Bayesian inference of kinetic schemes for ion channels by Kalman filtering

Abstract

Inferring adequate kinetic schemes for ion channel gating from ensemble currents is a daunting task due to limited information in the data. We address this problem by using a parallelized Bayesian filter to specify hidden Markov models for current and fluorescence data. We demonstrate the flexibility of this algorithm by including different noise distributions. Our generalized Kalman filter outperforms both a classical Kalman filter and a rate equation approach when applied to patch-clamp data exhibiting realistic open-channel noise. The derived generalization also enables inclusion of orthogonal fluorescence data, making unidentifiable parameters identifiable and increasing the accuracy of the parameter estimates by an order of magnitude. By using Bayesian highest credibility volumes, we found that our approach, in contrast to the rate equation approach, yields a realistic uncertainty quantification. Furthermore, the Bayesian filter delivers negligibly biased estimates for a wider range of data quality. For some data sets it identifies more parameters than the rate equation approach. These results also demonstrate the power of assessing the validity of algorithms by Bayesian credibility volumes in general. Finally, we show that our Bayesian filter is more robust against errors induced by either analog filtering before analog-to-digital conversion or by limited time resolution of fluorescence data than a rate equation approach.

Minimally and vaguely informative priors to combat practical parameter non-identifiability of hidden Markov models exemplified by ion channel data

“…Adding birth and death processes requires additional convolution with Poisson distributions [74]. Traditionally, ensemble data on CRNs are analyzed by considering only the mean value of the CME, in the form of deterministic rate equations (REs) [75] thereby losing the Markov property [41]. This simplification of discrete stochastic events by a continuous deterministic process of the mean value inevitably leads to a likelihood misspecification [41], even with the correct CRN topology.…”

“…This simplification of discrete stochastic events by a continuous deterministic process of the mean value inevitably leads to a likelihood misspecification [41], even with the correct CRN topology. This causes a less accurate and over-confident parameter inference [41] independently of the number of molecules, as long as the intrinsic fluctuations in the signal are not vanishing compared to the measurement noise [41]. A better approximation of the CME is the Fokker-Planck approximation (FPa) [76].…”

“…To our knowledge, the infinite HMM [37,38] only applies to single-molecule data but cannot be extended to ensemble data or continuous time HMMs. Notably, the hidden variable of a HMM does not have to be discrete but can be used to approximate a discrete CRN [40,41] A Kalman filter [42,43] also defines a valid HMM, as demonstrated for ensemble patch-clamp (PC) data [40] using a continuous hidden variable [44,45,46,47]. Here, we build on a generalization of the Kalman filter [41], necessary to employ the ideas of [40] on actual PC data, which uses a continuous hidden variable and continuous time HMM to analyze ensemble PC data of LGICs as well as ensemble binding data [41].…”

From Average Transient Transporter Currents to Microscopic Mechanism─A Bayesian Analysis

“…Building on related work for ion channels , and methods developed for computational systems biology, , and molecular biophysics, − we implement a BI data analysis pipeline (Figure ) to address the gap in knowledge about membrane transporter mechanisms and SSME data sets. To our knowledge, this is the first application of BI for the transporter mechanism.…”

“…Here, we utilize a recently developed sampling approach that combines powerful ideas from physics (annealing) and from machine-learning (normalizing flows) 27 to overcome convergence challenges. Building on related work for ion channels 28,29 and methods developed for computational systems biology, 30,31 and molecular biophysics, 32−34 we implement a BI data analysis pipeline (Figure 1) to address the gap in knowledge about membrane transporter mechanisms and SSME data sets. To our knowledge, this is the first application of BI for the transporter mechanism.…”