Estimation of ion Channel Kinetics from Macroscopic Recordings

MOFFAT, LUCIANO

Baltimore Maryland

Congreso; 55th Biophysical meeting; 2011

Biophysical Society

A sizeable portion of the kinetic information present on macroscopic record-ings is discarded by standard statistical analyses based on least-squares minimization. A more general approach that uses all the kinetic information present in the recording consists in maximizing the likelihood function, the probability of obtaining the data as a function of the parameters of the kinetic model. The exact likelihood function can be calculated only for a very small number of channels. Approximations proposed for preparations above 30 channels work fine when the acquisition time is smaller than the time the preparation needs to change its state, but this is not usually the case on experimental recordings. To overcome this limitation we developed the Integrated Macroscopic Recursive algorithm an approximation that can be applied to experimental data. This algorithm assumes for each measurement an a priori knowledge of the possible state of the ensemble of channels at the beginning and at the end of each measurement. This knowledge is modeled by a multivariate normal distribution of the ratio of channels in each possible pair of starting and ending states, the later predicted by the kinetic model under test. By using Bayes theorem we calculate the posterior distribution that result after taking into account the current measurement and we calculate the partial likelihood of each measurement. The distribution of channels at the end of the measurements is then used to calculate the prior distribution of starting state-ending state pair of the next measurement interval. We present a reliable approximation to the likelihood function that opens the door to several possibilities: a) estimate the kinetic parameters that best represent the experimental data with their error rates, b) to choose between alternative kinetic models and c) to optimize the experimental protocols.