Maximum likelihood estimation of biophysical parameters of synaptic receptors from macroscopic currents

Abstract

Dendritic integration and neuronal firing patterns strongly depend on biophysical properties of synaptic ligand-gated channels. However, precise estimation of biophysical parameters of these channels in their intrinsic environment is complicated and still unresolved problem. Here we describe a novel method based on a maximum likelihood approach that allows to estimate not only the unitary current of synaptic receptor channels but also their multiple conductance levels, kinetic constants, the number of receptors bound with a neurotransmitter, and the peak open probability from experimentally feasible number of postsynaptic currents. The new method also improves the accuracy of evaluation of unitary current as compared to the peak-scaled non-stationary fluctuation analysis, leading to a possibility to precisely estimate this important parameter from a few postsynaptic currents recorded in steady-state conditions. Estimation of unitary current with this method is robust even if postsynaptic currents are generated by receptors having different kinetic parameters, the case when peak-scaled non-stationary fluctuation analysis is not applicable. Thus, with the new method, routinely recorded postsynaptic currents could be used to study the properties of synaptic receptors in their native biochemical environment.

Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints

“…In turn, the kinetic mechanism describes the operation of the channel within the membrane, under stationary conditions or in response to stimuli. Markov models, computational algorithms, and software have been adapted and developed to extract the kinetic mechanism from experimental data ( Ball and Sansom, 1989 ; Hawkes et al, 1990 ; Qin et al, 1996 , 2000a , b ; Venkataramanan and Sigworth, 2002 ; Celentano and Hawkes, 2004 ; Qin and Li, 2004 ; Milescu et al, 2005 ; Csanády, 2006 ; Moffatt, 2007 ; Stepanyuk et al, 2011 , 2014 ), with two interrelated aims: to find an appropriate topology and to estimate the kinetic parameters.…”

“…A computational procedure for finding the “best” parameters for a proposed model topology combines an algorithm that measures how well a given model explains the data with an optimization engine that searches the parameter space for the “best” solution ( Fletcher, 2013 ). This optimal solution minimizes the error between the data and the prediction of the model (e.g., the sum of square errors) or maximizes a probability function (e.g., the likelihood that the experimental data were generated by the model or the Bayesian posterior probability; Horn and Lange, 1983 ; Hawkes et al, 1990 ; Qin et al, 1996 , 2000a ; Celentano and Hawkes, 2004 ; Milescu et al, 2005 ; Csanády, 2006 ; Moffatt, 2007 ; Calderhead et al, 2013 ; Stepanyuk et al, 2014 ; Epstein et al, 2016 ). Intuitively, the first approach can be described as minimizing a “cost function,” whereas the second, as maximizing a “goodness of fit.” Throughout this study, we will use the "cost function" term, but with the understanding that it could refer to either minimizing the sum of square errors or, equivalently, minimizing the negative log-likelihood.…”

Estimating kinetic mechanisms with prior knowledge II: Behavioral constraints and numerical tests

“…To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanism, defined as a set of interconvertible structural conformations, with transitions quantified by rate constants that depend on external variables (e.g., membrane potential, ligand concentration, etc.). Modeling molecular kinetics is not trivial, but sophisticated algorithms have been developed that can extract the rate constants for a given model from a variety of experimental data types, such as single-channel or whole-cell voltage-clamp currents ( Colquhoun and Hawkes, 1982 ; Colquhoun and Sigworth, 1995 ; Qin et al, 1996 , 2000 ; Venkataramanan and Sigworth, 2002 ; Colquhoun et al, 2003 ; Milescu et al, 2005 ; Csanády, 2006 ; Stepanyuk et al, 2011 , 2014 ), single-molecule fluorescence ( Weiss, 2000 ; Milescu et al, 2006a , b ; Liu et al, 2010 ), or even current-clamp recordings ( Milescu et al, 2008 ). Automated algorithms that can identify the model itself have also been attempted ( Gurkiewicz and Korngreen, 2007 ; Menon et al, 2009 ).…”

Bayesian inference of kinetic schemes for ion channels by Kalman filtering

“…Some rigorous attempts to incorporate the intrinsic noise of current data into the estimation 42 suffer from cubic computational complexity in the amount of data points, rendering the algorithm impractical for real data. Stepanyuk suggested a faster algorithm 43,44 . Advanced approaches to analyze singlemolecule data such as HMMs make use of solutions of the stochastic CME 45 13,14 .…”