Wang W et al. (2012), Optimal estimation of ion-channel kinetics from...

XB-ART-46119

PLoS One 2012 Jan 01;74:e35208. doi: 10.1371/journal.pone.0035208.

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Optimal estimation of ion-channel kinetics from macroscopic currents.

Wang W , Xiao F , Zeng X , Yao J , Yuchi M , Ding J .

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Markov modeling provides an effective approach for modeling ion channel kinetics. There are several search algorithms for global fitting of macroscopic or single-channel currents across different experimental conditions. Here we present a particle swarm optimization(PSO)-based approach which, when used in combination with golden section search (GSS), can fit macroscopic voltage responses with a high degree of accuracy (errors within 1%) and reasonable amount of calculation time (less than 10 hours for 20 free parameters) on a desktop computer. We also describe a method for initial value estimation of the model parameters, which appears to favor identification of global optimum and can further reduce the computational cost. The PSO-GSS algorithm is applicable for kinetic models of arbitrary topology and size and compatible with common stimulation protocols, which provides a convenient approach for establishing kinetic models at the macroscopic level.

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Species referenced: Xenopus
Genes referenced: gss

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	Figure 1. Fit a five-parameter voltage-dependent C-O model to the target current traces.(A) A five-parameter Markov model consisting of a closed state and an open state labeled with the letter C and O, respectively. The forward and backward rate constants separately are aexp(v/b) and cexp(−v/d). Here v represents voltage in mV, a and c the pre-exponential factors in ms−1 and b and d the exponential factors in mV. The fifth parameter is the channel number NC. (B) The errors relative to their target values were obtained by estimation of initial values (left) or by fit (right). (C) Convergence of PSO-GSS with (solid line) or without (dotted line) direct estimation. (D) In this model, target parameters a = 1 ms−1, b = 50 mV, c = 1 ms−1 and d = 200 mV; the reversal potential of channels Vr = 0 mV; the single-channel conductance G = 250 pS and the channel count NC = 1. The empty circles represent the target currents at the various voltages shown under each of current traces, and the solid lines represent fitted currents.
	Figure 2. Fit a 11-parameter BK-like C5-O5 model to the target current traces.(A) A 11-parameter Markov model consisting of five closed states and five open states labeled with the letter C and O, respectively. Each of parameters to be fitted is similar to that we described in Figure 1(A). (B–C) See the description in Figure 1B–C. (D) In this model, the target parameters c0 = 1.8225 ms−1, c1 = 1.215 ms−1, c2 = 0.855 ms−1, c3 = 0.49 ms−1, c4 = 0.11 ms−1, d = 200 mV, b = 36 mV, a4 = 0.396 ms−1, ko = 1.5 µM and kc = 13.5 µM; calcium concentration ca = 0.05, 1, 4, 10 and 100 µM, respectively; the reversal potential of channels Vr = 0 mV; the single-channel conductance G = 250 pS and the channel count NC = 1. Four dependent parameters are a0 = 0.001 ms−1, a1 = 0.006 ms−1, a2 = 0.038 ms−1 and a3 = 0.196 ms−1. The empty circles denote target currents and the solid lines represent fitted currents. The voltage protocols are placed below each of current traces.
	Figure 3. Fit a 13-parameter Nav-like C5-O-I-CI5 model to the target current traces.(A) A 13-parameter Markov model consisting of five closed states (C0, C1, C2, C3 and C4), an open state (O), an inactivation state (C10) and five closed-inactivation states (C5, C6, C7, C8 and C9). Each of parameters to be fitted is similar to that we described in Figure 1(A). (B–C) See the description in Figure 1B–C. (D) In this model, the target parameters m = 288.655598 ms−1, n = 12 mV, p = 22.144593 ms−1, q = 48 mV, r = 7.5 ms−1, s = 2 ms−1, g = 0.001, d = 0.5 ms−1, c = 4.436203, u = 0.9 ms−1, w = 0.006 ms−1 and j = 4 ms−1; the reversal potential of channels Vr = +55 mV; the single-channel conductance G = 250 pS and the channel count NC = 1. A dependent parameter i = 15 ms−1. The empty circles denote target currents and the solid lines represent fitted currents. The voltage protocols are placed below each of current traces.
	Figure 4. Fit a MWC model C5-O5 to the macroscopic currents of BK channels from Xenopus oocyte.(A) Activation traces of BK currents were recorded from an inside-out patch from a Xenopus oocyte injected with cRNA encoding mSlo1 α subunits. Channels were activated by voltage steps ranging from −200 to +200 mV with 10 mV increments from a holding potential of −180 mV with a cytosolic [Ca2+]i as indicated. The voltage protocol is not shown here. The red lines were coming from the globally fitting the model C5-O5 to BK currents by PSO-GSS algorithm. The channel count NC is 314 for 1 µM, 365 for 10 µM and 433 for 300 µM. The different Nc in the same patch is probably coming from the smaller single-channel conductance at the higher Ca2+, which will not change the channel kinetics. (B) Deactivation currents were obtained from the same patch as we described in (A). Currents were elicited by voltage steps ranging from −200 to +180 mV with 10 mV increments from a 20 ms-prepulse of +180 mV with a cytosolic [Ca2+]i as indicated. The red lines are fits by a PSO-GSS algorithm. The channel count NC is 301 for 1 µM, 354 for 10 µM and 387 for 300 µM. The score σ2 is 41.60. All the capacitive currents of 0.15 ms were pre-substituted with straight lines before run and not counted during run. The dash line is zero current.
	Figure 5. Comparison of kinetic characteristics between simulation data and target data.(A) The G-V curves of BK channels were plotted for data and best-fit, in the presence of 1, 10 and 300 µM Ca2+, respectively. (B) Time constants of activation (Left) and deactivation (Right) of BK channels were plotted for data and best-fit, in the presence of 1, 10 and 300 µM Ca2+, respectively. Here data are in black and fits in red.
	Figure 6. A 7-state BK model used for describing the same currents inFigure 4. (A) A 7-state BK model simplified from the 50-state MWC model of BK channels. (B) The parameters of the 7-state model were: a = 342.37 s−1; b = 67.90 mV; c = 56821.90 s−1; d = 168.47 mV; f = 10.21 s−1; i = 232.72 mV; g = 71130.28 s−1; j = 121.54 mV; h = 1330.129 s−1 M−1; c1 = 3.97; kO = 562.23 M; f1 = 105 s−1; g1 = 1323.36 s−1; f2 = 10.02 s−1; g2 = 99575.30 s−1. The score σ2 is 84.99. Compared with the 10-state MWC model, we have .
	Figure 7. Schematic diagram for GSS and PSO.(A) A schematic drawing for golden section search algorithm (GSS). (B) A flow graph for the PSO-GSS algorithm.

References [+] :

Colquhoun, How to impose microscopic reversibility in complex reaction mechanisms. 2004, Pubmed