Restoration of single-channel currents using the segmental k-means method based on hidden Markov modeling

Biophys J. 2004 Mar;86(3):1488-501. doi: 10.1016/S0006-3495(04)74217-4.


Patch-clamp recording provides an unprecedented means for study of detailed kinetics of ion channels at the single molecule level. Analysis of the recordings often begins with idealization of noisy recordings into continuous dwell-time sequences. Success of an analysis is contingent on accuracy of the idealization. I present here a statistical procedure based on hidden Markov modeling and k-means segmentation. The approach assumes a Markov scheme involving discrete conformational transitions for the kinetics of the channel and a white background noise for contamination of the observations. The idealization is sought to maximize a posteriori probability of the state sequence corresponding to the samples. The approach constitutes two fundamental steps. First, given a model, the Viterbi algorithm is applied to determine the most likely state sequence. With the resultant idealization, the model parameters are then empirically refined. The transition probabilities are calculated from the state sequences, and the current amplitudes and noise variances are determined from the ensemble means and variances of those samples belonging to the same conductance classes. The two steps are iterated until the likelihood is maximized. In practice, the algorithm converges rapidly, taking only a few iterations. Because the noise is taken into explicit account, it allows for a low signal/noise ratio, and consequently a relatively high bandwidth. The approach is applicable to data containing subconductance levels or multiple channels and permits state-dependent noises. Examples are given to elucidate its performance and practical applicability.

Publication types

  • Comparative Study
  • Evaluation Study
  • Research Support, U.S. Gov't, P.H.S.
  • Validation Study

MeSH terms

  • Animals
  • Cell Membrane / physiology*
  • Computer Simulation
  • Ion Channel Gating / physiology*
  • Ion Channels / physiology*
  • Kinetics
  • Markov Chains
  • Membrane Potentials / physiology
  • Mice
  • Models, Biological*
  • Models, Statistical*
  • Patch-Clamp Techniques / methods*
  • Potassium Channels, Calcium-Activated / physiology
  • Stochastic Processes


  • Ion Channels
  • Potassium Channels, Calcium-Activated