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de Sousa MPB, Cunha GM, Corso G, Dos Santos Lima GZ. Thermal effects and ephaptic entrainment in Hodgkin-Huxley model. Sci Rep 2024; 14:20075. [PMID: 39209942 PMCID: PMC11362309 DOI: 10.1038/s41598-024-70655-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2024] [Accepted: 08/20/2024] [Indexed: 09/04/2024] Open
Abstract
The brain is understood as an intricate biological system composed of numerous elements. It is susceptible to various physical and chemical influences, including temperature. The literature extensively explores the conditions that influence synapses in the context of cellular communication. However, the understanding of how the brain's global physical conditions can modulate ephaptic communication remains limited due to the poorly understood nature of ephapticity. This study proposes an adaptation of the Hodgkin and Huxley (HH) model to investigate the effects of ephaptic entrainment in response to thermal changes (HH-E). The analysis focuses on two distinct neuronal regimes: subthreshold and suprathreshold. In the subthreshold regime, circular statistics are used to demonstrate the dependence of phase differences with temperature. In the suprathreshold regime, the Inter-Spike Interval are employed to estimate phase preferences and changes in the spiking pattern. Temperature influences the model's ephaptic interactions and can modify its preferences for spiking frequency, with the direction of this change depending on specific model conditions and the temperature range under consideration. Furthermore, temperature enhance the anti-phase differences relationship between spikes and the external ephaptic signal. In the suprathreshold regime, ephaptic entrainment is also influenced by temperature, especially at low frequencies. This study reveals the susceptibility of ephaptic entrainment to temperature variations in both subthreshold and suprathreshold regimes and discusses the importance of ephaptic communication in the contexts where temperature may plays a significant role in neural physiology, such as inflammatory processes, fever, and epileptic seizures.
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Affiliation(s)
- Matheus Phellipe Brasil de Sousa
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
- Laboratório de Simulação e Modelagem Neurodinâmica, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Gabriel Moreno Cunha
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
- Laboratório de Simulação e Modelagem Neurodinâmica, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Gilberto Corso
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Gustavo Zampier Dos Santos Lima
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
- Laboratório de Simulação e Modelagem Neurodinâmica, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
- Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
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2
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Abdollahi N, Prescott SA. Impact of Extracellular Current Flow on Action Potential Propagation in Myelinated Axons. J Neurosci 2024; 44:e0569242024. [PMID: 38688722 PMCID: PMC11211723 DOI: 10.1523/jneurosci.0569-24.2024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Revised: 04/23/2024] [Accepted: 04/24/2024] [Indexed: 05/02/2024] Open
Abstract
Myelinated axons conduct action potentials, or spikes, in a saltatory manner. Inward current caused by a spike occurring at one node of Ranvier spreads axially to the next node, which regenerates the spike when depolarized enough for voltage-gated sodium channels to activate, and so on. The rate at which this process progresses dictates the velocity at which the spike is conducted and depends on several factors including axial resistivity and axon diameter that directly affect axial current. Here we show through computational simulations in modified double-cable axon models that conduction velocity also depends on extracellular factors whose effects can be explained by their indirect influence on axial current. Specifically, we show that a conventional double-cable model, with its outside layer connected to ground, transmits less axial current than a model whose outside layer is less absorptive. A more resistive barrier exists when an axon is packed tightly between other myelinated fibers, for example. We show that realistically resistive boundary conditions can significantly increase the velocity and energy efficiency of spike propagation, while also protecting against propagation failure. Certain factors like myelin thickness may be less important than typically thought if extracellular conditions are more resistive than normally considered. We also show how realistically resistive boundary conditions affect ephaptic interactions. Overall, these results highlight the unappreciated importance of extracellular conditions for axon function.
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Affiliation(s)
- Nooshin Abdollahi
- Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Ontario M5G 0A4, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario M5S 3G9, Canada
| | - Steven A Prescott
- Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Ontario M5G 0A4, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario M5S 3G9, Canada
- Department of Physiology, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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3
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Cunha GM, Corso G, Lima MMS, Dos Santos Lima GZ. Electrophysiological damage to neuronal membrane alters ephaptic entrainment. Sci Rep 2023; 13:11974. [PMID: 37488148 PMCID: PMC10366241 DOI: 10.1038/s41598-023-38738-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 07/13/2023] [Indexed: 07/26/2023] Open
Abstract
The brain is commonly understood as a complex network system with a particular organization and topology that can result in specific electrophysiological patterns. Among all the dynamic elements resulting from the circuits of the brain's network, ephapticity is a cellular communication mechanism that has received little attention. To understand the network's properties of ephaptic entrainment, we start investigating the ephaptic effect on a single neuron. In this study, we used numerical simulations to examine the relationship between alterations in ephaptic neuronal entrainment and impaired electrophysiological properties of the neuronal membrane, which can occur via spike field coherence (SFC). This change in frequency band amplitude is observed in some neurodegenerative diseases, such as Parkinson's or Alzheimer's. To further investigate these phenomena, we proposed a damaged model based on the impairment of both the resistance of the ion channels and the capacitance of the lipid membrane. Therefore, we simulated ephaptic entrainment with the hybrid neural model quadratic integrate-and-fire ephaptic (QIF-E), which mimics an ephaptic entrainment generated by an LFP (simulate a neuronal group). Our results indicate a link between peak entrainment (ephapticity) preference and a shift in frequency band when damage occurs mainly in ion channels. Finally, we discuss possible relationships between ephaptic entrainment and neurodegenerative diseases associated with aging factors.
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Affiliation(s)
- Gabriel Moreno Cunha
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Gilberto Corso
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Marcelo M S Lima
- Departamento de Fisiologia, Universidade Federal do Paraná, Curitiba, PR, 81531-980, Brazil
- Departamento de Farmacologia, Universidade Federal do Paraná, Curitiba, PR, 81531-980, Brazil
| | - Gustavo Zampier Dos Santos Lima
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
- Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
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4
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Schmidt H, R. Knösche T. Modelling the effect of ephaptic coupling on spike propagation in peripheral nerve fibres. BIOLOGICAL CYBERNETICS 2022; 116:461-473. [PMID: 35538379 PMCID: PMC9287264 DOI: 10.1007/s00422-022-00934-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 04/18/2022] [Indexed: 06/14/2023]
Abstract
Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of identical axons, whereas realistic peripheral nerve bundles contain numerous axons with different diameters. Here, we present a computationally efficient spike propagation model, which captures the essential features of propagating spikes and their ephaptic interaction, and facilitates the theoretical investigation of spike volleys in large, heterogeneous fibre bundles. We first lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model based on Hodgkin-Huxley dynamics. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that a higher level of heterogeneity requires stronger ephaptic coupling to achieve full synchronisation between spikes.
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Affiliation(s)
- Helmut Schmidt
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103 Leipzig, Germany
- Institute of Computer Science, The Czech Academy of Sciences, Pod Vodárenskou věží271/2, 182 07 Prague, Czech Republic
| | - Thomas R. Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103 Leipzig, Germany
- Institute of Biomedical Engineering and Informatics, University of Technology Ilmenau, Gustav-Kirchhoff Str. 2, 98693 Ilmenau, Germany
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5
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Cunha GM, Corso G, Miranda JGV, Dos Santos Lima GZ. Ephaptic entrainment in hybrid neuronal model. Sci Rep 2022; 12:1629. [PMID: 35102158 PMCID: PMC8803837 DOI: 10.1038/s41598-022-05343-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 01/04/2022] [Indexed: 11/17/2022] Open
Abstract
In recent decades, there has been a growing interest in the impact of electric fields generated in the brain. Transmembrane ionic currents originate electric fields in the extracellular space and are capable of affecting nearby neurons, a phenomenon called ephaptic neuronal communication. In the present work, the Quadratic Integrated-and-Fire model (QIF-E) underwent an adjustment/improvement to include the ephaptic entrainment behavior between neurons and electric fields. Indeed, the aim of our study is to validate the QIF-E model, which is a model to estimate the influence of electric fields on neurons. For this purpose, we evaluated whether the main properties observed in an experiment by Anastassiou et al. (Nat Neurosci 14:217-223, 2011), which analyzed the effect of an electric field on cortical pyramidal neurons, are reproduced with the QIF-E model. In this way, the analysis tools are employed according to the neuronal activity regime: (i) for the subthreshold regime, the circular statistic is used to describe the phase differences between the input stimulus signal (electrode) and the modeled membrane response; (ii) in the suprathreshold regime, the Population Vector and the Spike Field Coherence are used to estimate phase preferences and the entrainment intensity between the input stimulus and Action Potentials. The results observed are (i) in the subthreshold regime the values of the phase differences change with distinct frequencies of the input stimulus; (ii) in the supra-threshold regime the preferential phase of Action Potentials changes for different frequencies. In addition, we explore other parameters of the model, such as noise and membrane characteristic-time, in order to understand different types of neurons and extracellular environment related to ephaptic communication. Such results are consistent with results observed in empirical experiments based on ephaptic phenomenon. In addition, the QIF-E model allows further studies on the physiological importance of ephaptic communication in the brain, and its simplicity may open a door to simulate the ephaptic response in neuronal networks and assess the impact of ephaptic communication in such scenarios.
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Affiliation(s)
- Gabriel Moreno Cunha
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Gilberto Corso
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | | | - Gustavo Zampier Dos Santos Lima
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
- Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil.
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6
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Sætra MJ, Einevoll GT, Halnes G. An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain. PLoS Comput Biol 2021; 17:e1008143. [PMID: 34270543 PMCID: PMC8318289 DOI: 10.1371/journal.pcbi.1008143] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 07/28/2021] [Accepted: 06/28/2021] [Indexed: 11/29/2022] Open
Abstract
Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.
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Affiliation(s)
- Marte J. Sætra
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
| | - Gaute T. Einevoll
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
- Department of Physics, Norwegian University of Life Sciences, Ås, Norway
| | - Geir Halnes
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, Norwegian University of Life Sciences, Ås, Norway
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7
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Schmidt H, Hahn G, Deco G, Knösche TR. Ephaptic coupling in white matter fibre bundles modulates axonal transmission delays. PLoS Comput Biol 2021; 17:e1007858. [PMID: 33556058 PMCID: PMC7895385 DOI: 10.1371/journal.pcbi.1007858] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Revised: 02/19/2021] [Accepted: 10/06/2020] [Indexed: 11/19/2022] Open
Abstract
Axonal connections are widely regarded as faithful transmitters of neuronal signals with fixed delays. The reasoning behind this is that extracellular potentials caused by spikes travelling along axons are too small to have an effect on other axons. Here we devise a computational framework that allows us to study the effect of extracellular potentials generated by spike volleys in axonal fibre bundles on axonal transmission delays. We demonstrate that, although the extracellular potentials generated by single spikes are of the order of microvolts, the collective extracellular potential generated by spike volleys can reach several millivolts. As a consequence, the resulting depolarisation of the axonal membranes increases the velocity of spikes, and therefore reduces axonal delays between brain areas. Driving a neural mass model with such spike volleys, we further demonstrate that only ephaptic coupling can explain the reduction of stimulus latencies with increased stimulus intensities, as observed in many psychological experiments. Axonal fibre bundles that connect distant cortical areas contain millions of densely packed axons. When synchronous spike volleys travel through such fibre bundles, the extracellular potential within the bundles is perturbed. We use computer simulations to examine the magnitude and shape of this perturbation, and demonstrate that it is sufficiently strong to affect axonal transmission speeds. Since most spikes within a spike volley are positioned in an area where the extracellular potential is negative (relative to a distant reference), the resulting depolarisation of the axonal membranes accelerates the spike volley on average. This finding is in contrast to previous studies of ephaptic coupling effects between axons, where ephaptic coupling was found to slow down spike propagation. Our finding has consequences for information transmission and synchronisation between cortical areas.
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Affiliation(s)
- Helmut Schmidt
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- * E-mail:
| | - Gerald Hahn
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
- Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, Spain
- School of Psychological Sciences, Monash University, Melbourne, Australia
| | - Thomas R. Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Technische Universität Ilmenau, Institute of Biomedical Engineering and Informatics, Ilmenau, Germany
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8
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Sheheitli H, Jirsa VK. A mathematical model of ephaptic interactions in neuronal fiber pathways: Could there be more than transmission along the tracts? Netw Neurosci 2020; 4:595-610. [PMID: 32885117 PMCID: PMC7462434 DOI: 10.1162/netn_a_00134] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2019] [Accepted: 02/26/2020] [Indexed: 01/10/2023] Open
Abstract
While numerous studies of ephaptic interactions have focused on either axons of peripheral nerves or on cortical structures, no attention has been given to the possibility of ephaptic interactions in white matter tracts. Inspired by the highly organized, tightly packed geometry of axons in fiber pathways, we aim to investigate the potential effects of ephaptic interactions along these structures that are resilient to experimental probing. We use axonal cable theory to derive a minimal model of a sheet of N ephaptically coupled axons. Numerical solutions of the proposed model are explored as ephaptic coupling is varied. We demonstrate that ephaptic interactions can lead to local phase locking between adjacent traveling impulses and that, as coupling is increased, traveling impulses trigger new impulses along adjacent axons, resulting in finite size traveling fronts. For strong enough coupling, impulses propagate laterally and backwards, resulting in complex spatiotemporal patterns. While common large-scale brain network models often model fiber pathways as simple relays of signals between different brain regions, our work calls for a closer reexamination of the validity of such a view. The results suggest that in the presence of significant ephaptic interactions, the brain fiber tracts can act as a dynamic active medium. Starting from the FitzHugh-Nagumo cable model, we derive a system of nonlinear coupled partial differential equations (PDEs) to model a sheet of N ephaptically coupled axons. We also present a continuous limit approximation transforming the model into a two-dimensional field equation. We numerically solve the equations exploring the dynamics as coupling strength is varied. We observe phase locking of adjacent impulses and coordination of subthreshold dynamics. Strong enough coupling generates complex spatiotemporal patterns as new impulses form traveling fronts propagating laterally and backwards. The transition between different dynamic regimes happens abruptly at critical values of parameter. The results put into question the validity of assuming the role of fiber pathways to be that of mere interneuronal transmission and call for further investigation of the matter.
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Affiliation(s)
- Hiba Sheheitli
- Aix-Marseille University, Inserm, INS UMR_S 1106, Marseille, France
| | - Viktor K Jirsa
- Aix-Marseille University, Inserm, INS UMR_S 1106, Marseille, France
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9
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Capllonch-Juan M, Sepulveda F. Modelling the effects of ephaptic coupling on selectivity and response patterns during artificial stimulation of peripheral nerves. PLoS Comput Biol 2020; 16:e1007826. [PMID: 32479499 PMCID: PMC7263584 DOI: 10.1371/journal.pcbi.1007826] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2019] [Accepted: 03/27/2020] [Indexed: 11/18/2022] Open
Abstract
Artificial electrical stimulation of peripheral nerves for sensory feedback restoration can greatly benefit from computational models for simulation-based neural implant design in order to reduce the trial-and-error approach usually taken, thus potentially significantly reducing research and development costs and time. To this end, we built a computational model of a peripheral nerve trunk in which the interstitial space between the fibers and the tissues was modelled using a resistor network, thus enabling distance-dependent ephaptic coupling between myelinated axons and between fascicles as well. We used the model to simulate a) the stimulation of a nerve trunk model with a cuff electrode, and b) the propagation of action potentials along the axons. Results were used to investigate the effect of ephaptic interactions on recruitment and selectivity stemming from artificial (i.e., neural implant) stimulation and on the relative timing between action potentials during propagation. Ephaptic coupling was found to increase the number of fibers that are activated by artificial stimulation, thus reducing the artificial currents required for axonal recruitment, and it was found to reduce and shift the range of optimal stimulation amplitudes for maximum inter-fascicular selectivity. During propagation, while fibers of similar diameters tended to lock their action potentials and reduce their conduction velocities, as expected from previous knowledge on bundles of identical axons, the presence of many other fibers of different diameters was found to make their interactions weaker and unstable.
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10
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Ellingsrud AJ, Solbrå A, Einevoll GT, Halnes G, Rognes ME. Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries. Front Neuroinform 2020; 14:11. [PMID: 32269519 PMCID: PMC7109287 DOI: 10.3389/fninf.2020.00011] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 03/05/2020] [Indexed: 12/31/2022] Open
Abstract
Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.
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Affiliation(s)
- Ada J. Ellingsrud
- Department for Scientific Computing and Numerical Analysis, Simula Research Laboratory, Oslo, Norway
| | - Andreas Solbrå
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
| | - Gaute T. Einevoll
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
- Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Geir Halnes
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Marie E. Rognes
- Department for Scientific Computing and Numerical Analysis, Simula Research Laboratory, Oslo, Norway
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11
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Schmidt H, Knösche TR. Action potential propagation and synchronisation in myelinated axons. PLoS Comput Biol 2019; 15:e1007004. [PMID: 31622338 PMCID: PMC6818808 DOI: 10.1371/journal.pcbi.1007004] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Revised: 10/29/2019] [Accepted: 09/27/2019] [Indexed: 01/11/2023] Open
Abstract
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. With 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.
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Affiliation(s)
- Helmut Schmidt
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- * E-mail:
| | - Thomas R. Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, Ilmenau, Germany
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12
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Shifman AR, Lewis JE. E LFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models. Front Neuroinform 2019; 13:35. [PMID: 31214004 PMCID: PMC6555196 DOI: 10.3389/fninf.2019.00035] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Accepted: 04/24/2019] [Indexed: 12/18/2022] Open
Abstract
The transmembrane ionic currents that underlie changes in a cell's membrane potential give rise to electric fields in the extracellular space. In the context of brain activity, these electric fields form the basis for extracellularly recorded signals, such as multiunit activity, local field potentials and electroencephalograms. Understanding the underlying neuronal dynamics and localizing current sources using these signals is often challenging, and therefore effective computational modeling approaches are critical. Typically, the electric fields from neural activity are modeled in a post-hoc form, i.e., a traditional neuronal model is used to first generate the membrane currents, which in turn are then used to calculate the electric fields. When the conductivity of the extracellular space is high, the electric fields are weak, and therefore treating membrane currents and electric fields separately is justified. However, in brain regions of lower conductivity, extracellular fields can feed back and significantly influence the underlying transmembrane currents and dynamics of nearby neurons—this is often referred to as ephaptic coupling. The closed-loop nature of ephaptic coupling cannot be modeled using the post-hoc approaches implemented by existing software tools; instead, electric fields and neuronal dynamics must be solved simultaneously. To this end, we have developed a generalized modeling toolbox for studying ephaptic coupling in compartmental neuron models: ELFENN (ELectric Field Effects in Neural Networks). In open loop conditions, we validate the separate components of ELFENN for modeling membrane dynamics and associated field potentials against standard approaches (NEURON and LFPy). Unlike standard approaches however, ELFENN enables the closed-loop condition to be modeled as well, in that the field potentials can feed back and influence membrane dynamics. As an example closed-loop case, we use ELFENN to study phase-locking of action potentials generated by a population of axons running parallel in a bundle. Being able to efficiently explore ephaptic coupling from a computational perspective using tools, such as ELFENN will allow us to better understand the physical basis of electric fields in the brain, as well as the conditions in which these fields may influence neuronal dynamics in general.
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Affiliation(s)
- Aaron R Shifman
- Department of Biology, University of Ottawa, Ottawa, ON, Canada.,Center for Neural Dynamics, University of Ottawa, Ottawa, ON, Canada.,uOttawa Brain and Mind Research Institute, Ottawa, ON, Canada
| | - John E Lewis
- Department of Biology, University of Ottawa, Ottawa, ON, Canada.,Center for Neural Dynamics, University of Ottawa, Ottawa, ON, Canada.,uOttawa Brain and Mind Research Institute, Ottawa, ON, Canada
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Buccino AP, Kuchta M, Jæger KH, Ness TV, Berthet P, Mardal KA, Cauwenberghs G, Tveito A. How does the presence of neural probes affect extracellular potentials? J Neural Eng 2019; 16:026030. [PMID: 30703758 DOI: 10.1088/1741-2552/ab03a1] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
OBJECTIVE Mechanistic modeling of neurons is an essential component of computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach to simulation of extracellular neural recordings first computes transmembrane currents using the cable equation and then sums their contribution to model the extracellular potential. This two-step approach relies on the assumption that the extracellular space is an infinite and homogeneous conductive medium, while measurements are performed using neural probes. The main purpose of this paper is to assess to what extent the presence of the neural probes of varying shape and size impacts the extracellular field and how to correct for them. APPROACH We apply a detailed modeling framework allowing explicit representation of the neuron and the probe to study the effect of the probes and thereby estimate the effect of ignoring it. We use meshes with simplified neurons and different types of probe and compare the extracellular action potentials with and without the probe in the extracellular space. We then compare various solutions to account for the probes' presence and introduce an efficient probe correction method to include the probe effect in modeling of extracellular potentials. MAIN RESULTS Our computations show that microwires hardly influence the extracellular electric field and their effect can therefore be ignored. In contrast, multi-electrode arrays (MEAs) significantly affect the extracellular field by magnifying the recorded potential. While MEAs behave similarly to infinite insulated planes, we find that their effect strongly depends on the neuron-probe alignment and probe orientation. SIGNIFICANCE Ignoring the probe effect might be deleterious in some applications, such as neural localization and parameterization of neural models from extracellular recordings. Moreover, the presence of the probe can improve the interpretation of extracellular recordings, by providing a more accurate estimation of the extracellular potential generated by neuronal models.
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Affiliation(s)
- Alessio Paolo Buccino
- Center for Integrative Neuroplasticity (CINPLA), Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo, Norway. Department of Bioengineering, University of California San Diego, San Diego, CA, United States of America
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14
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Hagen E, Næss S, Ness TV, Einevoll GT. Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0. Front Neuroinform 2018; 12:92. [PMID: 30618697 PMCID: PMC6305460 DOI: 10.3389/fninf.2018.00092] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2018] [Accepted: 11/21/2018] [Indexed: 11/13/2022] Open
Abstract
Recordings of extracellular electrical, and later also magnetic, brain signals have been the dominant technique for measuring brain activity for decades. The interpretation of such signals is however nontrivial, as the measured signals result from both local and distant neuronal activity. In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons. Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed. This allows for the development of computational tools implementing forward models grounded in the biophysics underlying electrical and magnetic measurement modalities. LFPy (LFPy.readthedocs.io) incorporated a well-established scheme for predicting extracellular potentials of individual neurons with arbitrary levels of biological detail. It relies on NEURON (neuron.yale.edu) to compute transmembrane currents of multicompartment neurons which is then used in combination with an electrostatic forward model. Its functionality is now extended to allow for modeling of networks of multicompartment neurons with concurrent calculations of extracellular potentials and current dipole moments. The current dipole moments are then, in combination with suitable volume-conductor head models, used to compute non-invasive measures of neuronal activity, like scalp potentials (electroencephalographic recordings; EEG) and magnetic fields outside the head (magnetoencephalographic recordings; MEG). One such built-in head model is the four-sphere head model incorporating the different electric conductivities of brain, cerebrospinal fluid, skull and scalp. We demonstrate the new functionality of the software by constructing a network of biophysically detailed multicompartment neuron models from the Neocortical Microcircuit Collaboration (NMC) Portal (bbp.epfl.ch/nmc-portal) with corresponding statistics of connections and synapses, and compute in vivo-like extracellular potentials (local field potentials, LFP; electrocorticographical signals, ECoG) and corresponding current dipole moments. From the current dipole moments we estimate corresponding EEG and MEG signals using the four-sphere head model. We also show strong scaling performance of LFPy with different numbers of message-passing interface (MPI) processes, and for different network sizes with different density of connections. The open-source software LFPy is equally suitable for execution on laptops and in parallel on high-performance computing (HPC) facilities and is publicly available on GitHub.com.
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Affiliation(s)
- Espen Hagen
- Department of Physics, University of Oslo, Oslo, Norway.,Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Solveig Næss
- Department of Informatics, University of Oslo, Oslo, Norway
| | - Torbjørn V Ness
- Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Gaute T Einevoll
- Department of Physics, University of Oslo, Oslo, Norway.,Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
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15
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Han KS, Guo C, Chen CH, Witter L, Osorno T, Regehr WG. Ephaptic Coupling Promotes Synchronous Firing of Cerebellar Purkinje Cells. Neuron 2018; 100:564-578.e3. [PMID: 30293822 DOI: 10.1016/j.neuron.2018.09.018] [Citation(s) in RCA: 68] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2018] [Revised: 07/29/2018] [Accepted: 09/10/2018] [Indexed: 11/29/2022]
Abstract
Correlated neuronal activity at various timescales plays an important role in information transfer and processing. We find that in awake-behaving mice, an unexpectedly large fraction of neighboring Purkinje cells (PCs) exhibit sub-millisecond synchrony. Correlated firing usually arises from chemical or electrical synapses, but, surprisingly, neither is required to generate PC synchrony. We therefore assessed ephaptic coupling, a mechanism in which neurons communicate via extracellular electrical signals. In the neocortex, ephaptic signals from many neurons summate to entrain spiking on slow timescales, but extracellular signals from individual cells are thought to be too small to synchronize firing. Here we find that a single PC generates sufficiently large extracellular potentials to open sodium channels in nearby PC axons. Rapid synchronization is made possible because ephaptic signals generated by PCs peak during the rising phase of action potentials. These findings show that ephaptic coupling contributes to the prevalent synchronization of nearby PCs.
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Affiliation(s)
- Kyung-Seok Han
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Chong Guo
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Christopher H Chen
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Laurens Witter
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Tomas Osorno
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA
| | - Wade G Regehr
- Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA.
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16
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Baluška F, Miller, Jr WB. Senomic view of the cell: Senome versus Genome. Commun Integr Biol 2018; 11:1-9. [PMID: 30214674 PMCID: PMC6132427 DOI: 10.1080/19420889.2018.1489184] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Accepted: 06/11/2018] [Indexed: 12/25/2022] Open
Abstract
In the legacy of Thomas Henry Huxley, and his 'epigenetic' philosophy of biology, cells are proposed to represent a trinity of three memory-storing media: Senome, Epigenome, and Genome that together comprise a cell-wide informational architecture. Our current preferential focus on the Genome needs to be complemented by a similar focus on the Epigenome and a here proposed Senome, representing the sum of all the sensory experiences of the cognitive cell and its sensing apparatus. Only then will biology be in a position to embrace the whole complexity of the eukaryotic cell, understanding its true nature which allows the communicative assembly of cells in the form of sentient multicellular organisms.
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17
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Majhi S, Ghosh D. Alternating chimeras in networks of ephaptically coupled bursting neurons. CHAOS (WOODBURY, N.Y.) 2018; 28:083113. [PMID: 30180636 DOI: 10.1063/1.5022612] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Accepted: 07/26/2018] [Indexed: 06/08/2023]
Abstract
The distinctive phenomenon of the chimera state has been explored in neuronal systems under a variety of different network topologies during the last decade. Nevertheless, in all the works, the neurons are presumed to interact with each other directly with the help of synapses only. But, the influence of ephaptic coupling, particularly magnetic flux across the membrane, is mostly unexplored and should essentially be dealt with during the emergence of collective electrical activities and propagation of signals among the neurons in a network. Through this article, we report the development of an emerging dynamical state, namely, the alternating chimera, in a network of identical neuronal systems induced by an external electromagnetic field. Owing to this interaction scenario, the nonlinear neuronal oscillators are coupled indirectly via electromagnetic induction with magnetic flux, through which neurons communicate in spite of the absence of physical connections among them. The evolution of each neuron, here, is described by the three-dimensional Hindmarsh-Rose dynamics. We demonstrate that the presence of such non-locally and globally interacting external environments induces a stationary alternating chimera pattern in the ensemble of neurons, whereas in the local coupling limit, the network exhibits a transient chimera state whenever the local dynamics of the neurons is of the chaotic square-wave bursting type. For periodic square-wave bursting of the neurons, a similar qualitative phenomenon has been witnessed with the exception of the disappearance of cluster states for non-local and global interactions. Besides these observations, we advance our work while providing confirmation of the findings for neuronal ensembles exhibiting plateau bursting dynamics and also put forward the fact that the plateau pattern actually favors the alternating chimera more than others. These results may deliver better interpretations for different aspects of synchronization appearing in a network of neurons through field coupling that also relaxes the prerequisite of synaptic connectivity for realizing the chimera state in neuronal networks.
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Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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18
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West TO, Berthouze L, Halliday DM, Litvak V, Sharott A, Magill PJ, Farmer SF. Propagation of beta/gamma rhythms in the cortico-basal ganglia circuits of the parkinsonian rat. J Neurophysiol 2018; 119:1608-1628. [PMID: 29357448 PMCID: PMC6008089 DOI: 10.1152/jn.00629.2017] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Much of the motor impairment associated with Parkinson’s disease is thought to arise from pathological activity in the networks formed by the basal ganglia (BG) and motor cortex. To evaluate several hypotheses proposed to explain the emergence of pathological oscillations in parkinsonism, we investigated changes to the directed connectivity in BG networks following dopamine depletion. We recorded local field potentials (LFPs) in the cortex and basal ganglia of rats rendered parkinsonian by injection of 6-hydroxydopamine (6-OHDA) and in dopamine-intact controls. We performed systematic analyses of the networks using a novel tool for estimation of directed interactions (nonparametric directionality, NPD). We used a “conditioned” version of the NPD analysis that reveals the dependence of the correlation between two signals on a third reference signal. We find evidence of the dopamine dependency of both low-beta (14–20 Hz) and high-beta/low-gamma (20–40 Hz) directed network interactions. Notably, 6-OHDA lesions were associated with enhancement of the cortical “hyperdirect” connection to the subthalamic nucleus (STN) and its feedback to the cortex and striatum. We find that pathological beta synchronization resulting from 6-OHDA lesioning is widely distributed across the network and cannot be located to any individual structure. Furthermore, we provide evidence that high-beta/gamma oscillations propagate through the striatum in a pathway that is independent of STN. Rhythms at high beta/gamma show susceptibility to conditioning that indicates a hierarchical organization compared with those at low beta. These results further inform our understanding of the substrates for pathological rhythms in salient brain networks in parkinsonism. NEW & NOTEWORTHY We present a novel analysis of electrophysiological recordings in the cortico-basal ganglia network with the aim of evaluating several hypotheses concerning the origins of abnormal brain rhythms associated with Parkinson’s disease. We present evidence for changes in the directed connections within the network following chronic dopamine depletion in rodents. These findings speak to the plausibility of a “short-circuiting” of the network that gives rise to the conditions from which pathological synchronization may arise.
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Affiliation(s)
- Timothy O West
- Centre for Mathematics and Physics in the Life Sciences and Experimental Biology (CoMPLEX), Department of Physics and Astronomy, University College London , London , United Kingdom.,Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London , London , United Kingdom
| | - Luc Berthouze
- Centre for Computational Neuroscience and Robotics, University of Sussex , Falmer , United Kingdom.,UCL Great Ormond Street Institute of Child Health , London , United Kingdom
| | - David M Halliday
- Department of Electronic Engineering, University of York , York , United Kingdom
| | - Vladimir Litvak
- Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London , London , United Kingdom
| | - Andrew Sharott
- Medical Research Council Brain Network Dynamics Unit, University of Oxford , Oxford , United Kingdom
| | - Peter J Magill
- Medical Research Council Brain Network Dynamics Unit, University of Oxford , Oxford , United Kingdom.,Oxford Parkinson's Disease Centre, University of Oxford , Oxford , United Kingdom
| | - Simon F Farmer
- Department of Neurology, National Hospital for Neurology & Neurosurgery , London , United Kingdom.,Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, University College London , London , United Kingdom
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19
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Appukuttan S, Brain KL, Manchanda R. Modeling extracellular fields for a three-dimensional network of cells using NEURON. J Neurosci Methods 2017; 290:27-38. [DOI: 10.1016/j.jneumeth.2017.07.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Revised: 07/07/2017] [Accepted: 07/09/2017] [Indexed: 10/19/2022]
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20
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Signatures of Somatic Inhibition and Dendritic Excitation in Auditory Brainstem Field Potentials. J Neurosci 2017; 37:10451-10467. [PMID: 28947575 DOI: 10.1523/jneurosci.0600-17.2017] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Revised: 09/12/2017] [Accepted: 09/14/2017] [Indexed: 01/20/2023] Open
Abstract
Extracellular voltage recordings (Ve ; field potentials) provide an accessible view of in vivo neural activity, but proper interpretation of field potentials is a long-standing challenge. Computational modeling can aid in identifying neural generators of field potentials. In the auditory brainstem of cats, spatial patterns of sound-evoked Ve can resemble, strikingly, Ve generated by current dipoles. Previously, we developed a biophysically-based model of a binaural brainstem nucleus, the medial superior olive (MSO), that accounts qualitatively for observed dipole-like Ve patterns in sustained responses to monaural tones with frequencies >∼1000 Hz (Goldwyn et al., 2014). We have observed, however, that Ve patterns in cats of both sexes appear more monopole-like for lower-frequency tones. Here, we enhance our theory to accurately reproduce dipole and non-dipole features of Ve responses to monaural tones with frequencies ranging from 600 to 1800 Hz. By applying our model to data, we estimate time courses of paired input currents to MSO neurons. We interpret these inputs as dendrite-targeting excitation and soma-targeting inhibition (the latter contributes non-dipole-like features to Ve responses). Aspects of inferred inputs are consistent with synaptic inputs to MSO neurons including the tendencies of inhibitory inputs to attenuate in response to high-frequency tones and to precede excitatory inputs. Importantly, our updated theory can be tested experimentally by blocking synaptic inputs. MSO neurons perform a critical role in sound localization and binaural hearing. By solving an inverse problem to uncover synaptic inputs from Ve patterns we provide a new perspective on MSO physiology.SIGNIFICANCE STATEMENT Extracellular voltages (field potentials) are a common measure of brain activity. Ideally, one could infer from these data the activity of neurons and synapses that generate field potentials, but this "inverse problem" is not easily solved. We study brainstem field potentials in the region of the medial superior olive (MSO); a critical center in the auditory pathway. These field potentials exhibit distinctive spatial and temporal patterns in response to pure tone sounds. We use mathematical modeling in combination with physiological and anatomical knowledge of MSO neurons to plausibly explain how dendrite-targeting excitation and soma-targeting inhibition generate these field potentials. Inferring putative synaptic currents from field potentials advances our ability to study neural processing of sound in the MSO.
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Tveito A, Jæger KH, Lines GT, Paszkowski Ł, Sundnes J, Edwards AG, Māki-Marttunen T, Halnes G, Einevoll GT. An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons. Front Comput Neurosci 2017; 11:27. [PMID: 28484385 PMCID: PMC5401906 DOI: 10.3389/fncom.2017.00027] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Accepted: 03/31/2017] [Indexed: 11/20/2022] Open
Abstract
Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant-at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.
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Affiliation(s)
- Aslak Tveito
- Simula Research Laboratory, Center for Biomedical ComputingOslo, Norway
- Department of Informatics, University of OsloOslo, Norway
| | - Karoline H. Jæger
- Simula Research Laboratory, Center for Biomedical ComputingOslo, Norway
| | - Glenn T. Lines
- Simula Research Laboratory, Center for Biomedical ComputingOslo, Norway
| | | | - Joakim Sundnes
- Simula Research Laboratory, Center for Biomedical ComputingOslo, Norway
- Department of Informatics, University of OsloOslo, Norway
| | - Andrew G. Edwards
- Simula Research Laboratory, Center for Biomedical ComputingOslo, Norway
- Department of Biosciences, University of OsloOslo, Norway
| | - Tuomo Māki-Marttunen
- NORMENT, K.G. Jebsen Center for Psychosis Research, Institute of Clinical Medicine, University of OsloOslo, Norway
| | - Geir Halnes
- Department of Mathematical Sciences and Technology, Norwegian University of Life SciencesÅs, Norway
| | - Gaute T. Einevoll
- Department of Mathematical Sciences and Technology, Norwegian University of Life SciencesÅs, Norway
- Department of Physics, University of OsloOslo, Norway
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McColgan T, Liu J, Kuokkanen PT, Carr CE, Wagner H, Kempter R. Dipolar extracellular potentials generated by axonal projections. eLife 2017; 6:26106. [PMID: 28871959 PMCID: PMC5617635 DOI: 10.7554/elife.26106] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2017] [Accepted: 09/01/2017] [Indexed: 01/27/2023] Open
Abstract
Extracellular field potentials (EFPs) are an important source of information in neuroscience, but their physiological basis is in many cases still a matter of debate. Axonal sources are typically discounted in modeling and data analysis because their contributions are assumed to be negligible. Here, we established experimentally and theoretically that contributions of axons to EFPs can be significant. Modeling action potentials propagating along axons, we showed that EFPs were prominent in the presence of terminal zones where axons branch and terminate in close succession, as found in many brain regions. Our models predicted a dipolar far field and a polarity reversal at the center of the terminal zone. We confirmed these predictions using EFPs from the barn owl auditory brainstem where we recorded in nucleus laminaris using a multielectrode array. These results demonstrate that axonal terminal zones can produce EFPs with considerable amplitude and spatial reach.
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Affiliation(s)
- Thomas McColgan
- Department for Biology, Institute for Theoretical BiologyHumboldt-Universität zu BerlinBerlinGermany
| | - Ji Liu
- Department of BiologyUniversity of MarylandCollege ParkUnited States
| | - Paula Tuulia Kuokkanen
- Department for Biology, Institute for Theoretical BiologyHumboldt-Universität zu BerlinBerlinGermany,Bernstein Center for Computational NeuroscienceBerlinGermany
| | | | | | - Richard Kempter
- Department for Biology, Institute for Theoretical BiologyHumboldt-Universität zu BerlinBerlinGermany,Bernstein Center for Computational NeuroscienceBerlinGermany,Einstein Center for NeurosciencesBerlinGermany
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