SCALCS

Pure Python implementations of Q-matrix formalisms for single ion channel kinetic analysis.

Modules

Module	Description
scalcslib	Core calculations: asymptotic roots, dwell-time pdfs, P(open)
firstlatency	First-latency (first-opening) pdf after a concentration jump
cjumps	Concentration-jump macroscopic current calculations
qmatlib	Q-matrix algebra: eigendecomposition, matrix exponentials
pdfs	Exponential mixture pdf evaluation
scburst	Burst-length and cluster distributions
popen	Equilibrium open probability
mechanism	Ion channel mechanism (state/rate) representation
scalcsio	HJCFIT / DC_PyPs file I/O

First-latency pdf (firstlatency)

Computes the distribution of times from a rapid agonist concentration jump to the first channel opening, at three levels of approximation:

• Ideal — no missed events; mixture of kF exponentials.
• Asymptotic — HJC approximation valid for t >> tres; kF components with roots from det[W_F(s)] = 0.
• Exact — HJC exact correction for tres ≤ t < 3·tres, asymptotic beyond.

Usage example:

from scalcs import firstlatency as fl
from scalcs import qmatlib as qml
import numpy as np

# phi_shut: shut-state occupancies at c0 = 0
phi_shut = qml.pinf(mec.Q)[mec.kA:]
tres = 1e-3  # 1 ms dead time

roots = fl.asymptotic_roots(tres, mec)
areas = fl.asymptotic_areas(tres, roots, phi_shut, mec)
tau   = -1.0 / roots

t = np.linspace(tres, 0.1, 500)
f_asym  = fl.asymptotic_pdf(t, tres, tau, areas)

eigvals, g00, g10, g11 = fl.gamma_coefficients(tres, phi_shut, mec)
f_exact = fl.exact_pdf(t, tres, roots, areas, eigvals, g00, g10, g11)

References

CH82: Colquhoun D, Hawkes AG (1982) On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Phil Trans R Soc Lond B 300, 1-59.

HJC92: Hawkes AG, Jalali A, Colquhoun D (1992) Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events. Phil Trans R Soc Lond B 337, 383-404.

CHME97: Colquhoun D, Hawkes AG, Merlushkin A, Edmonds B (1997) Properties of single ion channel currents elicited by a pulse of agonist concentration or voltage. Phil Trans R Soc Lond A 355, 1743-1786.

CH95a: Colquhoun D, Hawkes AG (1995a) The principles of the stochastic interpretation of ion channel mechanisms. In: Single-channel recording. 2nd ed. (Eds: Sakmann B, Neher E) Plenum Press, New York, pp. 397-482.

CH95b: Colquhoun D, Hawkes AG (1995b) A Q-Matrix Cookbook. In: Single-channel recording. 2nd ed. (Eds: Sakmann B, Neher E) Plenum Press, New York, pp. 589-633.

CHS96: Colquhoun D, Hawkes AG, Srodzinski K (1996) Joint distributions of apparent open and shut times of single-ion channels and maximum likelihood fitting of mechanisms. Phil Trans R Soc Lond A 354, 2555-2590.