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Izzi JVR, Ferreira RF, Girardi VA, Pena RFO. Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator. Brain Sci 2024; 14:442. [PMID: 38790421 PMCID: PMC11119028 DOI: 10.3390/brainsci14050442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2024] [Revised: 04/22/2024] [Accepted: 04/26/2024] [Indexed: 05/26/2024] Open
Abstract
Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.
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Affiliation(s)
- João V. R. Izzi
- Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, SP, Brazil
| | - Ricardo F. Ferreira
- Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, SP, Brazil
| | - Victor A. Girardi
- Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, SP, Brazil
| | - Rodrigo F. O. Pena
- Department of Biological Sciences, Florida Atlantic University, Jupiter, FL 33458, USA
- Stiles-Nicholson Brain Institute, Florida Atlantic University, Jupiter, FL 33458, USA
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Borges FS, Protachevicz PR, Souza DLM, Bittencourt CF, Gabrick EC, Bentivoglio LE, Szezech JD, Batista AM, Caldas IL, Dura-Bernal S, Pena RFO. The Roles of Potassium and Calcium Currents in the Bistable Firing Transition. Brain Sci 2023; 13:1347. [PMID: 37759949 PMCID: PMC10527161 DOI: 10.3390/brainsci13091347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Revised: 09/13/2023] [Accepted: 09/15/2023] [Indexed: 09/29/2023] Open
Abstract
Healthy brains display a wide range of firing patterns, from synchronized oscillations during slow-wave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking (RS) cells with frequency adaptation and do not exhibit bursts in current-clamp experiments (in vitro). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings (gsyn) and external current inputs (I). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to the bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold (IL) and low-threshold (IT) ion channels play a role in increasing and decreasing the parameter conditions (gsyn and I) in which bistable dynamics occur, respectively. For high values of IL conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance IT increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.
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Affiliation(s)
- Fernando S. Borges
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, NY 11203, USA
- Center for Mathematics, Computation and Cognition, Federal University of ABC, São Bernardo do Campo 09606-045, Brazil
| | | | - Diogo L. M. Souza
- Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84010-330, Brazil
| | - Conrado F. Bittencourt
- Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84010-330, Brazil
| | - Enrique C. Gabrick
- Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84010-330, Brazil
| | - Lucas E. Bentivoglio
- Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84010-330, Brazil
| | - José D. Szezech
- Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84010-330, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa 84030-900, Brazil
| | - Antonio M. Batista
- Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84010-330, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa 84030-900, Brazil
| | - Iberê L. Caldas
- Institute of Physics, University of São Paulo, São Paulo 05508-090, Brazil
| | - Salvador Dura-Bernal
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, NY 11203, USA
- Center for Biomedical Imaging and Neuromodulation, The Nathan S. Kline Institute for Psychiatric Research, Orangeburg, NY 10962, USA
| | - Rodrigo F. O. Pena
- Department of Biological Sciences, Florida Atlantic University, Jupiter, FL 33458, USA
- Stiles-Nicholson Brain Institute, Florida Atlantic University, Jupiter, FL 33458, USA
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Borges FS, Protachevicz PR, Souza DLM, Bittencourt CF, Gabrick EC, Bentivoglio LE, Szezech JD, Batista AM, Caldas IL, Dura-Bernal S, Pena RFO. The Role of Potassium and Calcium Currents in the Bistable Firing Transition. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.16.553625. [PMID: 37645875 PMCID: PMC10462112 DOI: 10.1101/2023.08.16.553625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Healthy brains display a wide range of firing patterns, from synchronized oscillations during slowwave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking cells (RS) with frequency adaptation and do not exhibit bursts in current-clamp experiments ( in vitro ). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings ( g syn ) and external current inputs ( I ). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold ( I L ) and low-threshold ( I T ) ion channels play a role in increasing and decreasing the parameter conditions ( g syn and I ) in which bistable dynamics occur, respectively. For high values of I L conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance I T increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.
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Affiliation(s)
- Fernando S Borges
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, New York, USA
- Center for Mathematics, Computation, and Cognition, Federal University of ABC, 09606-045 São Bernardo do Campo, SP, Brazil
| | | | - Diogo L M Souza
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Conrado F Bittencourt
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Enrique C Gabrick
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Lucas E Bentivoglio
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - José D Szezech
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil
| | - Antonio M Batista
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil
| | - Iberê L Caldas
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
| | - Salvador Dura-Bernal
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, New York, USA
- Center for Biomedical Imaging and Neuromodulation, The Nathan S. Kline Institute for Psychiatric Research, New York, USA
| | - Rodrigo F O Pena
- Department of Biological Sciences, Florida Atlantic University, Jupiter, Florida, USA
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Dimitriadis SI. Latest Advances in Human Brain Dynamics. Brain Sci 2021; 11:brainsci11111476. [PMID: 34827475 PMCID: PMC8615593 DOI: 10.3390/brainsci11111476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2021] [Accepted: 10/29/2021] [Indexed: 11/16/2022] Open
Abstract
It is paramount for every neuroscientist to understand the nature of emerging technologies and approaches in investigating functional brain dynamics [...].
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Affiliation(s)
- Stavros I. Dimitriadis
- Integrative Neuroimaging Lab, 55133 Thessaloniki, Greece; or
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, College of Biomedical and Life Sciences, Cardiff University, Cardiff CF24 4HQ, UK
- Neuroinformatics Group, Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, College of Biomedical and Life Sciences, Cardiff CF24 4HQ, UK
- Division of Psychological Medicine and Clinical Neurosciences, School of Medicine, College of Biomedical and Life Sciences, Cardiff University, Cardiff CF24 4HQ, UK
- Neuroscience and Mental Health Research Institute, School of Medicine, College of Biomedical and Life Sciences, Cardiff University, Cardiff CF24 4HQ, UK
- MRC Centre for Neuropsychiatric Genetics and Genomics, School of Medicine, College of Biomedical and Life Sciences, Cardiff University, Cardiff CF24 4HQ, UK
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