
"""
t = np.arange(0, reclen, step)
c = cfunc(t, cargs)
mec.set_eff('c', cargs[1])
pi = qml.pinf(mec.Q)
Pt = np.array([pi.copy()])
for i in range(1, t.shape[0]):
mec.set_eff('c', c[i])
eigenvals, A = qml.eigs_sorted(mec.Q)
w = coefficient_calc(mec.k, A, pi)
pi = P_t(step, eigenvals, w)
Pt = np.append(Pt, [pi.copy()], axis=0)
P = Pt.transpose()
Popen = np.sum(P[: mec.kA], axis=0)
return t, c, Popen, P
def exact_GAMAxx(mec, tres, open):
"""
Calculate gama coeficients for the exact open time pdf (Eq. 3.22, HJC90).
Parameters
----------
tres : float
mec : dcpyps.Mechanism
The mechanism to be analysed.
open : bool
True for open time pdf and False for shut time pdf.
Returns
-------
eigen : ndarray, shape (k,)
Eigenvalues of -Q matrix.
gama00, gama10, gama11 : ndarrays
Constants for the exact open/shut time pdf.
"""
expQFF = qml.expQt(mec.QII, tres)
expQAA = qml.expQt(mec.QAA, tres)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kI)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kI, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kI, mec.kA, expQAA)
eigs, A = qml.eigs_sorted(-mec.Q)
if open:
phi = qml.phiHJC(eGAF, eGFA, mec.kA)
eigen, Z00, Z10, Z11 = qml.Zxx(mec.Q, eigs, A, mec.kA,
mec.QII, mec.QAI, mec.QIA, expQFF, open)
u = np.ones((mec.kI,1))
else:
phi = qml.phiHJC(eGFA, eGAF, mec.kI)
eigen, Z00, Z10, Z11 = qml.Zxx(mec.Q, eigs, A, mec.kA,
mec.QAA, mec.QIA, mec.QAI, expQAA, open)
u = np.ones((mec.kA, 1))
gama00 = (np.dot(np.dot(phi, Z00), u)).T[0]
gama10 = (np.dot(np.dot(phi, Z10), u)).T[0]
gama11 = (np.dot(np.dot(phi, Z11), u)).T[0]
return eigen, gama00, gama10, gama11
def printout(mec, cmax, width, eff='c'):
"""
"""
#TODO: on/off binding
#TODO: move some of calculations from here to separate functions
str = ('\n*******************************************\n' +
'CONCENTRATION JUMPS\n')
gamma = 30 # Conductance in pS
Vm = -80e-3 # Transmembrane potential in V.
mec.set_eff(eff, 0)
P0 = qml.pinf(mec.Q)
eigs0, A0 = qml.eigs_sorted(mec.Q)
str += ('\nEquilibrium occupancies before t=0, at concentration = 0.0:\n')
for i in range(mec.k):
str += ('p00({0:d}) = {1:.5g}\n'.format(i+1, P0[i]))
mec.set_eff(eff, cmax)
Pinf = qml.pinf(mec.Q)
eigsInf, Ainf = qml.eigs_sorted(mec.Q)
w_on = coefficient_calc(mec.k, Ainf, P0)
str += ('\nEquilibrium occupancies at maximum concentration = {0:.5g} mM:\n'
.format(cmax * 1000))
for i in range(mec.k):
str += ('pinf({0:d}) = '.format(i+1) + '{0:.5g}\n'.format(Pinf[i]))
Pt = P_t(width, eigsInf, w_on)
str += ('\nOccupancies at the end of {0:.5g} ms pulse:\n'.
format(width * 1000))
for i in range(mec.k):
str += ('pt({0:d}) = '.format(i+1) + '{0:.5g}\n'.format(Pt[i]))
tau_on_weighted, tau_on, tau_off_weighted, tau_off = weighted_taus(mec, cmax, width, eff='c')
str += ('\nON-RELAXATION for ideal step:\n' +
'Time course for current\n' +
'\nComp\tEigen\t\tTau (ms)\n')
for i in range(mec.k-1):
str += ('{0:d}\t'.format(i+1) +
'{0:.5g}\t\t'.format(eigsInf[i]) +
'{0:.5g}\t\n'.format(-1000 / eigsInf[i])) # convert to ms
ampl_on = np.sum(w_on[:, :mec.kA], axis=1)
cur_on = ampl_on * gamma * Vm
max_ampl_on = np.max(np.abs(ampl_on))
rel_ampl_on = ampl_on / max_ampl_on
area_on = -cur_on[:-1] / eigsInf[:-1]
str += ('\nAmpl.(t=0,pA)\tRel.ampl.\t\tArea(pC)\n')
for i in range(mec.k-1):
str += ('{0:.5g}\t\t'.format(cur_on[i]) +
'{0:.5g}\t\t'.format(rel_ampl_on[i]) +
'{0:.5g}\t\n'.format(area_on[i] * 1000))
str += ('\nWeighted On Tau (ms) = {0:.5g}\n'.format(tau_on_weighted * 1000))
str += ('\nTotal current at t=0 (pA) = {0:.5g}\n'.
format(np.sum(cur_on)))
str += ('Total current at equilibrium (pA) = {0:.5g}\n'.
format(cur_on[-1]))
str += ('Total area (pC) = {0:.5g}\n'.
format(np.sum(area_on)))
#TODO: Current at the end of pulse
ct = cur_on[:-1] * np.exp(width * eigsInf[:-1])
str += ('Current at the end of {0:.5g}'.format(width
* 1000) + ' ms pulse = {0:.5g}\n'.format(np.sum(ct) + cur_on[-1]))
# Calculate off- relaxation.
str += ('\nOFF-RELAXATION for ideal step:\n' +
'Time course for current\n' +
'\nComp\tEigen\t\tTau (ms)\n')
for i in range(mec.k-1):
str += ('{0:d}\t'.format(i+1) +
'{0:.5g}\t\t'.format(eigs0[i]) +
'{0:.5g}\t\n'.format(-1000 / eigs0[i]))
w_off = coefficient_calc(mec.k, A0, Pt)
ampl_off = np.sum(w_off[:, :mec.kA], axis=1)
cur_off = ampl_off * gamma * Vm
max_ampl_off = np.max(np.abs(ampl_off))
rel_ampl_off = ampl_off / max_ampl_off
area_off = np.zeros((mec.k-1))
str += ('\nAmpl.(t=0,pA)\tRel.ampl.\t\tArea(pC)\n')
for i in range(mec.k-1):
area_off[i] = -1000 * cur_off[i] / eigs0[i]
str += ('{0:.5g}\t\t'.format(cur_off[i]) +
'{0:.5g}\t\t'.format(rel_ampl_off[i]) +
'{0:.5g}\t\n'.format(area_off[i]))
str += ('\nWeighted Off Tau (ms) = {0:.5g}\n'.format(tau_off_weighted * 1000))
str += ('\nTotal current at t=0 (pA) = {0:.5g}\n'.
format(np.sum(cur_off)))
str += ('Total current at equilibrium (pA) = {0:.5g}\n'.
format(cur_off[-1]))
str += ('Total area (pC) = {0:.5g}\n'.format(np.sum(area_off)))
return str