Estimation of ionic currents and compensation mechanisms from recursive piecewise assimilation of electrophysiological data

Abstract

The identification of ion channels expressed in neuronal function and neuronal dynamics is critical to understanding neurological disease. This program calls for advanced parameter estimation methods that infer ion channel properties from the electrical oscillations they induce across the cell membrane. Characterization of the expressed ion channels would allow detecting channelopathies and help devise more effective therapies for neurological and cardiac disease. Here, we describe Recursive Piecewise Data Assimilation (RPDA), as a computational method that successfully deconvolutes the ionic current waveforms of a hippocampal neuron from the assimilation of current-clamp recordings. The strength of this approach is to simultaneously estimate all ionic currents in the cell from a small but high-quality dataset. RPDA allows us to quantify collateral alterations in non-targeted ion channels that demonstrate the potential of the method as a drug toxicity counter-screen. The method is validated by estimating the selectivity and potency of known ion channel inhibitors in agreement with the standard pharmacological assay of inhibitor potency (IC50).

Keywords: data assimilation; dynamical systems; ion channels; neurons and networks; parameter estimation.

Figure 1

Stimulation protocols applied to rodent hippocampal neurons (CA1). (A) Calibration protocol consisting of a sequence of current steps of increasing amplitude. (B) Protocol mixing a chaotic signal (Lorenz) and random current steps. (C) Protocol mixing a hyperchaotic current and random steps. Inset: Power spectra I(f) of current protocols in panels (B) and (C).

Figure 2

Estimation of the ion channel parameters in a pharmacologically altered neuron. (A) Hippocampal neuron recorded before and after blocking an ion channel with an antagonist of known selectivity and molar concentration (potency). The pre-drug and post-drug recordings are stimulated by the same current protocol (brown trace). (B) Recursive Piecewise Data Assimilation (RPDA) estimates 67 parameters by synchronizing the neuron-based conductance model to an 800 ms long recording of the membrane voltage. Rather than a single set, we constructed a statistical sample of R parameter sets by assimilating R 800 ms long windows offset from by 20 ms. We thus obtained R-parameter sets from pre-drug data {${\mathrm{p}}_{1,\dots ,\mathrm{R}}^{\mathrm{P}\mathrm{r}\mathrm{e}}$} and R-parameter sets from post-drug data {${\mathrm{p}}_{1,\dots ,\mathrm{R}}^{\mathrm{Post}}$}.

Algorithm

Recursive piecewise data assimilation.

Figure 3

Measured and Predicted membrane voltage. (A) 2,000 ms long epoch comparing the experimental membrane voltage oscillations of a CA1 hippocampal neuron (black line) to the membrane voltage oscillations predicted by the conductance model (red line). The first 1,000 ms of this epoch are also shown in Figure 1 with the stimulation current. (B) Measured and predicted membrane voltage after the application of iberiotoxin (IbTX: 100 nM).

Figure 4

Predicted ion current waveforms pre- and post-inhibition. (A) Predicted BK current waveforms before and after application of Iberiotoxin (100 nM). The pre-IbTX current trace is the average of 15 waveforms obtained by integrating the conductance model with parameters {${\mathrm{p}}_{1,\dots ,15}^{\mathrm{P}\mathrm{r}\mathrm{e}}$}. The post IbTX traces were similarly obtained from parameters {${\mathrm{p}}_{1,\dots ,15}^{\mathrm{Post}}$}. (B) Predicted ionic charge transferred through each ion channel of the CA1 neuron before and after IbTX. Each dot is obtained from the integration of a BK current waveform predicted by the model constructed from one of the R = 15 assimilation windows in Figure 2. The green dots are the charge predictions pre-drug and the blue dots are the charge predictions after 100 nM IbTX was applied. The median charge is shown by the horizontal bars. Asterisks (***) indicate multiplicity adjusted q values from multiple Mann–Whitney U tests using a False Discovery Rate approach of 1%. (C) Predicted A-type current waveforms before and after application of the 4-aminopyridin. (D) Predicted ionic charge transferred through each ion channel of the CA1 neuron before and after 4-AP. The data in (A,B) were generated from one animal and the data in (C,D) from another animal. These data are exemplar of the recordings taken on the 13 animals we have studied in total.