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Wen W, Turrigiano GG. Modular Arrangement of Synaptic and Intrinsic Homeostatic Plasticity within Visual Cortical Circuits. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.01.596982. [PMID: 38853882 PMCID: PMC11160741 DOI: 10.1101/2024.06.01.596982] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2024]
Abstract
Neocortical circuits use synaptic and intrinsic forms of homeostatic plasticity to stabilize key features of network activity, but whether these different homeostatic mechanisms act redundantly, or can be independently recruited to stabilize different network features, is unknown. Here we used pharmacological and genetic perturbations both in vitro and in vivo to determine whether synaptic scaling and intrinsic homeostatic plasticity (IHP) are arranged and recruited in a hierarchical or modular manner within L2/3 pyramidal neurons in rodent V1. Surprisingly, although the expression of synaptic scaling and IHP was dependent on overlapping trafficking pathways, they could be independently recruited by manipulating spiking activity or NMDAR signaling, respectively. Further, we found that changes in visual experience that affect NMDAR activation but not mean firing selectively trigger IHP, without recruiting synaptic scaling. These findings support a modular model in which synaptic and intrinsic homeostatic plasticity respond to and stabilize distinct aspects of network activity.
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Phan NA, Wang Y. Mixed-mode oscillations in a three-timescale coupled Morris-Lecar system. CHAOS (WOODBURY, N.Y.) 2024; 34:053119. [PMID: 38717416 PMCID: PMC11087137 DOI: 10.1063/5.0181308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 04/19/2024] [Indexed: 05/12/2024]
Abstract
Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris-Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.
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Affiliation(s)
- Ngoc Anh Phan
- Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA
| | - Yangyang Wang
- Department of Mathematics, Brandeis University, Waltham, Massachusetts 02453, USA
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3
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Alonso LM, Rue MCP, Marder E. Gating of homeostatic regulation of intrinsic excitability produces cryptic long-term storage of prior perturbations. Proc Natl Acad Sci U S A 2023; 120:e2222016120. [PMID: 37339223 PMCID: PMC10293857 DOI: 10.1073/pnas.2222016120] [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: 12/29/2022] [Accepted: 05/16/2023] [Indexed: 06/22/2023] Open
Abstract
Neurons and neuronal circuits must maintain their function throughout the life of the organism despite changing environments. Previous theoretical and experimental work suggests that neurons monitor their activity using intracellular calcium concentrations to regulate their intrinsic excitability. Models with multiple sensors can distinguish among different patterns of activity, but previous work using models with multiple sensors produced instabilities that lead the models' conductances to oscillate and then to grow without bound and diverge. We now introduce a nonlinear degradation term that explicitly prevents the maximal conductances to grow beyond a bound. We combine the sensors' signals into a master feedback signal that can be used to modulate the timescale of conductance evolution. Effectively, this means that the negative feedback can be gated on and off according to how far the neuron is from its target. The modified model recovers from multiple perturbations. Interestingly, depolarizing the models to the same membrane potential with current injection or with simulated high extracellular K+ produces different changes in conductances, arguing that caution must be used in interpreting manipulations that serve as a proxy for increased neuronal activity. Finally, these models accrue traces of prior perturbations that are not visible in their control activity after perturbation but that shape their responses to subsequent perturbations. These cryptic or hidden changes may provide insight into disorders such as posttraumatic stress disorder that only become visible in response to specific perturbations.
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Affiliation(s)
- Leandro M. Alonso
- Volen Center and Biology Department, Brandeis University, Waltham, MA02454
| | - Mara C. P. Rue
- Volen Center and Biology Department, Brandeis University, Waltham, MA02454
| | - Eve Marder
- Volen Center and Biology Department, Brandeis University, Waltham, MA02454
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Estacion M, Liu S, Cheng X, Dib-Hajj S, Waxman SG. Kv7-specific activators hyperpolarize resting membrane potential and modulate human iPSC-derived sensory neuron excitability. Front Pharmacol 2023; 14:1138556. [PMID: 36923357 PMCID: PMC10008904 DOI: 10.3389/fphar.2023.1138556] [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: 01/05/2023] [Accepted: 02/13/2023] [Indexed: 03/02/2023] Open
Abstract
Chronic pain is highly prevalent and remains a significant unmet global medical need. As part of a search for modulatory genes that confer pain resilience, we have studied two family cohorts where one individual reported much less pain than other family members that share the same pathogenic gain-of-function Nav1.7 mutation that confers hyperexcitability on pain-signaling dorsal root ganglion (DRG) neurons. In each of these kindreds, the pain-resilient individual carried a gain-of-function variant in Kv7.2 or Kv7.3, two potassium channels that stabilize membrane potential and reduce excitability. Our observation in this molecular genetic study that these gain-of-function Kv7.2 and 7.3 variants reduce DRG neuron excitability suggests that agents that activate or open Kv7 channels should attenuate sensory neuron firing. In the present study, we assess the effects on sensory neuron excitability of three Kv7 modulators-retigabine (Kv7.2 thru Kv7.5 activator), ICA-110381 (Kv7.2/Kv7.3 specific activator), and as a comparator ML277 (Kv7.1 specific activator)-in a "human-pain-in-a-dish" model (human iPSC-derived sensory neurons, iPSC-SN). Multi-electrode-array (MEA) recordings demonstrated inhibition of firing with retigabine and ICA-110381 (but not with ML277), with the concentration-response curve indicating that retigabine can achieve a 50% reduction of firing with sub-micromolar concentrations. Current-clamp recording demonstrated that retigabine hyperpolarized iPSC-SN resting potential and increased threshold. This study implicates Kv7.2/Kv7.3 channels as effective modulators of sensory neuron excitability, and suggest that compounds that specifically target Kv7.2/Kv7.3 currents in sensory neurons, including human sensory neurons, might provide an effective approach toward pain relief.
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Affiliation(s)
- Mark Estacion
- Department of Neurology and Center for Neuroscience and Regeneration Research, Yale University School of Medicine, New Haven, CT, United States
- Rehabilitation Research Center, Veterans Affairs Connecticut Healthcare System, West Haven, CT, United States
| | - Shujun Liu
- Department of Neurology and Center for Neuroscience and Regeneration Research, Yale University School of Medicine, New Haven, CT, United States
- Rehabilitation Research Center, Veterans Affairs Connecticut Healthcare System, West Haven, CT, United States
| | - Xiaoyang Cheng
- Department of Neurology and Center for Neuroscience and Regeneration Research, Yale University School of Medicine, New Haven, CT, United States
- Rehabilitation Research Center, Veterans Affairs Connecticut Healthcare System, West Haven, CT, United States
| | - Sulayman Dib-Hajj
- Department of Neurology and Center for Neuroscience and Regeneration Research, Yale University School of Medicine, New Haven, CT, United States
- Rehabilitation Research Center, Veterans Affairs Connecticut Healthcare System, West Haven, CT, United States
| | - Stephen G. Waxman
- Department of Neurology and Center for Neuroscience and Regeneration Research, Yale University School of Medicine, New Haven, CT, United States
- Rehabilitation Research Center, Veterans Affairs Connecticut Healthcare System, West Haven, CT, United States
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Zang Y, Marder E. Neuronal morphology enhances robustness to perturbations of channel densities. Proc Natl Acad Sci U S A 2023; 120:e2219049120. [PMID: 36787352 PMCID: PMC9974411 DOI: 10.1073/pnas.2219049120] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 01/14/2023] [Indexed: 02/15/2023] Open
Abstract
Biological neurons show significant cell-to-cell variability but have the striking ability to maintain their key firing properties in the face of unpredictable perturbations and stochastic noise. Using a population of multi-compartment models consisting of soma, neurites, and axon for the lateral pyloric neuron in the crab stomatogastric ganglion, we explore how rebound bursting is preserved when the 14 channel conductances in each model are all randomly varied. The coupling between the axon and other compartments is critical for the ability of the axon to spike during bursts and consequently determines the set of successful solutions. When the coupling deviates from a biologically realistic range, the neuronal tolerance of conductance variations is lessened. Thus, the gross morphological features of these neurons enhance their robustness to perturbations of channel densities and expand the space of individual variability that can maintain a desired output pattern.
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Affiliation(s)
- Yunliang Zang
- Volen Center, Brandeis University, Waltham, MA02454
- Department of Biology, Brandeis University, Waltham, MA02454
| | - Eve Marder
- Volen Center, Brandeis University, Waltham, MA02454
- Department of Biology, Brandeis University, Waltham, MA02454
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Marder E, Kedia S, Morozova EO. New insights from small rhythmic circuits. Curr Opin Neurobiol 2022; 76:102610. [PMID: 35986971 DOI: 10.1016/j.conb.2022.102610] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Revised: 06/20/2022] [Accepted: 06/28/2022] [Indexed: 11/30/2022]
Abstract
Small rhythmic circuits, such as those found in invertebrates, have provided fundamental insights into how circuit dynamics depend on individual neuronal and synaptic properties. Degenerate circuits are those with different network parameters and similar behavior. New work on degenerate circuits and their modulation illustrates some of the rules that help maintain stable and robust circuit function despite environmental perturbations. Advances in neuropeptide isolation and identification provide enhanced understanding of the neuromodulation of circuits for behavior. The advent of molecular studies of mRNA expression provides new insight into animal-to-animal variability and the homeostatic regulation of excitability in neurons and networks.
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Affiliation(s)
- Eve Marder
- Volen Center and Biology Department, Brandeis University, Waltham, MA 02454, USA
| | - Sonal Kedia
- Volen Center and Biology Department, Brandeis University, Waltham, MA 02454, USA. https://twitter.com/Sonal_Kedia
| | - Ekaterina O Morozova
- Volen Center and Biology Department, Brandeis University, Waltham, MA 02454, USA.
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Self-healing codes: How stable neural populations can track continually reconfiguring neural representations. Proc Natl Acad Sci U S A 2022; 119:2106692119. [PMID: 35145024 PMCID: PMC8851551 DOI: 10.1073/pnas.2106692119] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/29/2021] [Indexed: 12/19/2022] Open
Abstract
The brain is capable of adapting while maintaining stable long-term memories and learned skills. Recent experiments show that neural responses are highly plastic in some circuits, while other circuits maintain consistent responses over time, raising the question of how these circuits interact coherently. We show how simple, biologically motivated Hebbian and homeostatic mechanisms in single neurons can allow circuits with fixed responses to continuously track a plastic, changing representation without reference to an external learning signal. As an adaptive system, the brain must retain a faithful representation of the world while continuously integrating new information. Recent experiments have measured population activity in cortical and hippocampal circuits over many days and found that patterns of neural activity associated with fixed behavioral variables and percepts change dramatically over time. Such “representational drift” raises the question of how malleable population codes can interact coherently with stable long-term representations that are found in other circuits and with relatively rigid topographic mappings of peripheral sensory and motor signals. We explore how known plasticity mechanisms can allow single neurons to reliably read out an evolving population code without external error feedback. We find that interactions between Hebbian learning and single-cell homeostasis can exploit redundancy in a distributed population code to compensate for gradual changes in tuning. Recurrent feedback of partially stabilized readouts could allow a pool of readout cells to further correct inconsistencies introduced by representational drift. This shows how relatively simple, known mechanisms can stabilize neural tuning in the short term and provides a plausible explanation for how plastic neural codes remain integrated with consolidated, long-term representations.
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Niemeyer N, Schleimer JH, Schreiber S. Biophysical models of intrinsic homeostasis: Firing rates and beyond. Curr Opin Neurobiol 2021; 70:81-88. [PMID: 34454303 DOI: 10.1016/j.conb.2021.07.011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2021] [Revised: 06/14/2021] [Accepted: 07/14/2021] [Indexed: 12/01/2022]
Abstract
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.
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Affiliation(s)
- Nelson Niemeyer
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany; Einstein Center for Neurosciences Berlin, Charitéplatz 1, 10117, Berlin, Germany; Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany; Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany
| | - Susanne Schreiber
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany; Einstein Center for Neurosciences Berlin, Charitéplatz 1, 10117, Berlin, Germany; Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany.
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9
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Schubert F, Gros C. Nonlinear Dendritic Coincidence Detection for Supervised Learning. Front Comput Neurosci 2021; 15:718020. [PMID: 34421566 PMCID: PMC8372750 DOI: 10.3389/fncom.2021.718020] [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: 05/31/2021] [Accepted: 07/13/2021] [Indexed: 11/25/2022] Open
Abstract
Cortical pyramidal neurons have a complex dendritic anatomy, whose function is an active research field. In particular, the segregation between its soma and the apical dendritic tree is believed to play an active role in processing feed-forward sensory information and top-down or feedback signals. In this work, we use a simple two-compartment model accounting for the nonlinear interactions between basal and apical input streams and show that standard unsupervised Hebbian learning rules in the basal compartment allow the neuron to align the feed-forward basal input with the top-down target signal received by the apical compartment. We show that this learning process, termed coincidence detection, is robust against strong distractions in the basal input space and demonstrate its effectiveness in a linear classification task.
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Affiliation(s)
- Fabian Schubert
- Institute for Theoretical Physics, Goethe University Frankfurt am Main, Frankfurt am Main, Germany
| | - Claudius Gros
- Institute for Theoretical Physics, Goethe University Frankfurt am Main, Frankfurt am Main, Germany
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10
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Wason TD. A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area. Biosystems 2021; 205:104403. [PMID: 33746019 DOI: 10.1016/j.biosystems.2021.104403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 03/05/2021] [Indexed: 12/14/2022]
Abstract
What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.
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Affiliation(s)
- Thomas D Wason
- North Carolina State University, Department of Biological Sciences, Meitzen Laboratory, Campus Box 7617, 128 David Clark Labs, Raleigh, NC 27695-7617, USA.
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Schubert F, Gros C. Local Homeostatic Regulation of the Spectral Radius of Echo-State Networks. Front Comput Neurosci 2021; 15:587721. [PMID: 33732127 PMCID: PMC7958921 DOI: 10.3389/fncom.2021.587721] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 01/25/2020] [Indexed: 12/02/2022] Open
Abstract
Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius toward the desired value. For both mechanisms the spectral radius is autonomously adapted while the network receives and processes inputs under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols. Moreover, we evaluated the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using set point homeostatic feedback controls of neural firing.
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Affiliation(s)
- Fabian Schubert
- Institute for Theoretical Physics, Goethe University Frankfurt am Main, Frankfurt am Main, Germany
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12
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Melnykova A. Parametric inference for hypoelliptic ergodic diffusions with full observations. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2020. [DOI: 10.1007/s11203-020-09222-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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13
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Peterson EJ, Voytek B. Homeostatic mechanisms may shape the type and duration of oscillatory modulation. J Neurophysiol 2020; 124:168-177. [PMID: 32490710 DOI: 10.1152/jn.00119.2020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Neural oscillations are observed ubiquitously in the mammalian brain, but their stability is known to be rather variable. Some oscillations are tonic and last for seconds or even minutes. Other oscillations appear as unstable bursts. Likewise, some oscillations rely on excitatory AMPAergic synapses, but others are GABAergic and inhibitory. Why this diversity exists is not clear. We hypothesized Ca2+-dependent homeostasis could be important in finding an explanation. We tested this hypothesis in a highly simplified model of hippocampal neurons. In this model homeostasis profoundly alters the modulatory effect of neural oscillations. Under homeostasis, tonic AMPAergic oscillations actually decrease excitability and desynchronize firing. Tonic oscillations that are synaptically GABAergic-like those in real hippocampus-don't provoke a homeostatic response, however. If our simple model is correct, homeostasis can explain why the theta rhythm in the hippocampus is synaptically inhibitory: GABA has little to no intrinsic homeostatic response and so can preserve the pyramidal cell's natural dynamic range. Based on these results we speculate that homeostasis may explain why AMPAergic oscillations in cortex, and in hippocampus, often appear as bursts. Bursts do not interact with the slow homeostatic time constant and so retain their normal excitatory effect.NEW & NOTEWORTHY The intricate interplay of neuromodulators, like acetylcholine, with homeostasis is well known. The interplay between oscillatory modulation and homeostasis is not. We studied oscillatory modulation and homeostasis for the first time using a simplified model of hippocampus. We report a paradoxical result: Ca-mediated homeostasis causes AMPAergic oscillations to become effectively inhibitory. This result, along with other new observations, means homeostasis might be just as complex and important for oscillations as it is for other neuromodulators.
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Affiliation(s)
- Erik J Peterson
- Department of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania.,Department of Cognitive Science, University of California, San Diego, California
| | - Bradley Voytek
- Department of Cognitive Science, University of California, San Diego, California.,Neurosciences Graduate Program, University of California, San Diego, California.,Halıcıoğlu Data Science Institute, University of California, San Diego, California
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Miller P, Cannon J. Combined mechanisms of neural firing rate homeostasis. BIOLOGICAL CYBERNETICS 2019; 113:47-59. [PMID: 29955960 PMCID: PMC6510813 DOI: 10.1007/s00422-018-0768-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2018] [Accepted: 06/19/2018] [Indexed: 05/22/2023]
Abstract
Spikes in the membrane potential of neurons comprise the currency of information processing in the brain. The ability of neurons to convert any information present across their multiple inputs into a significant modification to the pattern of their emitted spikes depends on the rate at which they emit spikes. If the mean rate is near the neuron's maximum, or if the rate is near zero, then changes in the inputs have minimal impact on the neuron's firing rate. Therefore, a neuron needs to control its mean rate. Protocols that either dramatically increase or decrease a neuron's firing rate lead to multiple compensatory changes that return the neuron's mean rate toward its prior value. In this primer, first as a summary of our previous work (Cannon and Miller in J Neurophysiol 116(5):2004-2022, 2016; Cannon and Miller in J Math Neurosci 7(1):1, 2017), we describe the advantages and disadvantages of having more than one such control mechanism responding to the neuron's firing rate. We suggest how problems of two, coexisting, potentially competing mechanisms can be overcome. Key requirements are: (1) the control be of a distribution of values, which the controlled variable achieves over a fast timescale compared to the timescale of the control system; (2) at least one of the control mechanisms be nonlinear; and (3) the two control systems are satisfied by a stable distribution or range of values that can be achieved by the variable. We show examples of functional control systems, including the previously studied integral feedback controller and new simulations of a "bang-bang" controller, that allow for compensation when inputs to the system change. Finally, we present new results describing how the underlying signal processing pathways would produce mechanisms of dual control, as opposed to a single mechanism with two outputs, and compare the responses of these systems to changes of input statistics.
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Affiliation(s)
- Paul Miller
- Department of Biology and Volen National Center for Complex Systems, MS013, Brandeis University, Waltham, MA, 02454, USA.
| | - Jonathan Cannon
- Department of Biology and Volen National Center for Complex Systems, MS013, Brandeis University, Waltham, MA, 02454, USA
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Thomas PJ, Olufsen M, Sepulchre R, Iglesias PA, Ijspeert A, Srinivasan M. Control theory in biology and medicine : Introduction to the special issue. BIOLOGICAL CYBERNETICS 2019; 113:1-6. [PMID: 30701314 DOI: 10.1007/s00422-018-00791-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
From September-December 2017, the Mathematical Biosciences Institute at Ohio State University hosted a series of workshops on control theory in biology and medicine, including workshops on control and modulation of neuronal and motor systems, control of cellular and molecular systems, control of disease / personalized medicine across heterogeneous populations, and sensorimotor control of animals and robots. This special issue presents tutorials and research articles by several of the participants in the MBI workshops.
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Affiliation(s)
- Peter J Thomas
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio, USA.
| | - Mette Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA
| | | | - Pablo A Iglesias
- Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland, USA
| | - Auke Ijspeert
- Institute of Bioengineering, EPFL, Lausanne, Switzerland
| | - Manoj Srinivasan
- Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, Ohio, USA
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16
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Abstract
In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.
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Affiliation(s)
- Gabriele Scheler
- Carl Correns Foundation for Mathematical Biology, Mountain View, CA, 94040, USA
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17
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Abstract
In this paper, we document lognormal distributions for spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears as a functional property that is present everywhere. Secondly, we created a generic neural model to show that Hebbian learning will create and maintain lognormal distributions. We could prove with the model that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This settles a long-standing question about the type of plasticity exhibited by intrinsic excitability.
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Affiliation(s)
- Gabriele Scheler
- Carl Correns Foundation for Mathematical Biology, Mountain View, CA, 94040, USA
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