Maximum Likelihood Estimation of Ion Channel Kinetics from Macroscopic Currents

Abstract

We describe a maximum likelihood method for direct estimation of rate constants from macroscopic ion channel data for kinetic models of arbitrary size and topology. The number of channels in the preparation, and the mean and standard deviation of the unitary current can be estimated, and a priori constraints can be imposed on rate constants. The method allows for arbitrary stimulation protocols, including stimuli with finite rise time, trains of ligand or voltage steps, and global fitting across different experimental conditions. The initial state occupancies can be optimized from the fit kinetics. Utilizing arbitrary stimulation protocols and using the mean and the variance of the current reduce or eliminate problems of model identifiability (Kienker, 1989). The algorithm is faster than a recent method that uses the full autocovariance matrix (Celentano and Hawkes, 2004), in part due to the analytical calculation of the likelihood gradients. We tested the method with simulated data and with real macroscopic currents from acetylcholine receptors, elicited in response to brief pulses of carbachol. Given appropriate stimulation protocols, our method chose a reasonable model size and topology.

Unraveling Mechanisms Underlying Partial Agonism in 5-HT3A Receptors

“…Agonist association and dissociation rate constants were estimated by using the macroscopic rate optimizer (MAC) algorithm included in the QuB package (Milescu et al, 2005). Simulation of single-channel and macroscopic currents were performed using QuB software based on the model proposed and using the rate constants for desensitization and recovery experimentally determined.…”

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

“…The availability of simple methods like the Simplex and Levenberg-Marquardt algorithms provided in Matlab™ or a recently developed CellML-based tool (Hui et al 2007) and their limited need for significant computational resources would make them good candidates but their ability to find global minima is very restricted given the number of parameters to fit. Similar computational needs and problems with large numbers of parameters apply for the maximum likelihood method which is used for single channel measurements as in the software package QuB (Milescu et al 2005). Sequential quadratic programming methods also can be used to find a constrained minimum with superlinear convergence (Gill 1981, Fletcher 1987 for model parameters using Matlab™ (Bueno-Orovio et al 2008).…”

“…For example, the JSim package incorporates sophisticated optimisation routines for parameter estimation as well as the ability to automatically calculate sensitivity functions and generate multiple simulations by looping through ranges of parameter values. The QuB (Milescu et al 2005) and Neuron (Brette et al 2007) packages provide the ability to simulate and fit models of ion channels or cells. Yet none of these packages provide the means to systematically interrogate parameter identifiability.…”

Statistical properties of ion channel records. Part I: Relationship to the macroscopic current

“…Different calibration procedures (mostly numerical) have been developed to find the transition rates between kinetic states of a particular Markov structure to optimally replicate a set of single channel records. These procedures are based on maximum likelihood techniques [6] for matching the statistical properties of the model to the single channel records [7] or the macroscopic current [8,9] (The macroscopic current is the summation current through a large ensemble of ion channels). There are in theory infinite number of stochastic models (including many Markov structures) that can be calibrated to a set of single channel records to replicate certain statistical properties of the records and/or the resultant macroscopic current.…”