Identifiability analysis and parameter estimation of a single Hodgkin–Huxley type voltage dependent ion channel under voltage step measurement conditions

Csercsik, Dávid; Hangos, Katalin M.; Szederkényi, Gábor

doi:10.1016/j.neucom.2011.09.006

Cited by 34 publications

(30 citation statements)

References 32 publications

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“…Model simplification is related to the question of parameter identifiability and over-parameterisation (see e.g. [7, 11]). This is an important issue with larger models, which we touched upon in Section 3.1 where we showed that the two-parameter model (10) of steady state inactivation gives essentially the same results as the 12 parameter version in the original Fox et al model.…”

Section: Discussionmentioning

confidence: 99%

Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology

Pathmanathan

Shotwell

Gavaghan

et al. 2015

Progress in Biophysics and Molecular Biology

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Perhaps the most mature area of multi-scale systems biology is the modelling of the heart. Current models are grounded in over fifty years of research in the development of biophysically detailed models of the electrophysiology (EP) of cardiac cells, but one aspect which is inadequately addressed is the incorporation of uncertainty and physiological variability. Uncertainty quantification (UQ) is the identification and characterisation of the uncertainty in model parameters derived from experimental data, and the computation of the resultant uncertainty in model outputs. It is a necessary tool for establishing the credibility of computational models, and will likely be expected of EP models for future safety-critical clinical applications. The focus of this paper is formal UQ of one major sub-component of cardiac EP models, the steady-state inactivation of the fast sodium current, INa. To better capture average behaviour and quantify variability across cells, we have applied for the first time an ‘individual-based’ statistical methodology to assess voltage clamp data. Advantages of this approach over a more traditional ‘population-averaged’ approach are highlighted. The method was used to characterise variability amongst cells isolated from canine epi and endocardium, and this variability was then ‘propagated forward’ through a canine model to determine the resultant uncertainty in model predictions at different scales, such as of upstroke velocity and spiral wave dynamics. Statistically significant differences between epi and endocardial cells (greater half-inactivation and less steep slope of steady state inactivation curve for endo) was observed, and the forward propagation revealed a lack of robustness of the model to underlying variability, but also surprising robustness to variability at the tissue scale. Overall, the methodology can be used to: (i) better analyse voltage clamp data; (ii) characterise underlying population variability; (iii) investigate consequences of variability; and (iv) improve the ability to validate a model. To our knowledge this article is the first to quantify population variability in membrane dynamics in this manner, and the first to perform formal UQ for a component of a cardiac model. The approach is likely to find much wider applicability across systems biology as current application domains reach greater levels of maturity.

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Section: Discussionmentioning

confidence: 99%

Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology

Pathmanathan

Shotwell

Gavaghan

et al. 2015

Progress in Biophysics and Molecular Biology

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“…Willms et al (29) highlighted advantages of Method 3 over Method 1, and provided a software tool for Method 3 fitting (54), while an extensive analysis for voltage-independent channels was given by Milescu et al (55). Csercsik et al (56) investigated a procedure falling somewhere between Methods 1 and 3, where the parameters underlying voltage-dependence of steady states were determined, but time constants were fit separately for different voltages. Walch and Eisenberg (57) considered the problem of estimating both time constants and steady states independently for several voltages, and concluded that in this case only the time constants were identifiable.…”

Section: Introductionmentioning

confidence: 99%

Four ways to fit an ion channel model

Clerx

Beattie

Gavaghan

et al. 2019

Preprint

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Computational models of the cardiac action potential are increasingly being used to investigate the effects of 4 genetic mutations, predict pro-arrhythmic risk in drug development, and to guide clinical interventions. These safety-critical 5 applications, and indeed our understanding of the cardiac action potential, depend on accurate characterisation of the underlying 6 ionic currents. Four different methods can be found in the literature to fit ionic current models to single-cell measurements: 7 (Method 1) fitting model equations directly to time constant, steady-state, and I-V summary curves; (Method 2) fitting by comparing 8 simulated versions of these summary curves to their experimental counterparts; (Method 3) fitting to the current traces themselves 9 from a range of protocols; and (Method 4) fitting to a single current trace from an information-rich voltage clamp protocol. We 10 compare these methods using a set of experiments in which hERG1a current from single Chinese Hamster Ovary (CHO) cells 11 was characterised using multiple fitting protocols and an independent validation protocol. We show that Methods 3 and 4 provide 12 the best predictions on the independent validation set, and that the short information-rich protocols of Method 4 can replace 13 much longer conventional protocols without loss of predictive ability. While data for Method 2 is most readily available from the 14 literature, we find it performs poorly compared to Methods 3 and 4 both in accuracy of predictions and computational efficiency. 15 Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in 16 safety-critical applications. 17 Statement of Significance 18Mathematical models have been constructed to capture and share our understanding of the kinetics of ion channel currents 19 for almost 70 years, and hundreds of models have been developed, using a variety of techniques. We compare how well four 20 of the main methods fit data, how reliable and efficient the process of fitting is, and how predictive the resulting models are 21 for physiological situations. The most widely-used traditional approaches based on current-voltage and time constant-voltage 22 curves do not produce the most predictive models. Short, optimised experimental voltage clamp protocols can be used to create 23 models that are as predictive as ones derived from traditional protocols, opening up possibilities for measuring ion channel 24 kinetics faster, more accurately and in single cells. As these models often form part of larger multi-scale action potential and 25 tissue electrophysiology models, improved ion channel kinetics models could influence the findings of thousands of simulation 26 studies. 27Computational models of ionic currents have been used to understand the formation of the action potential (AP) (1-3), the 29 effects of genetic mutations (4), and the action of drugs on the rhythm of the heart (5). By fitting a mathematical model to 30 experimentally measured currents w...

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“…Although HH models can indeed capture such behavior, the mechanistic HH framework is not ideally suited for statistical analysis of spike train data in sensory systems as HH model parameters are difficult to interpret in terms of computation and coding. Moreover, fitting HH models to intracellular data is difficult (Buhry et al, 2011; Csercsik et al, 2012; Vavoulis et al, 2012; Lankarany et al, 2014), and only recently methods that fit HH models to spike trains alone have been gaining success (Meng et al, 2011, 2014).…”

Section: Introductionmentioning

confidence: 99%

Capturing multiple timescales of adaptation to second-order statistics with generalized linear models: gain scaling and fractional differentiation

Latimer

Fairhall

2019

Preprint

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6 Single neurons can dynamically change the gain of their spiking responses to account for shifts 7 in stimulus variance. Moreover, gain adaptation can occur across multiple timescales. Here, we 8 examine the ability of a simple statistical model of spike trains, the generalized linear model (GLM), 9 to account for these adaptive effects. The GLM describes spiking as a Poisson process whose 10 rate depends on a linear combination of the stimulus and recent spike history. The GLM success-11 fully replicates gain scaling observed in Hodgkin-Huxley simulations of cortical neurons that occurs 12 when the ratio of spike-generating potassium and sodium conductances approaches one. Gain 13 scaling in the GLM depends on the length and shape of the spike history filter. Additionally, the GLM 14 captures adaptation that occurs over multiple timescales as a fractional derivative of the stimulus 15 variance, which has been observed in neurons that include long timescale afterhyperpolarization 16 conductances. Fractional differentiation in GLMs requires long spike history that span several sec-17 onds. Together, these results demonstrate that the GLM provides a tractable statistical approach for 18 examining single-neuron adaptive computations in response to changes in stimulus variance.19

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Identifiability analysis and parameter estimation of a single Hodgkin–Huxley type voltage dependent ion channel under voltage step measurement conditions

Cited by 34 publications

References 32 publications

Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology

Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology

Four ways to fit an ion channel model

Capturing multiple timescales of adaptation to second-order statistics with generalized linear models: gain scaling and fractional differentiation

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