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Becker LA, Li B, Priebe NJ, Seidemann E, Taillefumier T. Exact Analysis of the Subthreshold Variability for Conductance-Based Neuronal Models with Synchronous Synaptic Inputs. PHYSICAL REVIEW. X 2024; 14:011021. [PMID: 38911939 PMCID: PMC11194039 DOI: 10.1103/physrevx.14.011021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/25/2024]
Abstract
The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically, we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects postspiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime yields realistic subthreshold variability (voltage variance ≃4-9 mV2) only when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that, without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.
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Affiliation(s)
- Logan A. Becker
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Baowang Li
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Center for Perceptual Systems, The University of Texas at Austin, Austin, Texas 78712, USA
- Center for Learning and Memory, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Psychology, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Nicholas J. Priebe
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Center for Learning and Memory, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Eyal Seidemann
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Center for Perceptual Systems, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Psychology, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Thibaud Taillefumier
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Neuroscience, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA
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Becker LA, Li B, Priebe NJ, Seidemann E, Taillefumier T. Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs. ARXIV 2023:arXiv:2304.09280v3. [PMID: 37131877 PMCID: PMC10153295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≃ 4 - 9 m V 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.
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Affiliation(s)
- Logan A. Becker
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin
- Department of Neuroscience, The University of Texas at Austin
| | - Baowang Li
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin
- Department of Neuroscience, The University of Texas at Austin
- Center for Perceptual Systems, The University of Texas at Austin
- Center for Learning and Memory, The University of Texas at Austin
- Department of Psychology, The University of Texas at Austin
| | - Nicholas J. Priebe
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin
- Department of Neuroscience, The University of Texas at Austin
- Center for Learning and Memory, The University of Texas at Austin
| | - Eyal Seidemann
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin
- Department of Neuroscience, The University of Texas at Austin
- Center for Perceptual Systems, The University of Texas at Austin
- Department of Psychology, The University of Texas at Austin
| | - Thibaud Taillefumier
- Center for Theoretical and Computational Neuroscience, The University of Texas at Austin
- Department of Neuroscience, The University of Texas at Austin
- Department of Mathematics, The University of Texas at Austin
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Becker LA, Li B, Priebe NJ, Seidemann E, Taillefumier T. Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.04.17.536739. [PMID: 37131647 PMCID: PMC10153111 DOI: 10.1101/2023.04.17.536739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≅ 4-9mV 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.
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