Statistical modelling and analysis of ion channel data

The gating behaviour of a single ion channel can be described by a hidden Markov model (HMM), and this forms a basis for statistical analysis of single channel patch clamp data. We analysed extensive high bandwidth (25 kHz and 50 kHz) data from the mechanosensitive channel of large conductance (MscL) in E. coli; the bandwidth refers to the low-pass filter used for the purpose of removing high frequency noise in recordings. The data were modelled using HMMs, and HMMs with a moving average adjustment for filtering.

MscL is a multi-level channel and the number of levels is not easily discerned based on the recorded noisy currents. The basic aims of the analysis are to determine the number of conducting levels, together with mean current, mean dwell time and proportion of time at each level. Comprehensive data analyses and comparisons across all our data sets were consistent with seven conductance levels for this channel.

Parameter estimates for HMMs with a moving average adjustment for filtering were obtained using an EM (expectation-maximisation) based algorithm which depends on a generalisation of the Baum forward-backward algorithm. The resulting improved algorithm is simpler than that of Khan et al. (2005) because the dimension of the parameter space is much smaller, and consequently the computational complexity is substantially reduced.

We present an approach that extends the HMM with an adjustment for filtering to allow for correlated noise, using deconvolution to pre-whiten the noise. This results in a standard HMM. Simulation studies were conducted to investigate and compare the performance of this method to the HMM and HMM with a moving average adjustment for the low-pass filter.

The standard errors of parameter estimates for the three types of model were obtained using an algorithm due to Khan (2003).