Hodgkin–Huxley type modelling and parameter estimation of GnRH neurons

Csercsik, Dávid; Farkas, Imre; Szederkényi, Gábor; Hrabovszky, Erik; Liposits, Zsolt; Hangos, Katalin M.

doi:10.1016/j.biosystems.2010.03.004

Cited by 10 publications

(16 citation statements)

References 59 publications

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“…Over the years, it has seen several modifications and 120 improvements such as the one by Frankenhaeuser and Huxley [16], or the incorporation 121 of additional ion currents [41] given the multitude of ion channel types [42,43]. Also, 122 attempts were made to provide better fits by modifying the exponents of the gating 123 variables [44]. In essence, it is difficult to determine what is the 'right' Hodgkin-Huxley 124 model for specific neuron types.…”

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confidence: 99%

Action Potential Propagation and Synchronisation in Myelinated Axons

Schmidt

Knösche

2019

Preprint

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With the advent of advanced MRI techniques it has become possible to study axonal white matter non-invasively and in great detail. Measuring the various parameters of the long-range connections of the brain opens up the possibility to build and refine detailed models of large-scale neuronal activity. One particular challenge is to find a mathematical description of action potential propagation that is sufficiently simple, yet still biologically plausible to model signal transmission across entire axonal fibre bundles. We develop a mathematical framework in which we replace the Hodgkin-Huxley dynamics by a spike-diffuse-spike model with passive sub-threshold dynamics and explicit, threshold-activated ion channel currents. This allows us to study in detail the influence of the various model parameters on the action potential velocity and on the entrainment of action potentials between ephaptically coupled fibres without having to recur to numerical simulations. Specifically, we recover known results regarding the influence of axon diameter, node of Ranvier length and internode length on the velocity of action potentials. Additionally, we find that the velocity depends more strongly on the thickness of the myelin sheath than was suggested by previous theoretical studies. We further explain the slowing down and synchronisation of action potentials in ephaptically coupled fibres by their dynamic interaction. In summary, this study presents a solution to incorporate detailed axonal parameters into a whole-brain modelling framework. Author summaryWith more and more data becoming available on white-matter tracts, the need arises to develop modelling frameworks that incorporate these data at the whole-brain level. This requires the development of efficient mathematical schemes to study parameter dependencies that can then be matched with data, in particular the speed of action potentials that cause delays between brain regions. Here, we develop a method that describes the formation of action potentials by threshold activated currents, often referred to as spike-diffuse-spike modelling. A particular focus of our study is the dependence of the speed of action potentials on structural parameters. We find that the diameter of axons and the thickness of the myelin sheath have a strong influence on the speed, whereas the length of myelinated segments and node of Ranvier length have a lesser effect. In addition to examining single axons, we demonstrate that action potentials between nearby axons can synchronise and slow down their propagation speed. August 8, 2019 1/35 48 the spatial discretisation must be relatively coarse to ensure numerical stability, which 49 can be remedied to some extent by advanced numerical methods and computational 50 effort [34]. The other problem, however, cannot be remedied that easily: it is the lack of 51 insight into how the model parameters influence the results, since there is a large 52 August 8, 2019 2/35 number of parameters involved. A way to illustrate parameter dependencies in an 53 effici...

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confidence: 99%

Action Potential Propagation and Synchronisation in Myelinated Axons

Schmidt

Knösche

2019

Preprint

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“…This approach has the benefit, that it can describe subthreshold behavior and the depolarizing phase of AP generation with only an amplifying and a resonant variable, which is the minimal model of excitability. In addition, the number of parameters is significantly lower compared to the case of a detailed conventional Hodgkin-Huxley type model (Csercsik et al, 2010). The tradeoff is that we are not able to handle the appearing voltage gated currents separately (except for the calcium current, as we will see, which has a leading role in the model).…”

Section: Introductionmentioning

confidence: 98%

“…A couple of models have been constructed so far to describe the ionic currents and short term (considering scales of milliseconds) general electrophysiological (Csercsik et al, 2010), and dendritic properties (Roberts et al, 2006;Roberts, Hemond, & Suter, 2008;Roberts et al, 2009) of GnRH neurons based on measurements performed on cells from hypothalamic slices. Other mathematical models (LeBeau *Manuscript Click here to download Manuscript: GnRH_neuron_RR_2_bbl.tex Click here to view linked References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 et Van Goor et al, 2000;Fletcher & Li, 2009) have been proposed to explain experimental data obtained on GT1 cells.…”

Section: Introductionmentioning

confidence: 99%

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A simple integrative electrophysiological model of bursting GnRH neurons

et al. 2011

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In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.

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“…Most treatments of HH parameter estimation have tackled the problem with a focus on practicality-estimating parameters given noisy and limited data. However, there has been relatively little examination [5] of the more basic but essential question of structural identifiability: given perfect, noise-free data, can the parameters in the model be uniquely determined? While such perfect data is of course unrealistic, structural identifiability is a prerequisite for practical identifiability and successful Email addresses: ojwalch@umich.edu (Olivia J. Walch), marisae@umich.edu (Marisa C. Eisenberg) parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

Parameter identifiability and identifiable combinations in generalized Hodgkin–Huxley models

Walch

Eisenberg

2016

Neurocomputing

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The use of Hodgkin-Huxley (HH) equations abounds in the literature, but the identifiability of the HH model parameters has not been broadly considered. Identifiability analysis addresses the question of whether it is possible to estimate the model parameters for a given choice of measurement data and experimental inputs. Here we explore the structural identifiability properties of a generalized form of HH from voltage clamp data. Through a scaling argument, we conclude that the steady-state gating variables are not identifiable from voltage clamp data, and then further show that their product together with the conductance term forms an identifiable combination. We additionally show that these parameters become identifiable when the initial conditions for each of the gating variables are known. The time constants for each gating variable are shown to be identifiable, and a novel method for estimating them is presented. Finally, the exponents of the gating variables are shown to be identifiable in the two-gate case, and we conjecture these to be identifiable in the general case. These results are broadly applicable to models using HH-like formalisms, and show in general which parameters and combinations of parameters are possible to estimate from voltage clamp data.

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Hodgkin–Huxley type modelling and parameter estimation of GnRH neurons

Cited by 10 publications

References 59 publications

Action Potential Propagation and Synchronisation in Myelinated Axons

Action Potential Propagation and Synchronisation in Myelinated Axons

A simple integrative electrophysiological model of bursting GnRH neurons

Parameter identifiability and identifiable combinations in generalized Hodgkin–Huxley models

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