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Peace ST, Johnson BC, Werth JC, Li G, Kaiser ME, Fukunaga I, Schaefer AT, Molnar AC, Cleland TA. Coherent olfactory bulb gamma oscillations arise from coupling independent columnar oscillators. J Neurophysiol 2024; 131:492-508. [PMID: 38264784 PMCID: PMC7615692 DOI: 10.1152/jn.00361.2023] [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: 09/29/2023] [Revised: 01/19/2024] [Accepted: 01/20/2024] [Indexed: 01/25/2024] Open
Abstract
Spike timing-based representations of sensory information depend on embedded dynamical frameworks within neuronal networks that establish the rules of local computation and interareal communication. Here, we investigated the dynamical properties of olfactory bulb circuitry in mice of both sexes using microelectrode array recordings from slice and in vivo preparations. Neurochemical activation or optogenetic stimulation of sensory afferents evoked persistent gamma oscillations in the local field potential. These oscillations arose from slower, GABA(A) receptor-independent intracolumnar oscillators coupled by GABA(A)-ergic synapses into a faster, broadly coherent network oscillation. Consistent with the theoretical properties of coupled-oscillator networks, the spatial extent of zero-phase coherence was bounded in slices by the reduced density of lateral interactions. The intact in vivo network, however, exhibited long-range lateral interactions that suffice in simulation to enable zero-phase gamma coherence across the olfactory bulb. The timing of action potentials in a subset of principal neurons was phase-constrained with respect to evoked gamma oscillations. Coupled-oscillator dynamics in olfactory bulb thereby enable a common clock, robust to biological heterogeneities, that is capable of supporting gamma-band spike synchronization and phase coding across the ensemble of activated principal neurons.NEW & NOTEWORTHY Odor stimulation evokes rhythmic gamma oscillations in the field potential of the olfactory bulb, but the dynamical mechanisms governing these oscillations have remained unclear. Establishing these mechanisms is important as they determine the biophysical capacities of the bulbar circuit to, for example, maintain zero-phase coherence across a spatially extended network, or coordinate the timing of action potentials in principal neurons. These properties in turn constrain and suggest hypotheses of sensory coding.
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Affiliation(s)
- Shane T Peace
- Department of Neurobiology & Behavior, Cornell University, Ithaca, New York, United States
| | - Benjamin C Johnson
- Department of Electrical and Computer Engineering, Cornell University, Ithaca, New York, United States
| | - Jesse C Werth
- Department of Psychology, Cornell University, Ithaca, New York, United States
| | - Guoshi Li
- Department of Psychology, Cornell University, Ithaca, New York, United States
| | - Martin E Kaiser
- Behavioural Neurophysiology, Max Planck Institute for Medical Research, Heidelberg, Germany
| | - Izumi Fukunaga
- Behavioural Neurophysiology, Max Planck Institute for Medical Research, Heidelberg, Germany
- Neurophysiology of Behaviour Laboratory, The Francis Crick Institute, London, United Kingdom
- Sensory and Behavioural Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Japan
| | - Andreas T Schaefer
- Behavioural Neurophysiology, Max Planck Institute for Medical Research, Heidelberg, Germany
- Neurophysiology of Behaviour Laboratory, The Francis Crick Institute, London, United Kingdom
- Department of Neuroscience, Physiology & Pharmacology, University College London, London, United Kingdom
- Department of Anatomy and Cell Biology, Faculty of Medicine, University of Heidelberg, Heidelberg, Germany
| | - Alyosha C Molnar
- Department of Electrical and Computer Engineering, Cornell University, Ithaca, New York, United States
| | - Thomas A Cleland
- Department of Psychology, Cornell University, Ithaca, New York, United States
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2
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Lefebvre J, Hutt A. Induced synchronization by endogenous noise modulation in finite-size random neural networks: A stochastic mean-field study. CHAOS (WOODBURY, N.Y.) 2023; 33:123110. [PMID: 38055720 DOI: 10.1063/5.0167771] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 11/09/2023] [Indexed: 12/08/2023]
Abstract
Event-related synchronization and desynchronization (ERS/ERD) are well-known features found experimentally in brain signals during cognitive tasks. Their understanding promises to have much better insights into neural information processes in cognition. Under the hypothesis that neural information affects the endogenous neural noise level in populations, we propose to employ a stochastic mean-field model to explain ERS/ERD in the γ-frequency range. The work extends previous mean-field studies by deriving novel effects from finite network size. Moreover, numerical simulations of ERS/ERD and their analytical explanation by the mean-field model suggest several endogenous noise modulation schemes, which may modulate the system's synchronization.
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Affiliation(s)
- J Lefebvre
- Krembil Brain Institute, University Health Network, Toronto, Ontario M5T 0S8, Canada
- Department of Biology, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
| | - A Hutt
- ICube, MLMS, University of Strasbourg, MIMESIS Team, Inria Nancy-Grand Est, 67000 Strasbourg, France
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3
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Franzen J, Ramlow L, Lindner B. The steady state and response to a periodic stimulation of the firing rate for a theta neuron with correlated noise. J Comput Neurosci 2023; 51:107-128. [PMID: 36273087 PMCID: PMC9840600 DOI: 10.1007/s10827-022-00836-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Revised: 07/29/2022] [Accepted: 09/01/2022] [Indexed: 01/18/2023]
Abstract
The stochastic activity of neurons is caused by various sources of correlated fluctuations and can be described in terms of simplified, yet biophysically grounded, integrate-and-fire models. One paradigmatic model is the quadratic integrate-and-fire model and its equivalent phase description by the theta neuron. Here we study the theta neuron model driven by a correlated Ornstein-Uhlenbeck noise and by periodic stimuli. We apply the matrix-continued-fraction method to the associated Fokker-Planck equation to develop an efficient numerical scheme to determine the stationary firing rate as well as the stimulus-induced modulation of the instantaneous firing rate. For the stationary case, we identify the conditions under which the firing rate decreases or increases by the effect of the colored noise and compare our results to existing analytical approximations for limit cases. For an additional periodic signal we demonstrate how the linear and nonlinear response terms can be computed and report resonant behavior for some of them. We extend the method to the case of two periodic signals, generally with incommensurable frequencies, and present a particular case for which a strong mixed response to both signals is observed, i.e. where the response to the sum of signals differs significantly from the sum of responses to the single signals. We provide Python code for our computational method: https://github.com/jannikfranzen/theta_neuron .
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Affiliation(s)
- Jannik Franzen
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, Berlin, 12489 Germany
| | - Lukas Ramlow
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, Berlin, 12489 Germany ,Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 2, Berlin, 10115 Germany
| | - Benjamin Lindner
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, Berlin, 12489 Germany ,Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 2, Berlin, 10115 Germany
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4
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The Effects of Background Noise on a Biophysical Model of Olfactory Bulb Mitral Cells. Bull Math Biol 2022; 84:107. [PMID: 36008641 DOI: 10.1007/s11538-022-01066-8] [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: 03/03/2022] [Accepted: 08/03/2022] [Indexed: 11/02/2022]
Abstract
The spiking activity of mitral cells (MC) in the olfactory bulb is a key attribute in olfactory sensory information processing to downstream cortical areas. A more detailed understanding of the modulation of MC spike statistics could shed light on mechanistic studies of olfactory bulb circuits and olfactory coding. We study the spike response of a recently developed single-compartment biophysical MC model containing seven known ionic currents and calcium dynamics subject to constant current input with background white noise. We observe rich spiking dynamics even with constant current input, including multimodal peaks in the interspike interval distribution (ISI). Although weak-to-moderate background noise for a fixed current input does not change the firing rate much, the spike dynamics can change dramatically, exhibiting non-monotonic spike variability not commonly observed in standard neuron models. We explain these dynamics with a phenomenological model of the ISI probability density function. Our study clarifies some of the complexities of MC spiking dynamics.
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5
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Adam EM, Brown EN, Kopell N, McCarthy MM. Deep brain stimulation in the subthalamic nucleus for Parkinson's disease can restore dynamics of striatal networks. Proc Natl Acad Sci U S A 2022; 119:e2120808119. [PMID: 35500112 PMCID: PMC9171607 DOI: 10.1073/pnas.2120808119] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 03/25/2022] [Indexed: 12/03/2022] Open
Abstract
Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is highly effective in alleviating movement disability in patients with Parkinson’s disease (PD). However, its therapeutic mechanism of action is unknown. The healthy striatum exhibits rich dynamics resulting from an interaction of beta, gamma, and theta oscillations. These rhythms are essential to selection and execution of motor programs, and their loss or exaggeration due to dopamine (DA) depletion in PD is a major source of behavioral deficits. Restoring the natural rhythms may then be instrumental in the therapeutic action of DBS. We develop a biophysical networked model of a BG pathway to study how abnormal beta oscillations can emerge throughout the BG in PD and how DBS can restore normal beta, gamma, and theta striatal rhythms. Our model incorporates STN projections to the striatum, long known but understudied, found to preferentially target fast-spiking interneurons (FSI). We find that DBS in STN can normalize striatal medium spiny neuron activity by recruiting FSI dynamics and restoring the inhibitory potency of FSIs observed in normal conditions. We also find that DBS allows the reexpression of gamma and theta rhythms, thought to be dependent on high DA levels and thus lost in PD, through cortical noise control. Our study highlights that DBS effects can go beyond regularizing BG output dynamics to restoring normal internal BG dynamics and the ability to regulate them. It also suggests how gamma and theta oscillations can be leveraged to supplement DBS treatment and enhance its effectiveness.
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Affiliation(s)
- Elie M. Adam
- Picower Institute for Learning and Memory, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Emery N. Brown
- Picower Institute for Learning and Memory, Massachusetts Institute of Technology, Cambridge, MA 02139
- Department of Anesthesia, Critical Care, and Pain Medicine, Massachusetts General Hospital, Boston, MA 02114
| | - Nancy Kopell
- Department of Mathematics and Statistics, Boston University, Boston, MA 02215
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6
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Pérez-Cervera A, Lindner B, Thomas PJ. Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators. BIOLOGICAL CYBERNETICS 2022; 116:219-234. [PMID: 35320405 PMCID: PMC9068686 DOI: 10.1007/s00422-022-00929-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 02/16/2022] [Indexed: 05/10/2023]
Abstract
Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.
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Affiliation(s)
- Alberto Pérez-Cervera
- National Research University Higher School of Economics, Moscow, Russia
- Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Institute of Physics, Humboldt University, Berlin, Germany
| | - Peter J. Thomas
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH USA
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7
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Afterhyperpolarization Promotes the Firing of Mitral Cells through a Voltage-Dependent Modification of Action Potential Threshold. eNeuro 2022; 9:ENEURO.0401-21.2021. [PMID: 35277450 PMCID: PMC8982644 DOI: 10.1523/eneuro.0401-21.2021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Revised: 11/22/2021] [Accepted: 12/13/2021] [Indexed: 11/21/2022] Open
Abstract
In the olfactory bulb, mitral cells (MCs) display a spontaneous firing that is characterized by bursts of action potentials (APs) intermixed with silent periods. Intraburst firing frequency and duration are heterogeneous among MCs and increase with membrane depolarization. By using patch-clamp recording on rat slices, we dissected out the intrinsic properties responsible for this bursting activity. We showed that the threshold of AP generation dynamically changes as a function of the preceding trajectory of the membrane potential. In fact, the AP threshold became more negative when the membrane was hyperpolarized and had a recovery rate inversely proportional to the membrane repolarization rate. Such variations appeared to be produced by changes in the inactivation state of voltage-dependent Na+ channels. Thus, AP initiation was favored by hyperpolarizing events, such as negative membrane oscillations or inhibitory synaptic input. After the first AP, the following fast afterhyperpolarization (AHP) brought the threshold to more negative values and then promoted the emission of the following AP. This phenomenon was repeated for each AP of the burst making the fast AHP a regenerative mechanism that sustained the firing, AHP with larger amplitudes and faster repolarizations being associated with larger and higher-frequency bursts. Burst termination was found to be because of the development of a slow repolarization component of the AHP (slow AHP). Overall, the AHP characteristics appeared as a major determinant of the bursting properties.
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8
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Rebscher L, Obermayer K, Metzner C. Synchronization Through Uncorrelated Noise in Excitatory-Inhibitory Networks. Front Comput Neurosci 2022; 16:825865. [PMID: 35185505 PMCID: PMC8855529 DOI: 10.3389/fncom.2022.825865] [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: 11/30/2021] [Accepted: 01/12/2022] [Indexed: 11/13/2022] Open
Abstract
Gamma rhythms play a major role in many different processes in the brain, such as attention, working memory, and sensory processing. While typically considered detrimental, counterintuitively noise can sometimes have beneficial effects on communication and information transfer. Recently, Meng and Riecke showed that synchronization of interacting networks of inhibitory neurons in the gamma band (i.e., gamma generated through an ING mechanism) increases while synchronization within these networks decreases when neurons are subject to uncorrelated noise. However, experimental and modeling studies point towardz an important role of the pyramidal-interneuronal network gamma (PING) mechanism in the cortex. Therefore, we investigated the effect of uncorrelated noise on the communication between excitatory-inhibitory networks producing gamma oscillations via a PING mechanism. Our results suggest that, at least in a certain range of noise strengths and natural frequency differences between the regions, synaptic noise can have a supporting role in facilitating inter-regional communication, similar to the ING case for a slightly larger parameter range. Furthermore, the noise-induced synchronization between networks is generated via a different mechanism than when synchronization is mediated by strong synaptic coupling. Noise-induced synchronization is achieved by lowering synchronization within networks which allows the respective other network to impose its own gamma rhythm resulting in synchronization between networks.
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Affiliation(s)
- Lucas Rebscher
- Neural Information Processing Group, Technische Universität Berlin, Berlin, Germany
| | - Klaus Obermayer
- Neural Information Processing Group, Technische Universität Berlin, Berlin, Germany
| | - Christoph Metzner
- Neural Information Processing Group, Technische Universität Berlin, Berlin, Germany
- Biocomputation Group, School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, United Kingdom
- *Correspondence: Christoph Metzner
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9
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Holzhausen K, Thomas PJ, Lindner B. Analytical approach to the mean-return-time phase of isotropic stochastic oscillators. Phys Rev E 2022; 105:024202. [PMID: 35291171 DOI: 10.1103/physreve.105.024202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT isochrons.
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Affiliation(s)
- Konstantin Holzhausen
- Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
| | - Peter J Thomas
- Department of Mathematics, Applied Mathematics and Statistics, 212 Yost Hall, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio, USA
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
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10
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Ogawa S, Parhar IS. Heterogeneity in GnRH and kisspeptin neurons and their significance in vertebrate reproductive biology. Front Neuroendocrinol 2022; 64:100963. [PMID: 34798082 DOI: 10.1016/j.yfrne.2021.100963] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Revised: 10/11/2021] [Accepted: 10/31/2021] [Indexed: 02/07/2023]
Abstract
Vertebrate reproduction is essentially controlled by the hypothalamus-pituitary-gonadal (HPG) axis, which is a central dogma of reproductive biology. Two major hypothalamic neuroendocrine cell groups containing gonadotropin-releasing hormone (GnRH) and kisspeptin are crucial for control of the HPG axis in vertebrates. GnRH and kisspeptin neurons exhibit high levels of heterogeneity including their cellular morphology, biochemistry, neurophysiology and functions. However, the molecular foundation underlying heterogeneities in GnRH and kisspeptin neurons remains unknown. More importantly, the biological and physiological significance of their heterogeneity in reproductive biology is poorly understood. In this review, we first describe the recent advances in the neuroendocrine functions of kisspeptin-GnRH pathways. We then view the recent emerging progress in the heterogeneity of GnRH and kisspeptin neurons using morphological and single-cell transcriptomic analyses. Finally, we discuss our views on the significance of functional heterogeneity of reproductive endocrine cells and their potential relevance to reproductive health.
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Affiliation(s)
- Satoshi Ogawa
- Brain Research Institute, Jeffrey Cheah School of Medicine and Health Sciences, Monash University Malaysia, 47500 Bandar Sunway, Selangor, Malaysia
| | - Ishwar S Parhar
- Brain Research Institute, Jeffrey Cheah School of Medicine and Health Sciences, Monash University Malaysia, 47500 Bandar Sunway, Selangor, Malaysia.
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11
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Burton SD, Urban NN. Cell and circuit origins of fast network oscillations in the mammalian main olfactory bulb. eLife 2021; 10:74213. [PMID: 34658333 PMCID: PMC8553344 DOI: 10.7554/elife.74213] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2021] [Accepted: 10/09/2021] [Indexed: 11/13/2022] Open
Abstract
Neural synchrony generates fast network oscillations throughout the brain, including the main olfactory bulb (MOB), the first processing station of the olfactory system. Identifying the mechanisms synchronizing neurons in the MOB will be key to understanding how network oscillations support the coding of a high-dimensional sensory space. Here, using paired recordings and optogenetic activation of glomerular sensory inputs in MOB slices, we uncovered profound differences in principal mitral cell (MC) vs. tufted cell (TC) spike-time synchrony: TCs robustly synchronized across fast- and slow-gamma frequencies, while MC synchrony was weaker and concentrated in slow-gamma frequencies. Synchrony among both cell types was enhanced by shared glomerular input but was independent of intraglomerular lateral excitation. Cell-type differences in synchrony could also not be traced to any difference in the synchronization of synaptic inhibition. Instead, greater TC than MC synchrony paralleled the more periodic firing among resonant TCs than MCs and emerged in patterns consistent with densely synchronous network oscillations. Collectively, our results thus reveal a mechanism for parallel processing of sensory information in the MOB via differential TC vs. MC synchrony, and further contrast mechanisms driving fast network oscillations in the MOB from those driving the sparse synchronization of irregularly firing principal cells throughout cortex.
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Affiliation(s)
- Shawn D Burton
- Department of Neurobiology, University of Pittsburgh, Pittsburgh, United States.,Center for the Neural Basis of Cognition, Pittsburgh, United States
| | - Nathaniel N Urban
- Department of Neurobiology, University of Pittsburgh, Pittsburgh, United States.,Center for the Neural Basis of Cognition, Pittsburgh, United States
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12
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Ramlow L, Lindner B. Interspike interval correlations in neuron models with adaptation and correlated noise. PLoS Comput Biol 2021; 17:e1009261. [PMID: 34449771 PMCID: PMC8428727 DOI: 10.1371/journal.pcbi.1009261] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Revised: 09/09/2021] [Accepted: 07/08/2021] [Indexed: 11/19/2022] Open
Abstract
The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.
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Affiliation(s)
- Lukas Ramlow
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
- Physics Department, Humboldt University zu Berlin, Berlin, Germany
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
- Physics Department, Humboldt University zu Berlin, Berlin, Germany
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13
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Zirkle J, Rubchinsky LL. Noise effect on the temporal patterns of neural synchrony. Neural Netw 2021; 141:30-39. [PMID: 33857688 DOI: 10.1016/j.neunet.2021.03.032] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Revised: 03/13/2021] [Accepted: 03/22/2021] [Indexed: 01/03/2023]
Abstract
Neural synchrony in the brain is often present in an intermittent fashion, i.e., there are intervals of synchronized activity interspersed with intervals of desynchronized activity. A series of experimental studies showed that this kind of temporal patterning of neural synchronization may be very specific and may be correlated with behaviour (even if the average synchrony strength is not changed). Prior studies showed that a network with many short desynchronized intervals may be functionally different from a network with few long desynchronized intervals as it may be more sensitive to synchronizing input signals. In this study, we investigated the effect of channel noise on the temporal patterns of neural synchronization. We employed a small network of conductance-based model neurons that were mutually connected via excitatory synapses. The resulting dynamics of the network was studied using the same time-series analysis methods as used in prior experimental and computational studies. While it is well known that synchrony strength generally degrades with noise, we found that noise also affects the temporal patterning of synchrony. Noise, at a sufficient intensity (yet too weak to substantially affect synchrony strength), promotes dynamics with predominantly short (although potentially very numerous) desynchronizations. Thus, channel noise may be one of the mechanisms contributing to the short desynchronization dynamics observed in multiple experimental studies.
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Affiliation(s)
- Joel Zirkle
- Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN, USA
| | - Leonid L Rubchinsky
- Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN, USA; Stark Neurosciences Research Institute, Indiana University School of Medicine, Indianapolis, IN, USA.
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14
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Mishra P, Narayanan R. Heterogeneities in intrinsic excitability and frequency-dependent response properties of granule cells across the blades of the rat dentate gyrus. J Neurophysiol 2020; 123:755-772. [PMID: 31913748 PMCID: PMC7052640 DOI: 10.1152/jn.00443.2019] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2019] [Revised: 12/25/2019] [Accepted: 01/07/2020] [Indexed: 12/18/2022] Open
Abstract
The dentate gyrus (DG), the input gate to the hippocampus proper, is anatomically segregated into three different sectors, namely, the suprapyramidal blade, the crest region, and the infrapyramidal blade. Although there are well-established differences between these sectors in terms of neuronal morphology, connectivity patterns, and activity levels, differences in electrophysiological properties of granule cells within these sectors have remained unexplored. Here, employing somatic whole cell patch-clamp recordings from the rat DG, we demonstrate that granule cells in these sectors manifest considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, these neurons showed positive temporal summation of their responses to inputs mimicking excitatory postsynaptic currents and showed little to no sag in their voltage responses to pulse currents. Consistently, the impedance amplitude profile manifested low-pass characteristics and the impedance phase profile lacked positive phase values at all measured frequencies and voltages and for all sectors. Granule cells in all sectors exhibited class I excitability, with broadly linear firing rate profiles, and granule cells in the crest region fired significantly fewer action potentials compared with those in the infrapyramidal blade. Finally, we found weak pairwise correlations across the 18 different measurements obtained individually from each of the three sectors, providing evidence that these measurements are indeed reporting distinct aspects of neuronal physiology. Together, our analyses show that granule cells act as integrators of afferent information and emphasize the need to account for the considerable physiological heterogeneities in assessing their roles in information encoding and processing.NEW & NOTEWORTHY We employed whole cell patch-clamp recordings from granule cells in the three subregions of the rat dentate gyrus to demonstrate considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, granule cells did not express membrane potential resonance, and their impedance profiles lacked inductive phase leads at all measured frequencies. Our analyses also show that granule cells manifest class I excitability characteristics, categorizing them as integrators of afferent information.
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Affiliation(s)
- Poonam Mishra
- Cellular Neurophysiology Laboratory, Molecular Biophysics Unit, Indian Institute of Science, Bangalore, India
| | - Rishikesh Narayanan
- Cellular Neurophysiology Laboratory, Molecular Biophysics Unit, Indian Institute of Science, Bangalore, India
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15
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Ly C, Weinberg SH. Analysis of heterogeneous cardiac pacemaker tissue models and traveling wave dynamics. J Theor Biol 2018; 459:18-35. [PMID: 30248329 DOI: 10.1016/j.jtbi.2018.09.023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2018] [Revised: 09/12/2018] [Accepted: 09/20/2018] [Indexed: 01/06/2023]
Abstract
The sinoatrial-node (SAN) is a complex heterogeneous tissue that generates a stable rhythm in healthy hearts, yet a general mechanistic explanation for when and how this tissue remains stable is lacking. Although computational and theoretical analyses could elucidate these phenomena, such methods have rarely been used in realistic (large-dimensional) gap-junction coupled heterogeneous pacemaker tissue models. In this study, we adapt a recent model of pacemaker cells (Severi et al., 2012), incorporating biophysical representations of ion channel and intracellular calcium dynamics, to capture physiological features of a heterogeneous population of pacemaker cells, in particular "center" and "peripheral" cells with distinct intrinsic frequencies and action potential morphology. Large-scale simulations of the SAN tissue, represented by a heterogeneous tissue structure of pacemaker cells, exhibit a rich repertoire of behaviors, including complete synchrony, traveling waves of activity originating from periphery to center, and transient traveling waves originating from the center. We use phase reduction methods that do not require fully simulating the large-scale model to capture these observations. Moreover, the phase reduced models accurately predict key properties of the tissue electrical dynamics, including wave frequencies when synchronization occurs, and wave propagation direction in a variety of tissue models. With the reduced phase models, we analyze the relationship between cell distributions and coupling strengths and the resulting transient dynamics. Further, the reduced phase model predicts parameter regimes of irregular electrical dynamics. Thus, we demonstrate that phase reduced oscillator models applied to realistic pacemaker tissue is a useful tool for investigating the spatial-temporal dynamics of cardiac pacemaker activity.
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Affiliation(s)
- Cheng Ly
- Department of Statistical Sciences & Operations Research, Virginia Commonwealth University, USA.
| | - Seth H Weinberg
- Department of Biomedical Engineering, Virginia Commonwealth University USA. http://www.shweinberglab.com
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16
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Mittal D, Narayanan R. Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells. J Neurophysiol 2018; 120:576-600. [PMID: 29718802 PMCID: PMC6101195 DOI: 10.1152/jn.00136.2018] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Biological heterogeneities are ubiquitous and play critical roles in the emergence of physiology at multiple scales. Although neurons in layer II (LII) of the medial entorhinal cortex (MEC) express heterogeneities in channel properties, the impact of such heterogeneities on the robustness of their cellular-scale physiology has not been assessed. Here, we performed a 55-parameter stochastic search spanning nine voltage- or calcium-activated channels to assess the impact of channel heterogeneities on the concomitant emergence of 10 in vitro electrophysiological characteristics of LII stellate cells (SCs). We generated 150,000 models and found a heterogeneous subpopulation of 449 valid models to robustly match all electrophysiological signatures. We employed this heterogeneous population to demonstrate the emergence of cellular-scale degeneracy in SCs, whereby disparate parametric combinations expressing weak pairwise correlations resulted in similar models. We then assessed the impact of virtually knocking out each channel from all valid models and demonstrate that the mapping between channels and measurements was many-to-many, a critical requirement for the expression of degeneracy. Finally, we quantitatively predict that the spike-triggered average of SCs should be endowed with theta-frequency spectral selectivity and coincidence detection capabilities in the fast gamma-band. We postulate this fast gamma-band coincidence detection as an instance of cellular-scale-efficient coding, whereby SC response characteristics match the dominant oscillatory signals in LII MEC. The heterogeneous population of valid SC models built here unveils the robust emergence of cellular-scale physiology despite significant channel heterogeneities, and forms an efficacious substrate for evaluating the impact of biological heterogeneities on entorhinal network function. NEW & NOTEWORTHY We assessed the impact of heterogeneities in channel properties on the robustness of cellular-scale physiology of medial entorhinal cortical stellate neurons. We demonstrate that neuronal models with disparate channel combinations were endowed with similar physiological characteristics, as a consequence of the many-to-many mapping between channel properties and the physiological characteristics that they modulate. We predict that the spike-triggered average of stellate cells should be endowed with theta-frequency spectral selectivity and fast gamma-band coincidence detection capabilities.
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Affiliation(s)
- Divyansh Mittal
- Cellular Neurophysiology Laboratory, Molecular Biophysics Unit, Indian Institute of Science , Bangalore , India
| | - Rishikesh Narayanan
- Cellular Neurophysiology Laboratory, Molecular Biophysics Unit, Indian Institute of Science , Bangalore , India
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17
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Lowet E, Roberts MJ, Peter A, Gips B, De Weerd P. A quantitative theory of gamma synchronization in macaque V1. eLife 2017; 6:26642. [PMID: 28857743 PMCID: PMC5779232 DOI: 10.7554/elife.26642] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Accepted: 08/21/2017] [Indexed: 12/13/2022] Open
Abstract
Gamma-band synchronization coordinates brief periods of excitability in oscillating neuronal populations to optimize information transmission during sensation and cognition. Commonly, a stable, shared frequency over time is considered a condition for functional neural synchronization. Here, we demonstrate the opposite: instantaneous frequency modulations are critical to regulate phase relations and synchronization. In monkey visual area V1, nearby local populations driven by different visual stimulation showed different gamma frequencies. When similar enough, these frequencies continually attracted and repulsed each other, which enabled preferred phase relations to be maintained in periods of minimized frequency difference. Crucially, the precise dynamics of frequencies and phases across a wide range of stimulus conditions was predicted from a physics theory that describes how weakly coupled oscillators influence each other's phase relations. Hence, the fundamental mathematical principle of synchronization through instantaneous frequency modulations applies to gamma in V1 and is likely generalizable to other brain regions and rhythms.
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Affiliation(s)
- Eric Lowet
- Faculty of Psychology and Neuroscience, Maastricht University, Maastricht, Netherlands
| | - Mark J Roberts
- Faculty of Psychology and Neuroscience, Maastricht University, Maastricht, Netherlands
| | - Alina Peter
- Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Frankfurt, Germany
| | - Bart Gips
- Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, Nijmegen, Netherlands
| | - Peter De Weerd
- Faculty of Psychology and Neuroscience, Maastricht University, Maastricht, Netherlands.,Maastricht Centre for Systems Biology, Maastricht University, Maastricht, Netherlands
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18
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Stiefel KM, Ermentrout GB. Neurons as oscillators. J Neurophysiol 2016; 116:2950-2960. [PMID: 27683887 DOI: 10.1152/jn.00525.2015] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Accepted: 09/27/2016] [Indexed: 01/03/2023] Open
Abstract
Regularly spiking neurons can be described as oscillators. In this article we review some of the insights gained from this conceptualization and their relevance for systems neuroscience. First, we explain how a regularly spiking neuron can be viewed as an oscillator and how the phase-response curve (PRC) describes the response of the neuron's spike times to small perturbations. We then discuss the meaning of the PRC for a single neuron's spiking behavior and review the PRCs measured from a variety of neurons in a range of spiking regimes. Next, we show how the PRC can be related to a number of common measures used to quantify neuronal firing, such as the spike-triggered average and the peristimulus histogram. We further show that the response of a neuron to correlated inputs depends on the shape of the PRC. We then explain how the PRC of single neurons can be used to predict neural network behavior. Given the PRC, conduction delays, and the waveform and time course of the synaptic potentials, it is possible to predict neural population behavior such as synchronization. The PRC also allows us to quantify the robustness of the synchronization to heterogeneity and noise. We finally ask how to combine the measured PRCs and the predictions based on PRC to further the understanding of systems neuroscience. As an example, we discuss how the change of the PRC by the neuromodulator acetylcholine could lead to a destabilization of cortical network dynamics. Although all of these studies are grounded in mathematical abstractions that do not strictly hold in biology, they provide good estimates for the emergence of the brain's network activity from the properties of individual neurons. The study of neurons as oscillators can provide testable hypotheses and mechanistic explanations for systems neuroscience.
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Affiliation(s)
| | - G Bard Ermentrout
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania
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19
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Kawamura Y, Nakao H. Optimization of noise-induced synchronization of oscillator networks. Phys Rev E 2016; 94:032201. [PMID: 27739705 DOI: 10.1103/physreve.94.032201] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Indexed: 11/07/2022]
Abstract
We investigate common-noise-induced synchronization between two identical networks of coupled phase oscillators exhibiting fully locked collective oscillations. Using the collective phase description method for fully locked oscillators, we demonstrate that two noninteracting networks of coupled phase oscillators can exhibit in-phase synchronization between the networks when driven by weak common noise. We derive the Lyapunov exponent characterizing the relaxation time for synchronization and develop a method of obtaining the optimal input pattern of common noise to achieve fast synchronization. We illustrate the theory using three representative networks with heterogeneous, global, and local coupling. The theoretical results are validated by direct numerical simulations.
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Affiliation(s)
- Yoji Kawamura
- Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan and Research and Development Center for Marine Biosciences, Japan Agency for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan
| | - Hiroya Nakao
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
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20
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Eaton JA, Moths B, Witten TA. Criterion for noise-induced synchronization: Application to colloidal alignment. Phys Rev E 2016; 94:032207. [PMID: 27739814 DOI: 10.1103/physreve.94.032207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2016] [Indexed: 06/06/2023]
Abstract
Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using programed forcing. We use the notion of statistical entropy to derive bounds on the rate of synchronization. These bounds apply generally to dynamical systems with stable periodic motion with a phase ϕ(t), when subjected to an impulsive perturbation. The impulse causes a change of phase expressible as a phase map ψ(ϕ). We derive an upper limit on the average change of entropy 〈ΔH〉 in terms of this phase map; when this limit is negative, alignment must occur. For systems that have achieved a low entropy, the 〈ΔH〉 approaches this upper limit.
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Affiliation(s)
- Jonah A Eaton
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Brian Moths
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Thomas A Witten
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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21
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Doiron B, Litwin-Kumar A, Rosenbaum R, Ocker GK, Josić K. The mechanics of state-dependent neural correlations. Nat Neurosci 2016; 19:383-93. [PMID: 26906505 DOI: 10.1038/nn.4242] [Citation(s) in RCA: 173] [Impact Index Per Article: 21.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2015] [Accepted: 01/12/2016] [Indexed: 12/12/2022]
Abstract
Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.
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Affiliation(s)
- Brent Doiron
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.,Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, USA
| | - Ashok Litwin-Kumar
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.,Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, USA.,Center for Theoretical Neuroscience, Columbia University, New York, New York, USA
| | - Robert Rosenbaum
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.,Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, USA.,Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana, USA.,Interdisciplinary Center for Network Science and Applications, University of Notre Dame, Notre Dame, Indiana, USA
| | - Gabriel K Ocker
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.,Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, USA.,Allen Institute for Brain Science, Seattle, Washington, USA
| | - Krešimir Josić
- Department of Mathematics, University of Houston, Houston, Texas, USA.,Department of Biology and Biochemistry, University of Houston, Houston, Texas, USA
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22
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Ly C. Interplay of intrinsic and network heterogeneity in strongly recurrent spiking networks. BMC Neurosci 2015. [PMCID: PMC4697603 DOI: 10.1186/1471-2202-16-s1-p150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
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23
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Verduzco-Flores S. Stochastic Synchronization in Purkinje Cells with Feedforward Inhibition Could Be Studied with Equivalent Phase-Response Curves. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2015; 5:25. [PMID: 26084702 PMCID: PMC4471077 DOI: 10.1186/s13408-015-0025-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/22/2014] [Accepted: 05/25/2015] [Indexed: 06/04/2023]
Abstract
Simple-spike synchrony between Purkinje cells projecting to a common neuron in the deep cerebellar nucleus is emerging as an important factor in the encoding of output information from cerebellar cortex. A phenomenon known as stochastic synchronization happens when uncoupled oscillators synchronize due to correlated inputs. Stochastic synchronization is a viable mechanism through which simple-spike synchrony could be generated, but it has received scarce attention, perhaps because the presence of feedforward inhibition in the input to Purkinje cells makes insights difficult. This paper presents a method to account for feedforward inhibition so the usual mathematical approaches to stochastic synchronization can be applied. The method consists in finding a single Phase Response Curve, called the equivalent PRC, that accounts for the effects of both excitatory inputs and delayed feedforward inhibition from molecular layer interneurons. The results suggest that a theory of stochastic synchronization for the case of feedforward inhibition may not be necessary, since this case can be approximately reduced to the case of inputs characterized by a single PRC. Moreover, feedforward inhibition could in many situations increase the level of synchrony experienced by Purkinje cells.
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Affiliation(s)
- Sergio Verduzco-Flores
- Computational Cognitive Neuroscience Laboratory, Department of Psychology and Neuroscience, University of Colorado Boulder, Boulder, CO, USA,
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24
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Phase-resetting as a tool of information transmission. Curr Opin Neurobiol 2014; 31:206-13. [PMID: 25529003 DOI: 10.1016/j.conb.2014.12.003] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Revised: 11/26/2014] [Accepted: 12/01/2014] [Indexed: 11/23/2022]
Abstract
Models of information transmission in the brain largely rely on firing rate codes. The abundance of oscillatory activity in the brain suggests that information may be also encoded using the phases of ongoing oscillations. Sensory perception, working memory and spatial navigation have been hypothesized to use phase codes, and cross-frequency coordination and phase synchronization between brain areas have been proposed to gate the flow of information. Phase codes generally require the phase of the oscillations to be reset at specific reference points for consistent coding, and coordination between oscillators requires favorable phase resetting characteristics. Recent evidence supports a role for neural oscillations in providing temporal reference windows that allow for correct parsing of phase-coded information.
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25
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Climer JR, DiTullio R, Newman EL, Hasselmo ME, Eden UT. Examination of rhythmicity of extracellularly recorded neurons in the entorhinal cortex. Hippocampus 2014; 25:460-73. [PMID: 25331248 DOI: 10.1002/hipo.22383] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/14/2014] [Indexed: 12/16/2022]
Abstract
A number of studies have examined the theta-rhythmic modulation of neuronal firing in the hippocampal circuit. For extracellular recordings, this is often done by examining spectral properties of the spike-time autocorrelogram, most significantly, for validating the presence or absence of theta modulation across species. These techniques can show significant rhythmicity for high firing rate, highly rhythmic neurons; however, they are substantially biased by several factors including the peak firing rate of the neuron, the amount of time spent in the neuron's receptive field, and other temporal properties of the rhythmicity such as cycle-skipping. These limitations make it difficult to examine rhythmic modulation in neurons with low firing rates or when an animal has short dwell times within the firing field and difficult to compare rhythmicity under disparate experimental conditions when these factors frequently differ. Here, we describe in detail the challenges that researchers face when using these techniques and apply our findings to recent recordings from bat entorhinal grid cells, suggesting that they may have lacked enough data to examine theta rhythmicity robustly. We describe a more sensitive and statistically rigorous method using maximum likelihood estimation (MLE) of a parametric model of the lags within the autocorrelation window, which helps to alleviate some of the problems of traditional methods and was also unable to detect rhythmicity in bat grid cells. Using large batteries of simulated data, we explored the boundaries for which the MLE technique and the theta index can detect rhythmicity. The MLE technique is less sensitive to many features of the autocorrelogram and provides a framework for statistical testing to detect rhythmicity as well as changes in rhythmicity in individual sessions providing a substantial improvement over previous methods.
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Affiliation(s)
- Jason R Climer
- Department of Psychological and Brain Sciences, Center for Memory and Brain, Boston University, Massachusetts
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26
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Rosenbaum R, Tchumatchenko T, Moreno-Bote R. Correlated neuronal activity and its relationship to coding, dynamics and network architecture. Front Comput Neurosci 2014; 8:102. [PMID: 25221504 PMCID: PMC4145255 DOI: 10.3389/fncom.2014.00102] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2014] [Accepted: 08/07/2014] [Indexed: 11/13/2022] Open
Affiliation(s)
- Robert Rosenbaum
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame Notre Dame, IN, USA ; Center for the Neural Basis of Cognition Pittsburgh, PA, USA
| | - Tatjana Tchumatchenko
- Department Theory of Neural Dynamics, Max Planck Institute for Brain Research Frankfurt am Main, Germany
| | - Rubén Moreno-Bote
- Research Unit, Parc Sanitari Sant Joan de Déu and Universitat de Barcelona Barcelona, Spain ; Centro de Investigación Biomédica en Red de Salud Mental (CIBERSAM) Barcelona, Spain
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