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Zheng Y, Kang S, O'Neill J, Bojak I. Spontaneous slow wave oscillations in extracellular field potential recordings reflect the alternating dominance of excitation and inhibition. J Physiol 2024; 602:713-736. [PMID: 38294945 DOI: 10.1113/jp284587] [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: 02/23/2023] [Accepted: 01/15/2024] [Indexed: 02/02/2024] Open
Abstract
In the resting state, cortical neurons can fire action potentials spontaneously but synchronously (Up state), followed by a quiescent period (Down state) before the cycle repeats. Extracellular recordings in the infragranular layer of cortex with a micro-electrode display a negative deflection (depth-negative) during Up states and a positive deflection (depth-positive) during Down states. The resulting slow wave oscillation (SWO) has been studied extensively during sleep and under anaesthesia. However, recent research on the balanced nature of synaptic excitation and inhibition has highlighted our limited understanding of its genesis. Specifically, are excitation and inhibition balanced during SWOs? We analyse spontaneous local field potentials (LFPs) during SWOs recorded from anaesthetised rats via a multi-channel laminar micro-electrode and show that the Down state consists of two distinct synaptic states: a Dynamic Down state associated with depth-positive LFPs and a prominent dipole in the extracellular field, and a Static Down state with negligible (≈ 0 mV $ \approx 0{\mathrm{\;mV}}$ ) LFPs and a lack of dipoles extracellularly. We demonstrate that depth-negative and -positive LFPs are generated by a shift in the balance of synaptic excitation and inhibition from excitation dominance (depth-negative) to inhibition dominance (depth-positive) in the infragranular layer neurons. Thus, although excitation and inhibition co-tune overall, differences in their timing lead to an alternation of dominance, manifesting as SWOs. We further show that Up state initiation is significantly faster if the preceding Down state is dynamic rather than static. Our findings provide a coherent picture of the dependence of SWOs on synaptic activity. KEY POINTS: Cortical neurons can exhibit repeated cycles of spontaneous activity interleaved with periods of relative silence, a phenomenon known as 'slow wave oscillation' (SWO). During SWOs, recordings of local field potentials (LFPs) in the neocortex show depth-negative deflection during the active period (Up state) and depth-positive deflection during the silent period (Down state). Here we further classified the Down state into a dynamic phase and a static phase based on a novel method of classification and revealed non-random, stereotypical sequences of the three states occurring with significantly different transitional kinetics. Our results suggest that the positive and negative deflections in the LFP reflect the shift of the instantaneous balance between excitatory and inhibitory synaptic activity of the local cortical neurons. The differences in transitional kinetics may imply distinct synaptic mechanisms for Up state initiation. The study may provide a new approach for investigating spontaneous brain rhythms.
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Affiliation(s)
- Ying Zheng
- School of Biological Sciences, Whiteknights, University of Reading, Reading, UK
- Centre for Integrative Neuroscience and Neurodynamics (CINN), University of Reading, Reading, UK
| | - Sungmin Kang
- School of Psychology, Cardiff University, Cardiff, UK
| | | | - Ingo Bojak
- Centre for Integrative Neuroscience and Neurodynamics (CINN), University of Reading, Reading, UK
- School of Psychology and Clinical Language Science, Whiteknights, University of Reading, Reading, UK
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2
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Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes. J Neurosci Methods 2022; 372:109550. [PMID: 35247493 DOI: 10.1016/j.jneumeth.2022.109550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 02/22/2022] [Accepted: 02/26/2022] [Indexed: 11/21/2022]
Abstract
BACKGROUND In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron. NEW METHOD We provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. To the best of our knowledge, this is the first time that a Hawkes-diffusion model is investigated on such complex data. The first step of the proposed procedure is to select a subnetwork of neurons impacting the central neuron using a multivariate Hawkes process. Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkes process, the occurrences of which correspond to the spike trains of the aforementioned subset of neurons that interact with the central neuron. RESULTS From the Hawkes estimation step we recover a small connectivity graph which contains the central neuron, and we show that taking into account this information improves the inference of membrane potential through the proposed jump-diffusion model. A goodness of fit test is applied to validate the relevance of the Hawkes model in such context. COMPARISON WITH EXISTING METHODS We compare an empirical inference method and two sparse estimation procedures based on the Hawkes assumption for the reconstruction of the connectivity graph using the spike-trains. Then, the Hawkes-diffusion model is competed with the simple diffusion in terms of best fit to describe the behavior of the membrane potential of a central neuron surrounded by a network. CONCLUSIONS The present method takes advantage of both spike trains and membrane potential to understand the behavior of a fixed neuron. The entire code has been developed and is freely available on GitHub.
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Müller-Komorowska D, Parabucki A, Elyasaf G, Katz Y, Beck H, Lampl I. A novel theoretical framework for simultaneous measurement of excitatory and inhibitory conductances. PLoS Comput Biol 2021; 17:e1009725. [PMID: 34962935 PMCID: PMC8746761 DOI: 10.1371/journal.pcbi.1009725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Revised: 01/10/2022] [Accepted: 12/06/2021] [Indexed: 11/20/2022] Open
Abstract
The firing of neurons throughout the brain is determined by the precise relations between excitatory and inhibitory inputs, and disruption of their balance underlies many psychiatric diseases. Whether or not these inputs covary over time or between repeated stimuli remains unclear due to the lack of experimental methods for measuring both inputs simultaneously. We developed a new analytical framework for instantaneous and simultaneous measurements of both the excitatory and inhibitory neuronal inputs during a single trial under current clamp recording. This can be achieved by injecting a current composed of two high frequency sinusoidal components followed by analytical extraction of the conductances. We demonstrate the ability of this method to measure both inputs in a single trial under realistic recording constraints and from morphologically realistic CA1 pyramidal model cells. Future experimental implementation of our new method will facilitate the understanding of fundamental questions about the health and disease of the nervous system. Most neurons in the brain receive synaptic inputs from both excitatory and inhibitory neurons. Together, these inputs determine neuronal activity: excitatory synapses shift the electrical potential across the membrane towards the threshold for generation of action potentials, whereas inhibitory synapses lower this potential away from the threshold. Action potentials are the rapid electrochemical signals that transmit information to other neurons and they are critical for the information processing abilities of the brain. Although there are many ways to measure either excitatory or inhibitory inputs, these methods have been unable to measure both at the same time. Measuring both inputs together is essential towards understanding how neurons integrate information. We developed a new analytical method to measure excitatory and inhibitory inputs at the same time from the voltage response to injection of an alternating current into a neuron. We describe the foundation of this new method and find that it works in biologically realistic simulations of neurons. By using this technique in real neurons, scientists could investigate basic principles of information processing in the healthy and diseased brain.
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Affiliation(s)
- Daniel Müller-Komorowska
- Institute of Experimental Epileptology and Cognition Research, Life and Brain Center, University of Bonn Medical Center, Bonn, Germany.,International Max Planck Research School for Brain and Behavior, University of Bonn, Bonn, Germany
| | - Ana Parabucki
- Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel
| | - Gal Elyasaf
- Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel
| | - Yonatan Katz
- Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel
| | - Heinz Beck
- Institute of Experimental Epileptology and Cognition Research, Life and Brain Center, University of Bonn Medical Center, Bonn, Germany
| | - Ilan Lampl
- Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel
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4
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Inference for biomedical data by using diffusion models with covariates and mixed effects. J R Stat Soc Ser C Appl Stat 2019. [DOI: 10.1111/rssc.12386] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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5
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Berg RW, Willumsen A, Lindén H. When networks walk a fine line: balance of excitation and inhibition in spinal motor circuits. CURRENT OPINION IN PHYSIOLOGY 2019. [DOI: 10.1016/j.cophys.2019.01.006] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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6
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Ditlevsen S, Samson A. Hypoelliptic diffusions: filtering and inference from complete and partial observations. J R Stat Soc Series B Stat Methodol 2018. [DOI: 10.1111/rssb.12307] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Adeline Samson
- Université Grenoble Alpes, and Centre National de la Recherche Scientifique Grenoble France
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7
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Berg RW. Commentary: Synaptic Excitation in Spinal Motoneurons Alternates with Synaptic Inhibition and Is Balanced by Outward Rectification during Rhythmic Motor Network Activity. Front Neural Circuits 2018; 12:1. [PMID: 29403360 PMCID: PMC5778114 DOI: 10.3389/fncir.2018.00001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2017] [Accepted: 01/04/2018] [Indexed: 01/20/2023] Open
Affiliation(s)
- Rune W Berg
- Department of Neuroscience, University of Copenhagen, Copenhagen, Denmark
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8
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Wright NC, Hoseini MS, Yasar TB, Wessel R. Coupling of synaptic inputs to local cortical activity differs among neurons and adapts after stimulus onset. J Neurophysiol 2017; 118:3345-3359. [PMID: 28931610 DOI: 10.1152/jn.00398.2017] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Cortical activity contributes significantly to the high variability of sensory responses of interconnected pyramidal neurons, which has crucial implications for sensory coding. Yet, largely because of technical limitations of in vivo intracellular recordings, the coupling of a pyramidal neuron's synaptic inputs to the local cortical activity has evaded full understanding. Here we obtained excitatory synaptic conductance ( g) measurements from putative pyramidal neurons and local field potential (LFP) recordings from adjacent cortical circuits during visual processing in the turtle whole brain ex vivo preparation. We found a range of g-LFP coupling across neurons. Importantly, for a given neuron, g-LFP coupling increased at stimulus onset and then relaxed toward intermediate values during continued visual stimulation. A model network with clustered connectivity and synaptic depression reproduced both the diversity and the dynamics of g-LFP coupling. In conclusion, these results establish a rich dependence of single-neuron responses on anatomical, synaptic, and emergent network properties. NEW & NOTEWORTHY Cortical neurons are strongly influenced by the networks in which they are embedded. To understand sensory processing, we must identify the nature of this influence and its underlying mechanisms. Here we investigate synaptic inputs to cortical neurons, and the nearby local field potential, during visual processing. We find a range of neuron-to-network coupling across cortical neurons. This coupling is dynamically modulated during visual processing via biophysical and emergent network properties.
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Affiliation(s)
- Nathaniel C Wright
- Department of Physics, Washington University in St. Louis , St. Louis, Missouri
| | - Mahmood S Hoseini
- Department of Physics, Washington University in St. Louis , St. Louis, Missouri
| | - Tansel Baran Yasar
- Department of Physics, Washington University in St. Louis , St. Louis, Missouri
| | - Ralf Wessel
- Department of Physics, Washington University in St. Louis , St. Louis, Missouri
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9
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Kobayashi R, Nishimaru H, Nishijo H, Lansky P. A single spike deteriorates synaptic conductance estimation. Biosystems 2017; 161:41-45. [PMID: 28756162 DOI: 10.1016/j.biosystems.2017.07.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Revised: 07/19/2017] [Accepted: 07/20/2017] [Indexed: 11/19/2022]
Abstract
We investigated the estimation accuracy of synaptic conductances by analyzing simulated voltage traces generated by a Hodgkin-Huxley type model. We show that even a single spike substantially deteriorates the estimation. We also demonstrate that two approaches, namely, negative current injection and spike removal, can ameliorate this deterioration.
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Affiliation(s)
- Ryota Kobayashi
- Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan; Department of Informatics, Graduate University for Advanced Studies (Sokendai), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan.
| | - Hiroshi Nishimaru
- System Emotional Science, Graduate School of Medicine and Pharmaceutical Sciences, University of Toyama, Sugitani 2630, Toyama 930-0194, Japan
| | - Hisao Nishijo
- System Emotional Science, Graduate School of Medicine and Pharmaceutical Sciences, University of Toyama, Sugitani 2630, Toyama 930-0194, Japan
| | - Petr Lansky
- Institute of Physiology, The Czech Academy of Sciences, 142 20 Prague 4, Czech Republic
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10
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Vich C, Berg RW, Guillamon A, Ditlevsen S. Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents. Front Comput Neurosci 2017; 11:69. [PMID: 28790909 PMCID: PMC5524927 DOI: 10.3389/fncom.2017.00069] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2016] [Accepted: 07/07/2017] [Indexed: 11/13/2022] Open
Abstract
Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.
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Affiliation(s)
- Catalina Vich
- Departament de Matemàtiques i Informàtica, Universitat de les Illes BalearsPalma, Spain
| | - Rune W Berg
- Center for Neuroscience, University of CopenhagenCopenhagen, Denmark
| | - Antoni Guillamon
- Departament de Matemàtiques, Universitat Politècnica de CatalunyaBarcelona, Spain
| | - Susanne Ditlevsen
- Department of Mathematical Sciences, University of CopenhagenCopenhagen, Denmark
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11
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12
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Lankarany M, Heiss JE, Lampl I, Toyoizumi T. Simultaneous Bayesian Estimation of Excitatory and Inhibitory Synaptic Conductances by Exploiting Multiple Recorded Trials. Front Comput Neurosci 2016; 10:110. [PMID: 27867353 PMCID: PMC5095134 DOI: 10.3389/fncom.2016.00110] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2016] [Accepted: 10/03/2016] [Indexed: 12/04/2022] Open
Abstract
Advanced statistical methods have enabled trial-by-trial inference of the underlying excitatory and inhibitory synaptic conductances (SCs) of membrane-potential recordings. Simultaneous inference of both excitatory and inhibitory SCs sheds light on the neural circuits underlying the neural activity and advances our understanding of neural information processing. Conventional Bayesian methods can infer excitatory and inhibitory SCs based on a single trial of observed membrane potential. However, if multiple recorded trials are available, this typically leads to suboptimal estimation because they neglect common statistics (of synaptic inputs (SIs)) across trials. Here, we establish a new expectation maximization (EM) algorithm that improves such single-trial Bayesian methods by exploiting multiple recorded trials to extract common SI statistics across the trials. In this paper, the proposed EM algorithm is embedded in parallel Kalman filters or particle filters for multiple recorded trials to integrate their outputs to iteratively update the common SI statistics. These statistics are then used to infer the excitatory and inhibitory SCs of individual trials. We demonstrate the superior performance of multiple-trial Kalman filtering (MtKF) and particle filtering (MtPF) relative to that of the corresponding single-trial methods. While relative estimation error of excitatory and inhibitory SCs is known to depend on the level of current injection into a cell, our numerical simulations using MtKF show that both excitatory and inhibitory SCs are reliably inferred using an optimal level of current injection. Finally, we validate the robustness and applicability of our technique through simulation studies, and we apply MtKF to in vivo data recorded from the rat barrel cortex.
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Affiliation(s)
- Milad Lankarany
- Neurosciences and Mental Health, Department of Physiology and the Institute of Biomaterials and Biomedical Engineering, University of Toronto, The Hospital for Sick ChildrenToronto, ON, Canada; RIKEN Brain Science InstituteSaitama, Japan
| | - Jaime E Heiss
- Center for Neuroscience, Biosciences Division, SRI International Menlo Park, CA, USA
| | - Ilan Lampl
- Department of Neurobiology, Weizmann Institute of Science Rehovot, Israel
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13
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Petersen PC, Berg RW. Lognormal firing rate distribution reveals prominent fluctuation-driven regime in spinal motor networks. eLife 2016; 5:e18805. [PMID: 27782883 PMCID: PMC5135395 DOI: 10.7554/elife.18805] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Accepted: 10/25/2016] [Indexed: 12/15/2022] Open
Abstract
When spinal circuits generate rhythmic movements it is important that the neuronal activity remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we simultaneously record from hundreds of neurons in lumbar spinal circuits of turtles and establish the neuronal fraction that operates within either a 'mean-driven' or a 'fluctuation-driven' regime. Fluctuation-driven neurons have a 'supralinear' input-output curve, which enhances sensitivity, whereas the mean-driven regime reduces sensitivity. We find a rich diversity of firing rates across the neuronal population as reflected in a lognormal distribution and demonstrate that half of the neurons spend at least 50 % of the time in the 'fluctuation-driven' regime regardless of behavior. Because of the disparity in input-output properties for these two regimes, this fraction may reflect a fine trade-off between stability and sensitivity in order to maintain flexibility across behaviors.
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Affiliation(s)
- Peter C Petersen
- Department of Neuroscience and Pharmacology, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Rune W Berg
- Department of Neuroscience and Pharmacology, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
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14
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Tuckwell HC, Ditlevsen S. The Space-Clamped Hodgkin-Huxley System with Random Synaptic Input: Inhibition of Spiking by Weak Noise and Analysis with Moment Equations. Neural Comput 2016; 28:2129-61. [PMID: 27557099 DOI: 10.1162/neco_a_00881] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only, there is a critical value of the steady-state excitatory conductance for repetitive spiking without noise, and for values of the conductance near the critical value, small noise has a powerfully inhibitory effect. For a given level of inhibition, there is also a critical value of the steady-state excitatory conductance for repetitive firing, and it is demonstrated that noise in either the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of deterministic differential equations for the approximate first- and second-order moments of the model is derived. They are solved using Runge-Kutta methods, and the solutions are compared with the results obtained by simulation for various sets of parameters, including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells, the assumptions underlying the moment equation approach are not satisfied. The simulation results show that noisy synaptic input of either an excitatory or inhibitory character or both may lead to the suppression of firing in neurons operating near a critical point and this has possible implications for cortical networks. Although suppression of firing is corroborated for the system of moment equations, there seem to be substantial differences between the dynamical properties of the original system of stochastic differential equations and the much larger system of moment equations.
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Affiliation(s)
- Henry C Tuckwell
- School of Electrical and Electronic Engineering, University of Adelaide SA 5005, Australia, and School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia
| | - Susanne Ditlevsen
- Department of Mathematical Sciences, University of Copenhagen, DK 2100 Copenhagen, Denmark
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15
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Kobayashi R, Nishimaru H, Nishijo H. Estimation of excitatory and inhibitory synaptic conductance variations in motoneurons during locomotor-like rhythmic activity. Neuroscience 2016; 335:72-81. [PMID: 27561702 DOI: 10.1016/j.neuroscience.2016.08.027] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Revised: 08/06/2016] [Accepted: 08/12/2016] [Indexed: 11/28/2022]
Abstract
The rhythmic activity of motoneurons (MNs) that underlies locomotion in mammals is generated by synaptic inputs from the locomotor network in the spinal cord. Thus, the quantitative estimation of excitatory and inhibitory synaptic conductances is essential to understand the mechanism by which the network generates the functional motor output. Conductance estimation is obtained from the voltage-current relationship measured by voltage-clamp- or current-clamp-recording with knowledge of the leak parameters of the recorded neuron. However, it is often difficult to obtain sufficient data to estimate synaptic conductances due to technical difficulties in electrophysiological experiments using in vivo or in vitro preparations. To address this problem, we estimated the average variations in excitatory and inhibitory synaptic conductance during a locomotion cycle from a single voltage trace without measuring the leak parameters. We found that the conductance variations can be accurately reconstructed from a voltage trace of 10 cycles by analyzing synthetic data generated from a computational model. Next, the conductance variations were estimated from mouse spinal MNs in vitro during drug-induced-locomotor-like activity. We found that the peak of excitatory conductance occurred during the depolarizing phase of the locomotor cycle, whereas the peak of inhibitory conductance occurred during the hyperpolarizing phase. These results suggest that the locomotor-like activity is generated by push-pull modulation via excitatory and inhibitory synaptic inputs.
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Affiliation(s)
- Ryota Kobayashi
- Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-0003, Japan; Department of Informatics, SOKENDAI (The Graduate University for Advanced Studies), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan.
| | - Hiroshi Nishimaru
- System Emotional Science, Graduate School of Medicine and Pharmaceutical Sciences, University of Toyama, Sugitani 2630, Toyama 930-0194, Japan; Faculty of Medicine, University of Tsukuba, Tsukuba 305-8575, Japan.
| | - Hisao Nishijo
- System Emotional Science, Graduate School of Medicine and Pharmaceutical Sciences, University of Toyama, Sugitani 2630, Toyama 930-0194, Japan
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16
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Yaşar TB, Wright NC, Wessel R. Inferring presynaptic population spiking from single-trial membrane potential recordings. J Neurosci Methods 2016; 259:13-21. [PMID: 26658223 DOI: 10.1016/j.jneumeth.2015.11.019] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2015] [Revised: 11/20/2015] [Accepted: 11/23/2015] [Indexed: 10/22/2022]
Abstract
BACKGROUND The time-varying membrane potential of a cortical neuron contains important information about the network activity. Extracting this information requires separating excitatory and inhibitory synaptic inputs from single-trial membrane potential recordings without averaging across trials. NEW METHOD We propose a method to extract the time course of excitatory and inhibitory synaptic inputs to a neuron from a single-trial membrane potential recording. The method takes advantage of the differences in the time constants and the reversal potentials of the excitatory and inhibitory synaptic currents, which allows the untangling of the two conductance types. RESULTS We evaluate the applicability of the method on a leaky integrate-and-fire model neuron and find high quality of estimation of excitatory synaptic conductance changes and presynaptic population spikes. Application of the method to a real cortical neuron with known synaptic inputs in a brain slice returns high-quality estimation of the time course of the excitatory synaptic conductance. Application of the method to membrane potential recordings from a cortical pyramidal neuron of an intact brain reveals complex network activity. COMPARISON WITH EXISTING METHODS Existing methods are based on repeated trials and thus are limited to estimating the statistical features of synaptic conductance changes, or, when based on single trials, are limited to special cases, have low temporal resolution, or are impractically complicated. CONCLUSIONS We propose and test an efficient method for estimating the full time course of excitatory and inhibitory synaptic conductances from single-trial membrane potential recordings. The method is sufficiently simple to ensure widespread use in neuroscience.
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Affiliation(s)
- Tansel Baran Yaşar
- Department of Physics, Campus Box 1105, Washington University, Saint Louis, MO 63130-4899, USA.
| | - Nathaniel Caleb Wright
- Department of Physics, Campus Box 1105, Washington University, Saint Louis, MO 63130-4899, USA.
| | - Ralf Wessel
- Department of Physics, Campus Box 1105, Washington University, Saint Louis, MO 63130-4899, USA.
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17
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Dissecting estimation of conductances in subthreshold regimes. J Comput Neurosci 2015; 39:271-87. [PMID: 26432075 DOI: 10.1007/s10827-015-0576-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Revised: 09/03/2015] [Accepted: 09/09/2015] [Indexed: 10/24/2022]
Abstract
We study the influence of subthreshold activity in the estimation of synaptic conductances. It is known that differences between actual conductances and the estimated ones using linear regression methods can be huge in spiking regimes, so caution has been taken to remove spiking activity from experimental data before proceeding to linear estimation. However, not much attention has been paid to the influence of ionic currents active in the non-spiking regime where such linear methods are still profusely used. In this paper, we use conductance-based models to test this influence using several representative mechanisms to induce ionic subthreshold activity. In all the cases, we show that the currents activated during subthreshold activity can lead to significant errors when estimating synaptic conductance linearly. Thus, our results add a new warning message when extracting conductance traces from intracellular recordings and the conclusions concerning neuronal activity that can be drawn from them. Additionally, we present, as a proof of concept, an alternative method that takes into account the main nonlinear effects of specific ionic subthreshold currents. This method, based on the quadratization of the subthreshold dynamics, allows us to reduce the relative errors of the estimated conductances by more than one order of magnitude. In experimental conditions, under appropriate fitting to canonical models, it could be useful to obtain better estimations as well even under the presence of noise.
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Hoang H, Yamashita O, Tokuda IT, Sato MA, Kawato M, Toyama K. Segmental Bayesian estimation of gap-junctional and inhibitory conductance of inferior olive neurons from spike trains with complicated dynamics. Front Comput Neurosci 2015; 9:56. [PMID: 26052280 PMCID: PMC4439545 DOI: 10.3389/fncom.2015.00056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2014] [Accepted: 04/26/2015] [Indexed: 11/13/2022] Open
Abstract
The inverse problem for estimating model parameters from brain spike data is an ill-posed problem because of a huge mismatch in the system complexity between the model and the brain as well as its non-stationary dynamics, and needs a stochastic approach that finds the most likely solution among many possible solutions. In the present study, we developed a segmental Bayesian method to estimate the two parameters of interest, the gap-junctional (gc ) and inhibitory conductance (gi ) from inferior olive spike data. Feature vectors were estimated for the spike data in a segment-wise fashion to compensate for the non-stationary firing dynamics. Hierarchical Bayesian estimation was conducted to estimate the gc and gi for every spike segment using a forward model constructed in the principal component analysis (PCA) space of the feature vectors, and to merge the segmental estimates into single estimates for every neuron. The segmental Bayesian estimation gave smaller fitting errors than the conventional Bayesian inference, which finds the estimates once across the entire spike data, or the minimum error method, which directly finds the closest match in the PCA space. The segmental Bayesian inference has the potential to overcome the problem of non-stationary dynamics and resolve the ill-posedness of the inverse problem because of the mismatch between the model and the brain under the constraints based, and it is a useful tool to evaluate parameters of interest for neuroscience from experimental spike train data.
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Affiliation(s)
- Huu Hoang
- Department of Mechanical Engineering, Ritsumeikan UniversityShiga, Japan
- ATR Neural Information Analysis LaboratoriesKyoto, Japan
| | - Okito Yamashita
- ATR Neural Information Analysis LaboratoriesKyoto, Japan
- Brain Functional Imaging Technologies Group, CiNetOsaka, Japan
| | - Isao T. Tokuda
- Department of Mechanical Engineering, Ritsumeikan UniversityShiga, Japan
| | - Masa-aki Sato
- ATR Neural Information Analysis LaboratoriesKyoto, Japan
| | - Mitsuo Kawato
- ATR Computational Neuroscience LaboratoriesKyoto, Japan
| | - Keisuke Toyama
- ATR Neural Information Analysis LaboratoriesKyoto, Japan
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Kobayashi R, He J, Lansky P. Estimation of the synaptic input firing rates and characterization of the stimulation effects in an auditory neuron. Front Comput Neurosci 2015; 9:59. [PMID: 26042025 PMCID: PMC4435043 DOI: 10.3389/fncom.2015.00059] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Accepted: 04/30/2015] [Indexed: 11/15/2022] Open
Abstract
To understand information processing in neuronal circuits, it is important to infer how a sensory stimulus impacts on the synaptic input to a neuron. An increase in neuronal firing during the stimulation results from pure excitation or from a combination of excitation and inhibition. Here, we develop a method for estimating the rates of the excitatory and inhibitory synaptic inputs from a membrane voltage trace of a neuron. The method is based on a modified Ornstein-Uhlenbeck neuronal model, which aims to describe the stimulation effects on the synaptic input. The method is tested using a single-compartment neuron model with a realistic description of synaptic inputs, and it is applied to an intracellular voltage trace recorded from an auditory neuron in vivo. We find that the excitatory and inhibitory inputs increase during stimulation, suggesting that the acoustic stimuli are encoded by a combination of excitation and inhibition.
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Affiliation(s)
- Ryota Kobayashi
- Principles of Informatics Research Division, National Institute of InformaticsTokyo, Japan
- Department of Informatics, SOKENDAI (The Graduate University for Advanced Studies)Tokyo, Japan
| | - Jufang He
- Department of Biomedical Sciences, City University of Hong KongHong Kong, China
| | - Petr Lansky
- Institute of Physiology, The Czech Academy of SciencesPrague, Czech Republic
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Abstract
OBJECTIVE External control of spike times in single neurons can reveal important information about a neuron's sub-threshold dynamics that lead to spiking, and has the potential to improve brain-machine interfaces and neural prostheses. The goal of this paper is the design of optimal electrical stimulation of a neuron to achieve a target spike train under the physiological constraint to not damage tissue. APPROACH We pose a stochastic optimal control problem to precisely specify the spike times in a leaky integrate-and-fire (LIF) model of a neuron with noise assumed to be of intrinsic or synaptic origin. In particular, we allow for the noise to be of arbitrary intensity. The optimal control problem is solved using dynamic programming when the controller has access to the voltage (closed-loop control), and using a maximum principle for the transition density when the controller only has access to the spike times (open-loop control). MAIN RESULTS We have developed a stochastic optimal control algorithm to obtain precise spike times. It is applicable in both the supra-threshold and sub-threshold regimes, under open-loop and closed-loop conditions and with an arbitrary noise intensity; the accuracy of control degrades with increasing intensity of the noise. Simulations show that our algorithms produce the desired results for the LIF model, but also for the case where the neuron dynamics are given by more complex models than the LIF model. This is illustrated explicitly using the Morris-Lecar spiking neuron model, for which an LIF approximation is first obtained from a spike sequence using a previously published method. We further show that a related control strategy based on the assumption that there is no noise performs poorly in comparison to our noise-based strategies. The algorithms are numerically intensive and may require efficiency refinements to achieve real-time control; in particular, the open-loop context is more numerically demanding than the closed-loop one. SIGNIFICANCE Our main contribution is the online feedback control of a noisy neuron through modulation of the input, taking into account physiological constraints on the control. A precise and robust targeting of neural activity based on stochastic optimal control has great potential for regulating neural activity in e.g. prosthetic applications and to improve our understanding of the basic mechanisms by which neuronal firing patterns can be controlled in vivo.
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Affiliation(s)
- Alexandre Iolov
- Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada. Department of Mathematical Sciences, University of Copenhagen, DK-1165 Copenhagen, Denmark
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Ditlevsen S, Samson A. Estimation in the partially observed stochastic Morris–Lecar neuronal model with particle filter and stochastic approximation methods. Ann Appl Stat 2014. [DOI: 10.1214/14-aoas729] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Premotor spinal network with balanced excitation and inhibition during motor patterns has high resilience to structural division. J Neurosci 2014; 34:2774-84. [PMID: 24553920 DOI: 10.1523/jneurosci.3349-13.2014] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Direct measurements of synaptic inhibition (I) and excitation (E) to spinal motoneurons can provide an important insight into the organization of premotor networks. Such measurements of flexor motoneurons participating in motor patterns in turtles have recently demonstrated strong concurrent E and I as well as stochastic membrane potentials and irregular spiking in the adult turtle spinal cord. These findings represent a departure from the widespread acceptance of feedforward reciprocal rate models for spinal motor function. The apparent discrepancy has been reviewed as an experimental artifact caused by the distortion of local networks in the transected turtle spinal cord. We tested this assumption in the current study by performing experiments to assess the integrity of motor functions in the intact spinal cord and the cord transected at segments D9/D10. Excitatory and inhibitory synaptic inputs to motoneurons were estimated during rhythmic motor activity and demonstrated primarily intense inputs that consisted of qualitatively similar mixed E/I before and after the transection. To understand this high functional resilience, we used mathematical modeling of networks with recurrent connectivity that could potentially explain the balanced E/I. Both experimental and modeling data support the concept of a locally balanced premotor network consisting of recurrent E/I connectivity, in addition to the well known reciprocal network activity. The multifaceted synaptic connections provide spinal networks with a remarkable ability to remain functional after structural divisions.
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