Single shot detection of alterations across multiple ionic currents from assimilation of cell membrane dynamics

Abstract

The dysfunction of ion channels is a causative factor in a variety of neurological diseases, thereby defining the implicated channels as key drug targets. The detection of functional changes in multiple specific ionic currents currently presents a challenge, particularly when the neurological causes are either a priori unknown, or are unexpected. Traditional patch clamp electrophysiology is a powerful tool in this regard but is low throughput. Here, we introduce a single-shot method for detecting alterations amongst a range of ion channel types from subtle changes in membrane voltage in response to a short chaotically driven current clamp protocol. We used data assimilation to estimate the parameters of individual ion channels and from these we reconstructed ionic currents which exhibit significantly lower error than the parameter estimates. Such reconstructed currents thereby become sensitive predictors of functional alterations in biological ion channels. The technique correctly predicted which ionic current was altered, and by approximately how much, following pharmacological blockade of BK, SK, A-type K⁺ and HCN channels in hippocampal CA1 neurons. We anticipate this assay technique could aid in the detection of functional changes in specific ionic currents during drug screening, as well as in research targeting ion channel dysfunction.

Figure 1

Estimation of ion current alterations from current clamp recordings. (a) Membrane voltage of a (hippocampal) neuron recorded before and after a pharmacological inhibitor is applied to partially block a specific ion channel (black traces). The same current protocol (brown trace) is applied to elicit pre-drug and post-drug oscillations. (b) Data assimilation (IPOPT) was used to synchronize a nine-ion channel Hodgkin–Huxley model to the data over a 800 ms long time window and obtain one set of pre-drug parameters {p^*_Pre} and one set of post-drug parameters {p^*_Post}. Each set has K = 67 parameters. This approach was repeated over R assimilation windows offset by 80 ms to generate a statistical sample of parameter sets {p^*_Pre}_1,…,R and {p^*_Post}_1,…,R where R = 15–19 depending on the antagonist applied. (c–e) The Hodgkin–Huxley model configured with each set of estimated parameters was used to predict the ionic current waveforms and membrane voltage oscillations through forward integration of the current protocol with an adaptive step-size fifth order Runge–Kutta method (RK5). (c, d) The degree of channel block was predicted by calculating the amount of ionic charge transferred per action potential, $Q_{Pre-drug}$ and $Q_{Post-drug}$, for all nine ion channels of the model. Predictions were validated by comparing the median and mean reductions in charge transfer to the known selectivity and potency of the antagonist. (e) Predictions were also validated by comparing the predicted membrane voltage to the measured one.

Figure 2

Comparing the uncertainty on estimated ionic currents and parameter. (a) Deviations of parameter estimates from their true values ($p_k^{\ast }$), $k=1\dots 67$, when Gaussian noise is added to the membrane voltage. Parameter deviations $\mathrm{\Delta }{p}_{k,r}=\left(p_{k,r}-p_k^{\ast }\right)$ were computed from a statistical sample of ℜ = 100 assimilations of the same 800 ms window with 100 different realizations of added noise (0.25 mV r.m.s.) (red dots). The greater the dispersion, the greater the parameter sensitivity to data (and model) error. (b) Covariance matrix of parameter deviations: ${\mathrm{\sigma }}_{k{k}^{\prime }}=\frac{1}{\mathcal{R}-1}{\sum }_{r=1}\left(\frac{\mathrm{\Delta }{p}_{k,r}}{p_k^{\ast }}\right)\left(\frac{\mathrm{\Delta }{p}_{k^{\prime },r}}{p_{k^{\prime }}^{\ast }}\right)$. Correlations occur within blocks of parameters pertaining to the same ionic current. In contrast, correlations between the parameters of different ionic currents are weaker. (c) Comparison of the standard deviations of predicted ionic currents and of their underlying parameters. The parameter standard deviation (red dot) is an average of the relative standard deviations of the 67 parameters each calculated over the statistical sample of 100 noise realizations. The current standard deviation (black dot) was calculated by integrating the 100 sodium current waveforms over the assimilation window and computing the relative standard deviation of the integral charge. The uncertainty on ionic currents is three times smaller than on parameters. (d) Spectrum of eigenvalues of the covariance matrix. The 6 outliers determine the 6 directions of parameter correlations in parameter space.

Figure 3

Single-shot prediction of ionic current block by Iberiotoxin (IbTX). (a) Predicted ionic charge transferred per action potential, per ion channel, across the complement of ion channels of a CA1 neuron. The green dots are the charge predictions computed from R = 15 assimilation windows of pre-drug neuron recordings. The blue dots are the charge predictions computed similarly from the same neuron after 100 nM IbTX was applied. Horizontal bars show median charge values. Asterisks (***) indicate multiplicity adjusted q values from multiple Mann–Whitney U tests using a False Discovery Rate approach of 1%. (b) Predicted change in BK charge transfer showing the effect of IbTX as the nominal BK antagonist. (c) Effect of IbTX measured in one action potential. Inhibition of the BK channels reduces afterhyperpolarization (fAHP). (d) Effect of IbTX predicted for the same action potential. Each voltage trace is the average of 15 waveforms computed from 15 assimilations windows. (e) Predicted BK current waveforms and their alteration by IbTX. Each waveform is the average of 15 BK current waveforms reconstructed from 15 assimilation windows.

Figure 4

Single shot prediction of ionic current block by apamin. (a) Predicted ionic charge transferred per action potential, per ion channel, of a CA1 neuron. The green dots are the ionic charges predicted from R = 18 assimilation windows of pre-drug recordings. The blue dots are the predictions computed similarly after 150 nM apamin was applied to the neuron. Horizontal bars are the median charge values. Asterisks (***) represent multiplicity adjusted q values from multiple Mann–Whitney U tests. (b) Predicted change in SK charge transfer showing the effect of apamin as the nominal SK antagonist. (c) Effect of apamin on one action potential. Inset: same for multiple action potentials. (d) Effect of apamin predicted for the same action potential. (e) Predicted SK current waveforms and their alteration by apamin.

Figure 5

Single shot prediction of ionic current block by 4-Aminopyridine (4-AP). (a) Predicted ionic charge transferred per action potential, per ion channel of a CA1 neuron. The green dots show the charge predicted from R = 19 assimilation windows of pre-drug recordings. The blue dots show the same after 300 µM 4-AP after was applied to the neuron. (b) Predicted change in A-type charge transfer showing the effect of 4-APP as the nominal A-type antagonist. (c) Effect of 4-AP on one action potential. Inset: 4-AP increases the speed of adaptation of the neuron to stimulation following removal of the A-current-mediated delay. (d) Effect of 4-AP predicted for the same action potential. (e) Predicted A-type current waveforms and their alteration by 4-AP.

Figure 6

Single shot prediction of the ionic current block by ZD7288. (a) Predicted ionic charge transferred per ion channel over an entire 800 ms long assimilation window for a CA1 neuron. The green dots are the charge predicted from R = 19 assimilations of pre-drug recordings. The blue dots are the charge predictions computed similarly after 50 µM ZD7288 was applied. (b) Predicted change in HCN-type charge transfer showing the effect of ZD7288 as the nominal HCN antagonist. (c) Effect of ZD7288 observed during a hyperpolarizing current step activating the HCN channel. (d) Effect of the ZD7288 antagonist predicted in response to the same hyperpolarizing step.