def stf_fit(p0, lsfunc):
data = stf.get_trace()[stf.get_fit_start():stf.get_fit_end()]
dt = stf.get_sampling_interval()
x = np.arange(0, len(data) * dt, dt)
plsq = leastsq(leastsq_stf, p0, args=(data, lsfunc, x))
return plsq[0]
def crop():
si = stf.get_sampling_interval()
start = stf.get_fit_start() * si
end = stf.get_fit_end() * si
spells.cut_sweeps(start, end - start)
return
def stf_fit( p0, lsfunc ):
data = stf.get_trace()[ stf.get_fit_start() : stf.get_fit_end() ]
dt = stf.get_sampling_interval()
x = np.arange(0, len(data)*dt, dt)
plsq = leastsq(leastsq_stf, p0, args=(data, lsfunc, x))
return plsq[0]
def monoexpfit(optimization=True, Tn=20):
"""
Fits monoexponential function with offset to data between the fit cursors
in the current trace of the active channel using a Chebyshev-Levenberg-
Marquardt hybrid algorithm. Optimization requires Scipy. Setting optimization
to False forces this function to use just the Chebyshev algorithm. The maximum
order of the Chebyshev polynomials can be set using Tn.
"""
# Get data
fit_start = stf.get_fit_start()
fit_end = stf.get_fit_end()
y = np.double(stf.get_trace()[fit_start:fit_end])
si = stf.get_sampling_interval()
l = len(y)
t = si * np.arange(0, l, 1, np.double)
# Define monoexponential function
def f(t, *p):
return p[0] + p[1] * np.exp(-t / p[2])
# Get initial values from Chebyshev transform fit
init = chebexp(1, Tn)
p0 = (init.get('Offset'), )
p0 += (init.get('Amp_0'), )
p0 += (init.get('Tau_0'), )
# Optimize (if applicable)
if optimization == True:
# Optimize fit using Levenberg-Marquardt algorithm
options = {"ftol": 2.22e-16, "xtol": 2.22e-16, "gtol": 2.22e-16}
[p, pcov] = optimize.curve_fit(f, t, y, p0, **options)
elif optimization == False:
p = list(p0)
fit = f(t, *p)
# Calculate SSE
SSE = np.sum((y - fit)**2)
# Plot fit in a new window
matrix = np.zeros((2, stf.get_size_trace())) * np.nan
matrix[0, :] = stf.get_trace()
matrix[1, fit_start:fit_end] = fit
stf.new_window_matrix(matrix)
# Create table of results
retval = [("p0_Offset", p[0])]
retval += [("p1_Amp_0", p[1])]
retval += [("p2_Tau_0", p[2])]
retval += [("SSE", SSE)]
retval += [("dSSE", 1.0 - np.sum((y - f(t, *p0))**2) / SSE)]
retval += [("Time fit begins", fit_start * si)]
retval += [("Time fit ends", fit_end * si)]
retval = dict(retval)
stf.show_table(
retval, "monoexpfit, Section #%i" % float(stf.get_trace_index() + 1))
return
def batch_integration():
"""
Perform batch integration between the decay/fit cursors of all traces
in the active window
"""
n = int(stf.get_fit_end() + 1 - stf.get_fit_start())
x = [i * stf.get_sampling_interval() for i in range(n)]
dictlist = []
for i in range(stf.get_size_channel()):
stf.set_trace(i)
y = stf.get_trace()[int(stf.get_fit_start()):int(stf.get_fit_end() +
1)]
auc = np.trapz(y - stf.get_base(), x)
dictlist += [("%i" % (i + 1), auc)]
retval = dict(dictlist)
stf.show_table(retval, "Area Under Curve")
stf.set_trace(0)
return
def yvalue(origin, interval):
stf.set_fit_start(origin, True)
stf.set_fit_end(origin + interval, True)
stf.measure()
x = int(stf.get_fit_end(False))
y = []
for i in range(stf.get_size_channel()):
stf.set_trace(i)
y.append(stf.get_trace(i)[x])
return y
def blankstim():
"""
Blank values between fit cursors in all traces in the active channel.
Typically used to blank stimulus artifacts.
"""
fit_start = stf.get_fit_start()
fit_end = stf.get_fit_end()
blanked_traces = []
for i in range(stf.get_size_channel()):
tmp = stf.get_trace(i)
tmp[fit_start:fit_end] = np.nan
blanked_traces.append(tmp)
stf.new_window_list(blanked_traces)
return
def interpstim():
"""
Interpolate values between fit cursors in all traces in the active channel.
Typically used to remove stimulus artifacts.
"""
x = np.array(
[i * stf.get_sampling_interval() for i in range(stf.get_size_trace())])
fit_start = int(stf.get_fit_start())
fit_end = int(stf.get_fit_end())
interp_traces = []
for i in range(stf.get_size_channel()):
tmp = stf.get_trace(i)
tmp[fit_start:fit_end] = np.interp(x[fit_start:fit_end],
[x[fit_start], x[fit_end]],
[tmp[fit_start], tmp[fit_end]])
interp_traces.append(tmp)
stf.new_window_list(interp_traces)
return
def chebexp(n, Tn=20):
"""
Fits sums of exponentials with offset to the current trace in the
active channel using the Chebyshev tranform algorithm. The maximum
order of the Chebyshev polynomials can be set using Tn.
Reference:
Malachowski, Clegg and Redford (2007) J Microsc 228(3): 282-95
"""
# Get data trace between fit/decay cursors
y = stf.get_trace()[stf.get_fit_start():stf.get_fit_end()].astype(
np.double)
si = np.double(stf.get_sampling_interval())
l = len(y)
N = np.double(l - 1)
# Calculate time dimension with unit 1
t = np.arange(0, l, 1, np.double)
# Check the maximum order Chebyshev polynomials to generate
if l < Tn:
raise ValueError('Tn exceeds the number of data points')
# Generate the polynomials T and coefficients d
T0 = np.ones((l), np.double)
R0 = np.sum(T0**2)
d0 = np.sum((T0 * y) / R0)
T = np.zeros((l, Tn), np.double)
T[:, 0] = 1 - 2 * t / N
T[:, 1] = 1 - 6 * t / (N - 1) + 6 * t**2 / (N * (N - 1))
R = np.zeros((Tn), np.double)
d = np.zeros((Tn), np.double)
for j in range(Tn):
if j > 1:
A = (j + 1) * (N - j)
B = 2 * (j + 1) - 1
C = j * (N + j + 1)
T[:, j] = (B * (N - 2 * t) * T[:, j - 1] - C * T[:, j - 2]) / A
R[j] = np.sum(T[:, j]**2)
d[j] = np.sum(T[:, j] * y / R[j])
# Generate additional coefficients dn that describe the relationship
# between the Chebyshev coefficients d and the constant k, which is
# directly related to the exponent time constant
dn = np.zeros((n, Tn), np.double)
for i in range(1, n + 1):
for j in range(1 + i, Tn - i + 1):
if i > 1:
dn[i - 1, j - 1] = (((N + j + 2) * dn[i - 2, j] /
(2 * j + 3)) - dn[i - 2, j - 1] -
((N - j + 1) * dn[i - 2, j - 2] /
(2 * j - 1))) / 2
else:
dn[i - 1,
j - 1] = (((N + j + 2) * d[j] / (2 * j + 3)) - d[j - 1] -
((N - j + 1) * d[j - 2] / (2 * j - 1))) / 2
for i in range(n):
dn[i, :] = dn[i, :] * np.double(np.all(dn, 0))
# Form the regression model to find the time constants of each exponent
Mn = np.zeros((n, n), np.double)
b = np.zeros(n, np.double)
for i in range(n):
b[i] = np.sum(d * dn[i, :])
for m in range(n):
Mn[i, m] = -np.sum(dn[i, :] * dn[m, :])
# Solve the linear problem
try:
x = np.linalg.solve(Mn, b)
except:
x = np.linalg.lstsq(Mn, b)[0]
k = np.roots(np.hstack((1, x)))
if any(k != np.real(k)):
raise ValueError("Result is not a sum of %d real exponents" % n)
tau = -1 / np.log(1 + k)
# Generate the Chebyshev coefficients df for each exponent
df0 = np.zeros(n, np.double)
df = np.zeros((n, Tn), np.double)
for i in range(n):
for j in range(Tn):
df[i, j] = np.sum(np.exp(-t / tau[i]) * T[:, j] / R[j])
df0[i] = np.sum(np.exp(-t / tau[i]) * T0 / R0)
# Form the regression model to find the amplitude of each exponent
Mf = np.zeros((n, n), np.double)
b = np.zeros(n, np.double)
for i in range(n):
b[i] = np.sum(d * df[i, :])
for m in range(n):
Mf[i, m] = np.sum(df[i, :] * df[m, :])
# Solve the linear problem
try:
a = np.linalg.solve(Mf, b)
except:
a = np.linalg.lstsq(Mf, b)[0]
# Calculate the offset for the fit
offset = d0 - np.sum(df0 * a.T)
# Prepare output
retval = [("Amp_%d" % i, a[i]) for i in range(n)]
retval += [("Tau_%d" % i, si * tau[i]) for i in range(n)]
retval += [("Offset", np.double(offset))]
retval = dict(retval)
return retval
def EPSPtrains(latency=200,
numStim=4,
intvlList=[1, 0.8, 0.6, 0.4, 0.2, 0.1, 0.08, 0.06, 0.04, 0.02]):
# Initialize
numTrains = len(intvlList) # Number of trains
intvlArray = np.array(intvlList) * 1000 # Units in ms
si = stf.get_sampling_interval() # Units in ms
# Background subtraction
traceBaselines = []
subtractedTraces = []
k = 1e-4
x = [i * stf.get_sampling_interval() for i in range(stf.get_size_trace())]
for i in range(numTrains):
stf.set_trace(i)
z = x
y = stf.get_trace()
traceBaselines.append(y)
ridx = []
if intvlArray[i] > 500:
for j in range(numStim):
ridx += range(
int(round(((intvlArray[i] * j) + latency - 1) / si)),
int(round(
((intvlArray[i] * (j + 1)) + latency - 1) / si)) - 1)
else:
ridx += range(
int(round((latency - 1) / si)),
int(
round(((intvlArray[i] *
(numStim - 1)) + latency + 500) / si)) - 1)
ridx += range(int(round(4999 / si)), int(round(5199 / si)))
z = np.delete(z, ridx, 0)
y = np.delete(y, ridx, 0)
yi = np.interp(x, z, y)
yf = signal.symiirorder1(yi, (k**2), 1 - k)
traceBaselines.append(yf)
subtractedTraces.append(stf.get_trace() - yf)
stf.new_window_list(traceBaselines)
stf.new_window_list(subtractedTraces)
# Measure depolarization
# Initialize variables
a = []
b = []
# Set baseline start and end cursors
stf.set_base_start(np.round(
(latency - 50) / si)) # Average during 50 ms period before stimulus
stf.set_base_end(np.round(latency / si))
# Set fit start cursor
stf.set_fit_start(np.round(latency / si))
stf.set_fit_end(
np.round(((intvlArray[1] * (numStim - 1)) + latency + 1000) /
si)) # Include a 1 second window after last stimulus
# Start AUC calculations
for i in range(numTrains):
stf.set_trace(i)
stf.measure()
b.append(stf.get_base())
n = int(stf.get_fit_end() + 1 - stf.get_fit_start())
x = np.array([k * stf.get_sampling_interval() for k in range(n)])
y = stf.get_trace()[int(stf.get_fit_start()):int(stf.get_fit_end() +
1)]
a.append(np.trapz(y - b[i], x)) # Units in V.s
return a
def wcp(V_step=-5, step_start=10, step_duration=20):
"""
Measures whole cell properties. Specifically, this function returns the
voltage clamp step estimates of series resistance, input resistance, cell
membrane resistance, cell membrane capacitance, cell surface area and
specific membrane resistance.
The series (or access) resistance is obtained my dividing the voltage step
by the peak amplitude of the current transient (Ogden, 1994): Rs = V / Ip
The input resistance is obtained by dividing the voltage step by the average
amplitude of the steady-state current (Barbour, 2014): Rin = V / Iss
The cell membrane resistance is calculated by subtracting the series
resistance from the input resistance (Barbour, 1994): Rm = Rin - Rs
The cell membrane capacitance is estimated by dividing the transient charge
by the size of the voltage-clamp step (Taylor et al. 2012): Cm = Q / V
The cell surface area is estimated by dividing the cell capacitance by the
specific cell capacitance, c (1.0 uF/cm^2; Gentet et al. 2000; Niebur, 2008):
Area = Cm / c
The specific membrane resistance is calculated by multiplying the cell
membrane resistance with the cell surface area: rho = Rm * Area
Users should be aware of the approximate nature of determining cell
capacitance and derived parameters from the voltage-clamp step method
(Golowasch, J. et al., 2009)
References:
Barbour, B. (2014) Electronics for electrophysiologists. Microelectrode
Techniques workshop tutorial.
www.biologie.ens.fr/~barbour/electronics_for_electrophysiologists.pdf
Gentet, L.J., Stuart, G.J., and Clements, J.D. (2000) Direct measurement
of specific membrane capacitance in neurons. Biophys J. 79(1):314-320
Golowasch, J. et al. (2009) Membrane Capacitance Measurements Revisited:
Dependence of Capacitance Value on Measurement Method in Nonisopotential
Neurons. J Neurophysiol. 2009 Oct; 102(4): 2161-2175.
Niebur, E. (2008), Scholarpedia, 3(6):7166. doi:10.4249/scholarpedia.7166
www.scholarpedia.org/article/Electrical_properties_of_cell_membranes
(revision #13938, last accessed 30 April 2018)
Ogden, D. Chapter 16: Microelectrode electronics, in Ogden, D. (ed.)
Microelectrode Techniques. 1994. 2nd Edition. Cambridge: The Company
of Biologists Limited.
Taylor, A.L. (2012) What we talk about when we talk about capacitance
measured with the voltage-clamp step method J Comput Neurosci.
32(1):167-175
"""
# Error checking
if stf.get_yunits() != "pA":
raise ValueError('The recording is not voltage clamp')
# Prepare variables from input arguments
si = stf.get_sampling_interval()
t0 = step_start / si
l = step_duration / si
# Set cursors and update measurements
stf.set_base_start((step_start - 1) / si)
stf.set_base_end(t0 - 1)
stf.set_peak_start(t0)
stf.set_peak_end((step_start + 1) / si)
stf.set_fit_start(t0)
stf.set_fit_end(t0 + l - 1)
stf.set_peak_direction("both")
stf.measure()
# Calculate series resistance (Rs) from initial transient
b = stf.get_base()
Rs = 1000 * V_step / (stf.get_peak() - b) # in Mohm
# Calculate charge delivered during the voltage clamp step
n = int(stf.get_fit_end() + 1 - stf.get_fit_start())
x = [i * stf.get_sampling_interval() for i in range(n)]
y = stf.get_trace()[int(stf.get_fit_start()):int(stf.get_fit_end() + 1)]
Q = np.trapz(y - b, x)
# Set cursors and update measurements
stf.set_base_start(t0 + l - 1 - (step_duration / 4) / si)
stf.set_base_end(t0 + l - 1)
stf.measure()
# Measure steady state current and calculate input resistance
I = stf.get_base() - b
Rin = 1000 * V_step / I # in Mohm
# Calculate cell membrane resistance
Rm = Rin - Rs # in Mohm
# Calculate voltage-clamp step estimate of the cell capacitance
t = x[-1] - x[0]
Cm = (Q - I * t) / V_step # in pF
# Estimate membrane surface area, where the capacitance per unit area is 1.0 uF/cm^2
A = Cm * 1e-06 / 1.0 # in cm^2
# Calculate specific membrane resistance
rho = 1e+03 * Rm * A # in kohm.cm^2; usually 10 at rest
# Create table of results
retval = []
retval += [("Holding current (pA)", b)]
retval += [("Series resistance (Mohm)", Rs)]
retval += [("Input resistance (Mohm)", Rin)]
retval += [("Cell resistance (Mohm)", Rm)]
retval += [("Cell capacitance (pF)", Cm)]
retval += [("Surface area (um^2)", A * 1e+04**2)]
retval += [("Membrane resistivity (kohm.cm^2)", rho)]
retval = dict(retval)
stf.show_table(retval, "Whole-cell properties")
return retval
