Analysis of Single Channel Currents Using Signal Processing Techniques Based on Hidden Markov

Principal Investigator

Shin-Ho Chung

Department of Chemistry,The Faculties


Toby W. Allen

Ben Corry

Matthew Hoyles

Department of Chemistry,The Faculties

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The 'giga-seal' patch-clamp technique has so far
proved to be a powerful tool for studying
movements of ions across biological ion channels. A tight seal between the rim of the electrode tip and the cell membrane drastically reduces the leakage current and extraneous background noise, so enabling the resolution of discrete changes in conductance which occur when single channels open and close. Even with this technique, the current across a single channel is relatively small compared to the background measurement noise. There is a need to measure and characterize, not only relatively large ionic currents, but also microscopic conductance fluctuations that are occurring in the noise.

To detect and characterize small membrane channel currents that are heavily contaminated by random and deterministic noise, we have introduced a novel signal processing technique based on hidden Markov models. One complication arises when applying this technique to the analysis of channel currents. A channel, when it opens, does not always open fully but sometimes opens partially. Thus, the opening and closing of the channel is not instantaneous but the transit sometimes is achieved in several steps, with brief pauses in the intermediate states. In order for our signal processing method to be of use in the study of biophysical problems, we needed to formulate a method of determining the state dimension of a hidden Markov chain.


What are the results to date and the future work?

We formulated a new technique for determining the number of states required for the Markov chain to characterize the observed process. We derived a realization theorem showing that observations on a finite Markov chain embedded in continuous noise can be synthesized as values obtained from an auto-regressive moving-average data generating mechanism. We then used this realization result to motivate the construction of a procedure for identifying the state dimension of the hidden Markov chain. With the aid of this procedure, we have been able to extract small signals representing the opening and closing of single ion channels with an unprecedented accuracy. For example, conductance and subconductance levels of voltage-

- Appendix A



activated sodium channels recorded using patch-clamp techniques from isolated myocytes were determined this way. From the tabulated amplitude distributions, we inferred that the conductance sublevels normally seen are evenly spaced. This finding provides an important clue to understanding the mechanisms that give rise to conductance substates in channel currents. It also has implications for the structure of this channel, in particular whether the channel operates as a single pore or a number of coupled parallel pathways.

We plan to carry out patch-clamp recordings various types of ion channels. Each recorded current trace will be analyzed using this processing technique and the results of experiments will be compared with the predictions derived from computer simulations.

What computational techniques are used?

The core of the processing method we use for extracting signals from noise is the expectation-maximization (EM) algorithm, an iterative procedure composed of the E-step and the M-step. There are alternative numerical methods for calculating the maximum likelihood estimates. One approach we have considered, and rejected, is the Newton-Raphson algorithm which, when it converges, does so quadratically and thus rapidly. The EM algorithm, on the other hand, converges linearly, and so convergence is slow. However, with the Newton-Raphson algorithm, the computational steps involved tend to be complicated and the memory requirements to obtain the estimates are large, especially since the Hessian matrix needs to be inverted. Moreover, successive iterations with the Newton-Raphson algorithm do not necessarily improve the likelihood function. In contrast, the EM algorithm is simple to implement and satisfies the appealing property that the likelihood function is always improved after each iteration.


D. Poskitt, K. Dogancay and S. H. Chung. Double blind deconvolution: the analysis of postsynaptic currents in nerve cells. J. Royal Stat. Soc. B. 61, 191-212, 1999.

S. H. Chung and P. W. Gage. Signal processing techniques for channel current analysis based on hidden Markov models. Methods in Enzymol. 293, 420-438, 1998.

D. A. Saint and S. H. Chung. Variability of channel subconductance states of the cardiac sodium channel induced by protease. Receptors & Channels (in press, 1999).

Appendix A -