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Chizhov AV, Amakhin DV, Sagtekin AE, Desroches M. Single-compartment model of a pyramidal neuron, fitted to recordings with current and conductance injection. BIOLOGICAL CYBERNETICS 2023; 117:433-451. [PMID: 37755465 DOI: 10.1007/s00422-023-00976-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 09/07/2023] [Indexed: 09/28/2023]
Abstract
For single neuron models, reproducing characteristics of neuronal activity such as the firing rate, amplitude of spikes, and threshold potentials as functions of both synaptic current and conductance is a challenging task. In the present work, we measure these characteristics of regular spiking cortical neurons using the dynamic patch-clamp technique, compare the data with predictions from the standard Hodgkin-Huxley and Izhikevich models, and propose a relatively simple five-dimensional dynamical system model, based on threshold criteria. The model contains a single sodium channel with slow inactivation, fast activation and moderate deactivation, as well as, two fast repolarizing and slow shunting potassium channels. The model quantitatively reproduces characteristics of steady-state activity that are typical for a cortical pyramidal neuron, namely firing rate not exceeding 30 Hz; critical values of the stimulating current and conductance which induce the depolarization block not exceeding 80 mV and 3, respectively (both values are scaled by the resting input conductance); extremum of hyperpolarization close to the midpoint between spikes. The analysis of the model reveals that the spiking regime appears through a saddle-node-on-invariant-circle bifurcation, and the depolarization block is reached through a saddle-node bifurcation of cycles. The model can be used for realistic network simulations, and it can also be implemented within the so-called mean-field, refractory density framework.
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Affiliation(s)
- Anton V Chizhov
- MathNeuro Team, Inria Centre at Universite Cote d'Azur, Sophia Antipolis, France.
- Computational Physics Laboratory, Ioffe Institute, Saint Petersburg, Russia.
| | - Dmitry V Amakhin
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
| | - A Erdem Sagtekin
- Istanbul Technical University, Istanbul, Turkey
- University of Tuebingen, Tuebingen, Germany
| | - Mathieu Desroches
- MathNeuro Team, Inria Centre at Universite Cote d'Azur, Sophia Antipolis, France
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Xiao J, Chen Z, Yu B. A Potential Mechanism of Sodium Channel Mediating the General Anesthesia Induced by Propofol. Front Cell Neurosci 2020; 14:593050. [PMID: 33343303 PMCID: PMC7746837 DOI: 10.3389/fncel.2020.593050] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2020] [Accepted: 11/10/2020] [Indexed: 12/19/2022] Open
Abstract
General anesthesia has revolutionized healthcare over the past 200 years and continues to show advancements. However, many phenomena induced by general anesthetics including paradoxical excitation are still poorly understood. Voltage-gated sodium channels (NaV) were believed to be one of the proteins targeted during general anesthesia. Based on electrophysiological measurements before and after propofol treatments of different concentrations, we mathematically modified the Hodgkin–Huxley sodium channel formulations and constructed a thalamocortical model to investigate the potential roles of NaV. The ion channels of individual neurons were modeled using the Hodgkin–Huxley type equations. The enhancement of propofol-induced GABAa current was simulated by increasing the maximal conductance and the time-constant of decay. Electroencephalogram (EEG) was evaluated as the post-synaptic potential from pyramidal (PY) cells. We found that a left shift in activation of NaV was induced primarily by a low concentration of propofol (0.3–10 μM), while a left shift in inactivation of NaV was induced by an increasing concentration (0.3–30 μM). Mathematical simulation indicated that a left shift of NaV activation produced a Hopf bifurcation, leading to cell oscillations. Left shift of NaV activation around a value of 5.5 mV in the thalamocortical models suppressed normal bursting of thalamocortical (TC) cells by triggering its chaotic oscillations. This led to irregular spiking of PY cells and an increased frequency in EEG readings. This observation suggests a mechanism leading to paradoxical excitation during general anesthesia. While a left shift in inactivation led to light hyperpolarization in individual cells, it inhibited the activity of the thalamocortical model after a certain depth of anesthesia. This finding implies that high doses of propofol inhibit the network partly by accelerating NaV toward inactivation. Additionally, this result explains why the application of sodium channel blockers decreases the requirement for general anesthetics. Our study provides an insight into the roles that NaV plays in the mechanism of general anesthesia. Since the activation and inactivation of NaV are structurally independent, it should be possible to avoid side effects by state-dependent binding to the NaV to achieve precision medicine in the future.
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Affiliation(s)
- Jinglei Xiao
- Department of Anesthesiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Zhengguo Chen
- College of Computer, National University of Defence Technology, Changsha, China
| | - Buwei Yu
- Department of Anesthesiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
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Fernandez FR, Rahsepar B, White JA. Differences in the Electrophysiological Properties of Mouse Somatosensory Layer 2/3 Neurons In Vivo and Slice Stem from Intrinsic Sources Rather than a Network-Generated High Conductance State. eNeuro 2018; 5:ENEURO.0447-17.2018. [PMID: 29662946 PMCID: PMC5898699 DOI: 10.1523/eneuro.0447-17.2018] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2017] [Revised: 03/01/2018] [Accepted: 03/20/2018] [Indexed: 01/29/2023] Open
Abstract
Synaptic activity in vivo can potentially alter the integration properties of neurons. Using recordings in awake mice, we targeted somatosensory layer 2/3 pyramidal neurons and compared neuronal properties with those from slices. Pyramidal cells in vivo had lower resistance and gain values, as well as broader spikes and increased spike frequency adaptation compared to the same cells in slices. Increasing conductance in neurons using dynamic clamp to levels observed in vivo, however, did not lessen the differences between in vivo and slice conditions. Further, local application of tetrodotoxin (TTX) in vivo blocked synaptic-mediated membrane voltage fluctuations but had little impact on pyramidal cell membrane input resistance and time constant values. Differences in electrophysiological properties of layer 2/3 neurons in mouse somatosensory cortex, therefore, stem from intrinsic sources separate from synaptic-mediated membrane voltage fluctuations.
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Affiliation(s)
- Fernando R Fernandez
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215
| | - Bahar Rahsepar
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215
| | - John A White
- Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215
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Balbi P, Massobrio P, Hellgren Kotaleski J. A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms. PLoS Comput Biol 2017; 13:e1005737. [PMID: 28863150 PMCID: PMC5599066 DOI: 10.1371/journal.pcbi.1005737] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2017] [Revised: 09/14/2017] [Accepted: 08/23/2017] [Indexed: 11/19/2022] Open
Abstract
Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour.
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Affiliation(s)
- Pietro Balbi
- Department of Neurorehabilitation, Scientific Institute of Pavia via Boezio IRCCS, Istituti Clinici Scientifici Maugeri SpA, Pavia, Italy
| | - Paolo Massobrio
- Department of Informatics, Bioengineering, Robotics and System Engineering (DIBRIS), University of Genova, Genova, Italy
| | - Jeanette Hellgren Kotaleski
- Department of Neuroscience, Karolinska Institute, Stockholm, Sweden
- Department of Computational Science and Technology, School of Computer Science and Communication, KTH The Royal Institute of Technology, Stockholm, Sweden
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Wang L, Wang H, Yu L, Chen Y. Spike-Threshold Variability Originated from Separatrix-Crossing in Neuronal Dynamics. Sci Rep 2016; 6:31719. [PMID: 27546614 PMCID: PMC4992847 DOI: 10.1038/srep31719] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2016] [Accepted: 07/26/2016] [Indexed: 11/09/2022] Open
Abstract
The threshold voltage for action potential generation is a key regulator of neuronal signal processing, yet the mechanism of its dynamic variation is still not well described. In this paper, we propose that threshold phenomena can be classified as parameter thresholds and state thresholds. Voltage thresholds which belong to the state threshold are determined by the 'general separatrix' in state space. We demonstrate that the separatrix generally exists in the state space of neuron models. The general form of separatrix was assumed as the function of both states and stimuli and the previously assumed threshold evolving equation versus time is naturally deduced from the separatrix. In terms of neuronal dynamics, the threshold voltage variation, which is affected by different stimuli, is determined by crossing the separatrix at different points in state space. We suggest that the separatrix-crossing mechanism in state space is the intrinsic dynamic mechanism for threshold voltages and post-stimulus threshold phenomena. These proposals are also systematically verified in example models, three of which have analytic separatrices and one is the classic Hodgkin-Huxley model. The separatrix-crossing framework provides an overview of the neuronal threshold and will facilitate understanding of the nature of threshold variability.
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Affiliation(s)
- Longfei Wang
- Institute of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Hengtong Wang
- College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Lianchun Yu
- Institute of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Yong Chen
- Center of Soft Matter Physics and its Application, Beihang University, Beijing 100191, China.,School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
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Smirnova EY, Zaitsev AV, Kim KK, Chizhov AV. The domain of neuronal firing on a plane of input current and conductance. J Comput Neurosci 2015; 39:217-33. [PMID: 26278407 DOI: 10.1007/s10827-015-0573-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Revised: 08/04/2015] [Accepted: 08/06/2015] [Indexed: 10/23/2022]
Abstract
The activation of neurotransmitter receptors increases the current flow and membrane conductance and thus controls the firing rate of a neuron. In the present work, we justified the two-dimensional representation of a neuronal input by voltage-independent current and conductance and obtained experimentally and numerically a complete input-output (I/O) function. The dependence of the steady-state firing rate on the input current and conductance was studied as a two-parameter I/O function. We employed the dynamic patch clamp technique in slices to get this dependence for the whole domain of two input signals that evoke stationary spike trains in a single neuron (Ω-domain). As found, the Ω-domain is finite and an additional conductance decreases the range of spike-evoking currents. The I/O function has been reproduced in a Hodgkin-Huxley-like model. Among the simulated effects of different factors on the I/O function, including passive and active membrane properties, external conditions and input signal properties, the most interesting were: the shift of the right boundary of the Ω-domain (corresponding to the exCitation block) leftwards due to the decrease of the maximal potassium conductance; and the reduction of the Ω-domain by the decrease of the maximal sodium concentration. As found in experiments and simulations, the Ω-domain is reduced by the decrease of extracellular sodium concentration, by cooling, and by adding slow potassium currents providing interspike interval adaptation; the Ω-domain height is increased by adding color noise. Our modeling data provided a generalization of I/O dependencies that is consistent with previous studies and our experiments. Our results suggest that both current flow and membrane conductance should be taken into account when determining neuronal firing activity.
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Affiliation(s)
- E Yu Smirnova
- Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Politekhnicheskaya str., 26, 194021, St.-Petersburg, Russia.
| | - A V Zaitsev
- Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint-Petersburg, Russia
| | - K Kh Kim
- Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint-Petersburg, Russia
| | - A V Chizhov
- Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Politekhnicheskaya str., 26, 194021, St.-Petersburg, Russia.,Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint-Petersburg, Russia
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